def activeCells(self):
if getattr(self, '_activeCells', None) is None:
if getattr(self, 'topofile', None) is not None:
topo = np.genfromtxt(self.basePath + self.topofile,
skip_header=1)
# Find the active cells
active = Utils.surface2ind_topo(self.mesh, topo, 'N')
elif isinstance(self._staticInput, float):
active = self.m0 != self._staticInput
else:
# Read from file active cells with 0:air, 1:dynamic, -1 static
active = self.activeModel != 0
inds = np.asarray(
[inds for inds, elem in enumerate(active, 1) if elem],
dtype=int) - 1
self._activeCells = inds
# Reduce m0 to active space
if len(self.m0) > len(self._activeCells):
self._m0 = self.m0[self._activeCells]
return self._activeCells
def drapeTopotoLoc(mesh, pts, actind=None, option="top", topo=None):
"""
Drape location right below (cell center) the topography
"""
if mesh.dim == 2:
if pts.ndim > 1:
raise Exception("pts should be 1d array")
elif mesh.dim == 3:
if pts.shape[1] == 3:
raise Exception("shape of pts should be (x,3)")
else:
raise NotImplementedError()
if actind is None:
actind = Utils.surface2ind_topo(mesh, topo)
if mesh._meshType == "TENSOR":
meshtemp, topoCC = gettopoCC(mesh, actind, option=option)
inds = Utils.closestPoints(meshtemp, pts)
elif mesh._meshType == "TREE":
if mesh.dim == 3:
uniqXYlocs, topoCC = gettopoCC(mesh, actind, option=option)
inds = closestPointsGrid(uniqXYlocs, pts)
else:
raise NotImplementedError()
else:
raise NotImplementedError()
out = np.c_[pts, topoCC[inds]]
return out
def activeCells(self):
if getattr(self, '_activeCells', None) is None:
if getattr(self, 'topofile', None) is not None:
topo = np.genfromtxt(
self.basePath + self.topofile, skip_header=1
)
# Find the active cells
active = Utils.surface2ind_topo(self.mesh, topo, 'N')
elif isinstance(self._staticInput, float):
active = self.m0 != self._staticInput
else:
# Read from file active cells with 0:air, 1:dynamic, -1 static
active = self.activeModel != 0
inds = np.where(active)[0]
self._activeCells = inds
# Reduce m0 to active space
if len(self.m0) > len(self._activeCells):
self._m0 = self.m0[self._activeCells]
return self._activeCells
def drapeTopotoLoc(mesh, pts, actind=None, option="top", topo=None):
"""
Drape location right below (cell center) the topography
"""
if mesh.dim == 2:
if pts.ndim > 1:
raise Exception("pts should be 1d array")
elif mesh.dim == 3:
if pts.shape[1] == 3:
raise Exception("shape of pts should be (x,3)")
else:
raise NotImplementedError()
if actind is None:
actind = Utils.surface2ind_topo(mesh, topo)
if mesh._meshType == "TENSOR":
meshtemp, topoCC = gettopoCC(mesh, actind, option=option)
inds = Utils.closestPoints(meshtemp, pts)
elif mesh._meshType == "TREE":
if mesh.dim == 3:
uniqXYlocs, topoCC = gettopoCC(mesh, actind, option=option)
inds = closestPointsGrid(uniqXYlocs, pts)
else:
raise NotImplementedError()
else:
raise NotImplementedError()
out = np.c_[pts, topoCC[inds]]
return out
def activeCells(self):
if getattr(self, '_activeCells', None) is None:
if getattr(self, 'topofile', None) is not None:
topo = np.genfromtxt(self.basePath + self.topofile,
skip_header=1)
# Find the active cells
active = Utils.surface2ind_topo(self.mesh, topo, 'N')
elif isinstance(self._staticInput, float):
active = self.m0 != self._staticInput
else:
# Read from file active cells with 0:air, 1:dynamic, -1 static
active = self.activeModel != 0
inds = np.asarray([inds for inds,
elem in enumerate(active, 1)
if elem], dtype=int) - 1
self._activeCells = inds
# Reduce m0 to active space
self._m0 = self.m0[self._activeCells]
return self._activeCells
def create_local_mesh(
src_location,
rx_location,
topo_location,
topo,
h = [10., 10., 5.],
x_core_lim = (-100., 100.),
y_core_lim = (-20., 20.),
):
# TODO: All parameters used for generating this mesh should be input parameters
# Currently fixed for a specific case
xyz = np.vstack((rx_location, src_location))
x = np.linspace(x_core_lim[0], x_core_lim[1]) + src_location[0]
y = np.linspace(y_core_lim[0], y_core_lim[1]) + src_location[1]
dem = Utils.ndgrid(x, y, np.r_[topo_location[2]])
mesh_local = discretize.utils.mesh_builder_xyz(
dem,
h,
padding_distance=[[2000., 2000.], [2000., 2000.], [2000., 2000.]],
base_mesh=None,
depth_core=None,
expansion_factor=1.3,
mesh_type='tree'
)
mesh_local = discretize.utils.refine_tree_xyz(
mesh_local,
dem,
method='surface',
octree_levels=[5, 10, 10],
octree_levels_padding=None,
finalize=False,
min_level=0,
max_distance=np.inf,
)
mesh_local = discretize.utils.refine_tree_xyz(
mesh_local,
xyz,
method='radial',
octree_levels=[2, 0, 0],
octree_levels_padding=None,
finalize=True,
min_level=1,
max_distance=np.inf,
)
actv_local = Utils.surface2ind_topo(mesh_local, topo)
return mesh_local, actv_local
def activeCells(self):
if getattr(self, '_activeCells', None) is None:
if self.topofile == 'null':
self._activeCells = np.arange(mesh.nC)
else:
topo = np.genfromtxt(self.basePath + self.topofile, skip_header=1)
# Find the active cells
active = Utils.surface2ind_topo(self.mesh,topo,'N')
inds = np.asarray([inds for inds, elem in enumerate(active, 1) if elem], dtype = int) - 1
self._activeCells = inds
return self._activeCells
def readSeepageModel(fname, mesh=None, xsurf=None, ysurf=None):
fluiddata = pd.read_csv(fname)
header = fluiddata.keys()
xyz = np.c_[fluiddata['X (m)'].values,fluiddata['Y (m)'].values]
h = fluiddata['Total Head (m)'].values
Ux = fluiddata['X-Velocity Magnitude (m/sec)'].values
Uy = fluiddata['Y-Velocity Magnitude (m/sec)'].values
Gradx = fluiddata['X-Gradient'].values
Grady = fluiddata['Y-Gradient'].values
Pressure = fluiddata['Pressure Head (m)'].values
Sw = fluiddata[fluiddata.keys()[17]].values
Kx = fluiddata["X-Conductivity (m/sec)"]
Ky = fluiddata["Y-Conductivity (m/sec)"]
if mesh is None:
# TODO: this is a specific set up ...
xmin, ymin = xyz[:,0].min(), xyz[:,1].min()
cs = 0.5
ncx = 152*2
ncy = 36*2
npad = 5
hx = [(cs,npad, -1.3),(cs,ncx),(cs,npad, 1.3)]
hy = [(cs,npad, -1.3),(cs,ncy)]
mesh = Mesh.TensorMesh([hx, hy], x0 = [xmin, ymin])
mesh._x0 = np.r_[xmin-mesh.hx[:10].sum(), xmin-mesh.hy[:10].sum()]
# ...
xsurf = np.r_[-1e10, 55, 90, 94, 109, 112, 126.5, +1e10]
ysurf = np.r_[27.5, 27.5, 43.2, 43.2, 35, 35, 27.5, 27.5]
yup = np.ones_like(ysurf)*45
actind = Utils.surface2ind_topo(mesh, np.c_[xsurf, ysurf])
waterheight = 40.
waterind = (np.logical_and(~actind, mesh.gridCC[:,1]<40.)) & (mesh.gridCC[:,0]<90.)
F_hlin = LinearNDInterpolator(xyz, h)
hccIn = F_hlin(mesh.gridCC[actind,:])
F_hnear = NearestNDInterpolator(mesh.gridCC[actind,:], hccIn)
hcc = F_hnear(mesh.gridCC)
fluiddata = {"xyz": xyz, "h":h, "Sw":Sw, "Kx":Kx, "Ky":Ky, "P":Pressure, "Ux":Ux, "Uy":Uy,\
"Gradx":Gradx, "Grady":Grady, \
"hcc": hcc, "mesh":mesh, "actind":actind, "waterind": waterind, \
"xsurf":xsurf, "ysurf":ysurf, "yup":yup}
return fluiddata
def readSeepageModel(fname, mesh=None, xsurf=None, ysurf=None):
fluiddata = pd.read_csv(fname)
header = fluiddata.keys()
xyz = np.c_[fluiddata['X (m)'].values, fluiddata['Y (m)'].values]
h = fluiddata['Total Head (m)'].values
Ux = fluiddata['X-Velocity Magnitude (m/sec)'].values
Uy = fluiddata['Y-Velocity Magnitude (m/sec)'].values
Gradx = fluiddata['X-Gradient'].values
Grady = fluiddata['Y-Gradient'].values
Pressure = fluiddata['Pressure Head (m)'].values
Sw = fluiddata[fluiddata.keys()[17]].values
Kx = fluiddata["X-Conductivity (m/sec)"]
Ky = fluiddata["Y-Conductivity (m/sec)"]
if mesh is None:
# TODO: this is a specific set up ...
xmin, ymin = xyz[:, 0].min(), xyz[:, 1].min()
cs = 0.5
ncx = 152 * 2
ncy = 36 * 2
npad = 5
hx = [(cs, npad, -1.3), (cs, ncx), (cs, npad, 1.3)]
hy = [(cs, npad, -1.3), (cs, ncy)]
mesh = Mesh.TensorMesh([hx, hy], x0=[xmin, ymin])
mesh._x0 = np.r_[xmin - mesh.hx[:10].sum(), xmin - mesh.hy[:10].sum()]
# ...
xsurf = np.r_[-1e10, 55, 90, 94, 109, 112, 126.5, +1e10]
ysurf = np.r_[27.5, 27.5, 43.2, 43.2, 35, 35, 27.5, 27.5]
yup = np.ones_like(ysurf) * 45
actind = Utils.surface2ind_topo(mesh, np.c_[xsurf, ysurf])
waterheight = 40.
waterind = (np.logical_and(
~actind, mesh.gridCC[:, 1] < 40.)) & (mesh.gridCC[:, 0] < 90.)
F_hlin = LinearNDInterpolator(xyz, h)
hccIn = F_hlin(mesh.gridCC[actind, :])
F_hnear = NearestNDInterpolator(mesh.gridCC[actind, :], hccIn)
hcc = F_hnear(mesh.gridCC)
fluiddata = {"xyz": xyz, "h":h, "Sw":Sw, "Kx":Kx, "Ky":Ky, "P":Pressure, "Ux":Ux, "Uy":Uy,\
"Gradx":Gradx, "Grady":Grady, \
"hcc": hcc, "mesh":mesh, "actind":actind, "waterind": waterind, \
"xsurf":xsurf, "ysurf":ysurf, "yup":yup}
return fluiddata
def get_interpolation_matrix(
self,
npts=20,
epsilon=None
):
tree_2d = kdtree(self.topography[:, :2])
xy = Utils.ndgrid(self.mesh_3d.vectorCCx, self.mesh_3d.vectorCCy)
distance, inds = tree_2d.query(xy, k=npts)
if epsilon is None:
epsilon = np.min([self.mesh_3d.hx.min(), self.mesh_3d.hy.min()])
w = 1. / (distance + epsilon)**2
w = Utils.sdiag(1./np.sum(w, axis=1)) * (w)
I = Utils.mkvc(
np.arange(inds.shape[0]).reshape([-1, 1]).repeat(npts, axis=1)
)
J = Utils.mkvc(inds)
self._P = sp.coo_matrix(
(Utils.mkvc(w), (I, J)),
shape=(inds.shape[0], self.topography.shape[0])
)
mesh_1d = Mesh.TensorMesh([np.r_[self.hz[:-1], 1e20]])
z = self.P*self.topography[:, 2]
self._actinds = Utils.surface2ind_topo(self.mesh_3d, np.c_[xy, z])
Z = np.empty(self.mesh_3d.vnC, dtype=float, order='F')
Z = self.mesh_3d.gridCC[:, 2].reshape(
(self.mesh_3d.nCx*self.mesh_3d.nCy, self.mesh_3d.nCz), order='F'
)
ACTIND = self._actinds.reshape(
(self.mesh_3d.nCx*self.mesh_3d.nCy, self.mesh_3d.nCz), order='F'
)
self._Pz = []
# This part can be cythonized or parallelized
for i_xy in range(self.mesh_3d.nCx*self.mesh_3d.nCy):
actind_temp = ACTIND[i_xy, :]
z_temp = -(Z[i_xy, :] - z[i_xy])
self._Pz.append(mesh_1d.getInterpolationMat(z_temp[actind_temp]))
def drapeTopotoLoc(mesh, topo, pts):
"""
Drape
"""
if mesh.dim == 2:
if pts.ndim > 1:
raise Exception("pts should be 1d array")
elif mesh.dim == 3:
if pts.shape[1] == 3:
raise Exception("shape of pts should be (x,3)")
else:
raise NotImplementedError()
airind = Utils.surface2ind_topo(mesh, topo)
meshtemp, topoCC = gettopoCC(mesh, ~airind)
inds = Utils.closestPoints(meshtemp, pts)
return np.c_[pts, topoCC[inds]]
def drapeTopotoLoc(mesh, topo, pts):
"""
Drape
"""
if mesh.dim ==2:
if pts.ndim > 1:
raise Exception("pts should be 1d array")
elif mesh.dim ==3:
if pts.shape[1] == 3:
raise Exception("shape of pts should be (x,3)")
else:
raise NotImplementedError()
airind = Utils.surface2ind_topo(mesh, topo)
meshtemp, topoCC = gettopoCC(mesh, ~airind)
inds = Utils.closestPoints(meshtemp, pts)
return np.c_[pts, topoCC[inds]]
def get_interpolation_matrix(
self,
npts=20,
epsilon=None
):
tree_2d = kdtree(self.topography[:, :2])
xy = Utils.ndgrid(self.mesh_3d.vectorCCx, self.mesh_3d.vectorCCy)
distance, inds = tree_2d.query(xy, k=npts)
if epsilon is None:
epsilon = np.min([self.mesh_3d.hx.min(), self.mesh_3d.hy.min()])
w = 1. / (distance + epsilon)**2
w = Utils.sdiag(1./np.sum(w, axis=1)) * (w)
I = Utils.mkvc(
np.arange(inds.shape[0]).reshape([-1, 1]).repeat(npts, axis=1)
)
J = Utils.mkvc(inds)
self._P = sp.coo_matrix(
(Utils.mkvc(w), (I, J)),
shape=(inds.shape[0], self.topography.shape[0])
)
mesh_1d = Mesh.TensorMesh([np.r_[self.hz[:-1], 1e20]])
z = self.P*self.topography[:, 2]
self._actinds = Utils.surface2ind_topo(self.mesh_3d, np.c_[xy, z])
Z = np.empty(self.mesh_3d.vnC, dtype=float, order='F')
Z = self.mesh_3d.gridCC[:, 2].reshape(
(self.mesh_3d.nCx*self.mesh_3d.nCy, self.mesh_3d.nCz), order='F'
)
ACTIND = self._actinds.reshape(
(self.mesh_3d.nCx*self.mesh_3d.nCy, self.mesh_3d.nCz), order='F'
)
self._Pz = []
# This part can be cythonized or parallelized
for i_xy in range(self.mesh_3d.nCx*self.mesh_3d.nCy):
actind_temp = ACTIND[i_xy, :]
z_temp = -(Z[i_xy, :] - z[i_xy])
self._Pz.append(mesh_1d.getInterpolationMat(z_temp[actind_temp]))
def setUp(self):
ndv = -100
# Create a self.mesh
dx = 5.
hxind = [(dx, 5, -1.3), (dx, 5), (dx, 5, 1.3)]
hyind = [(dx, 5, -1.3), (dx, 5), (dx, 5, 1.3)]
hzind = [(dx, 5, -1.3), (dx, 6)]
self.mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCC')
# Get index of the center
midx = int(self.mesh.nCx/2)
midy = int(self.mesh.nCy/2)
# Lets create a simple Gaussian topo and set the active cells
[xx, yy] = np.meshgrid(self.mesh.vectorNx, self.mesh.vectorNy)
zz = -np.exp((xx**2 + yy**2) / 75**2) + self.mesh.vectorNz[-1]
# Go from topo to actv cells
topo = np.c_[Utils.mkvc(xx), Utils.mkvc(yy), Utils.mkvc(zz)]
actv = Utils.surface2ind_topo(self.mesh, topo, 'N')
actv = np.where(actv)[0]
# Create active map to go from reduce space to full
self.actvMap = Maps.InjectActiveCells(self.mesh, actv, -100)
nC = len(actv)
# Create and array of observation points
xr = np.linspace(-20., 20., 20)
yr = np.linspace(-20., 20., 20)
X, Y = np.meshgrid(xr, yr)
# Move the observation points 5m above the topo
Z = -np.exp((X**2 + Y**2) / 75**2) + self.mesh.vectorNz[-1] + 5.
# Create a MAGsurvey
locXYZ = np.c_[Utils.mkvc(X.T), Utils.mkvc(Y.T), Utils.mkvc(Z.T)]
rxLoc = PF.BaseGrav.RxObs(locXYZ)
srcField = PF.BaseGrav.SrcField([rxLoc])
survey = PF.BaseGrav.LinearSurvey(srcField)
# We can now create a density model and generate data
# Here a simple block in half-space
model = np.zeros((self.mesh.nCx, self.mesh.nCy, self.mesh.nCz))
model[(midx-2):(midx+2), (midy-2):(midy+2), -6:-2] = 0.5
model = Utils.mkvc(model)
self.model = model[actv]
# Create active map to go from reduce set to full
actvMap = Maps.InjectActiveCells(self.mesh, actv, ndv)
# Create reduced identity map
idenMap = Maps.IdentityMap(nP=nC)
# Create the forward model operator
prob = PF.Gravity.GravityIntegral(
self.mesh,
rhoMap=idenMap,
actInd=actv
)
# Pair the survey and problem
survey.pair(prob)
# Compute linear forward operator and compute some data
d = prob.fields(self.model)
# Add noise and uncertainties (1nT)
data = d + np.random.randn(len(d))*0.001
wd = np.ones(len(data))*.001
survey.dobs = data
survey.std = wd
# PF.Gravity.plot_obs_2D(survey.srcField.rxList[0].locs, d=data)
# Create sensitivity weights from our linear forward operator
wr = PF.Magnetics.get_dist_wgt(self.mesh, locXYZ, actv, 2., 2.)
wr = wr**2.
# Create a regularization
reg = Regularization.Sparse(self.mesh, indActive=actv, mapping=idenMap)
reg.cell_weights = wr
reg.norms = np.c_[0, 0, 0, 0]
reg.gradientType = 'component'
# reg.eps_p, reg.eps_q = 5e-2, 1e-2
# Data misfit function
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.W = 1/wd
# Add directives to the inversion
opt = Optimization.ProjectedGNCG(maxIter=100, lower=-1., upper=1.,
maxIterLS=20, maxIterCG=10,
tolCG=1e-3)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=1e+8)
# Here is where the norms are applied
IRLS = Directives.Update_IRLS(f_min_change=1e-4,
minGNiter=1)
update_Jacobi = Directives.UpdatePreconditioner()
self.inv = Inversion.BaseInversion(invProb,
directiveList=[IRLS,
update_Jacobi])
# level means number of layers in current OcTree level
for level in range(int(nCpad[ii])):
mesh.insert_cells(
np.c_[mkvc(CCx), mkvc(CCy), z-zOffset],
np.ones_like(z)*maxLevel-ii,
finalize=False
)
zOffset += dx
mesh.finalize()
# Define an active cells from topo
actv = Utils.surface2ind_topo(mesh, topo)
nC = int(actv.sum())
###########################################################################
# Forward modeling data
# ---------------------
#
# We can now generate TMI data
#
# Convert the inclination declination to vector in Cartesian
M_xyz = Utils.matutils.dip_azimuth2cartesian(np.ones(nC)*M[0], np.ones(nC)*M[1])
# Get the indicies of the magnetized block
ind = Utils.ModelBuilder.getIndicesBlock(
np.r_[-20, -20, -10], np.r_[20, 20, 25],
def set_mesh(self, topo=None,
dx=None, dy=None, dz=None,
n_spacing=None, corezlength=None,
npad_x=7, npad_y=7, npad_z=7,
pad_rate_x=1.3, pad_rate_y=1.3, pad_rate_z=1.3,
ncell_per_dipole=4, mesh_type='TensorMesh',
dimension=2,
method='nearest'
):
"""
Set up a mesh for a given DC survey
"""
if mesh_type == 'TreeMesh':
raise NotImplementedError()
# 2D or 3D mesh
if dimension in [2, 3]:
if dimension == 2:
z_ind = 1
else:
z_ind = 2
a = abs(np.diff(np.sort(self.electrode_locations[:, 0]))).min()
lineLength = abs(
self.electrode_locations[:, 0].max() -
self.electrode_locations[:, 0].min()
)
dx_ideal = a/ncell_per_dipole
if dx is None:
dx = dx_ideal
warnings.warn(
"dx is set to {} m (samllest electrode spacing ({}) / {})".format(dx, a, ncell_per_dipole)
)
if dz is None:
dz = dx*0.5
warnings.warn(
"dz ({} m) is set to dx ({} m) / {}".format(dz, dx, 2)
)
x0 = self.electrode_locations[:, 0].min()
if topo is None:
# For 2D mesh
if dimension == 2:
# sort by x
row_idx = np.lexsort((self.electrode_locations[:, 0],))
# For 3D mesh
else:
# sort by x, then by y
row_idx = np.lexsort((self.electrode_locations[:, 1],
self.electrode_locations[:, 0]))
locs = self.electrode_locations[row_idx, :]
else:
# For 2D mesh
if dimension == 2:
# sort by x
mask = np.isin(self.electrode_locations[:, 0], topo[:, 0])
if np.any(mask):
raise RuntimeError("the x coordinates of some topo and electrodes are the same.")
locs_tmp = np.vstack((topo, self.electrode_locations[~mask, :]))
row_idx = np.lexsort((locs_tmp[:, 0],))
# For 3D mesh
else:
# sort by x, then by y
dtype = [('x', np.float64), ('y', np.float64)]
mask = np.isin(self.electrode_locations[:, [0, 1]].copy().view(dtype),
topo[:, [0, 1]].copy().view(dtype)).flatten()
if np.any(mask):
raise RuntimeError("the x and y coordinates of some topo and electrodes are the same.")
locs_tmp = np.vstack((topo, self.electrode_locations[~mask, :]))
row_idx = np.lexsort((locs_tmp[:, 1], locs_tmp[:, 0]))
locs = locs_tmp[row_idx, :]
if dx > dx_ideal:
# warnings.warn(
# "Input dx ({}) is greater than expected \n We recommend using {:0.1e} m cells, that is, {} cells per {0.1e} m dipole length".format(dx, dx_ideal, ncell_per_dipole, a)
# )
pass
self.dx = dx
self.dz = dz
self.npad_x = npad_x
self.npad_z = npad_z
self.pad_rate_x = pad_rate_x
self.pad_rate_z = pad_rate_z
self.ncell_per_dipole = ncell_per_dipole
zmax = locs[:, z_ind].max()
zmin = locs[:, z_ind].min()
# 3 cells each for buffer
corexlength = lineLength + dx * 6
if corezlength is None:
corezlength = self.grids[:, z_ind].max()
ncx = np.round(corexlength/dx)
ncz = np.round(corezlength/dz)
hx = [
(dx, npad_x, -pad_rate_x), (dx, ncx), (dx, npad_x, pad_rate_x)
]
hz = [(dz, npad_z, -pad_rate_z), (dz, ncz)]
x0_mesh = -(
(dx * pad_rate_x ** (np.arange(npad_x)+1)).sum() + dx * 3 - x0
)
z0_mesh = -((dz * pad_rate_z ** (np.arange(npad_z)+1)).sum() + dz * ncz) + zmax
# For 2D mesh
if dimension == 2:
h = [hx, hz]
x0_for_mesh = [x0_mesh, z0_mesh]
self.xyzlim = np.vstack((
np.r_[x0, x0+lineLength],
np.r_[zmax-corezlength, zmax]
))
fill_value = "extrapolate"
# For 3D mesh
else:
if dy is None:
raise Exception("You must input dy (m)")
self.dy = dy
self.npad_y = npad_y
self.pad_rate_y = pad_rate_y
ylocs = np.unique(self.electrode_locations[:, 1])
ymin, ymax = ylocs.min(), ylocs.max()
# 3 cells each for buffer in y-direction
coreylength = ymax-ymin+dy*6
ncy = np.round(coreylength/dy)
hy = [
(dy, npad_y, -pad_rate_y),
(dy, ncy),
(dy, npad_y, pad_rate_y)
]
y0 = ylocs.min()-dy/2.
y0_mesh = -(
(dy * pad_rate_y ** (np.arange(npad_y)+1)).sum()
+ dy*3 - y0
)
h = [hx, hy, hz]
x0_for_mesh = [x0_mesh, y0_mesh, z0_mesh]
self.xyzlim = np.vstack((
np.r_[x0, x0+lineLength],
np.r_[ymin-dy*3, ymax+dy*3],
np.r_[zmax-corezlength, zmax]
))
fill_value = np.nan
mesh = Mesh.TensorMesh(h, x0=x0_for_mesh)
actind = Utils.surface2ind_topo(mesh, locs, method=method, fill_value=fill_value)
else:
raise NotImplementedError()
return mesh, actind
def run(plotIt=True, survey_type="dipole-dipole"):
np.random.seed(1)
# Initiate I/O class for DC
IO = DC.IO()
# Obtain ABMN locations
xmin, xmax = 0., 200.
ymin, ymax = 0., 0.
zmin, zmax = 0, 0
endl = np.array([[xmin, ymin, zmin], [xmax, ymax, zmax]])
# Generate DC survey object
survey_dc = DC.Utils.gen_DCIPsurvey(endl,
survey_type=survey_type,
dim=2,
a=10,
b=10,
n=10)
survey_dc.getABMN_locations()
survey_dc = IO.from_ambn_locations_to_survey(survey_dc.a_locations,
survey_dc.b_locations,
survey_dc.m_locations,
survey_dc.n_locations,
survey_type,
data_dc_type='volt',
data_ip_type='volt')
# Obtain 2D TensorMesh
mesh, actind = IO.set_mesh()
topo, mesh1D = DC.Utils.genTopography(mesh, -10, 0, its=100)
actind = Utils.surface2ind_topo(mesh, np.c_[mesh1D.vectorCCx, topo])
survey_dc.drapeTopo(mesh, actind, option="top")
# Build conductivity and chargeability model
blk_inds_c = Utils.ModelBuilder.getIndicesSphere(np.r_[60., -25.], 12.5,
mesh.gridCC)
blk_inds_r = Utils.ModelBuilder.getIndicesSphere(np.r_[140., -25.], 12.5,
mesh.gridCC)
blk_inds_charg = Utils.ModelBuilder.getIndicesSphere(
np.r_[100., -25], 12.5, mesh.gridCC)
sigma = np.ones(mesh.nC) * 1. / 100.
sigma[blk_inds_c] = 1. / 10.
sigma[blk_inds_r] = 1. / 1000.
sigma[~actind] = 1. / 1e8
rho = 1. / sigma
charg = np.zeros(mesh.nC)
charg[blk_inds_charg] = 0.1
# Show the true conductivity model
if plotIt:
fig, axs = plt.subplots(2, 1, figsize=(12, 6))
temp_rho = rho.copy()
temp_rho[~actind] = np.nan
temp_charg = charg.copy()
temp_charg[~actind] = np.nan
out1 = mesh.plotImage(temp_rho,
grid=True,
ax=axs[0],
gridOpts={'alpha': 0.2},
clim=(10, 1000),
pcolorOpts={
"cmap": "viridis",
"norm": colors.LogNorm()
})
out2 = mesh.plotImage(temp_charg,
grid=True,
ax=axs[1],
gridOpts={'alpha': 0.2},
clim=(0, 0.1),
pcolorOpts={"cmap": "magma"})
for i in range(2):
axs[i].plot(survey_dc.electrode_locations[:, 0],
survey_dc.electrode_locations[:, 1], 'kv')
axs[i].set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
axs[i].set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
axs[i].set_aspect('equal')
cb = plt.colorbar(out1[0], ax=axs[0])
cb.set_label("Resistivity (ohm-m)")
cb = plt.colorbar(out2[0], ax=axs[1])
cb.set_label("Chargeability")
plt.show()
# Use Exponential Map: m = log(rho)
actmap = Maps.InjectActiveCells(mesh,
indActive=actind,
valInactive=np.log(1e8))
mapping = Maps.ExpMap(mesh) * actmap
# Generate mtrue_dc for resistivity
mtrue_dc = np.log(rho[actind])
# Generate 2.5D DC problem
# "N" means potential is defined at nodes
prb = DC.Problem2D_N(mesh, rhoMap=mapping, storeJ=True, Solver=Solver)
# Pair problem with survey
try:
prb.pair(survey_dc)
except:
survey_dc.unpair()
prb.pair(survey_dc)
# Make synthetic DC data with 5% Gaussian noise
dtrue_dc = survey_dc.makeSyntheticData(mtrue_dc, std=0.05, force=True)
IO.data_dc = dtrue_dc
# Generate mtrue_ip for chargability
mtrue_ip = charg[actind]
# Generate 2.5D DC problem
# "N" means potential is defined at nodes
prb_ip = IP.Problem2D_N(mesh,
etaMap=actmap,
storeJ=True,
rho=rho,
Solver=Solver)
survey_ip = IP.from_dc_to_ip_survey(survey_dc, dim="2.5D")
prb_ip.pair(survey_ip)
dtrue_ip = survey_ip.makeSyntheticData(mtrue_ip, std=0.05)
IO.data_ip = dtrue_ip
# Show apparent resisitivty pseudo-section
if plotIt:
IO.plotPseudoSection(data_type='apparent_resistivity',
scale='log',
cmap='viridis')
plt.show()
# Show apparent chargeability pseudo-section
if plotIt:
IO.plotPseudoSection(data_type='apparent_chargeability',
scale='linear',
cmap='magma')
plt.show()
# Show apparent resisitivty histogram
if plotIt:
fig = plt.figure(figsize=(10, 4))
ax1 = plt.subplot(121)
out = hist(np.log10(abs(IO.voltages)), bins=20)
ax1.set_xlabel("log10 DC voltage (V)")
ax2 = plt.subplot(122)
out = hist(IO.apparent_resistivity, bins=20)
ax2.set_xlabel("Apparent Resistivity ($\Omega$m)")
plt.tight_layout()
plt.show()
# Set initial model based upon histogram
m0_dc = np.ones(actmap.nP) * np.log(100.)
# Set uncertainty
# floor
eps_dc = 10**(-3.2)
# percentage
std_dc = 0.05
mopt_dc, pred_dc = DC.run_inversion(m0_dc,
survey_dc,
actind,
mesh,
std_dc,
eps_dc,
beta0_ratio=1e0,
use_sensitivity_weight=True)
# Convert obtained inversion model to resistivity
# rho = M(m), where M(.) is a mapping
rho_est = mapping * mopt_dc
rho_est[~actind] = np.nan
rho_true = rho.copy()
rho_true[~actind] = np.nan
# show recovered conductivity
if plotIt:
vmin, vmax = rho.min(), rho.max()
fig, ax = plt.subplots(2, 1, figsize=(20, 6))
out1 = mesh.plotImage(rho_true,
clim=(10, 1000),
pcolorOpts={
"cmap": "viridis",
"norm": colors.LogNorm()
},
ax=ax[0])
out2 = mesh.plotImage(rho_est,
clim=(10, 1000),
pcolorOpts={
"cmap": "viridis",
"norm": colors.LogNorm()
},
ax=ax[1])
out = [out1, out2]
for i in range(2):
ax[i].plot(survey_dc.electrode_locations[:, 0],
survey_dc.electrode_locations[:, 1], 'kv')
ax[i].set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax[i].set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[i][0], ax=ax[i])
cb.set_label("Resistivity ($\Omega$m)")
ax[i].set_xlabel("Northing (m)")
ax[i].set_ylabel("Elevation (m)")
ax[i].set_aspect('equal')
plt.tight_layout()
plt.show()
# Show apparent resisitivty histogram
if plotIt:
fig = plt.figure(figsize=(10, 4))
ax1 = plt.subplot(121)
out = hist(np.log10(abs(IO.voltages_ip)), bins=20)
ax1.set_xlabel("log10 IP voltage (V)")
ax2 = plt.subplot(122)
out = hist(IO.apparent_chargeability, bins=20)
ax2.set_xlabel("Apparent Chargeability (V/V)")
plt.tight_layout()
plt.show()
# Set initial model based upon histogram
m0_ip = np.ones(actmap.nP) * 1e-10
# Set uncertainty
# floor
eps_ip = 10**(-4)
# percentage
std_ip = 0.05
# Clean sensitivity function formed with true resistivity
prb_ip._Jmatrix = None
# Input obtained resistivity to form sensitivity
prb_ip.rho = mapping * mopt_dc
mopt_ip, _ = IP.run_inversion(m0_ip,
survey_ip,
actind,
mesh,
std_ip,
eps_ip,
upper=np.Inf,
lower=0.,
beta0_ratio=1e0,
use_sensitivity_weight=True)
# Convert obtained inversion model to chargeability
# charg = M(m), where M(.) is a mapping for cells below topography
charg_est = actmap * mopt_ip
charg_est[~actind] = np.nan
charg_true = charg.copy()
charg_true[~actind] = np.nan
# show recovered chargeability
if plotIt:
fig, ax = plt.subplots(2, 1, figsize=(20, 6))
out1 = mesh.plotImage(charg_true,
clim=(0, 0.1),
pcolorOpts={"cmap": "magma"},
ax=ax[0])
out2 = mesh.plotImage(charg_est,
clim=(0, 0.1),
pcolorOpts={"cmap": "magma"},
ax=ax[1])
out = [out1, out2]
for i in range(2):
ax[i].plot(survey_dc.electrode_locations[:, 0],
survey_dc.electrode_locations[:, 1], 'rv')
ax[i].set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax[i].set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[i][0], ax=ax[i])
cb.set_label("Resistivity ($\Omega$m)")
ax[i].set_xlabel("Northing (m)")
ax[i].set_ylabel("Elevation (m)")
ax[i].set_aspect('equal')
plt.tight_layout()
plt.show()
def run(plotIt=True):
# Define the inducing field parameter
H0 = (50000, 90, 0)
# Create a mesh
dx = 5.
hxind = [(dx, 5, -1.3), (dx, 10), (dx, 5, 1.3)]
hyind = [(dx, 5, -1.3), (dx, 10), (dx, 5, 1.3)]
hzind = [(dx, 5, -1.3), (dx, 10)]
mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCC')
# Get index of the center
midx = int(mesh.nCx / 2)
midy = int(mesh.nCy / 2)
# Lets create a simple Gaussian topo and set the active cells
[xx, yy] = np.meshgrid(mesh.vectorNx, mesh.vectorNy)
zz = -np.exp((xx**2 + yy**2) / 75**2) + mesh.vectorNz[-1]
# We would usually load a topofile
topo = np.c_[Utils.mkvc(xx), Utils.mkvc(yy), Utils.mkvc(zz)]
# Go from topo to array of indices of active cells
actv = Utils.surface2ind_topo(mesh, topo, 'N')
actv = np.where(actv)[0]
nC = len(actv)
# Create and array of observation points
xr = np.linspace(-20., 20., 20)
yr = np.linspace(-20., 20., 20)
X, Y = np.meshgrid(xr, yr)
# Move the observation points 5m above the topo
Z = -np.exp((X**2 + Y**2) / 75**2) + mesh.vectorNz[-1] + 5.
# Create a MAGsurvey
rxLoc = np.c_[Utils.mkvc(X.T), Utils.mkvc(Y.T), Utils.mkvc(Z.T)]
rxLoc = PF.BaseMag.RxObs(rxLoc)
srcField = PF.BaseMag.SrcField([rxLoc], param=H0)
survey = PF.BaseMag.LinearSurvey(srcField)
# We can now create a susceptibility model and generate data
# Here a simple block in half-space
model = np.zeros((mesh.nCx, mesh.nCy, mesh.nCz))
model[(midx - 2):(midx + 2), (midy - 2):(midy + 2), -6:-2] = 0.02
model = Utils.mkvc(model)
model = model[actv]
# Create active map to go from reduce set to full
actvMap = Maps.InjectActiveCells(mesh, actv, -100)
# Create reduced identity map
idenMap = Maps.IdentityMap(nP=nC)
# Create the forward model operator
prob = PF.Magnetics.MagneticIntegral(mesh, chiMap=idenMap, actInd=actv)
# Pair the survey and problem
survey.pair(prob)
# Compute linear forward operator and compute some data
d = prob.fields(model)
# Add noise and uncertainties
# We add some random Gaussian noise (1nT)
data = d + np.random.randn(len(d))
wd = np.ones(len(data)) * 1. # Assign flat uncertainties
survey.dobs = data
survey.std = wd
survey.mtrue = model
# Create sensitivity weights from our linear forward operator
rxLoc = survey.srcField.rxList[0].locs
wr = np.sum(prob.G**2., axis=0)**0.5
wr = (wr / np.max(wr))
# Create a regularization
reg = Regularization.Sparse(mesh, indActive=actv, mapping=idenMap)
reg.cell_weights = wr
reg.mref = np.zeros(nC)
reg.norms = np.c_[0, 0, 0, 0]
# reg.eps_p, reg.eps_q = 1e-0, 1e-0
# Data misfit function
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.W = 1 / wd
# Add directives to the inversion
opt = Optimization.ProjectedGNCG(maxIter=100,
lower=0.,
upper=1.,
maxIterLS=20,
maxIterCG=20,
tolCG=1e-3)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1e-1)
# Here is where the norms are applied
# Use pick a threshold parameter empirically based on the distribution of
# model parameters
IRLS = Directives.Update_IRLS(f_min_change=1e-4, maxIRLSiter=40)
saveDict = Directives.SaveOutputEveryIteration(save_txt=False)
update_Jacobi = Directives.UpdatePreconditioner()
inv = Inversion.BaseInversion(
invProb, directiveList=[IRLS, betaest, update_Jacobi, saveDict])
# Run the inversion
m0 = np.ones(nC) * 1e-4 # Starting model
mrec = inv.run(m0)
if plotIt:
# Here is the recovered susceptibility model
ypanel = midx
zpanel = -5
m_l2 = actvMap * invProb.l2model
m_l2[m_l2 == -100] = np.nan
m_lp = actvMap * mrec
m_lp[m_lp == -100] = np.nan
m_true = actvMap * model
m_true[m_true == -100] = np.nan
# Plot the data
Utils.PlotUtils.plot2Ddata(rxLoc, d)
plt.figure()
# Plot L2 model
ax = plt.subplot(321)
mesh.plotSlice(m_l2,
ax=ax,
normal='Z',
ind=zpanel,
grid=True,
clim=(model.min(), model.max()))
plt.plot(([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCy[ypanel], mesh.vectorCCy[ypanel]]),
color='w')
plt.title('Plan l2-model.')
plt.gca().set_aspect('equal')
plt.ylabel('y')
ax.xaxis.set_visible(False)
plt.gca().set_aspect('equal', adjustable='box')
# Vertica section
ax = plt.subplot(322)
mesh.plotSlice(m_l2,
ax=ax,
normal='Y',
ind=midx,
grid=True,
clim=(model.min(), model.max()))
plt.plot(([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCz[zpanel], mesh.vectorCCz[zpanel]]),
color='w')
plt.title('E-W l2-model.')
plt.gca().set_aspect('equal')
ax.xaxis.set_visible(False)
plt.ylabel('z')
plt.gca().set_aspect('equal', adjustable='box')
# Plot Lp model
ax = plt.subplot(323)
mesh.plotSlice(m_lp,
ax=ax,
normal='Z',
ind=zpanel,
grid=True,
clim=(model.min(), model.max()))
plt.plot(([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCy[ypanel], mesh.vectorCCy[ypanel]]),
color='w')
plt.title('Plan lp-model.')
plt.gca().set_aspect('equal')
ax.xaxis.set_visible(False)
plt.ylabel('y')
plt.gca().set_aspect('equal', adjustable='box')
# Vertical section
ax = plt.subplot(324)
mesh.plotSlice(m_lp,
ax=ax,
normal='Y',
ind=midx,
grid=True,
clim=(model.min(), model.max()))
plt.plot(([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCz[zpanel], mesh.vectorCCz[zpanel]]),
color='w')
plt.title('E-W lp-model.')
plt.gca().set_aspect('equal')
ax.xaxis.set_visible(False)
plt.ylabel('z')
plt.gca().set_aspect('equal', adjustable='box')
# Plot True model
ax = plt.subplot(325)
mesh.plotSlice(m_true,
ax=ax,
normal='Z',
ind=zpanel,
grid=True,
clim=(model.min(), model.max()))
plt.plot(([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCy[ypanel], mesh.vectorCCy[ypanel]]),
color='w')
plt.title('Plan true model.')
plt.gca().set_aspect('equal')
plt.xlabel('x')
plt.ylabel('y')
plt.gca().set_aspect('equal', adjustable='box')
# Vertical section
ax = plt.subplot(326)
mesh.plotSlice(m_true,
ax=ax,
normal='Y',
ind=midx,
grid=True,
clim=(model.min(), model.max()))
plt.plot(([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCz[zpanel], mesh.vectorCCz[zpanel]]),
color='w')
plt.title('E-W true model.')
plt.gca().set_aspect('equal')
plt.xlabel('x')
plt.ylabel('z')
plt.gca().set_aspect('equal', adjustable='box')
# Plot convergence curves
fig, axs = plt.figure(), plt.subplot()
axs.plot(saveDict.phi_d, 'k', lw=2)
axs.plot(np.r_[IRLS.iterStart, IRLS.iterStart],
np.r_[0, np.max(saveDict.phi_d)], 'k:')
twin = axs.twinx()
twin.plot(saveDict.phi_m, 'k--', lw=2)
axs.text(IRLS.iterStart,
0,
'IRLS Steps',
va='bottom',
ha='center',
rotation='vertical',
size=12,
bbox={'facecolor': 'white'})
axs.set_ylabel('$\phi_d$', size=16, rotation=0)
axs.set_xlabel('Iterations', size=14)
twin.set_ylabel('$\phi_m$', size=16, rotation=0)
def run(plotIt=True,
survey_type="dipole-dipole",
rho_background=1e3,
rho_block=1e2,
block_x0=100,
block_dx=10,
block_y0=-10,
block_dy=5):
np.random.seed(1)
# Initiate I/O class for DC
IO = DC.IO()
# Obtain ABMN locations
xmin, xmax = 0., 200.
ymin, ymax = 0., 0.
zmin, zmax = 0, 0
endl = np.array([[xmin, ymin, zmin], [xmax, ymax, zmax]])
# Generate DC survey object
survey = DC.Utils.gen_DCIPsurvey(endl,
survey_type=survey_type,
dim=2,
a=10,
b=10,
n=10)
survey.getABMN_locations()
survey = IO.from_ambn_locations_to_survey(survey.a_locations,
survey.b_locations,
survey.m_locations,
survey.n_locations,
survey_type,
data_dc_type='volt')
# Obtain 2D TensorMesh
mesh, actind = IO.set_mesh()
# Flat topography
actind = Utils.surface2ind_topo(mesh, np.c_[mesh.vectorCCx,
mesh.vectorCCx * 0.])
survey.drapeTopo(mesh, actind, option="top")
# Use Exponential Map: m = log(rho)
actmap = Maps.InjectActiveCells(mesh,
indActive=actind,
valInactive=np.log(1e8))
parametric_block = Maps.ParametricBlock(mesh, slopeFact=1e2)
mapping = Maps.ExpMap(mesh) * parametric_block
# Set true model
# val_background,val_block, block_x0, block_dx, block_y0, block_dy
mtrue = np.r_[np.log(1e3), np.log(10), 100, 10, -20, 10]
# Set initial model
m0 = np.r_[np.log(rho_background),
np.log(rho_block), block_x0, block_dx, block_y0, block_dy]
rho = mapping * mtrue
rho0 = mapping * m0
# Show the true conductivity model
fig = plt.figure(figsize=(12, 3))
ax = plt.subplot(111)
temp = rho.copy()
temp[~actind] = np.nan
out = mesh.plotImage(temp,
grid=False,
ax=ax,
gridOpts={'alpha': 0.2},
clim=(10, 1000),
pcolorOpts={
"cmap": "viridis",
"norm": colors.LogNorm()
})
ax.plot(survey.electrode_locations[:, 0], survey.electrode_locations[:, 1],
'k.')
ax.set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax.set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[0])
cb.set_label("Resistivity (ohm-m)")
ax.set_aspect('equal')
ax.set_title("True resistivity model")
plt.show()
# Show the true conductivity model
fig = plt.figure(figsize=(12, 3))
ax = plt.subplot(111)
temp = rho0.copy()
temp[~actind] = np.nan
out = mesh.plotImage(temp,
grid=False,
ax=ax,
gridOpts={'alpha': 0.2},
clim=(10, 1000),
pcolorOpts={
"cmap": "viridis",
"norm": colors.LogNorm()
})
ax.plot(survey.electrode_locations[:, 0], survey.electrode_locations[:, 1],
'k.')
ax.set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax.set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[0])
cb.set_label("Resistivity (ohm-m)")
ax.set_aspect('equal')
ax.set_title("Initial resistivity model")
plt.show()
# Generate 2.5D DC problem
# "N" means potential is defined at nodes
prb = DC.Problem2D_N(mesh, rhoMap=mapping, storeJ=True, Solver=Solver)
# Pair problem with survey
try:
prb.pair(survey)
except:
survey.unpair()
prb.pair(survey)
# Make synthetic DC data with 5% Gaussian noise
dtrue = survey.makeSyntheticData(mtrue, std=0.05, force=True)
# Show apparent resisitivty pseudo-section
IO.plotPseudoSection(data=survey.dobs / IO.G,
data_type='apparent_resistivity')
# Show apparent resisitivty histogram
fig = plt.figure()
out = hist(survey.dobs / IO.G, bins=20)
plt.show()
# Set uncertainty
# floor
eps = 10**(-3.2)
# percentage
std = 0.05
dmisfit = DataMisfit.l2_DataMisfit(survey)
uncert = abs(survey.dobs) * std + eps
dmisfit.W = 1. / uncert
# Map for a regularization
mesh_1d = Mesh.TensorMesh([parametric_block.nP])
# Related to inversion
reg = Regularization.Simple(mesh_1d, alpha_x=0.)
opt = Optimization.InexactGaussNewton(maxIter=10)
invProb = InvProblem.BaseInvProblem(dmisfit, reg, opt)
beta = Directives.BetaSchedule(coolingFactor=5, coolingRate=2)
betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1e0)
target = Directives.TargetMisfit()
updateSensW = Directives.UpdateSensitivityWeights()
update_Jacobi = Directives.UpdatePreconditioner()
invProb.beta = 0.
inv = Inversion.BaseInversion(invProb, directiveList=[target])
prb.counter = opt.counter = Utils.Counter()
opt.LSshorten = 0.5
opt.remember('xc')
# Run inversion
mopt = inv.run(m0)
# Convert obtained inversion model to resistivity
# rho = M(m), where M(.) is a mapping
rho_est = mapping * mopt
rho_true = rho.copy()
# show recovered conductivity
vmin, vmax = rho.min(), rho.max()
fig, ax = plt.subplots(2, 1, figsize=(20, 6))
out1 = mesh.plotImage(rho_true,
clim=(10, 1000),
pcolorOpts={
"cmap": "viridis",
"norm": colors.LogNorm()
},
ax=ax[0])
out2 = mesh.plotImage(rho_est,
clim=(10, 1000),
pcolorOpts={
"cmap": "viridis",
"norm": colors.LogNorm()
},
ax=ax[1])
out = [out1, out2]
for i in range(2):
ax[i].plot(survey.electrode_locations[:, 0],
survey.electrode_locations[:, 1], 'kv')
ax[i].set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax[i].set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[i][0], ax=ax[i])
cb.set_label("Resistivity ($\Omega$m)")
ax[i].set_xlabel("Northing (m)")
ax[i].set_ylabel("Elevation (m)")
ax[i].set_aspect('equal')
ax[0].set_title("True resistivity model")
ax[1].set_title("Recovered resistivity model")
plt.tight_layout()
plt.show()
#%% ## TESTING CODE
# Generate survey using two tiles, compute solution using UBC-DCIP3D
# and compare by using the pre-computed grid
padxy = np.r_[dx[1]*expf**(np.asarray(range(npadxy['DC']))+1)]
padz = np.r_[dx[1]*expf**(np.asarray(range(npadz['DC']))+1)]
hx = np.r_[padxy[::-1], core['DC'], padxy]
hy = np.r_[padxy[::-1], core['DC'],core['DC'], padxy]
hz = np.r_[padz[::-1],[33],np.ones(25)*30,[23,18,15,12], np.ones(15)*10,[12,15,18,23],30*expf**(np.asarray(range(npadz['DC'])))]
mesh = Mesh.TensorMesh([hx,hy,hz], 'CC0')
mesh._x0 = (mesh.x0[0] + np.mean(X[tID]), mesh.x0[1]+np.mean(Y[tID]), mesh.x0[2]-(np.sum(hz[:(npadz['DC']+20)])))
# Extract model from global tolocal mesh
actv2 = Utils.surface2ind_topo(mesh, topo, 'N')
P = Maps.Mesh2MeshTopo([mesh_global,mesh],[actv,actv2],nIterpPts = 12)
model = mesh_global.readModelUBC(work_dir + '\\' + modelfile['DC'])
model_Tile = P*(model[actv])
m = np.ones(mesh.nC)*1e-8
m[actv2] = model_Tile
# mtemp = m.reshape(mesh.vnC, order='F')
Mesh.TensorMesh.writeUBC(mesh,work_dir +'\\MeshTile.msh')
Mesh.TensorMesh.writeModelUBC(mesh,work_dir +'\\MeshTile.mod',m)
# Create survey
def run(plotIt=True, survey_type="dipole-dipole", p=0., qx=2., qz=2.):
np.random.seed(1)
# Initiate I/O class for DC
IO = DC.IO()
# Obtain ABMN locations
xmin, xmax = 0., 200.
ymin, ymax = 0., 0.
zmin, zmax = 0, 0
endl = np.array([[xmin, ymin, zmin], [xmax, ymax, zmax]])
# Generate DC survey object
survey = DC.Utils.gen_DCIPsurvey(endl, survey_type=survey_type, dim=2,
a=10, b=10, n=10)
survey.getABMN_locations()
survey = IO.from_ambn_locations_to_survey(
survey.a_locations, survey.b_locations,
survey.m_locations, survey.n_locations,
survey_type, data_dc_type='volt'
)
# Obtain 2D TensorMesh
mesh, actind = IO.set_mesh()
topo, mesh1D = DC.Utils.genTopography(mesh, -10, 0, its=100)
actind = Utils.surface2ind_topo(mesh, np.c_[mesh1D.vectorCCx, topo])
survey.drapeTopo(mesh, actind, option="top")
# Build a conductivity model
blk_inds_c = Utils.ModelBuilder.getIndicesSphere(
np.r_[60., -25.], 12.5, mesh.gridCC
)
blk_inds_r = Utils.ModelBuilder.getIndicesSphere(
np.r_[140., -25.], 12.5, mesh.gridCC
)
layer_inds = mesh.gridCC[:, 1] > -5.
sigma = np.ones(mesh.nC)*1./100.
sigma[blk_inds_c] = 1./10.
sigma[blk_inds_r] = 1./1000.
sigma[~actind] = 1./1e8
rho = 1./sigma
# Show the true conductivity model
if plotIt:
fig = plt.figure(figsize=(12, 3))
ax = plt.subplot(111)
temp = rho.copy()
temp[~actind] = np.nan
out = mesh.plotImage(
temp, grid=True, ax=ax, gridOpts={'alpha': 0.2},
clim=(10, 1000),
pcolorOpts={"cmap": "viridis", "norm": colors.LogNorm()}
)
ax.plot(
survey.electrode_locations[:, 0],
survey.electrode_locations[:, 1], 'k.'
)
ax.set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax.set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[0])
cb.set_label("Resistivity (ohm-m)")
ax.set_aspect('equal')
plt.show()
# Use Exponential Map: m = log(rho)
actmap = Maps.InjectActiveCells(
mesh, indActive=actind, valInactive=np.log(1e8)
)
mapping = Maps.ExpMap(mesh) * actmap
# Generate mtrue
mtrue = np.log(rho[actind])
# Generate 2.5D DC problem
# "N" means potential is defined at nodes
prb = DC.Problem2D_N(
mesh, rhoMap=mapping, storeJ=True,
Solver=Solver, verbose=True
)
# Pair problem with survey
try:
prb.pair(survey)
except:
survey.unpair()
prb.pair(survey)
# Make synthetic DC data with 5% Gaussian noise
dtrue = survey.makeSyntheticData(mtrue, std=0.05, force=True)
IO.data_dc = dtrue
# Show apparent resisitivty pseudo-section
if plotIt:
IO.plotPseudoSection(
data=survey.dobs/IO.G, data_type='apparent_resistivity'
)
# Show apparent resisitivty histogram
if plotIt:
fig = plt.figure()
out = hist(survey.dobs/IO.G, bins=20)
plt.xlabel("Apparent Resisitivty ($\Omega$m)")
plt.show()
# Set initial model based upon histogram
m0 = np.ones(actmap.nP)*np.log(100.)
# Set uncertainty
# floor
eps = 10**(-3.2)
# percentage
std = 0.05
dmisfit = DataMisfit.l2_DataMisfit(survey)
uncert = abs(survey.dobs) * std + eps
dmisfit.W = 1./uncert
# Map for a regularization
regmap = Maps.IdentityMap(nP=int(actind.sum()))
# Related to inversion
reg = Regularization.Sparse(
mesh, indActive=actind, mapping=regmap,
gradientType='components'
)
# gradientType = 'components'
reg.norms = np.c_[p, qx, qz, 0.]
IRLS = Directives.Update_IRLS(
maxIRLSiter=20, minGNiter=1,
betaSearch=False, fix_Jmatrix=True
)
opt = Optimization.InexactGaussNewton(maxIter=40)
invProb = InvProblem.BaseInvProblem(dmisfit, reg, opt)
beta = Directives.BetaSchedule(coolingFactor=5, coolingRate=2)
betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1e0)
target = Directives.TargetMisfit()
update_Jacobi = Directives.UpdatePreconditioner()
inv = Inversion.BaseInversion(
invProb, directiveList=[
betaest, IRLS
]
)
prb.counter = opt.counter = Utils.Counter()
opt.LSshorten = 0.5
opt.remember('xc')
# Run inversion
mopt = inv.run(m0)
rho_est = mapping*mopt
rho_est_l2 = mapping*invProb.l2model
rho_est[~actind] = np.nan
rho_est_l2[~actind] = np.nan
rho_true = rho.copy()
rho_true[~actind] = np.nan
# show recovered conductivity
if plotIt:
vmin, vmax = rho.min(), rho.max()
fig, ax = plt.subplots(3, 1, figsize=(20, 9))
out1 = mesh.plotImage(
rho_true, clim=(10, 1000),
pcolorOpts={"cmap": "viridis", "norm": colors.LogNorm()},
ax=ax[0]
)
out2 = mesh.plotImage(
rho_est_l2, clim=(10, 1000),
pcolorOpts={"cmap": "viridis", "norm": colors.LogNorm()},
ax=ax[1]
)
out3 = mesh.plotImage(
rho_est, clim=(10, 1000),
pcolorOpts={"cmap": "viridis", "norm": colors.LogNorm()},
ax=ax[2]
)
out = [out1, out2, out3]
titles = ["True", "L2", ("L%d, Lx%d, Lz%d")%(p, qx, qz)]
for i in range(3):
ax[i].plot(
survey.electrode_locations[:, 0],
survey.electrode_locations[:, 1], 'kv'
)
ax[i].set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax[i].set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[i][0], ax=ax[i])
cb.set_label("Resistivity ($\Omega$m)")
ax[i].set_xlabel("Northing (m)")
ax[i].set_ylabel("Elevation (m)")
ax[i].set_aspect('equal')
ax[i].set_title(titles[i])
plt.tight_layout()
plt.show()
def run(plotIt=True):
# Create a mesh
dx = 5.
hxind = [(dx, 5, -1.3), (dx, 15), (dx, 5, 1.3)]
hyind = [(dx, 5, -1.3), (dx, 15), (dx, 5, 1.3)]
hzind = [(dx, 5, -1.3), (dx, 7), (3.5, 1), (2, 5)]
mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCC')
# Get index of the center
midx = int(mesh.nCx/2)
midy = int(mesh.nCy/2)
# Lets create a simple Gaussian topo and set the active cells
[xx, yy] = np.meshgrid(mesh.vectorNx, mesh.vectorNy)
zz = -np.exp((xx**2 + yy**2) / 75**2) + mesh.vectorNz[-1]
# We would usually load a topofile
topo = np.c_[Utils.mkvc(xx), Utils.mkvc(yy), Utils.mkvc(zz)]
# Go from topo to array of indices of active cells
actv = Utils.surface2ind_topo(mesh, topo, 'N')
actv = np.where(actv)[0]
nC = len(actv)
# Create and array of observation points
xr = np.linspace(-30., 30., 20)
yr = np.linspace(-30., 30., 20)
X, Y = np.meshgrid(xr, yr)
# Move the observation points 5m above the topo
Z = -np.exp((X**2 + Y**2) / 75**2) + mesh.vectorNz[-1] + 0.1
# Create a GRAVsurvey
rxLoc = np.c_[Utils.mkvc(X.T), Utils.mkvc(Y.T), Utils.mkvc(Z.T)]
rxLoc = PF.BaseGrav.RxObs(rxLoc)
srcField = PF.BaseGrav.SrcField([rxLoc])
survey = PF.BaseGrav.LinearSurvey(srcField)
# We can now create a density model and generate data
# Here a simple block in half-space
model = np.zeros((mesh.nCx, mesh.nCy, mesh.nCz))
model[(midx-5):(midx-1), (midy-2):(midy+2), -10:-6] = 0.75
model[(midx+1):(midx+5), (midy-2):(midy+2), -10:-6] = -0.75
model = Utils.mkvc(model)
model = model[actv]
# Create active map to go from reduce set to full
actvMap = Maps.InjectActiveCells(mesh, actv, -100)
# Create reduced identity map
idenMap = Maps.IdentityMap(nP=nC)
# Create the forward model operator
prob = PF.Gravity.GravityIntegral(mesh, rhoMap=idenMap, actInd=actv)
# Pair the survey and problem
survey.pair(prob)
# Compute linear forward operator and compute some data
d = prob.fields(model)
# Add noise and uncertainties
# We add some random Gaussian noise (1nT)
data = d + np.random.randn(len(d))*1e-3
wd = np.ones(len(data))*1e-3 # Assign flat uncertainties
survey.dobs = data
survey.std = wd
survey.mtrue = model
# Create sensitivity weights from our linear forward operator
rxLoc = survey.srcField.rxList[0].locs
wr = np.sum(prob.G**2., axis=0)**0.5
wr = (wr/np.max(wr))
# Create a regularization
reg = Regularization.Sparse(mesh, indActive=actv, mapping=idenMap)
reg.cell_weights = wr
reg.norms = np.c_[0, 0, 0, 0]
# Data misfit function
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.W = Utils.sdiag(1/wd)
# Add directives to the inversion
opt = Optimization.ProjectedGNCG(maxIter=100, lower=-1., upper=1.,
maxIterLS=20, maxIterCG=10,
tolCG=1e-3)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1e-1)
# Here is where the norms are applied
# Use pick a threshold parameter empirically based on the distribution of
# model parameters
IRLS = Directives.Update_IRLS(
f_min_change=1e-4, maxIRLSiter=30, coolEpsFact=1.5, beta_tol=1e-1,
)
saveDict = Directives.SaveOutputEveryIteration(save_txt=False)
update_Jacobi = Directives.UpdatePreconditioner()
inv = Inversion.BaseInversion(
invProb, directiveList=[IRLS, betaest, update_Jacobi, saveDict]
)
# Run the inversion
m0 = np.ones(nC)*1e-4 # Starting model
mrec = inv.run(m0)
if plotIt:
# Here is the recovered susceptibility model
ypanel = midx
zpanel = -7
m_l2 = actvMap * invProb.l2model
m_l2[m_l2 == -100] = np.nan
m_lp = actvMap * mrec
m_lp[m_lp == -100] = np.nan
m_true = actvMap * model
m_true[m_true == -100] = np.nan
vmin, vmax = mrec.min(), mrec.max()
# Plot the data
Utils.PlotUtils.plot2Ddata(rxLoc, data)
plt.figure()
# Plot L2 model
ax = plt.subplot(321)
mesh.plotSlice(m_l2, ax=ax, normal='Z', ind=zpanel,
grid=True, clim=(vmin, vmax))
plt.plot(([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCy[ypanel], mesh.vectorCCy[ypanel]]), color='w')
plt.title('Plan l2-model.')
plt.gca().set_aspect('equal')
plt.ylabel('y')
ax.xaxis.set_visible(False)
plt.gca().set_aspect('equal', adjustable='box')
# Vertical section
ax = plt.subplot(322)
mesh.plotSlice(m_l2, ax=ax, normal='Y', ind=midx,
grid=True, clim=(vmin, vmax))
plt.plot(([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCz[zpanel], mesh.vectorCCz[zpanel]]), color='w')
plt.title('E-W l2-model.')
plt.gca().set_aspect('equal')
ax.xaxis.set_visible(False)
plt.ylabel('z')
plt.gca().set_aspect('equal', adjustable='box')
# Plot Lp model
ax = plt.subplot(323)
mesh.plotSlice(m_lp, ax=ax, normal='Z', ind=zpanel,
grid=True, clim=(vmin, vmax))
plt.plot(([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCy[ypanel], mesh.vectorCCy[ypanel]]), color='w')
plt.title('Plan lp-model.')
plt.gca().set_aspect('equal')
ax.xaxis.set_visible(False)
plt.ylabel('y')
plt.gca().set_aspect('equal', adjustable='box')
# Vertical section
ax = plt.subplot(324)
mesh.plotSlice(m_lp, ax=ax, normal='Y', ind=midx,
grid=True, clim=(vmin, vmax))
plt.plot(([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCz[zpanel], mesh.vectorCCz[zpanel]]), color='w')
plt.title('E-W lp-model.')
plt.gca().set_aspect('equal')
ax.xaxis.set_visible(False)
plt.ylabel('z')
plt.gca().set_aspect('equal', adjustable='box')
# Plot True model
ax = plt.subplot(325)
mesh.plotSlice(m_true, ax=ax, normal='Z', ind=zpanel,
grid=True, clim=(vmin, vmax))
plt.plot(([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCy[ypanel], mesh.vectorCCy[ypanel]]), color='w')
plt.title('Plan true model.')
plt.gca().set_aspect('equal')
plt.xlabel('x')
plt.ylabel('y')
plt.gca().set_aspect('equal', adjustable='box')
# Vertical section
ax = plt.subplot(326)
mesh.plotSlice(m_true, ax=ax, normal='Y', ind=midx,
grid=True, clim=(vmin, vmax))
plt.plot(([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCz[zpanel], mesh.vectorCCz[zpanel]]), color='w')
plt.title('E-W true model.')
plt.gca().set_aspect('equal')
plt.xlabel('x')
plt.ylabel('z')
plt.gca().set_aspect('equal', adjustable='box')
# Plot convergence curves
fig, axs = plt.figure(), plt.subplot()
axs.plot(saveDict.phi_d, 'k', lw=2)
axs.plot(
np.r_[IRLS.iterStart, IRLS.iterStart],
np.r_[0, np.max(saveDict.phi_d)], 'k:'
)
twin = axs.twinx()
twin.plot(saveDict.phi_m, 'k--', lw=2)
axs.text(
IRLS.iterStart, np.max(saveDict.phi_d)/2.,
'IRLS Steps', va='bottom', ha='center',
rotation='vertical', size=12,
bbox={'facecolor': 'white'}
)
axs.set_ylabel('$\phi_d$', size=16, rotation=0)
axs.set_xlabel('Iterations', size=14)
twin.set_ylabel('$\phi_m$', size=16, rotation=0)
def run(plotIt=True, survey_type="pole-dipole"):
np.random.seed(1)
# Initiate I/O class for DC
IO = DC.IO()
# Obtain ABMN locations
fileName1 = "/Users/juan/Documents/testData/fmdata-daf.con" # output mod
fileName2 = "/Users/juan/Documents/testData/forwardmodel.msh" # input mesh
mesh = Mesh.TensorMesh._readUBC_3DMesh(fileName2) # Read in/create mesh
print("Starting forward modeling")
start = clock()
# Define model Background
rx = getRxData() # rx locations
tx = getTxData() # tx locations
survey_dc = generateSurvey(rx, tx, 45, 55) # create survey object
survey_dc.survey_type = "pole-dipole"
survey_dc.getABMN_locations() # get locations
# survey_dc = IO.from_ambn_locations_to_survey(
# survey_dc.a_locations, survey_dc.b_locations,
# survey_dc.m_locations, survey_dc.n_locations,
# survey_type, data_dc_type='volt', data_ip_type='volt'
# )
uniq = Utils.uniqueRows(
np.vstack((survey_dc.a_locations, survey_dc.b_locations,
survey_dc.m_locations, survey_dc.n_locations)))
electrode_locations = uniq[0] # assign
actinds = Utils.surface2ind_topo(mesh, electrode_locations,
method='cubic') # active indicies
# survey_dc.drapeTopo(mesh, actinds)
IO.a_locations = survey_dc.a_locations.copy()
IO.b_locations = survey_dc.b_locations.copy()
IO.m_locations = survey_dc.m_locations.copy()
IO.n_locations = survey_dc.n_locations.copy() # drape topo
IO.data_dc_type = 'volt'
IO.G = IO.geometric_factor(survey_dc)
# =============================================================================
# create sphere for ice representation
x0 = (np.max(mesh.gridCC[:, 0]) +
np.min(mesh.gridCC[:, 0])) / 2. + 50 # x0 center point of sphere
y0 = (np.max(mesh.gridCC[:, 1]) +
np.min(mesh.gridCC[:, 1])) / 2. - 50 # y0 center point of sphere
z0 = 2350 # x0 center point of sphere
# (np.max(mesh.gridCC[:, 2]) + np.min(mesh.gridCC[:, 2])) / 2.
r0 = 500 # radius of sphere
print(x0, y0, z0)
csph = (np.sqrt((mesh.gridCC[:, 0] - x0)**2. +
(mesh.gridCC[:, 1] - y0)**2. +
(mesh.gridCC[:, 2] - z0)**2.)) < r0 # indicies of sphere
# sphere done =================================================================
# ============================================================================
# Create model
mx = np.ones(mesh.nC) * 0.018 # chargeability
sigma = np.ones(mesh.nC) * 1. / 15000.
# create dipping structure parameters
theta = 45. * np.pi / 180. # dipping angle
x0_d = 374700.
x1_d = 375000.
y0_d = 6275850.
y0_1d = 900. * np.sin(theta) + y0_d
y1_d = 6275900.
y1_1d = 900. * np.sin(theta) + y1_d
z0_d = 1900.
z1_d = z0_d - (900. * np.cos(theta))
m_ = (z0_d - z1_d) / (y0_1d - y0_d) # slope of dip
# loop through mesh and assign dipping structure conductivity
for idx in range(mesh.nC):
if z1_d <= mesh.gridCC[idx, 2] <= z0_d:
if (x0_d <= mesh.gridCC[idx, 0] <= x1_d):
yslope1 = y0_d + (1. / m_) * (mesh.gridCC[idx, 2] - z0_d)
yslope2 = y1_d + (1. / m_) * (mesh.gridCC[idx, 2] - z0_d)
if yslope1 <= mesh.gridCC[idx, 1] <= yslope2:
mx[idx] = 0.035
sigma[idx] = 1. / 300.
# mx[csph] = ((0.025) *
# np.ones_like(mx[csph])) # set sphere values
mx[~actinds] = 1. / 1e8 # flag air values
# sigma[csph] = ((5000.) *
# np.ones_like(sigma[csph])) # set sphere values
sigma[~actinds] = 1. / 1e8 # flag air values
rho = 1. / sigma
stop = clock()
print(stop)
# plot results
# Show the true conductivity model
if plotIt:
ncy = mesh.nCy
ncz = mesh.nCz
ncx = mesh.nCx
print(mesh.nC)
clim = [0, 0.04]
fig, ax = plt.subplots(2, 2, figsize=(12, 6))
ax = Utils.mkvc(ax)
dat = mesh.plotSlice(((mx)),
ax=ax[0],
normal='Z',
clim=clim,
ind=int(ncz / 2 - 14),
pcolorOpts={"cmap": "jet"})
ax[0].plot(rx[:, 0], rx[:, 1], 'or')
ax[0].plot(tx[:, 0], tx[:, 1], 'dk')
mesh.plotSlice(((mx)),
ax=ax[1],
normal='Y',
clim=clim,
ind=int(ncy / 2 + 2),
pcolorOpts={"cmap": "jet"})
mesh.plotSlice(((mx)),
ax=ax[2],
normal='X',
clim=clim,
ind=int(ncx / 2 + 4),
pcolorOpts={"cmap": "jet"})
mesh.plotSlice(((mx)),
ax=ax[3],
normal='X',
clim=clim,
ind=int(ncx / 2 + 8),
pcolorOpts={"cmap": "jet"})
cbar_ax = fig.add_axes([0.82, 0.15, 0.05, 0.7])
cb = plt.colorbar(dat[0], ax=cbar_ax)
fig.subplots_adjust(right=0.85)
cb.set_label('V/V')
cbar_ax.axis('off')
plt.show()
# print(mtrue.min(), mtrue.max())
# clim = [0, 20000]
# fig, ax = plt.subplots(2, 2, figsize=(12, 6))
# ax = Utils.mkvc(ax)
# dat = mesh.plotSlice(((mtrue)), ax=ax[0], normal='Z', clim=clim,
# ind=int(ncz / 2 - 4), pcolorOpts={"cmap": "jet"})
# ax[0].plot(rx[:, 0], rx[:, 1], 'or')
# mesh.plotSlice(((mtrue)), ax=ax[1], normal='Y', clim=clim,
# ind=int(ncy / 2), pcolorOpts={"cmap": "jet"})
# mesh.plotSlice(((mtrue)), ax=ax[2], normal='X', clim=clim,
# ind=int(ncx / 2 + 4), pcolorOpts={"cmap": "jet"})
# mesh.plotSlice(((mtrue)), ax=ax[3], normal='X', clim=clim,
# ind=int(ncx / 2 + 8), pcolorOpts={"cmap": "jet"})
# cbar_ax = fig.add_axes([0.82, 0.15, 0.05, 0.7])
# cb = plt.colorbar(dat[0], ax=cbar_ax)
# fig.subplots_adjust(right=0.85)
# cb.set_label('rho')
# cbar_ax.axis('off')
# plt.show()
# print(error.size, survey_ip.obs.size)
# error = np.asarray(survey_ip.dobs) * (np.random.randint(-1, 2, survey_ip.dobs) / 20.)
# survey_ip.dobs = survey_ip.dobs + error
# Use Exponential Map: m = log(rho)
actmap = Maps.InjectActiveCells(mesh,
indActive=actinds,
valInactive=np.log(1e8))
mapping = Maps.ExpMap(mesh) * actmap
# Generate mtrue_dc for resistivity
mtrue_dc = np.log(rho[actinds])
# Generate 3D DC problem
# "CC" means potential is defined at center
prb = DC.Problem3D_CC(mesh, rhoMap=mapping, storeJ=False, Solver=Solver)
# Pair problem with survey
# try:
prb.pair(survey_dc)
# except:
# survey_dc.unpair()
# prb.pair(survey_dc)
survey_dc.dpred(mtrue_dc)
# Make synthetic DC data with 5% Gaussian noise
dtrue_dc = survey_dc.makeSyntheticData(mtrue_dc, std=0.05, force=True)
IO.data_dc = dtrue_dc
# Generate mtrue_ip for chargability
mtrue_ip = mx[actinds]
# Generate 3D DC problem
# "CC" means potential is defined at center
prb_ip = IP.Problem3D_CC(mesh,
etaMap=actmap,
storeJ=False,
rho=rho,
Solver=Solver)
survey_ip = IP.from_dc_to_ip_survey(survey_dc, dim="3D")
survey_ip.survey_type = "pole-dipole"
survey_ip.getABMN_locations()
prb_ip.pair(survey_ip)
survey_ip.dpred(mtrue_ip)
dtrue_ip = survey_ip.makeSyntheticData(mtrue_ip, std=0.05)
survey_ip.std = np.ones_like(dtrue_ip) * 0.05
survey_ip.eps = np.ones_like(dtrue_ip) * 10**(-4)
IO.data_ip = dtrue_ip
DC.Utils.writeUBC_DCobs("fmip.obs", survey_ip, 3, 'GENERAL', 'pole-dipole')
def run(plotIt=True, survey_type="dipole-dipole"):
np.random.seed(1)
# Initiate I/O class for DC
IO = DC.IO()
# Obtain ABMN locations
xmin, xmax = 0., 200.
ymin, ymax = 0., 0.
zmin, zmax = 0, 0
endl = np.array([[xmin, ymin, zmin], [xmax, ymax, zmax]])
# Generate DC survey object
survey_dc = DC.Utils.gen_DCIPsurvey(endl, survey_type=survey_type, dim=2,
a=10, b=10, n=10)
survey_dc.getABMN_locations()
survey_dc = IO.from_ambn_locations_to_survey(
survey_dc.a_locations, survey_dc.b_locations,
survey_dc.m_locations, survey_dc.n_locations,
survey_type, data_dc_type='volt', data_ip_type='volt'
)
# Obtain 2D TensorMesh
mesh, actind = IO.set_mesh()
topo, mesh1D = DC.Utils.genTopography(mesh, -10, 0, its=100)
actind = Utils.surface2ind_topo(mesh, np.c_[mesh1D.vectorCCx, topo])
survey_dc.drapeTopo(mesh, actind, option="top")
# Build conductivity and chargeability model
blk_inds_c = Utils.ModelBuilder.getIndicesSphere(
np.r_[60., -25.], 12.5, mesh.gridCC
)
blk_inds_r = Utils.ModelBuilder.getIndicesSphere(
np.r_[140., -25.], 12.5, mesh.gridCC
)
blk_inds_charg = Utils.ModelBuilder.getIndicesSphere(
np.r_[100., -25], 12.5, mesh.gridCC
)
sigma = np.ones(mesh.nC)*1./100.
sigma[blk_inds_c] = 1./10.
sigma[blk_inds_r] = 1./1000.
sigma[~actind] = 1./1e8
rho = 1./sigma
charg = np.zeros(mesh.nC)
charg[blk_inds_charg] = 0.1
# Show the true conductivity model
if plotIt:
fig, axs = plt.subplots(2,1, figsize=(12, 6))
temp_rho = rho.copy()
temp_rho[~actind] = np.nan
temp_charg = charg.copy()
temp_charg[~actind] = np.nan
out1 = mesh.plotImage(
temp_rho, grid=True, ax=axs[0], gridOpts={'alpha': 0.2},
clim=(10, 1000),
pcolorOpts={"cmap": "viridis", "norm": colors.LogNorm()}
)
out2 = mesh.plotImage(
temp_charg, grid=True, ax=axs[1], gridOpts={'alpha': 0.2},
clim=(0, 0.1),
pcolorOpts={"cmap": "magma"}
)
for i in range(2):
axs[i].plot(
survey_dc.electrode_locations[:, 0],
survey_dc.electrode_locations[:, 1], 'kv'
)
axs[i].set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
axs[i].set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
axs[i].set_aspect('equal')
cb = plt.colorbar(out1[0], ax=axs[0])
cb.set_label("Resistivity (ohm-m)")
cb = plt.colorbar(out2[0], ax=axs[1])
cb.set_label("Chargeability")
plt.show()
# Use Exponential Map: m = log(rho)
actmap = Maps.InjectActiveCells(
mesh, indActive=actind, valInactive=np.log(1e8)
)
mapping = Maps.ExpMap(mesh) * actmap
# Generate mtrue_dc for resistivity
mtrue_dc = np.log(rho[actind])
# Generate 2.5D DC problem
# "N" means potential is defined at nodes
prb = DC.Problem2D_N(
mesh, rhoMap=mapping, storeJ=True,
Solver=Solver
)
# Pair problem with survey
try:
prb.pair(survey_dc)
except:
survey_dc.unpair()
prb.pair(survey_dc)
# Make synthetic DC data with 5% Gaussian noise
dtrue_dc = survey_dc.makeSyntheticData(mtrue_dc, std=0.05, force=True)
IO.data_dc = dtrue_dc
# Generate mtrue_ip for chargability
mtrue_ip = charg[actind]
# Generate 2.5D DC problem
# "N" means potential is defined at nodes
prb_ip = IP.Problem2D_N(
mesh, etaMap=actmap, storeJ=True, rho=rho,
Solver=Solver
)
survey_ip = IP.from_dc_to_ip_survey(survey_dc, dim="2.5D")
prb_ip.pair(survey_ip)
dtrue_ip = survey_ip.makeSyntheticData(mtrue_ip, std=0.05)
IO.data_ip = dtrue_ip
# Show apparent resisitivty pseudo-section
if plotIt:
IO.plotPseudoSection(
data_type='apparent_resistivity', scale='log',
cmap='viridis'
)
plt.show()
# Show apparent chargeability pseudo-section
if plotIt:
IO.plotPseudoSection(
data_type='apparent_chargeability', scale='linear',
cmap='magma'
)
plt.show()
# Show apparent resisitivty histogram
if plotIt:
fig = plt.figure(figsize=(10, 4))
ax1 = plt.subplot(121)
out = hist(np.log10(abs(IO.voltages)), bins=20)
ax1.set_xlabel("log10 DC voltage (V)")
ax2 = plt.subplot(122)
out = hist(IO.apparent_resistivity, bins=20)
ax2.set_xlabel("Apparent Resistivity ($\Omega$m)")
plt.tight_layout()
plt.show()
# Set initial model based upon histogram
m0_dc = np.ones(actmap.nP)*np.log(100.)
# Set uncertainty
# floor
eps_dc = 10**(-3.2)
# percentage
std_dc = 0.05
mopt_dc, pred_dc = DC.run_inversion(
m0_dc, survey_dc, actind, mesh, std_dc, eps_dc,
beta0_ratio=1e0,
use_sensitivity_weight=True
)
# Convert obtained inversion model to resistivity
# rho = M(m), where M(.) is a mapping
rho_est = mapping*mopt_dc
rho_est[~actind] = np.nan
rho_true = rho.copy()
rho_true[~actind] = np.nan
# show recovered conductivity
if plotIt:
vmin, vmax = rho.min(), rho.max()
fig, ax = plt.subplots(2, 1, figsize=(20, 6))
out1 = mesh.plotImage(
rho_true, clim=(10, 1000),
pcolorOpts={"cmap": "viridis", "norm": colors.LogNorm()},
ax=ax[0]
)
out2 = mesh.plotImage(
rho_est, clim=(10, 1000),
pcolorOpts={"cmap": "viridis", "norm": colors.LogNorm()},
ax=ax[1]
)
out = [out1, out2]
for i in range(2):
ax[i].plot(
survey_dc.electrode_locations[:, 0],
survey_dc.electrode_locations[:, 1], 'kv'
)
ax[i].set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax[i].set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[i][0], ax=ax[i])
cb.set_label("Resistivity ($\Omega$m)")
ax[i].set_xlabel("Northing (m)")
ax[i].set_ylabel("Elevation (m)")
ax[i].set_aspect('equal')
plt.tight_layout()
plt.show()
# Show apparent resisitivty histogram
if plotIt:
fig = plt.figure(figsize=(10, 4))
ax1 = plt.subplot(121)
out = hist(np.log10(abs(IO.voltages_ip)), bins=20)
ax1.set_xlabel("log10 IP voltage (V)")
ax2 = plt.subplot(122)
out = hist(IO.apparent_chargeability, bins=20)
ax2.set_xlabel("Apparent Chargeability (V/V)")
plt.tight_layout()
plt.show()
# Set initial model based upon histogram
m0_ip = np.ones(actmap.nP)*1e-10
# Set uncertainty
# floor
eps_ip = 10**(-4)
# percentage
std_ip = 0.05
# Clean sensitivity function formed with true resistivity
prb_ip._Jmatrix = None
# Input obtained resistivity to form sensitivity
prb_ip.rho = mapping*mopt_dc
mopt_ip, _ = IP.run_inversion(
m0_ip, survey_ip, actind, mesh, std_ip, eps_ip,
upper=np.Inf, lower=0.,
beta0_ratio=1e0,
use_sensitivity_weight=True
)
# Convert obtained inversion model to chargeability
# charg = M(m), where M(.) is a mapping for cells below topography
charg_est = actmap*mopt_ip
charg_est[~actind] = np.nan
charg_true = charg.copy()
charg_true[~actind] = np.nan
# show recovered chargeability
if plotIt:
fig, ax = plt.subplots(2, 1, figsize=(20, 6))
out1 = mesh.plotImage(
charg_true, clim=(0, 0.1),
pcolorOpts={"cmap": "magma"},
ax=ax[0]
)
out2 = mesh.plotImage(
charg_est, clim=(0, 0.1),
pcolorOpts={"cmap": "magma"},
ax=ax[1]
)
out = [out1, out2]
for i in range(2):
ax[i].plot(
survey_dc.electrode_locations[:, 0],
survey_dc.electrode_locations[:, 1], 'rv'
)
ax[i].set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax[i].set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[i][0], ax=ax[i])
cb.set_label("Resistivity ($\Omega$m)")
ax[i].set_xlabel("Northing (m)")
ax[i].set_ylabel("Elevation (m)")
ax[i].set_aspect('equal')
plt.tight_layout()
plt.show()
def setUp(self):
np.random.seed(0)
# First we need to define the direction of the inducing field
# As a simple case, we pick a vertical inducing field of magnitude
# 50,000nT.
# From old convention, field orientation is given as an
# azimuth from North (positive clockwise)
# and dip from the horizontal (positive downward).
H0 = (50000., 90., 0.)
# Create a mesh
h = [5, 5, 5]
padDist = np.ones((3, 2)) * 100
nCpad = [2, 4, 2]
# Create grid of points for topography
# Lets create a simple Gaussian topo and set the active cells
[xx, yy] = np.meshgrid(np.linspace(-200., 200., 50),
np.linspace(-200., 200., 50))
b = 100
A = 50
zz = A * np.exp(-0.5 * ((xx / b)**2. + (yy / b)**2.))
# We would usually load a topofile
topo = np.c_[Utils.mkvc(xx), Utils.mkvc(yy), Utils.mkvc(zz)]
# Create and array of observation points
xr = np.linspace(-100., 100., 20)
yr = np.linspace(-100., 100., 20)
X, Y = np.meshgrid(xr, yr)
Z = A * np.exp(-0.5 * ((X / b)**2. + (Y / b)**2.)) + 5
# Create a MAGsurvey
xyzLoc = np.c_[Utils.mkvc(X.T), Utils.mkvc(Y.T), Utils.mkvc(Z.T)]
rxLoc = PF.BaseMag.RxObs(xyzLoc)
srcField = PF.BaseMag.SrcField([rxLoc], param=H0)
survey = PF.BaseMag.LinearSurvey(srcField)
# self.mesh.finalize()
self.mesh = meshutils.mesh_builder_xyz(
xyzLoc,
h,
padding_distance=padDist,
mesh_type='TREE',
)
self.mesh = meshutils.refine_tree_xyz(
self.mesh,
topo,
method='surface',
octree_levels=nCpad,
octree_levels_padding=nCpad,
finalize=True,
)
# Define an active cells from topo
actv = Utils.surface2ind_topo(self.mesh, topo)
nC = int(actv.sum())
# We can now create a susceptibility model and generate data
# Lets start with a simple block in half-space
self.model = Utils.ModelBuilder.addBlock(self.mesh.gridCC,
np.zeros(self.mesh.nC),
np.r_[-20, -20, -15],
np.r_[20, 20, 20], 0.05)[actv]
# Create active map to go from reduce set to full
self.actvMap = Maps.InjectActiveCells(self.mesh, actv, np.nan)
# Creat reduced identity map
idenMap = Maps.IdentityMap(nP=nC)
# Create the forward model operator
prob = PF.Magnetics.MagneticIntegral(self.mesh,
chiMap=idenMap,
actInd=actv)
# Pair the survey and problem
survey.pair(prob)
# Compute linear forward operator and compute some data
data = prob.fields(self.model)
# Add noise and uncertainties (1nT)
noise = np.random.randn(len(data))
data += noise
wd = np.ones(len(data)) * 1.
survey.dobs = data
survey.std = wd
# Create sensitivity weights from our linear forward operator
rxLoc = survey.srcField.rxList[0].locs
wr = prob.getJtJdiag(self.model)**0.5
wr /= np.max(wr)
# Create a regularization
reg = Regularization.Sparse(self.mesh, indActive=actv, mapping=idenMap)
reg.norms = np.c_[0, 0, 0, 0]
reg.cell_weights = wr
reg.mref = np.zeros(nC)
# Data misfit function
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.W = 1. / survey.std
# Add directives to the inversion
opt = Optimization.ProjectedGNCG(maxIter=20,
lower=0.,
upper=10.,
maxIterLS=20,
maxIterCG=20,
tolCG=1e-4,
stepOffBoundsFact=1e-4)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=1e+6)
# Here is where the norms are applied
# Use pick a treshold parameter empirically based on the distribution of
# model parameters
IRLS = Directives.Update_IRLS(f_min_change=1e-3,
maxIRLSiter=20,
beta_tol=1e-1,
betaSearch=False)
update_Jacobi = Directives.UpdatePreconditioner()
# saveOuput = Directives.SaveOutputEveryIteration()
# saveModel.fileName = work_dir + out_dir + 'ModelSus'
self.inv = Inversion.BaseInversion(invProb,
directiveList=[IRLS, update_Jacobi])
def run(plotIt=True, survey_type="dipole-dipole"):
np.random.seed(1)
# Initiate I/O class for DC
IO = DC.IO()
# Obtain ABMN locations
xmin, xmax = 0., 200.
ymin, ymax = 0., 0.
zmin, zmax = 0, 0
endl = np.array([[xmin, ymin, zmin], [xmax, ymax, zmax]])
# Generate DC survey object
survey = DC.Utils.gen_DCIPsurvey(endl, survey_type=survey_type, dim=2,
a=10, b=10, n=10)
survey.getABMN_locations()
survey = IO.from_ambn_locations_to_survey(
survey.a_locations, survey.b_locations,
survey.m_locations, survey.n_locations,
survey_type, data_dc_type='volt'
)
# Obtain 2D TensorMesh
mesh, actind = IO.set_mesh()
topo, mesh1D = DC.Utils.genTopography(mesh, -10, 0, its=100)
actind = Utils.surface2ind_topo(mesh, np.c_[mesh1D.vectorCCx, topo])
survey.drapeTopo(mesh, actind, option="top")
# Build a conductivity model
blk_inds_c = Utils.ModelBuilder.getIndicesSphere(
np.r_[60., -25.], 12.5, mesh.gridCC
)
blk_inds_r = Utils.ModelBuilder.getIndicesSphere(
np.r_[140., -25.], 12.5, mesh.gridCC
)
layer_inds = mesh.gridCC[:, 1] > -5.
sigma = np.ones(mesh.nC)*1./100.
sigma[blk_inds_c] = 1./10.
sigma[blk_inds_r] = 1./1000.
sigma[~actind] = 1./1e8
rho = 1./sigma
# Show the true conductivity model
if plotIt:
fig = plt.figure(figsize=(12, 3))
ax = plt.subplot(111)
temp = rho.copy()
temp[~actind] = np.nan
out = mesh.plotImage(
temp, grid=True, ax=ax, gridOpts={'alpha': 0.2},
clim=(10, 1000),
pcolorOpts={"cmap": "viridis", "norm": colors.LogNorm()}
)
ax.plot(
survey.electrode_locations[:, 0],
survey.electrode_locations[:, 1], 'k.'
)
ax.set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax.set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[0])
cb.set_label("Resistivity (ohm-m)")
ax.set_aspect('equal')
plt.show()
# Use Exponential Map: m = log(rho)
actmap = Maps.InjectActiveCells(
mesh, indActive=actind, valInactive=np.log(1e8)
)
mapping = Maps.ExpMap(mesh) * actmap
# Generate mtrue
mtrue = np.log(rho[actind])
# Generate 2.5D DC problem
# "N" means potential is defined at nodes
prb = DC.Problem2D_N(
mesh, rhoMap=mapping, storeJ=True,
Solver=Solver
)
# Pair problem with survey
try:
prb.pair(survey)
except:
survey.unpair()
prb.pair(survey)
geometric_factor = survey.set_geometric_factor(
data_type="apparent_resistivity",
survey_type='dipole-dipole',
space_type='half-space'
)
# Make synthetic DC data with 5% Gaussian noise
dtrue = survey.makeSyntheticData(mtrue, std=0.05, force=True)
IO.data_dc = dtrue
# Show apparent resisitivty pseudo-section
if plotIt:
IO.plotPseudoSection(
data=survey.dobs, data_type='apparent_resistivity'
)
# Show apparent resisitivty histogram
if plotIt:
fig = plt.figure()
out = hist(survey.dobs, bins=20)
plt.xlabel("Apparent Resisitivty ($\Omega$m)")
plt.show()
# Set initial model based upon histogram
m0 = np.ones(actmap.nP)*np.log(100.)
# Set uncertainty
# floor (10 ohm-m)
eps = 1.
# percentage
std = 0.05
dmisfit = DataMisfit.l2_DataMisfit(survey)
uncert = abs(survey.dobs) * std + eps
dmisfit.W = 1./uncert
# Map for a regularization
regmap = Maps.IdentityMap(nP=int(actind.sum()))
# Related to inversion
reg = Regularization.Sparse(mesh, indActive=actind, mapping=regmap)
opt = Optimization.InexactGaussNewton(maxIter=15)
invProb = InvProblem.BaseInvProblem(dmisfit, reg, opt)
beta = Directives.BetaSchedule(coolingFactor=5, coolingRate=2)
betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1e0)
target = Directives.TargetMisfit()
updateSensW = Directives.UpdateSensitivityWeights()
update_Jacobi = Directives.UpdatePreconditioner()
inv = Inversion.BaseInversion(
invProb, directiveList=[
beta, betaest, target, updateSensW, update_Jacobi
]
)
prb.counter = opt.counter = Utils.Counter()
opt.LSshorten = 0.5
opt.remember('xc')
# Run inversion
mopt = inv.run(m0)
# Get diag(JtJ)
mask_inds = np.ones(mesh.nC, dtype=bool)
jtj = np.sqrt(updateSensW.JtJdiag[0])
jtj /= jtj.max()
temp = np.ones_like(jtj, dtype=bool)
temp[jtj > 0.005] = False
mask_inds[actind] = temp
actind_final = np.logical_and(actind, ~mask_inds)
jtj_cc = np.ones(mesh.nC)*np.nan
jtj_cc[actind] = jtj
# Show the sensitivity
if plotIt:
fig = plt.figure(figsize=(12, 3))
ax = plt.subplot(111)
temp = rho.copy()
temp[~actind] = np.nan
out = mesh.plotImage(
jtj_cc, grid=True, ax=ax,
gridOpts={'alpha': 0.2}, clim=(0.005, 0.5),
pcolorOpts={"cmap": "viridis", "norm": colors.LogNorm()}
)
ax.plot(
survey.electrode_locations[:, 0],
survey.electrode_locations[:, 1], 'k.'
)
ax.set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax.set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[0])
cb.set_label("Sensitivity")
ax.set_aspect('equal')
plt.show()
# Convert obtained inversion model to resistivity
# rho = M(m), where M(.) is a mapping
rho_est = mapping*mopt
rho_est[~actind_final] = np.nan
rho_true = rho.copy()
rho_true[~actind_final] = np.nan
# show recovered conductivity
if plotIt:
vmin, vmax = rho.min(), rho.max()
fig, ax = plt.subplots(2, 1, figsize=(20, 6))
out1 = mesh.plotImage(
rho_true, clim=(10, 1000),
pcolorOpts={"cmap": "viridis", "norm": colors.LogNorm()},
ax=ax[0]
)
out2 = mesh.plotImage(
rho_est, clim=(10, 1000),
pcolorOpts={"cmap": "viridis", "norm": colors.LogNorm()},
ax=ax[1]
)
out = [out1, out2]
for i in range(2):
ax[i].plot(
survey.electrode_locations[:, 0],
survey.electrode_locations[:, 1], 'kv'
)
ax[i].set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax[i].set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[i][0], ax=ax[i])
cb.set_label("Resistivity ($\Omega$m)")
ax[i].set_xlabel("Northing (m)")
ax[i].set_ylabel("Elevation (m)")
ax[i].set_aspect('equal')
plt.tight_layout()
plt.show()
def setUp(self):
np.random.seed(0)
H0 = (50000., 90., 0.)
# The magnetization is set along a different
# direction (induced + remanence)
M = np.array([45., 90.])
# Create grid of points for topography
# Lets create a simple Gaussian topo
# and set the active cells
[xx, yy] = np.meshgrid(
np.linspace(-200, 200, 50),
np.linspace(-200, 200, 50)
)
b = 100
A = 50
zz = A*np.exp(-0.5*((xx/b)**2. + (yy/b)**2.))
# We would usually load a topofile
topo = np.c_[Utils.mkvc(xx), Utils.mkvc(yy), Utils.mkvc(zz)]
# Create and array of observation points
xr = np.linspace(-100., 100., 20)
yr = np.linspace(-100., 100., 20)
X, Y = np.meshgrid(xr, yr)
Z = A*np.exp(-0.5*((X/b)**2. + (Y/b)**2.)) + 5
# Create a MAGsurvey
xyzLoc = np.c_[Utils.mkvc(X.T), Utils.mkvc(Y.T), Utils.mkvc(Z.T)]
rxLoc = PF.BaseMag.RxObs(xyzLoc)
srcField = PF.BaseMag.SrcField([rxLoc], param=H0)
survey = PF.BaseMag.LinearSurvey(srcField)
# Create a mesh
h = [5, 5, 5]
padDist = np.ones((3, 2)) * 100
nCpad = [2, 4, 2]
# Get extent of points
limx = np.r_[topo[:, 0].max(), topo[:, 0].min()]
limy = np.r_[topo[:, 1].max(), topo[:, 1].min()]
limz = np.r_[topo[:, 2].max(), topo[:, 2].min()]
# Get center of the mesh
midX = np.mean(limx)
midY = np.mean(limy)
midZ = np.mean(limz)
nCx = int(limx[0]-limx[1]) / h[0]
nCy = int(limy[0]-limy[1]) / h[1]
nCz = int(limz[0]-limz[1]+int(np.min(np.r_[nCx, nCy])/3)) / h[2]
# Figure out full extent required from input
extent = np.max(np.r_[nCx * h[0] + padDist[0, :].sum(),
nCy * h[1] + padDist[1, :].sum(),
nCz * h[2] + padDist[2, :].sum()])
maxLevel = int(np.log2(extent/h[0]))+1
# Number of cells at the small octree level
nCx, nCy, nCz = 2**(maxLevel), 2**(maxLevel), 2**(maxLevel)
# Define the mesh and origin
# For now cubic cells
mesh = Mesh.TreeMesh([np.ones(nCx)*h[0],
np.ones(nCx)*h[1],
np.ones(nCx)*h[2]])
# Set origin
mesh.x0 = np.r_[
-nCx*h[0]/2.+midX,
-nCy*h[1]/2.+midY,
-nCz*h[2]/2.+midZ
]
# Refine the mesh around topography
# Get extent of points
F = NearestNDInterpolator(topo[:, :2], topo[:, 2])
zOffset = 0
# Cycle through the first 3 octree levels
for ii in range(3):
dx = mesh.hx.min()*2**ii
nCx = int((limx[0]-limx[1]) / dx)
nCy = int((limy[0]-limy[1]) / dx)
# Create a grid at the octree level in xy
CCx, CCy = np.meshgrid(
np.linspace(limx[1], limx[0], nCx),
np.linspace(limy[1], limy[0], nCy)
)
z = F(mkvc(CCx), mkvc(CCy))
# level means number of layers in current OcTree level
for level in range(int(nCpad[ii])):
mesh.insert_cells(
np.c_[
mkvc(CCx),
mkvc(CCy),
z-zOffset
], np.ones_like(z)*maxLevel-ii,
finalize=False
)
zOffset += dx
mesh.finalize()
self.mesh = mesh
# Define an active cells from topo
actv = Utils.surface2ind_topo(mesh, topo)
nC = int(actv.sum())
model = np.zeros((mesh.nC, 3))
# Convert the inclination declination to vector in Cartesian
M_xyz = Utils.matutils.dip_azimuth2cartesian(M[0], M[1])
# Get the indicies of the magnetized block
ind = Utils.ModelBuilder.getIndicesBlock(
np.r_[-20, -20, -10], np.r_[20, 20, 25],
mesh.gridCC,
)[0]
# Assign magnetization values
model[ind, :] = np.kron(
np.ones((ind.shape[0], 1)), M_xyz*0.05
)
# Remove air cells
self.model = model[actv, :]
# Create active map to go from reduce set to full
self.actvMap = Maps.InjectActiveCells(mesh, actv, np.nan)
# Creat reduced identity map
idenMap = Maps.IdentityMap(nP=nC*3)
# Create the forward model operator
prob = PF.Magnetics.MagneticIntegral(
mesh, chiMap=idenMap, actInd=actv,
modelType='vector'
)
# Pair the survey and problem
survey.pair(prob)
# Compute some data and add some random noise
data = prob.fields(Utils.mkvc(self.model))
std = 5 # nT
data += np.random.randn(len(data))*std
wd = np.ones(len(data))*std
# Assigne data and uncertainties to the survey
survey.dobs = data
survey.std = wd
# Create an projection matrix for plotting later
actvPlot = Maps.InjectActiveCells(mesh, actv, np.nan)
# Create sensitivity weights from our linear forward operator
rxLoc = survey.srcField.rxList[0].locs
# This Mapping connects the regularizations for the three-component
# vector model
wires = Maps.Wires(('p', nC), ('s', nC), ('t', nC))
# Create sensitivity weights from our linear forward operator
# so that all cells get equal chance to contribute to the solution
wr = np.sum(prob.G**2., axis=0)**0.5
wr = (wr/np.max(wr))
# Create three regularization for the different components
# of magnetization
reg_p = Regularization.Sparse(mesh, indActive=actv, mapping=wires.p)
reg_p.mref = np.zeros(3*nC)
reg_p.cell_weights = (wires.p * wr)
reg_s = Regularization.Sparse(mesh, indActive=actv, mapping=wires.s)
reg_s.mref = np.zeros(3*nC)
reg_s.cell_weights = (wires.s * wr)
reg_t = Regularization.Sparse(mesh, indActive=actv, mapping=wires.t)
reg_t.mref = np.zeros(3*nC)
reg_t.cell_weights = (wires.t * wr)
reg = reg_p + reg_s + reg_t
reg.mref = np.zeros(3*nC)
# Data misfit function
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.W = 1./survey.std
# Add directives to the inversion
opt = Optimization.ProjectedGNCG(maxIter=30, lower=-10, upper=10.,
maxIterLS=20, maxIterCG=20, tolCG=1e-4)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
# A list of directive to control the inverson
betaest = Directives.BetaEstimate_ByEig()
# Here is where the norms are applied
# Use pick a treshold parameter empirically based on the distribution of
# model parameters
IRLS = Directives.Update_IRLS(
f_min_change=1e-3, maxIRLSiter=0, beta_tol=5e-1
)
# Pre-conditioner
update_Jacobi = Directives.UpdatePreconditioner()
inv = Inversion.BaseInversion(invProb,
directiveList=[IRLS, update_Jacobi, betaest])
# Run the inversion
m0 = np.ones(3*nC) * 1e-4 # Starting model
mrec_MVIC = inv.run(m0)
self.mstart = Utils.matutils.cartesian2spherical(mrec_MVIC.reshape((nC, 3), order='F'))
beta = invProb.beta
dmis.prob.coordinate_system = 'spherical'
dmis.prob.model = self.mstart
# Create a block diagonal regularization
wires = Maps.Wires(('amp', nC), ('theta', nC), ('phi', nC))
# Create a Combo Regularization
# Regularize the amplitude of the vectors
reg_a = Regularization.Sparse(mesh, indActive=actv,
mapping=wires.amp)
reg_a.norms = np.c_[0., 0., 0., 0.] # Sparse on the model and its gradients
reg_a.mref = np.zeros(3*nC)
# Regularize the vertical angle of the vectors
reg_t = Regularization.Sparse(mesh, indActive=actv,
mapping=wires.theta)
reg_t.alpha_s = 0. # No reference angle
reg_t.space = 'spherical'
reg_t.norms = np.c_[2., 0., 0., 0.] # Only norm on gradients used
# Regularize the horizontal angle of the vectors
reg_p = Regularization.Sparse(mesh, indActive=actv,
mapping=wires.phi)
reg_p.alpha_s = 0. # No reference angle
reg_p.space = 'spherical'
reg_p.norms = np.c_[2., 0., 0., 0.] # Only norm on gradients used
reg = reg_a + reg_t + reg_p
reg.mref = np.zeros(3*nC)
Lbound = np.kron(np.asarray([0, -np.inf, -np.inf]), np.ones(nC))
Ubound = np.kron(np.asarray([10, np.inf, np.inf]), np.ones(nC))
# Add directives to the inversion
opt = Optimization.ProjectedGNCG(maxIter=20,
lower=Lbound,
upper=Ubound,
maxIterLS=20,
maxIterCG=30,
tolCG=1e-3,
stepOffBoundsFact=1e-3,
)
opt.approxHinv = None
invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=beta*10.)
# Here is where the norms are applied
IRLS = Directives.Update_IRLS(f_min_change=1e-4, maxIRLSiter=20,
minGNiter=1, beta_tol=0.5,
coolingRate=1, coolEps_q=True,
betaSearch=False)
# Special directive specific to the mag amplitude problem. The sensitivity
# weights are update between each iteration.
ProjSpherical = Directives.ProjectSphericalBounds()
update_SensWeight = Directives.UpdateSensitivityWeights()
update_Jacobi = Directives.UpdatePreconditioner()
self.inv = Inversion.BaseInversion(
invProb,
directiveList=[
ProjSpherical, IRLS, update_SensWeight, update_Jacobi
]
)
if topo is not None:
meshLocal = meshutils.refine_tree_xyz(
meshLocal, topo, method='surface',
octree_levels=octree_levels_topo, finalize=False
)
meshLocal = meshutils.refine_tree_xyz(
meshLocal, topo_elevations_at_data_locs[ind_t, :],
method='surface',
max_distance=max_distance,
octree_levels=octree_levels_obs,
octree_levels_padding=octree_levels_padding,
finalize=True,
)
tileLayer = Utils.surface2ind_topo(meshLocal, topo)
# Calculate approximate problem size
nDt, nCt = ind_t.sum()*1. * len(survey.components), tileLayer.sum()*1.
nChunks = n_cpu # Number of chunks
cSa, cSb = int(nDt/nChunks), int(nCt/nChunks) # Chunk sizes
usedRAM = nDt * nCt * 8. * 1e-9
count += 1
print(nDt, nCt, usedRAM, binCount.min())
del meshLocal
nTiles = X1.shape[0]
# Loop through the tiles and generate all sensitivities
print("Number of tiles:" + str(nTiles))
if topo is not None:
mesh = meshutils.refine_tree_xyz(mesh,
topo,
method='surface',
octree_levels=octreeTopo,
finalize=False)
mesh = meshutils.refine_tree_xyz(mesh,
newTopo,
method='surface',
octree_levels=octreeObs,
octree_levels_padding=octree_levels_padding,
finalize=True)
# Compute active cells
activeCells = Utils.surface2ind_topo(mesh, topo, gridLoc='CC')
# activeCells = meshutils.activeTopoLayer(mesh, topo)
Mesh.TreeMesh.writeUBC(
mesh,
workDir + dsep + outDir + 'OctreeMeshGlobal.msh',
models={workDir + dsep + outDir + 'ActiveSurface.act': activeCells})
# Get the layer of cells directly below topo
#activeCells = Utils.actIndFull2layer(mesh, active)
nC = int(activeCells.sum()) # Number of active cells
print(nC)
# Create active map to go from reduce set to full
activeCellsMap = Maps.InjectActiveCells(mesh, activeCells, ndv)
def run(
plotIt=True, survey_type="dipole-dipole",
rho_background=1e3,
rho_block=1e2,
block_x0=100,
block_dx=10,
block_y0=-10,
block_dy=5
):
np.random.seed(1)
# Initiate I/O class for DC
IO = DC.IO()
# Obtain ABMN locations
xmin, xmax = 0., 200.
ymin, ymax = 0., 0.
zmin, zmax = 0, 0
endl = np.array([[xmin, ymin, zmin], [xmax, ymax, zmax]])
# Generate DC survey object
survey = DC.Utils.gen_DCIPsurvey(endl, survey_type=survey_type, dim=2,
a=10, b=10, n=10)
survey.getABMN_locations()
survey = IO.from_ambn_locations_to_survey(
survey.a_locations, survey.b_locations,
survey.m_locations, survey.n_locations,
survey_type, data_dc_type='volt'
)
# Obtain 2D TensorMesh
mesh, actind = IO.set_mesh()
# Flat topography
actind = Utils.surface2ind_topo(
mesh, np.c_[mesh.vectorCCx, mesh.vectorCCx*0.]
)
survey.drapeTopo(mesh, actind, option="top")
# Use Exponential Map: m = log(rho)
actmap = Maps.InjectActiveCells(
mesh, indActive=actind, valInactive=np.log(1e8)
)
parametric_block = Maps.ParametricBlock(mesh, slopeFact=1e2)
mapping = Maps.ExpMap(mesh) * parametric_block
# Set true model
# val_background,val_block, block_x0, block_dx, block_y0, block_dy
mtrue = np.r_[np.log(1e3), np.log(10), 100, 10, -20, 10]
# Set initial model
m0 = np.r_[
np.log(rho_background), np.log(rho_block),
block_x0, block_dx, block_y0, block_dy
]
rho = mapping * mtrue
rho0 = mapping * m0
# Show the true conductivity model
fig = plt.figure(figsize=(12, 3))
ax = plt.subplot(111)
temp = rho.copy()
temp[~actind] = np.nan
out = mesh.plotImage(
temp, grid=False, ax=ax, gridOpts={'alpha': 0.2},
clim=(10, 1000),
pcolorOpts={"cmap": "viridis", "norm": colors.LogNorm()}
)
ax.plot(
survey.electrode_locations[:, 0],
survey.electrode_locations[:, 1], 'k.'
)
ax.set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax.set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[0])
cb.set_label("Resistivity (ohm-m)")
ax.set_aspect('equal')
ax.set_title("True resistivity model")
plt.show()
# Show the true conductivity model
fig = plt.figure(figsize=(12, 3))
ax = plt.subplot(111)
temp = rho0.copy()
temp[~actind] = np.nan
out = mesh.plotImage(
temp, grid=False, ax=ax, gridOpts={'alpha': 0.2},
clim=(10, 1000),
pcolorOpts={"cmap": "viridis", "norm": colors.LogNorm()}
)
ax.plot(
survey.electrode_locations[:, 0],
survey.electrode_locations[:, 1], 'k.'
)
ax.set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax.set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[0])
cb.set_label("Resistivity (ohm-m)")
ax.set_aspect('equal')
ax.set_title("Initial resistivity model")
plt.show()
# Generate 2.5D DC problem
# "N" means potential is defined at nodes
prb = DC.Problem2D_N(
mesh, rhoMap=mapping, storeJ=True,
Solver=Solver
)
# Pair problem with survey
try:
prb.pair(survey)
except:
survey.unpair()
prb.pair(survey)
# Make synthetic DC data with 5% Gaussian noise
dtrue = survey.makeSyntheticData(mtrue, std=0.05, force=True)
# Show apparent resisitivty pseudo-section
IO.plotPseudoSection(
data=survey.dobs/IO.G, data_type='apparent_resistivity'
)
# Show apparent resisitivty histogram
fig = plt.figure()
out = hist(survey.dobs/IO.G, bins=20)
plt.show()
# Set uncertainty
# floor
eps = 10**(-3.2)
# percentage
std = 0.05
dmisfit = DataMisfit.l2_DataMisfit(survey)
uncert = abs(survey.dobs) * std + eps
dmisfit.W = 1./uncert
# Map for a regularization
mesh_1d = Mesh.TensorMesh([parametric_block.nP])
# Related to inversion
reg = Regularization.Simple(mesh_1d, alpha_x=0.)
opt = Optimization.InexactGaussNewton(maxIter=10)
invProb = InvProblem.BaseInvProblem(dmisfit, reg, opt)
beta = Directives.BetaSchedule(coolingFactor=5, coolingRate=2)
betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1e0)
target = Directives.TargetMisfit()
updateSensW = Directives.UpdateSensitivityWeights()
update_Jacobi = Directives.UpdatePreconditioner()
invProb.beta = 0.
inv = Inversion.BaseInversion(
invProb, directiveList=[
target
]
)
prb.counter = opt.counter = Utils.Counter()
opt.LSshorten = 0.5
opt.remember('xc')
# Run inversion
mopt = inv.run(m0)
# Convert obtained inversion model to resistivity
# rho = M(m), where M(.) is a mapping
rho_est = mapping*mopt
rho_true = rho.copy()
# show recovered conductivity
vmin, vmax = rho.min(), rho.max()
fig, ax = plt.subplots(2, 1, figsize=(20, 6))
out1 = mesh.plotImage(
rho_true, clim=(10, 1000),
pcolorOpts={"cmap": "viridis", "norm": colors.LogNorm()},
ax=ax[0]
)
out2 = mesh.plotImage(
rho_est, clim=(10, 1000),
pcolorOpts={"cmap": "viridis", "norm": colors.LogNorm()},
ax=ax[1]
)
out = [out1, out2]
for i in range(2):
ax[i].plot(
survey.electrode_locations[:, 0],
survey.electrode_locations[:, 1], 'kv'
)
ax[i].set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax[i].set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[i][0], ax=ax[i])
cb.set_label("Resistivity ($\Omega$m)")
ax[i].set_xlabel("Northing (m)")
ax[i].set_ylabel("Elevation (m)")
ax[i].set_aspect('equal')
ax[0].set_title("True resistivity model")
ax[1].set_title("Recovered resistivity model")
plt.tight_layout()
plt.show()
def set_mesh(self, topo=None,
dx=None, dy=None, dz=None,
n_spacing=None, corezlength=None,
npad_x=7, npad_y=7, npad_z=7,
pad_rate_x=1.3, pad_rate_y=1.3, pad_rate_z=1.3,
ncell_per_dipole=4, mesh_type='TensorMesh',
dimension=2,
method='nearest'
):
"""
Set up a mesh for a given DC survey
"""
if mesh_type == 'TreeMesh':
raise NotImplementedError()
# 2D or 3D mesh
if dimension in [2, 3]:
if dimension == 2:
z_ind = 1
else:
z_ind = 2
a = abs(np.diff(np.sort(self.electrode_locations[:, 0]))).min()
lineLength = abs(
self.electrode_locations[:, 0].max() -
self.electrode_locations[:, 0].min()
)
dx_ideal = a/ncell_per_dipole
if dx is None:
dx = dx_ideal
warnings.warn(
"dx is set to {} m (samllest electrode spacing ({}) / {})".format(dx, a, ncell_per_dipole)
)
if dz is None:
dz = dx*0.5
warnings.warn(
"dz ({} m) is set to dx ({} m) / {}".format(dz, dx, 2)
)
x0 = self.electrode_locations[:, 0].min()
if topo is None:
locs = self.electrode_locations
else:
locs = np.vstack((topo, self.electrode_locations))
if dx > dx_ideal:
# warnings.warn(
# "Input dx ({}) is greater than expected \n We recommend using {:0.1e} m cells, that is, {} cells per {0.1e} m dipole length".format(dx, dx_ideal, ncell_per_dipole, a)
# )
pass
self.dx = dx
self.dz = dz
self.npad_x = npad_x
self.npad_z = npad_z
self.pad_rate_x = pad_rate_x
self.pad_rate_z = pad_rate_z
self.ncell_per_dipole = ncell_per_dipole
zmax = locs[:, z_ind].max()
zmin = locs[:, z_ind].min()
# 3 cells each for buffer
corexlength = lineLength + dx * 6
if corezlength is None:
corezlength = self.grids[:, z_ind].max()
ncx = np.round(corexlength/dx)
ncz = np.round(corezlength/dz)
hx = [
(dx, npad_x, -pad_rate_x), (dx, ncx), (dx, npad_x, pad_rate_x)
]
hz = [(dz, npad_z, -pad_rate_z), (dz, ncz)]
x0_mesh = -(
(dx * pad_rate_x ** (np.arange(npad_x)+1)).sum() + dx * 3 - x0
)
z0_mesh = -((dz * pad_rate_z ** (np.arange(npad_z)+1)).sum() + dz * ncz) + zmax
# For 2D mesh
if dimension == 2:
h = [hx, hz]
x0_for_mesh = [x0_mesh, z0_mesh]
self.xyzlim = np.vstack((
np.r_[x0, x0+lineLength],
np.r_[zmax-corezlength, zmax]
))
# For 3D mesh
else:
if dy is None:
raise Exception("You must input dy (m)")
self.dy = dy
self.npad_y = npad_y
self.pad_rate_y = pad_rate_y
ylocs = np.unique(self.electrode_locations[:, 1])
ymin, ymax = ylocs.min(), ylocs.max()
# 3 cells each for buffer in y-direction
coreylength = ymax-ymin+dy*6
ncy = np.round(coreylength/dy)
hy = [
(dy, npad_y, -pad_rate_y),
(dy, ncy),
(dy, npad_y, pad_rate_y)
]
y0 = ylocs.min()-dy/2.
y0_mesh = -(
(dy * pad_rate_y ** (np.arange(npad_y)+1)).sum()
+ dy*3 - y0
)
h = [hx, hy, hz]
x0_for_mesh = [x0_mesh, y0_mesh, z0_mesh]
self.xyzlim = np.vstack((
np.r_[x0, x0+lineLength],
np.r_[ymin-dy*3, ymax+dy*3],
np.r_[zmax-corezlength, zmax]
))
mesh = Mesh.TensorMesh(h, x0=x0_for_mesh)
actind = Utils.surface2ind_topo(mesh, locs, method=method)
else:
raise NotImplementedError()
return mesh, actind
def run(plotIt=True):
# Define the inducing field parameter
H0 = (50000, 90, 0)
# Create a mesh
dx = 5.
hxind = [(dx, 5, -1.3), (dx, 10), (dx, 5, 1.3)]
hyind = [(dx, 5, -1.3), (dx, 10), (dx, 5, 1.3)]
hzind = [(dx, 5, -1.3), (dx, 10)]
mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCC')
# Get index of the center
midx = int(mesh.nCx/2)
midy = int(mesh.nCy/2)
# Lets create a simple Gaussian topo and set the active cells
[xx, yy] = np.meshgrid(mesh.vectorNx, mesh.vectorNy)
zz = -np.exp((xx**2 + yy**2) / 75**2) + mesh.vectorNz[-1]
# We would usually load a topofile
topo = np.c_[Utils.mkvc(xx), Utils.mkvc(yy), Utils.mkvc(zz)]
# Go from topo to actv cells
actv = Utils.surface2ind_topo(mesh, topo, 'N')
actv = np.asarray([inds for inds, elem in enumerate(actv, 1) if elem],
dtype=int) - 1
# Create active map to go from reduce space to full
actvMap = Maps.InjectActiveCells(mesh, actv, -100)
nC = len(actv)
# Create and array of observation points
xr = np.linspace(-20., 20., 20)
yr = np.linspace(-20., 20., 20)
X, Y = np.meshgrid(xr, yr)
# Move the observation points 5m above the topo
Z = -np.exp((X**2 + Y**2) / 75**2) + mesh.vectorNz[-1] + 5.
# Create a MAGsurvey
rxLoc = np.c_[Utils.mkvc(X.T), Utils.mkvc(Y.T), Utils.mkvc(Z.T)]
rxLoc = PF.BaseMag.RxObs(rxLoc)
srcField = PF.BaseMag.SrcField([rxLoc], param=H0)
survey = PF.BaseMag.LinearSurvey(srcField)
# We can now create a susceptibility model and generate data
# Here a simple block in half-space
model = np.zeros((mesh.nCx, mesh.nCy, mesh.nCz))
model[(midx-2):(midx+2), (midy-2):(midy+2), -6:-2] = 0.02
model = Utils.mkvc(model)
model = model[actv]
# Create active map to go from reduce set to full
actvMap = Maps.InjectActiveCells(mesh, actv, -100)
# Creat reduced identity map
idenMap = Maps.IdentityMap(nP=nC)
# Create the forward model operator
prob = PF.Magnetics.MagneticIntegral(mesh, chiMap=idenMap, actInd=actv)
# Pair the survey and problem
survey.pair(prob)
# Compute linear forward operator and compute some data
d = prob.fields(model)
# Add noise and uncertainties
# We add some random Gaussian noise (1nT)
data = d + np.random.randn(len(d))
wd = np.ones(len(data))*1. # Assign flat uncertainties
survey.dobs = data
survey.std = wd
survey.mtrue = model
# Create sensitivity weights from our linear forward operator
rxLoc = survey.srcField.rxList[0].locs
wr = np.sum(prob.G**2., axis=0)**0.5
wr = (wr/np.max(wr))
# Create a regularization
reg = Regularization.Sparse(mesh, indActive=actv, mapping=idenMap)
reg.cell_weights = wr
reg.norms = [0, 1, 1, 1]
reg.eps_p, reg.eps_q = 1e-3, 1e-3
# Data misfit function
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.W = 1/wd
# Add directives to the inversion
opt = Optimization.ProjectedGNCG(maxIter=100, lower=0., upper=1.,
maxIterLS=20, maxIterCG=10, tolCG=1e-3)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
betaest = Directives.BetaEstimate_ByEig()
# Here is where the norms are applied
# Use pick a treshold parameter empirically based on the distribution of
# model parameters
IRLS = Directives.Update_IRLS(f_min_change=1e-3, minGNiter=3)
update_Jacobi = Directives.Update_lin_PreCond()
inv = Inversion.BaseInversion(invProb,
directiveList=[IRLS, betaest, update_Jacobi])
# Run the inversion
m0 = np.ones(nC)*1e-4 # Starting model
mrec = inv.run(m0)
if plotIt:
# Here is the recovered susceptibility model
ypanel = midx
zpanel = -5
m_l2 = actvMap * IRLS.l2model
m_l2[m_l2 == -100] = np.nan
m_lp = actvMap * mrec
m_lp[m_lp == -100] = np.nan
m_true = actvMap * model
m_true[m_true == -100] = np.nan
# Plot the data
PF.Magnetics.plot_obs_2D(rxLoc, d=d)
plt.figure()
# Plot L2 model
ax = plt.subplot(321)
mesh.plotSlice(m_l2, ax=ax, normal='Z', ind=zpanel,
grid=True, clim=(model.min(), model.max()))
plt.plot(([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCy[ypanel], mesh.vectorCCy[ypanel]]), color='w')
plt.title('Plan l2-model.')
plt.gca().set_aspect('equal')
plt.ylabel('y')
ax.xaxis.set_visible(False)
plt.gca().set_aspect('equal', adjustable='box')
# Vertica section
ax = plt.subplot(322)
mesh.plotSlice(m_l2, ax=ax, normal='Y', ind=midx,
grid=True, clim=(model.min(), model.max()))
plt.plot(([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCz[zpanel], mesh.vectorCCz[zpanel]]), color='w')
plt.title('E-W l2-model.')
plt.gca().set_aspect('equal')
ax.xaxis.set_visible(False)
plt.ylabel('z')
plt.gca().set_aspect('equal', adjustable='box')
# Plot Lp model
ax = plt.subplot(323)
mesh.plotSlice(m_lp, ax=ax, normal='Z', ind=zpanel,
grid=True, clim=(model.min(), model.max()))
plt.plot(([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCy[ypanel], mesh.vectorCCy[ypanel]]), color='w')
plt.title('Plan lp-model.')
plt.gca().set_aspect('equal')
ax.xaxis.set_visible(False)
plt.ylabel('y')
plt.gca().set_aspect('equal', adjustable='box')
# Vertical section
ax = plt.subplot(324)
mesh.plotSlice(m_lp, ax=ax, normal='Y', ind=midx,
grid=True, clim=(model.min(), model.max()))
plt.plot(([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCz[zpanel], mesh.vectorCCz[zpanel]]), color='w')
plt.title('E-W lp-model.')
plt.gca().set_aspect('equal')
ax.xaxis.set_visible(False)
plt.ylabel('z')
plt.gca().set_aspect('equal', adjustable='box')
# Plot True model
ax = plt.subplot(325)
mesh.plotSlice(m_true, ax=ax, normal='Z', ind=zpanel,
grid=True, clim=(model.min(), model.max()))
plt.plot(([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCy[ypanel], mesh.vectorCCy[ypanel]]), color='w')
plt.title('Plan true model.')
plt.gca().set_aspect('equal')
plt.xlabel('x')
plt.ylabel('y')
plt.gca().set_aspect('equal', adjustable='box')
# Vertical section
ax = plt.subplot(326)
mesh.plotSlice(m_true, ax=ax, normal='Y', ind=midx,
grid=True, clim=(model.min(), model.max()))
plt.plot(([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCz[zpanel], mesh.vectorCCz[zpanel]]), color='w')
plt.title('E-W true model.')
plt.gca().set_aspect('equal')
plt.xlabel('x')
plt.ylabel('z')
plt.gca().set_aspect('equal', adjustable='box')
### make a mesh mesh = Mesh.TensorMesh([hx_ind, hy_ind, hz_ind], 'CCC') # Get index of the center mid_x = int(mesh.nCx/2) mid_y = int(mesh.nCy/2) # Lets create a simple Gaussian topo and set the active cells [xx, yy] = np.meshgrid(mesh.vectorNx, mesh.vectorNy) zz = -np.exp((xx**2 + yy**2) / 75**2) + mesh.vectorNz[-1] ### We would usually load a topofile topo = np.c_[Utils.mkvc(xx), Utils.mkvc(yy), Utils.mkvc(zz)] ### Go from topo to array of indices of active cells active_cells = Utils.surface2ind_topo(mesh, topo, 'N') active_cells = np.where(active_cells)[0] num_cells = len(active_cells) ### Create and array of observation points x_receiver = np.linspace(-30., 30., 20) y_receiver = np.linspace(-30., 30., 20) X_r, Y_r = np.meshgrid(x_receiver, y_receiver) ### Move the observation points 5m (?) above the topo Z_r = -np.exp((X_r**2 + Y_r**2) / 75**2) + mesh.vectorNz[-1] + 0.001 ### Create a GRAVsurvey ### make an array of station locations rx_loc = np.c_[Utils.mkvc(X_r.T), Utils.mkvc(Y_r.T), Utils.mkvc(Z_r.T)]
def run(plotIt=True):
H0 = (50000., 90., 0.)
# Create a mesh
dx = 5.
hxind = [(dx, 5, -1.3), (dx, 10), (dx, 5, 1.3)]
hyind = [(dx, 5, -1.3), (dx, 10), (dx, 5, 1.3)]
hzind = [(dx, 5, -1.3), (dx, 10)]
mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCC')
# Lets create a simple Gaussian topo and set the active cells
[xx, yy] = np.meshgrid(mesh.vectorNx, mesh.vectorNy)
zz = -np.exp((xx**2 + yy**2) / 75**2) + mesh.vectorNz[-1]
# We would usually load a topofile
topo = np.c_[Utils.mkvc(xx), Utils.mkvc(yy), Utils.mkvc(zz)]
# Go from topo to array of indices of active cells
actv = Utils.surface2ind_topo(mesh, topo, 'N')
actv = np.where(actv)[0]
# Create and array of observation points
xr = np.linspace(-20., 20., 20)
yr = np.linspace(-20., 20., 20)
X, Y = np.meshgrid(xr, yr)
# Move the observation points 5m above the topo
Z = -np.exp((X**2 + Y**2) / 75**2) + mesh.vectorNz[-1] + 5.
# Create a MAGsurvey
rxLoc = np.c_[Utils.mkvc(X.T), Utils.mkvc(Y.T), Utils.mkvc(Z.T)]
rxLoc = PF.BaseMag.RxObs(rxLoc)
srcField = PF.BaseMag.SrcField([rxLoc], param=H0)
survey = PF.BaseMag.LinearSurvey(srcField)
# We can now create a susceptibility model and generate data
model = np.zeros(mesh.nC)
# Change values in half the domain
model[mesh.gridCC[:,0] < 0] = 0.01
# Add a block in half-space
model = Utils.ModelBuilder.addBlock(mesh.gridCC, model, np.r_[-10,-10,20], np.r_[10,10,40], 0.05)
model = Utils.mkvc(model)
model = model[actv]
# Create active map to go from reduce set to full
actvMap = Maps.InjectActiveCells(mesh, actv, np.nan)
# Create reduced identity map
idenMap = Maps.IdentityMap(nP=len(actv))
# Create the forward model operator
prob = PF.Magnetics.MagneticIntegral(mesh, chiMap=idenMap, actInd=actv)
# Pair the survey and problem
survey.pair(prob)
# Compute linear forward operator and compute some data
d = prob.fields(model)
# Add noise and uncertainties
# We add some random Gaussian noise (1nT)
data = d + np.random.randn(len(d))
wd = np.ones(len(data))*1. # Assign flat uncertainties
survey.dobs = data
survey.std = wd
survey.mtrue = model
# Plot the data
rxLoc = survey.srcField.rxList[0].locs
# Create a homogenous maps for the two domains
domains = [mesh.gridCC[actv,0] < 0, mesh.gridCC[actv,0] >= 0]
homogMap = Maps.SurjectUnits(domains)
# Create a wire map for a second model space, voxel based
wires = Maps.Wires(('h**o', len(domains)), ('hetero', len(actv)))
# Create Sum map
sumMap = Maps.SumMap([homogMap*wires.h**o, wires.hetero])
# Create the forward model operator
prob = PF.Magnetics.MagneticIntegral(mesh, chiMap=sumMap, actInd=actv)
# Pair the survey and problem
survey.unpair()
survey.pair(prob)
# Make depth weighting
wr = np.zeros(sumMap.shape[1])
# Take the cell number out of the scaling.
# Want to keep high sens for large volumes
scale = Utils.sdiag(np.r_[Utils.mkvc(1./homogMap.P.sum(axis=0)),np.ones_like(actv)])
for ii in range(survey.nD):
wr += ((prob.G[ii, :]*prob.chiMap.deriv(np.ones(sumMap.shape[1])*1e-4)*scale)/survey.std[ii])**2.
# Scale the model spaces independently
wr[wires.h**o.index] /= (np.max((wires.h**o*wr)))
wr[wires.hetero.index] /= (np.max(wires.hetero*wr))
wr = wr**0.5
## Create a regularization
# For the homogeneous model
regMesh = Mesh.TensorMesh([len(domains)])
reg_m1 = Regularization.Sparse(regMesh, mapping=wires.h**o)
reg_m1.cell_weights = wires.h**o*wr
reg_m1.norms = np.c_[0, 2, 2, 2]
reg_m1.mref = np.zeros(sumMap.shape[1])
# Regularization for the voxel model
reg_m2 = Regularization.Sparse(mesh, indActive=actv, mapping=wires.hetero)
reg_m2.cell_weights = wires.hetero*wr
reg_m2.norms = np.c_[0, 1, 1, 1]
reg_m2.mref = np.zeros(sumMap.shape[1])
reg = reg_m1 + reg_m2
# Data misfit function
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.W = 1/wd
# Add directives to the inversion
opt = Optimization.ProjectedGNCG(maxIter=100, lower=0., upper=1.,
maxIterLS=20, maxIterCG=10, tolCG=1e-3, tolG=1e-3, eps=1e-6)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
betaest = Directives.BetaEstimate_ByEig()
# Here is where the norms are applied
# Use pick a threshold parameter empirically based on the distribution of
# model parameters
IRLS = Directives.Update_IRLS(f_min_change=1e-3, minGNiter=1)
update_Jacobi = Directives.UpdatePreconditioner()
inv = Inversion.BaseInversion(invProb,
directiveList=[IRLS, betaest, update_Jacobi])
# Run the inversion
m0 = np.ones(sumMap.shape[1])*1e-4 # Starting model
prob.model = m0
mrecSum = inv.run(m0)
if plotIt:
mesh.plot_3d_slicer(actvMap * model, aspect="equal", zslice=30, pcolorOpts={"cmap":'inferno_r'}, transparent='slider')
mesh.plot_3d_slicer(actvMap * sumMap * mrecSum, aspect="equal", zslice=30, pcolorOpts={"cmap":'inferno_r'}, transparent='slider')
def setUp(self):
np.random.seed(0)
# Define the inducing field parameter
H0 = (50000, 90, 0)
# Create a mesh
dx = 5.
hxind = [(dx, 5, -1.3), (dx, 5), (dx, 5, 1.3)]
hyind = [(dx, 5, -1.3), (dx, 5), (dx, 5, 1.3)]
hzind = [(dx, 5, -1.3), (dx, 6)]
mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCC')
# Get index of the center
midx = int(mesh.nCx / 2)
midy = int(mesh.nCy / 2)
# Lets create a simple Gaussian topo and set the active cells
[xx, yy] = np.meshgrid(mesh.vectorNx, mesh.vectorNy)
zz = -np.exp((xx**2 + yy**2) / 75**2) + mesh.vectorNz[-1]
# Go from topo to actv cells
topo = np.c_[Utils.mkvc(xx), Utils.mkvc(yy), Utils.mkvc(zz)]
actv = Utils.surface2ind_topo(mesh, topo, 'N')
actv = np.asarray([inds for inds, elem in enumerate(actv, 1) if elem],
dtype=int) - 1
# Create active map to go from reduce space to full
actvMap = Maps.InjectActiveCells(mesh, actv, -100)
nC = len(actv)
# Create and array of observation points
xr = np.linspace(-20., 20., 20)
yr = np.linspace(-20., 20., 20)
X, Y = np.meshgrid(xr, yr)
# Move the observation points 5m above the topo
Z = -np.exp((X**2 + Y**2) / 75**2) + mesh.vectorNz[-1] + 5.
# Create a MAGsurvey
rxLoc = np.c_[Utils.mkvc(X.T), Utils.mkvc(Y.T), Utils.mkvc(Z.T)]
rxLoc = PF.BaseMag.RxObs(rxLoc)
srcField = PF.BaseMag.SrcField([rxLoc], param=H0)
survey = PF.BaseMag.LinearSurvey(srcField)
# We can now create a susceptibility model and generate data
# Here a simple block in half-space
model = np.zeros((mesh.nCx, mesh.nCy, mesh.nCz))
model[(midx - 2):(midx + 2), (midy - 2):(midy + 2), -6:-2] = 0.02
model = Utils.mkvc(model)
self.model = model[actv]
# Create active map to go from reduce set to full
actvMap = Maps.InjectActiveCells(mesh, actv, -100)
# Creat reduced identity map
idenMap = Maps.IdentityMap(nP=nC)
# Create the forward model operator
prob = PF.Magnetics.MagneticIntegral(mesh, chiMap=idenMap, actInd=actv)
# Pair the survey and problem
survey.pair(prob)
# Compute linear forward operator and compute some data
d = prob.fields(self.model)
# Add noise and uncertainties (1nT)
data = d + np.random.randn(len(d))
wd = np.ones(len(data)) * 1.
survey.dobs = data
survey.std = wd
# Create sensitivity weights from our linear forward operator
wr = np.sum(prob.G**2., axis=0)**0.5
wr = (wr / np.max(wr))
# Create a regularization
reg = Regularization.Sparse(mesh, indActive=actv, mapping=idenMap)
reg.cell_weights = wr
reg.norms = np.c_[0, 0, 0, 0]
reg.gradientType = 'component'
# reg.eps_p, reg.eps_q = 1e-3, 1e-3
# Data misfit function
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.W = 1 / wd
# Add directives to the inversion
opt = Optimization.ProjectedGNCG(maxIter=100,
lower=0.,
upper=1.,
maxIterLS=20,
maxIterCG=10,
tolCG=1e-3)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
betaest = Directives.BetaEstimate_ByEig()
# Here is where the norms are applied
IRLS = Directives.Update_IRLS(f_min_change=1e-4, minGNiter=1)
update_Jacobi = Directives.UpdatePreconditioner()
self.inv = Inversion.BaseInversion(
invProb, directiveList=[IRLS, betaest, update_Jacobi])
def run(plotIt=True, survey_type="dipole-dipole", p=0., qx=2., qz=2.):
np.random.seed(1)
# Initiate I/O class for DC
IO = DC.IO()
# Obtain ABMN locations
xmin, xmax = 0., 200.
ymin, ymax = 0., 0.
zmin, zmax = 0, 0
endl = np.array([[xmin, ymin, zmin], [xmax, ymax, zmax]])
# Generate DC survey object
survey = DC.Utils.gen_DCIPsurvey(endl,
survey_type=survey_type,
dim=2,
a=10,
b=10,
n=10)
survey.getABMN_locations()
survey = IO.from_ambn_locations_to_survey(survey.a_locations,
survey.b_locations,
survey.m_locations,
survey.n_locations,
survey_type,
data_dc_type='volt')
# Obtain 2D TensorMesh
mesh, actind = IO.set_mesh()
topo, mesh1D = DC.Utils.genTopography(mesh, -10, 0, its=100)
actind = Utils.surface2ind_topo(mesh, np.c_[mesh1D.vectorCCx, topo])
survey.drapeTopo(mesh, actind, option="top")
# Build a conductivity model
blk_inds_c = Utils.ModelBuilder.getIndicesSphere(np.r_[60., -25.], 12.5,
mesh.gridCC)
blk_inds_r = Utils.ModelBuilder.getIndicesSphere(np.r_[140., -25.], 12.5,
mesh.gridCC)
layer_inds = mesh.gridCC[:, 1] > -5.
sigma = np.ones(mesh.nC) * 1. / 100.
sigma[blk_inds_c] = 1. / 10.
sigma[blk_inds_r] = 1. / 1000.
sigma[~actind] = 1. / 1e8
rho = 1. / sigma
# Show the true conductivity model
if plotIt:
fig = plt.figure(figsize=(12, 3))
ax = plt.subplot(111)
temp = rho.copy()
temp[~actind] = np.nan
out = mesh.plotImage(temp,
grid=True,
ax=ax,
gridOpts={'alpha': 0.2},
clim=(10, 1000),
pcolorOpts={
"cmap": "viridis",
"norm": colors.LogNorm()
})
ax.plot(survey.electrode_locations[:, 0],
survey.electrode_locations[:, 1], 'k.')
ax.set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax.set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[0])
cb.set_label("Resistivity (ohm-m)")
ax.set_aspect('equal')
plt.show()
# Use Exponential Map: m = log(rho)
actmap = Maps.InjectActiveCells(mesh,
indActive=actind,
valInactive=np.log(1e8))
mapping = Maps.ExpMap(mesh) * actmap
# Generate mtrue
mtrue = np.log(rho[actind])
# Generate 2.5D DC problem
# "N" means potential is defined at nodes
prb = DC.Problem2D_N(mesh,
rhoMap=mapping,
storeJ=True,
Solver=Solver,
verbose=True)
# Pair problem with survey
try:
prb.pair(survey)
except:
survey.unpair()
prb.pair(survey)
# Make synthetic DC data with 5% Gaussian noise
dtrue = survey.makeSyntheticData(mtrue, std=0.05, force=True)
IO.data_dc = dtrue
# Show apparent resisitivty pseudo-section
if plotIt:
IO.plotPseudoSection(data=survey.dobs / IO.G,
data_type='apparent_resistivity')
# Show apparent resisitivty histogram
if plotIt:
fig = plt.figure()
out = hist(survey.dobs / IO.G, bins=20)
plt.xlabel("Apparent Resisitivty ($\Omega$m)")
plt.show()
# Set initial model based upon histogram
m0 = np.ones(actmap.nP) * np.log(100.)
# Set uncertainty
# floor
eps = 10**(-3.2)
# percentage
std = 0.05
dmisfit = DataMisfit.l2_DataMisfit(survey)
uncert = abs(survey.dobs) * std + eps
dmisfit.W = 1. / uncert
# Map for a regularization
regmap = Maps.IdentityMap(nP=int(actind.sum()))
# Related to inversion
reg = Regularization.Sparse(mesh,
indActive=actind,
mapping=regmap,
gradientType='components')
# gradientType = 'components'
reg.norms = np.c_[p, qx, qz, 0.]
IRLS = Directives.Update_IRLS(maxIRLSiter=20,
minGNiter=1,
betaSearch=False,
fix_Jmatrix=True)
opt = Optimization.InexactGaussNewton(maxIter=40)
invProb = InvProblem.BaseInvProblem(dmisfit, reg, opt)
beta = Directives.BetaSchedule(coolingFactor=5, coolingRate=2)
betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1e0)
target = Directives.TargetMisfit()
update_Jacobi = Directives.UpdatePreconditioner()
inv = Inversion.BaseInversion(invProb, directiveList=[betaest, IRLS])
prb.counter = opt.counter = Utils.Counter()
opt.LSshorten = 0.5
opt.remember('xc')
# Run inversion
mopt = inv.run(m0)
rho_est = mapping * mopt
rho_est_l2 = mapping * invProb.l2model
rho_est[~actind] = np.nan
rho_est_l2[~actind] = np.nan
rho_true = rho.copy()
rho_true[~actind] = np.nan
# show recovered conductivity
if plotIt:
vmin, vmax = rho.min(), rho.max()
fig, ax = plt.subplots(3, 1, figsize=(20, 9))
out1 = mesh.plotImage(rho_true,
clim=(10, 1000),
pcolorOpts={
"cmap": "viridis",
"norm": colors.LogNorm()
},
ax=ax[0])
out2 = mesh.plotImage(rho_est_l2,
clim=(10, 1000),
pcolorOpts={
"cmap": "viridis",
"norm": colors.LogNorm()
},
ax=ax[1])
out3 = mesh.plotImage(rho_est,
clim=(10, 1000),
pcolorOpts={
"cmap": "viridis",
"norm": colors.LogNorm()
},
ax=ax[2])
out = [out1, out2, out3]
titles = ["True", "L2", ("L%d, Lx%d, Lz%d") % (p, qx, qz)]
for i in range(3):
ax[i].plot(survey.electrode_locations[:, 0],
survey.electrode_locations[:, 1], 'kv')
ax[i].set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max())
ax[i].set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min())
cb = plt.colorbar(out[i][0], ax=ax[i])
cb.set_label("Resistivity ($\Omega$m)")
ax[i].set_xlabel("Northing (m)")
ax[i].set_ylabel("Elevation (m)")
ax[i].set_aspect('equal')
ax[i].set_title(titles[i])
plt.tight_layout()
plt.show()
def setUp(self):
np.random.seed(0)
# First we need to define the direction of the inducing field
# As a simple case, we pick a vertical inducing field of magnitude
# 50,000nT.
# From old convention, field orientation is given as an
# azimuth from North (positive clockwise)
# and dip from the horizontal (positive downward).
H0 = (50000., 90., 0.)
# Create a mesh
h = [5, 5, 5]
padDist = np.ones((3, 2)) * 100
nCpad = [2, 4, 2]
# Create grid of points for topography
# Lets create a simple Gaussian topo and set the active cells
[xx, yy] = np.meshgrid(
np.linspace(-200., 200., 50),
np.linspace(-200., 200., 50)
)
b = 100
A = 50
zz = A*np.exp(-0.5*((xx/b)**2. + (yy/b)**2.))
# We would usually load a topofile
topo = np.c_[Utils.mkvc(xx), Utils.mkvc(yy), Utils.mkvc(zz)]
# Create and array of observation points
xr = np.linspace(-100., 100., 20)
yr = np.linspace(-100., 100., 20)
X, Y = np.meshgrid(xr, yr)
Z = A*np.exp(-0.5*((X/b)**2. + (Y/b)**2.)) + 5
# Create a MAGsurvey
xyzLoc = np.c_[Utils.mkvc(X.T), Utils.mkvc(Y.T), Utils.mkvc(Z.T)]
rxLoc = PF.BaseMag.RxObs(xyzLoc)
srcField = PF.BaseMag.SrcField([rxLoc], param=H0)
survey = PF.BaseMag.LinearSurvey(srcField)
# Get extent of points
limx = np.r_[topo[:, 0].max(), topo[:, 0].min()]
limy = np.r_[topo[:, 1].max(), topo[:, 1].min()]
limz = np.r_[topo[:, 2].max(), topo[:, 2].min()]
# Get center of the mesh
midX = np.mean(limx)
midY = np.mean(limy)
midZ = np.mean(limz)
nCx = int(limx[0]-limx[1]) / h[0]
nCy = int(limy[0]-limy[1]) / h[1]
nCz = int(limz[0]-limz[1]+int(np.min(np.r_[nCx, nCy])/3)) / h[2]
# Figure out full extent required from input
extent = np.max(np.r_[nCx * h[0] + padDist[0, :].sum(),
nCy * h[1] + padDist[1, :].sum(),
nCz * h[2] + padDist[2, :].sum()])
maxLevel = int(np.log2(extent/h[0]))+1
# Number of cells at the small octree level
# For now equal in 3D
nCx, nCy, nCz = 2**(maxLevel), 2**(maxLevel), 2**(maxLevel)
# nCy = 2**(int(np.log2(extent/h[1]))+1)
# nCz = 2**(int(np.log2(extent/h[2]))+1)
# Define the mesh and origin
# For now cubic cells
self.mesh = Mesh.TreeMesh([np.ones(nCx)*h[0],
np.ones(nCx)*h[1],
np.ones(nCx)*h[2]])
# Set origin
self.mesh.x0 = np.r_[
-nCx*h[0]/2.+midX, -nCy*h[1]/2.+midY, -nCz*h[2]/2.+midZ
]
# Refine the mesh around topography
# Get extent of points
F = NearestNDInterpolator(topo[:, :2], topo[:, 2])
zOffset = 0
# Cycle through the first 3 octree levels
for ii in range(3):
dx = self.mesh.hx.min()*2**ii
nCx = int((limx[0]-limx[1]) / dx)
nCy = int((limy[0]-limy[1]) / dx)
# Create a grid at the octree level in xy
CCx, CCy = np.meshgrid(
np.linspace(limx[1], limx[0], nCx),
np.linspace(limy[1], limy[0], nCy)
)
z = F(mkvc(CCx), mkvc(CCy))
# level means number of layers in current OcTree level
for _ in range(int(nCpad[ii])):
self.mesh.insert_cells(
np.c_[mkvc(CCx), mkvc(CCy), z-zOffset],
np.ones_like(z)*maxLevel-ii,
finalize=False
)
zOffset += dx
self.mesh.finalize()
# Define an active cells from topo
actv = Utils.surface2ind_topo(self.mesh, topo)
nC = int(actv.sum())
# We can now create a susceptibility model and generate data
# Lets start with a simple block in half-space
self.model = Utils.ModelBuilder.addBlock(
self.mesh.gridCC, np.zeros(self.mesh.nC),
np.r_[-20, -20, -5], np.r_[20, 20, 30], 0.05
)[actv]
# Create active map to go from reduce set to full
self.actvMap = Maps.InjectActiveCells(self.mesh, actv, np.nan)
# Creat reduced identity map
idenMap = Maps.IdentityMap(nP=nC)
# Create the forward model operator
prob = PF.Magnetics.MagneticIntegral(
self.mesh, chiMap=idenMap, actInd=actv
)
# Pair the survey and problem
survey.pair(prob)
# Compute linear forward operator and compute some data
data = prob.fields(self.model)
# Add noise and uncertainties (1nT)
noise = np.random.randn(len(data))
data += noise
wd = np.ones(len(data))*1.
survey.dobs = data
survey.std = wd
# Create sensitivity weights from our linear forward operator
rxLoc = survey.srcField.rxList[0].locs
wr = np.zeros(prob.G.shape[1])
for ii in range(survey.nD):
wr += (prob.G[ii, :]/survey.std[ii])**2.
# wr = (wr/np.max(wr))
wr = wr**0.5
# Create a regularization
reg = Regularization.Sparse(self.mesh, indActive=actv, mapping=idenMap)
reg.norms = np.c_[0, 0, 0, 0]
reg.cell_weights = wr
reg.mref = np.zeros(nC)
# Data misfit function
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.W = 1./survey.std
# Add directives to the inversion
opt = Optimization.ProjectedGNCG(
maxIter=20, lower=0., upper=10.,
maxIterLS=20, maxIterCG=20, tolCG=1e-4,
stepOffBoundsFact=1e-4
)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=1e+4)
# Here is where the norms are applied
# Use pick a treshold parameter empirically based on the distribution of
# model parameters
IRLS = Directives.Update_IRLS(
f_min_change=1e-3, maxIRLSiter=20, beta_tol=5e-1
)
update_Jacobi = Directives.UpdatePreconditioner()
# saveOuput = Directives.SaveOutputEveryIteration()
# saveModel.fileName = work_dir + out_dir + 'ModelSus'
self.inv = Inversion.BaseInversion(
invProb,
directiveList=[IRLS, update_Jacobi]
)
(mesh.gridCC[:, 2] - z0)**2.)) < r0 # indicies of sphere
# sphere done =================================================================
print("Starting forward modeling")
start = clock()
# Define model Background
ln_sigback = 0.023 # chargeability
rx = getRxData() # rx locations
tx = getTxData() # tx locations
survey = generateSurvey(rx, tx, 45, 65) # create survey object
survey.getABMN_locations() # get locations
uniq = Utils.uniqueRows(
np.vstack((survey.a_locations, survey.b_locations, survey.m_locations,
survey.n_locations))) # row the locations
electrode_locations = uniq[0] # assign
actinds = Utils.surface2ind_topo(mesh, electrode_locations,
method='cubic') # active indicies
survey.drapeTopo(mesh, actinds) # drape topo
# ============================================================================
# Create model
mx = np.ones(mesh.nC) * 0.015 # chargeability
sigma = np.ones(mesh.nC) * 1. / 33000.
# create dipping structure parameters
theta = 45. * np.pi / 180. # dipping angle
x0_d = 374700.
x1_d = 375000.
y0_d = 6275850.
y0_1d = 500. * np.sin(theta) + y0_d
y1_d = 6275900.
y1_1d = 500. * np.sin(theta) + y1_d
z0_d = 1860.
def run(plotIt=True, survey_type="pole-dipole"):
np.random.seed(1)
# Initiate I/O class for DC
IO = DC.IO()
# Obtain ABMN locations
fileName1 = "C:/Users/johnk/Projects/Seabridge/fmdataDC.con" # output mod
fileName1_ = "C:/Users/johnk/Projects/Seabridge/fmdataIP.chg" # output mod
fileName2 = "C:/Users/johnk/Projects/Seabridge/forwardmodel.msh" # in mesh
mesh = Mesh.TensorMesh._readUBC_3DMesh(fileName2) # Read in/create mesh
print("Starting forward modeling")
start = clock()
# Define model Background
rx = getRxData() # rx locations
tx = getTxData() # tx locations
survey_dc = generateSurvey(rx, tx, 45, 65) # create survey object
survey_dc.getABMN_locations() # get locations
# survey_dc = IO.from_ambn_locations_to_survey(
# survey_dc.a_locations, survey_dc.b_locations,
# survey_dc.m_locations, survey_dc.n_locations,
# survey_type, data_dc_type='volt', data_ip_type='volt'
# )
uniq = Utils.uniqueRows(np.vstack((survey_dc.a_locations,
survey_dc.b_locations,
survey_dc.m_locations,
survey_dc.n_locations)))
electrode_locations = uniq[0] # assign
actinds = Utils.surface2ind_topo(mesh,
electrode_locations,
method='cubic') # active indicies
survey_dc.drapeTopo(mesh, actinds) # drape topo
# =============================================================================
# create sphere for ice representation
x0 = (np.max(mesh.gridCC[:, 0]) +
np.min(mesh.gridCC[:, 0])) / 2. + 50 # x0 center point of sphere
y0 = (np.max(mesh.gridCC[:, 1]) +
np.min(mesh.gridCC[:, 1])) / 2. - 50 # y0 center point of sphere
z0 = 2350 # x0 center point of sphere
# (np.max(mesh.gridCC[:, 2]) + np.min(mesh.gridCC[:, 2])) / 2.
r0 = 500 # radius of sphere
print(x0, y0, z0)
csph = (np.sqrt((mesh.gridCC[:, 0] - x0)**2. +
(mesh.gridCC[:, 1] - y0)**2. +
(mesh.gridCC[:, 2] - z0)**2.)) < r0 # indicies of sphere
# sphere done =================================================================
# ============================================================================
# Create model
mx = np.ones(mesh.nC) * 0.020 # chargeability
sigma = np.ones(mesh.nC) * 1. / 15000.
# create dipping structure parameters
theta = 45. * np.pi / 180. # dipping angle
x0_d = 374700.
x1_d = 375000.
y0_d = 6275850.
y0_1d = 500. * np.sin(theta) + y0_d
y1_d = 6275900.
y1_1d = 500. * np.sin(theta) + y1_d
z0_d = 1860.
z1_d = z0_d - (500. * np.cos(theta))
m_ = (z0_d - z1_d) / (y0_1d - y0_d) # slope of dip
# loop through mesh and assign dipping structure conductivity
for idx in range(mesh.nC):
if z1_d <= mesh.gridCC[idx, 2] <= z0_d:
if (x0_d <= mesh.gridCC[idx, 0] <= x1_d):
yslope1 = y0_d + (1. / m_) * (mesh.gridCC[idx, 2] - z0_d)
yslope2 = y1_d + (1. / m_) * (mesh.gridCC[idx, 2] - z0_d)
if yslope1 <= mesh.gridCC[idx, 1] <= yslope2:
mx[idx] = 0.03
sigma[idx] = 1. / 300.
# mx[csph] = ((0.025) *
# np.ones_like(mx[csph])) # set sphere values
mx[~actinds] = 1. / 1e8 # flag air values
# sigma[csph] = ((5000.) *
# np.ones_like(sigma[csph])) # set sphere values
sigma[~actinds] = 1. / 1e8 # flag air values
rho = 1. / sigma
stop = clock()
print(stop)
# plot results
# Show the true conductivity model
if plotIt:
ncy = mesh.nCy
ncz = mesh.nCz
ncx = mesh.nCx
mtrue = mx
print(mtrue.min(), mtrue.max())
clim = [0, 0.04]
fig, ax = plt.subplots(2, 2, figsize=(12, 6))
ax = Utils.mkvc(ax)
dat = mesh.plotSlice(((mx)), ax=ax[0], normal='Z', clim=clim,
ind=int(ncz / 2), pcolorOpts={"cmap": "jet"})
ax[0].plot(rx[:, 0], rx[:, 1], 'or')
ax[0].plot(tx[:, 0], tx[:, 1], 'dk')
mesh.plotSlice(((mx)), ax=ax[1], normal='Y', clim=clim,
ind=int(ncy / 2 + 2), pcolorOpts={"cmap": "jet"})
mesh.plotSlice(((mx)), ax=ax[2], normal='X', clim=clim,
ind=int(ncx / 2 + 4), pcolorOpts={"cmap": "jet"})
mesh.plotSlice(((mx)), ax=ax[3], normal='X', clim=clim,
ind=int(ncx / 2 + 8), pcolorOpts={"cmap": "jet"})
cbar_ax = fig.add_axes([0.82, 0.15, 0.05, 0.7])
cb = plt.colorbar(dat[0], ax=cbar_ax)
fig.subplots_adjust(right=0.85)
cb.set_label('V/V')
cbar_ax.axis('off')
plt.show()
mtrue = 1. / sigma
print(mtrue.min(), mtrue.max())
clim = [0, 20000]
fig, ax = plt.subplots(2, 2, figsize=(12, 6))
ax = Utils.mkvc(ax)
dat = mesh.plotSlice(((mtrue)), ax=ax[0], normal='Z', clim=clim,
ind=int(ncz / 2 - 4), pcolorOpts={"cmap": "jet"})
ax[0].plot(rx[:, 0], rx[:, 1], 'or')
ax[0].plot(tx[:, 0], tx[:, 1], 'dk')
mesh.plotSlice(((mtrue)), ax=ax[1], normal='Y', clim=clim,
ind=int(ncy / 2), pcolorOpts={"cmap": "jet"})
mesh.plotSlice(((mtrue)), ax=ax[2], normal='X', clim=clim,
ind=int(ncx / 2 + 4), pcolorOpts={"cmap": "jet"})
mesh.plotSlice(((mtrue)), ax=ax[3], normal='X', clim=clim,
ind=int(ncx / 2 + 8), pcolorOpts={"cmap": "jet"})
cbar_ax = fig.add_axes([0.82, 0.15, 0.05, 0.7])
cb = plt.colorbar(dat[0], ax=cbar_ax)
fig.subplots_adjust(right=0.85)
cb.set_label('rho')
cbar_ax.axis('off')
plt.show()
# Use Exponential Map: m = log(rho)
actmap = Maps.InjectActiveCells(
mesh, indActive=actinds, valInactive=np.log(1e8)
)
mapping = Maps.ExpMap(mesh) * actmap
# Generate mtrue_dc for resistivity
mtrue_dc = np.log(rho[actinds])
# Generate 3D DC problem
# "CC" means potential is defined at center
prb = DC.Problem3D_CC(
mesh, rhoMap=mapping, storeJ=False,
Solver=Solver
)
# Pair problem with survey
try:
prb.pair(survey_dc)
except:
survey_dc.unpair()
prb.pair(survey_dc)
# Make synthetic DC data with 5% Gaussian noise
dtrue_dc = survey_dc.makeSyntheticData(mtrue_dc, std=0.05, force=True)
IO.data_dc = dtrue_dc
# Generate mtrue_ip for chargability
mtrue_ip = mx[actinds]
# Generate 3D DC problem
# "CC" means potential is defined at center
prb_ip = IP.Problem3D_CC(
mesh, etaMap=actmap, storeJ=False, rho=rho,
Solver=Solver
)
survey_ip = IP.from_dc_to_ip_survey(survey_dc, dim="3D")
prb_ip.pair(survey_ip)
dtrue_ip = survey_ip.makeSyntheticData(mtrue_ip, std=0.05)
IO.data_ip = dtrue_ip
# Show apparent resisitivty histogram
# if plotIt:
# fig = plt.figure(figsize=(10, 4))
# ax1 = plt.subplot(121)
# out = hist(np.log10(abs(IO.voltages)), bins=20)
# ax1.set_xlabel("log10 DC voltage (V)")
# ax2 = plt.subplot(122)
# out = hist(IO.apparent_resistivity, bins=20)
# ax2.set_xlabel("Apparent Resistivity ($\Omega$m)")
# plt.tight_layout()
# plt.show()
# Set initial model based upon histogram
m0_dc = np.ones(actmap.nP) * np.log(10000.)
# Set uncertainty
# floor
eps_dc = 10**(-3.2)
# percentage
std_dc = 0.05
mopt_dc, pred_dc = DC.run_inversion(
m0_dc, survey_dc, actinds, mesh, std_dc, eps_dc,
use_sensitivity_weight=False)
# Convert obtained inversion model to resistivity
# rho = M(m), where M(.) is a mapping
rho_est = mapping * mopt_dc
# rho_est[~actinds] = np.nan
rho_true = rho.copy()
rho_true[~actinds] = np.nan
# write data to file
out_file = open(fileName1, "w")
for i in range(rho_est.size):
out_file.write("%0.5e\n" % rho_est[i])
# Set initial model based upon histogram
m0_ip = np.ones(actmap.nP) * 1e-10
# Set uncertainty
# floor
eps_ip = 10**(-4)
# percentage
std_ip = 0.05
# Clean sensitivity function formed with true resistivity
prb_ip._Jmatrix = None
# Input obtained resistivity to form sensitivity
prb_ip.rho = mapping * mopt_dc
mopt_ip, _ = IP.run_inversion(
m0_ip, survey_ip, actinds, mesh, std_ip, eps_ip,
upper=np.Inf, lower=0.,
use_sensitivity_weight=False)
# Convert obtained inversion model to chargeability
# charg = M(m), where M(.) is a mapping for cells below topography
charg_est = actmap * mopt_ip
# charg_est[~actinds] = np.nan
charg_true = charg.copy()
charg_true[~actinds] = np.nan
# write IP data to file
out_file = open(fileName1_, "w")
for i in range(charg_est.size):
out_file.write("%0.5e\n" % charg_est[i])
def setUp(self):
ndv = -100
# Create a mesh
dx = 5.
hxind = [(dx, 5, -1.3), (dx, 5), (dx, 5, 1.3)]
hyind = [(dx, 5, -1.3), (dx, 5), (dx, 5, 1.3)]
hzind = [(dx, 5, -1.3), (dx, 6)]
mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCC')
# Get index of the center
midx = int(mesh.nCx/2)
midy = int(mesh.nCy/2)
# Lets create a simple Gaussian topo and set the active cells
[xx, yy] = np.meshgrid(mesh.vectorNx, mesh.vectorNy)
zz = -np.exp((xx**2 + yy**2) / 75**2) + mesh.vectorNz[-1]
# Go from topo to actv cells
topo = np.c_[Utils.mkvc(xx), Utils.mkvc(yy), Utils.mkvc(zz)]
actv = Utils.surface2ind_topo(mesh, topo, 'N')
actv = np.asarray([inds for inds, elem in enumerate(actv, 1)
if elem], dtype=int) - 1
# Create active map to go from reduce space to full
actvMap = Maps.InjectActiveCells(mesh, actv, -100)
nC = len(actv)
# Create and array of observation points
xr = np.linspace(-20., 20., 20)
yr = np.linspace(-20., 20., 20)
X, Y = np.meshgrid(xr, yr)
# Move the observation points 5m above the topo
Z = -np.exp((X**2 + Y**2) / 75**2) + mesh.vectorNz[-1] + 5.
# Create a MAGsurvey
locXYZ = np.c_[Utils.mkvc(X.T), Utils.mkvc(Y.T), Utils.mkvc(Z.T)]
rxLoc = PF.BaseGrav.RxObs(locXYZ)
srcField = PF.BaseGrav.SrcField([rxLoc])
survey = PF.BaseGrav.LinearSurvey(srcField)
# We can now create a density model and generate data
# Here a simple block in half-space
model = np.zeros((mesh.nCx, mesh.nCy, mesh.nCz))
model[(midx-2):(midx+2), (midy-2):(midy+2), -6:-2] = 0.5
model = Utils.mkvc(model)
self.model = model[actv]
# Create active map to go from reduce set to full
actvMap = Maps.InjectActiveCells(mesh, actv, ndv)
# Create reduced identity map
idenMap = Maps.IdentityMap(nP=nC)
# Create the forward model operator
prob = PF.Gravity.GravityIntegral(
mesh,
rhoMap=idenMap,
actInd=actv
)
# Pair the survey and problem
survey.pair(prob)
# Compute linear forward operator and compute some data
d = prob.fields(self.model)
# Add noise and uncertainties (1nT)
data = d + np.random.randn(len(d))*0.001
wd = np.ones(len(data))*.001
survey.dobs = data
survey.std = wd
# PF.Gravity.plot_obs_2D(survey.srcField.rxList[0].locs, d=data)
# Create sensitivity weights from our linear forward operator
wr = PF.Magnetics.get_dist_wgt(mesh, locXYZ, actv, 2., 2.)
wr = wr**2.
# Create a regularization
reg = Regularization.Sparse(mesh, indActive=actv, mapping=idenMap)
reg.cell_weights = wr
reg.norms = [0, 1, 1, 1]
reg.eps_p, reg.eps_q = 5e-2, 1e-2
# Data misfit function
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.W = 1/wd
# Add directives to the inversion
opt = Optimization.ProjectedGNCG(maxIter=100, lower=-1., upper=1.,
maxIterLS=20, maxIterCG=10,
tolCG=1e-3)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=1e+8)
# Here is where the norms are applied
IRLS = Directives.Update_IRLS(f_min_change=1e-3,
minGNiter=3)
update_Jacobi = Directives.Update_lin_PreCond(mapping=idenMap)
self.inv = Inversion.BaseInversion(invProb,
directiveList=[IRLS,
update_Jacobi])
def run(plotIt=True):
# Create a mesh
dx = 5.
hxind = [(dx, 5, -1.3), (dx, 15), (dx, 5, 1.3)]
hyind = [(dx, 5, -1.3), (dx, 15), (dx, 5, 1.3)]
hzind = [(dx, 5, -1.3), (dx, 7), (3.5, 1), (2, 5)]
mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCC')
# Get index of the center
midx = int(mesh.nCx/2)
midy = int(mesh.nCy/2)
# Lets create a simple Gaussian topo and set the active cells
[xx, yy] = np.meshgrid(mesh.vectorNx, mesh.vectorNy)
zz = -np.exp((xx**2 + yy**2) / 75**2) + mesh.vectorNz[-1]
# We would usually load a topofile
topo = np.c_[Utils.mkvc(xx), Utils.mkvc(yy), Utils.mkvc(zz)]
# Go from topo to actv cells
actv = Utils.surface2ind_topo(mesh, topo, 'N')
actv = np.asarray([inds for inds, elem in enumerate(actv, 1) if elem],
dtype=int) - 1
# Create active map to go from reduce space to full
actvMap = Maps.InjectActiveCells(mesh, actv, -100)
nC = len(actv)
# Create and array of observation points
xr = np.linspace(-30., 30., 20)
yr = np.linspace(-30., 30., 20)
X, Y = np.meshgrid(xr, yr)
# Move the observation points 5m above the topo
Z = -np.exp((X**2 + Y**2) / 75**2) + mesh.vectorNz[-1] + 0.1
# Create a MAGsurvey
rxLoc = np.c_[Utils.mkvc(X.T), Utils.mkvc(Y.T), Utils.mkvc(Z.T)]
rxLoc = PF.BaseGrav.RxObs(rxLoc)
srcField = PF.BaseGrav.SrcField([rxLoc])
survey = PF.BaseGrav.LinearSurvey(srcField)
# We can now create a susceptibility model and generate data
# Here a simple block in half-space
model = np.zeros((mesh.nCx, mesh.nCy, mesh.nCz))
model[(midx-5):(midx-1), (midy-2):(midy+2), -10:-6] = 0.5
model[(midx+1):(midx+5), (midy-2):(midy+2), -10:-6] = -0.5
model = Utils.mkvc(model)
model = model[actv]
# Create active map to go from reduce set to full
actvMap = Maps.InjectActiveCells(mesh, actv, -100)
# Create reduced identity map
idenMap = Maps.IdentityMap(nP=nC)
# Create the forward model operator
prob = PF.Gravity.GravityIntegral(mesh, rhoMap=idenMap, actInd=actv)
# Pair the survey and problem
survey.pair(prob)
# Compute linear forward operator and compute some data
d = prob.fields(model)
# Add noise and uncertainties
# We add some random Gaussian noise (1nT)
data = d + np.random.randn(len(d))*1e-3
wd = np.ones(len(data))*1e-3 # Assign flat uncertainties
survey.dobs = data
survey.std = wd
survey.mtrue = model
# Create sensitivity weights from our linear forward operator
rxLoc = survey.srcField.rxList[0].locs
wr = np.sum(prob.G**2., axis=0)**0.5
wr = (wr/np.max(wr))
# Create a regularization
reg = Regularization.Sparse(mesh, indActive=actv, mapping=idenMap)
reg.cell_weights = wr
reg.norms = [0, 1, 1, 1]
# Data misfit function
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.W = Utils.sdiag(1/wd)
# Add directives to the inversion
opt = Optimization.ProjectedGNCG(maxIter=100, lower=-1., upper=1.,
maxIterLS=20, maxIterCG=10,
tolCG=1e-3)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
betaest = Directives.BetaEstimate_ByEig()
# Here is where the norms are applied
# Use pick a treshold parameter empirically based on the distribution of
# model parameters
IRLS = Directives.Update_IRLS(f_min_change=1e-2, minGNiter=2)
update_Jacobi = Directives.UpdatePreconditioner()
inv = Inversion.BaseInversion(invProb, directiveList=[IRLS,
betaest,
update_Jacobi])
# Run the inversion
m0 = np.ones(nC)*1e-4 # Starting model
mrec = inv.run(m0)
if plotIt:
# Here is the recovered susceptibility model
ypanel = midx
zpanel = -7
m_l2 = actvMap * invProb.l2model
m_l2[m_l2 == -100] = np.nan
m_lp = actvMap * mrec
m_lp[m_lp == -100] = np.nan
m_true = actvMap * model
m_true[m_true == -100] = np.nan
vmin, vmax = mrec.min(), mrec.max()
# Plot the data
PF.Gravity.plot_obs_2D(rxLoc, d=data)
plt.figure()
# Plot L2 model
ax = plt.subplot(321)
mesh.plotSlice(m_l2, ax=ax, normal='Z', ind=zpanel,
grid=True, clim=(vmin, vmax))
plt.plot(([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCy[ypanel], mesh.vectorCCy[ypanel]]), color='w')
plt.title('Plan l2-model.')
plt.gca().set_aspect('equal')
plt.ylabel('y')
ax.xaxis.set_visible(False)
plt.gca().set_aspect('equal', adjustable='box')
# Vertica section
ax = plt.subplot(322)
mesh.plotSlice(m_l2, ax=ax, normal='Y', ind=midx,
grid=True, clim=(vmin, vmax))
plt.plot(([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCz[zpanel], mesh.vectorCCz[zpanel]]), color='w')
plt.title('E-W l2-model.')
plt.gca().set_aspect('equal')
ax.xaxis.set_visible(False)
plt.ylabel('z')
plt.gca().set_aspect('equal', adjustable='box')
# Plot Lp model
ax = plt.subplot(323)
mesh.plotSlice(m_lp, ax=ax, normal='Z', ind=zpanel,
grid=True, clim=(vmin, vmax))
plt.plot(([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCy[ypanel], mesh.vectorCCy[ypanel]]), color='w')
plt.title('Plan lp-model.')
plt.gca().set_aspect('equal')
ax.xaxis.set_visible(False)
plt.ylabel('y')
plt.gca().set_aspect('equal', adjustable='box')
# Vertical section
ax = plt.subplot(324)
mesh.plotSlice(m_lp, ax=ax, normal='Y', ind=midx,
grid=True, clim=(vmin, vmax))
plt.plot(([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCz[zpanel], mesh.vectorCCz[zpanel]]), color='w')
plt.title('E-W lp-model.')
plt.gca().set_aspect('equal')
ax.xaxis.set_visible(False)
plt.ylabel('z')
plt.gca().set_aspect('equal', adjustable='box')
# Plot True model
ax = plt.subplot(325)
mesh.plotSlice(m_true, ax=ax, normal='Z', ind=zpanel,
grid=True, clim=(vmin, vmax))
plt.plot(([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCy[ypanel], mesh.vectorCCy[ypanel]]), color='w')
plt.title('Plan true model.')
plt.gca().set_aspect('equal')
plt.xlabel('x')
plt.ylabel('y')
plt.gca().set_aspect('equal', adjustable='box')
# Vertical section
ax = plt.subplot(326)
mesh.plotSlice(m_true, ax=ax, normal='Y', ind=midx,
grid=True, clim=(vmin, vmax))
plt.plot(([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCz[zpanel], mesh.vectorCCz[zpanel]]), color='w')
plt.title('E-W true model.')
plt.gca().set_aspect('equal')
plt.xlabel('x')
plt.ylabel('z')
plt.gca().set_aspect('equal', adjustable='box')
def setUp(self):
# We will assume a vertical inducing field
H0 = (50000., 90., 0.)
# The magnetization is set along a different direction (induced + remanence)
M = np.array([90., 0.])
# Block with an effective susceptibility
chi_e = 0.05
# Create grid of points for topography
# Lets create a simple Gaussian topo and set the active cells
[xx, yy] = np.meshgrid(np.linspace(-200, 200, 50),
np.linspace(-200, 200, 50))
b = 100
A = 50
zz = A * np.exp(-0.5 * ((xx / b)**2. + (yy / b)**2.))
topo = np.c_[Utils.mkvc(xx), Utils.mkvc(yy), Utils.mkvc(zz)]
# Create and array of observation points
xr = np.linspace(-100., 100., 20)
yr = np.linspace(-100., 100., 20)
X, Y = np.meshgrid(xr, yr)
Z = A * np.exp(-0.5 * ((X / b)**2. + (Y / b)**2.)) + 5
# Create a MAGsurvey
rxLoc = np.c_[Utils.mkvc(X.T), Utils.mkvc(Y.T), Utils.mkvc(Z.T)]
Rx = PF.BaseMag.RxObs(rxLoc)
srcField = PF.BaseMag.SrcField([Rx], param=H0)
survey = PF.BaseMag.LinearSurvey(srcField)
# Create a mesh
h = [5, 5, 5]
padDist = np.ones((3, 2)) * 100
nCpad = [4, 4, 2]
# Get extent of points
limx = np.r_[topo[:, 0].max(), topo[:, 0].min()]
limy = np.r_[topo[:, 1].max(), topo[:, 1].min()]
limz = np.r_[topo[:, 2].max(), topo[:, 2].min()]
# Get center of the mesh
midX = np.mean(limx)
midY = np.mean(limy)
midZ = np.mean(limz)
nCx = int(limx[0] - limx[1]) / h[0]
nCy = int(limy[0] - limy[1]) / h[1]
nCz = int(limz[0] - limz[1] + int(np.min(np.r_[nCx, nCy]) / 3)) / h[2]
# Figure out full extent required from input
extent = np.max(np.r_[nCx * h[0] + padDist[0, :].sum(),
nCy * h[1] + padDist[1, :].sum(),
nCz * h[2] + padDist[2, :].sum()])
maxLevel = int(np.log2(extent / h[0])) + 1
# Number of cells at the small octree level
# For now equal in 3D
nCx, nCy, nCz = 2**(maxLevel), 2**(maxLevel), 2**(maxLevel)
# Define the mesh and origin
mesh = Mesh.TreeMesh(
[np.ones(nCx) * h[0],
np.ones(nCx) * h[1],
np.ones(nCx) * h[2]])
# Set origin
mesh.x0 = np.r_[-nCx * h[0] / 2. + midX, -nCy * h[1] / 2. + midY,
-nCz * h[2] / 2. + midZ]
# Refine the mesh around topography
# Get extent of points
F = NearestNDInterpolator(topo[:, :2], topo[:, 2])
zOffset = 0
# Cycle through the first 3 octree levels
for ii in range(3):
dx = mesh.hx.min() * 2**ii
nCx = int((limx[0] - limx[1]) / dx)
nCy = int((limy[0] - limy[1]) / dx)
# Create a grid at the octree level in xy
CCx, CCy = np.meshgrid(np.linspace(limx[1], limx[0], nCx),
np.linspace(limy[1], limy[0], nCy))
z = F(mkvc(CCx), mkvc(CCy))
# level means number of layers in current OcTree level
for level in range(int(nCpad[ii])):
mesh.insert_cells(np.c_[mkvc(CCx),
mkvc(CCy), z - zOffset],
np.ones_like(z) * maxLevel - ii,
finalize=False)
zOffset += dx
mesh.finalize()
# Define an active cells from topo
actv = Utils.surface2ind_topo(mesh, topo)
nC = int(actv.sum())
# Convert the inclination declination to vector in Cartesian
M_xyz = Utils.matutils.dip_azimuth2cartesian(
np.ones(nC) * M[0],
np.ones(nC) * M[1])
# Get the indicies of the magnetized block
ind = Utils.ModelBuilder.getIndicesBlock(
np.r_[-20, -20, -10],
np.r_[20, 20, 25],
mesh.gridCC,
)[0]
# Assign magnetization value, inducing field strength will
# be applied in by the :class:`SimPEG.PF.Magnetics` problem
model = np.zeros(mesh.nC)
model[ind] = chi_e
# Remove air cells
self.model = model[actv]
# Create active map to go from reduce set to full
self.actvPlot = Maps.InjectActiveCells(mesh, actv, np.nan)
# Creat reduced identity map
idenMap = Maps.IdentityMap(nP=nC)
# Create the forward model operator
prob = PF.Magnetics.MagneticIntegral(mesh,
M=M_xyz,
chiMap=idenMap,
actInd=actv)
# Pair the survey and problem
survey.pair(prob)
# Compute some data and add some random noise
data = prob.fields(self.model)
# Split the data in components
nD = rxLoc.shape[0]
std = 5 # nT
data += np.random.randn(nD) * std
wd = np.ones(nD) * std
# Assigne data and uncertainties to the survey
survey.dobs = data
survey.std = wd
######################################################################
# Equivalent Source
# Get the active cells for equivalent source is the top only
surf = Utils.modelutils.surface_layer_index(mesh, topo)
# Get the layer of cells directyl below topo
nC = np.count_nonzero(surf) # Number of active cells
# Create active map to go from reduce set to full
surfMap = Maps.InjectActiveCells(mesh, surf, np.nan)
# Create identity map
idenMap = Maps.IdentityMap(nP=nC)
# Create static map
prob = PF.Magnetics.MagneticIntegral(mesh,
chiMap=idenMap,
actInd=surf,
parallelized=False,
equiSourceLayer=True)
prob.solverOpts['accuracyTol'] = 1e-4
# Pair the survey and problem
if survey.ispaired:
survey.unpair()
survey.pair(prob)
# Create a regularization function, in this case l2l2
reg = Regularization.Sparse(mesh,
indActive=surf,
mapping=Maps.IdentityMap(nP=nC),
scaledIRLS=False)
reg.mref = np.zeros(nC)
# Specify how the optimization will proceed,
# set susceptibility bounds to inf
opt = Optimization.ProjectedGNCG(maxIter=20,
lower=-np.inf,
upper=np.inf,
maxIterLS=20,
maxIterCG=20,
tolCG=1e-3)
# Define misfit function (obs-calc)
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.W = 1. / survey.std
# Create the default L2 inverse problem from the above objects
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
# Specify how the initial beta is found
betaest = Directives.BetaEstimate_ByEig()
# Target misfit to stop the inversion,
# try to fit as much as possible of the signal,
# we don't want to lose anything
IRLS = Directives.Update_IRLS(f_min_change=1e-3,
minGNiter=1,
beta_tol=1e-1)
update_Jacobi = Directives.UpdatePreconditioner()
# Put all the parts together
inv = Inversion.BaseInversion(
invProb, directiveList=[betaest, IRLS, update_Jacobi])
# Run the equivalent source inversion
mstart = np.ones(nC) * 1e-4
mrec = inv.run(mstart)
# Won't store the sensitivity and output 'xyz' data.
prob.forwardOnly = True
prob.rx_type = 'xyz'
prob._G = None
prob.modelType = 'amplitude'
prob.model = mrec
pred = prob.fields(mrec)
bx = pred[:nD]
by = pred[nD:2 * nD]
bz = pred[2 * nD:]
bAmp = (bx**2. + by**2. + bz**2.)**0.5
# AMPLITUDE INVERSION
# Create active map to go from reduce space to full
actvMap = Maps.InjectActiveCells(mesh, actv, -100)
nC = int(actv.sum())
# Create identity map
idenMap = Maps.IdentityMap(nP=nC)
self.mstart = np.ones(nC) * 1e-4
# Create the forward model operator
prob = PF.Magnetics.MagneticIntegral(mesh,
chiMap=idenMap,
actInd=actv,
modelType='amplitude',
rx_type='xyz')
prob.model = self.mstart
# Change the survey to xyz components
surveyAmp = PF.BaseMag.LinearSurvey(survey.srcField)
# Pair the survey and problem
surveyAmp.pair(prob)
# Create a regularization function, in this case l2l2
wr = np.sum(prob.G**2., axis=0)**0.5
wr = (wr / np.max(wr))
# Re-set the observations to |B|
surveyAmp.dobs = bAmp
surveyAmp.std = wd
# Create a sparse regularization
reg = Regularization.Sparse(mesh, indActive=actv, mapping=idenMap)
reg.norms = np.c_[0, 0, 0, 0]
reg.mref = np.zeros(nC)
reg.cell_weights = wr
# Data misfit function
dmis = DataMisfit.l2_DataMisfit(surveyAmp)
dmis.W = 1. / surveyAmp.std
# Add directives to the inversion
opt = Optimization.ProjectedGNCG(maxIter=30,
lower=0.,
upper=1.,
maxIterLS=20,
maxIterCG=20,
tolCG=1e-3)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
# Here is the list of directives
betaest = Directives.BetaEstimate_ByEig()
# Specify the sparse norms
IRLS = Directives.Update_IRLS(f_min_change=1e-3,
minGNiter=1,
coolingRate=1,
betaSearch=False)
# The sensitivity weights are update between each iteration.
update_SensWeight = Directives.UpdateSensitivityWeights()
update_Jacobi = Directives.UpdatePreconditioner(threshold=1 - 3)
# Put all together
self.inv = Inversion.BaseInversion(
invProb,
directiveList=[betaest, IRLS, update_SensWeight, update_Jacobi])
self.mesh = mesh
rxLoc[:, 1] > ylim[0], rxLoc[:, 1] < ylim[1]], axis=0)
if np.sum(ind_t) < 20:
continue
rxLoc_t = PF.BaseMag.RxObs(rxLoc[ind_t, :])
srcField = PF.BaseMag.SrcField([rxLoc_t], param=survey.srcField.param)
survey_t = PF.BaseMag.LinearSurvey(srcField)
survey_t.dobs = survey.dobs[ind_t]
survey_t.std = survey.std[ind_t]
# Extract model from global to local mesh
if driver.topofile is not None:
topo = np.genfromtxt(work_dir + driver.topofile,
skip_header=1)
actv = Utils.surface2ind_topo(mesh_t, topo, 'N')
actv = np.asarray(np.where(mkvc(actv))[0], dtype=int)
else:
actv = np.ones(mesh_t.nC, dtype='bool')
nC = len(actv)
# print("Tile "+str(tt))
print(nC, np.sum(ind_t))
# Create active map to go from reduce space to full
actvMap = Maps.InjectActiveCells(mesh_t, actv, -100)
# Create identity map
idenMap = Maps.IdentityMap(nP=nC)
mstart = np.ones(nC)*1e-4
def createLocalProb(rxLoc, wrGlobal, lims):
# Grab the data for current tile
ind_t = np.all([
rxLoc[:, 0] >= lims[0], rxLoc[:, 0] <= lims[1],
rxLoc[:, 1] >= lims[2], rxLoc[:, 1] <= lims[3], surveyMask
],
axis=0)
# Remember selected data in case of tile overlap
surveyMask[ind_t] = False
# Create new survey
rxLoc_t = PF.BaseGrav.RxObs(rxLoc[ind_t, :])
srcField = PF.BaseGrav.SrcField([rxLoc_t])
survey_t = PF.BaseGrav.LinearSurvey(srcField)
survey_t.dobs = survey.dobs[ind_t]
survey_t.std = survey.std[ind_t]
survey_t.ind = ind_t
# mesh_t = meshTree.copy()
mesh_t = Utils.modelutils.meshBuilder(rxLoc[ind_t, :],
h,
padDist,
meshGlobal=meshInput,
meshType='TREE',
gridLoc='CC')
mesh_t = Utils.modelutils.refineTree(mesh_t,
topo,
dtype='surface',
nCpad=[0, 3, 2],
finalize=False)
mesh_t = Utils.modelutils.refineTree(mesh_t,
rxLoc[ind_t, :],
dtype='surface',
nCpad=[10, 5, 5],
finalize=False)
center = np.mean(rxLoc[ind_t, :], axis=0)
tileCenter = np.r_[np.mean(lims[0:2]), np.mean(lims[2:]), center[2]]
ind = closestPoints(mesh, tileCenter, gridLoc='CC')
shift = np.squeeze(mesh.gridCC[ind, :]) - center
mesh_t.x0 += shift
mesh_t.finalize()
print(mesh_t.nC)
actv_t = Utils.surface2ind_topo(mesh_t, topo)
# Create reduced identity map
tileMap = Maps.Tile((mesh, actv), (mesh_t, actv_t))
tileMap.nCell = 40
tileMap.nBlock = 1
# Create the forward model operator
prob = PF.Gravity.GravityIntegral(mesh_t,
rhoMap=tileMap,
actInd=actv_t,
memory_saving_mode=True,
parallelized=True)
survey_t.pair(prob)
# Data misfit function
dmis = DataMisfit.l2_DataMisfit(survey_t)
dmis.W = 1. / survey_t.std
wrGlobal += prob.getJtJdiag(np.ones(tileMap.P.shape[1]))
# Create combo misfit function
return dmis, wrGlobal
ind = Utils.ModelBuilder.getIndicesSphere(loc, radi, mesh.gridCC)
model[ind] = sig[1]
# Create quick topo
xtopo, ytopo = np.meshgrid(mesh.vectorNx, mesh.vectorNy)
ztopo = np.zeros_like(xtopo)
topo = np.c_[mkvc(xtopo), mkvc(ytopo), mkvc(ztopo)]
# Write out topo file
fid = open('Topo.topo', 'w')
fid.write(str(topo.shape[0]) + '\n')
np.savetxt(fid, topo, fmt='%f', delimiter=' ', newline='\n')
fid.close()
ind = Utils.surface2ind_topo(mesh, topo, gridLoc='N')
# Change aircells
model[ind == 0] = air
# Write out model
Mesh.TensorMesh.writeUBC(mesh, 'Mesh.msh')
Mesh.TensorMesh.writeModelUBC(mesh, mfile, model)
# Create survey locs centered about origin and write to file
locx, locy = np.meshgrid(np.linspace(-xlim, xlim, nstn),
np.linspace(-xlim, xlim, nstn))
locz = np.ones_like(locx) * rx_height
rxLoc = np.c_[mkvc(locx), mkvc(locy), mkvc(locz)]
def setUp(self):
np.random.seed(0)
# Define the inducing field parameter
H0 = (50000, 90, 0)
# Create a mesh
dx = 5.0
hxind = [(dx, 5, -1.3), (dx, 5), (dx, 5, 1.3)]
hyind = [(dx, 5, -1.3), (dx, 5), (dx, 5, 1.3)]
hzind = [(dx, 5, -1.3), (dx, 6)]
mesh = Mesh.TensorMesh([hxind, hyind, hzind], "CCC")
# Get index of the center
midx = int(mesh.nCx / 2)
midy = int(mesh.nCy / 2)
# Lets create a simple Gaussian topo and set the active cells
[xx, yy] = np.meshgrid(mesh.vectorNx, mesh.vectorNy)
zz = -np.exp((xx ** 2 + yy ** 2) / 75 ** 2) + mesh.vectorNz[-1]
# Go from topo to actv cells
topo = np.c_[Utils.mkvc(xx), Utils.mkvc(yy), Utils.mkvc(zz)]
actv = Utils.surface2ind_topo(mesh, topo, "N")
actv = np.asarray([inds for inds, elem in enumerate(actv, 1) if elem], dtype=int) - 1
# Create active map to go from reduce space to full
actvMap = Maps.InjectActiveCells(mesh, actv, -100)
nC = len(actv)
# Create and array of observation points
xr = np.linspace(-20.0, 20.0, 20)
yr = np.linspace(-20.0, 20.0, 20)
X, Y = np.meshgrid(xr, yr)
# Move the observation points 5m above the topo
Z = -np.exp((X ** 2 + Y ** 2) / 75 ** 2) + mesh.vectorNz[-1] + 5.0
# Create a MAGsurvey
rxLoc = np.c_[Utils.mkvc(X.T), Utils.mkvc(Y.T), Utils.mkvc(Z.T)]
rxLoc = PF.BaseMag.RxObs(rxLoc)
srcField = PF.BaseMag.SrcField([rxLoc], param=H0)
survey = PF.BaseMag.LinearSurvey(srcField)
# We can now create a susceptibility model and generate data
# Here a simple block in half-space
model = np.zeros((mesh.nCx, mesh.nCy, mesh.nCz))
model[(midx - 2) : (midx + 2), (midy - 2) : (midy + 2), -6:-2] = 0.02
model = Utils.mkvc(model)
self.model = model[actv]
# Create active map to go from reduce set to full
actvMap = Maps.InjectActiveCells(mesh, actv, -100)
# Creat reduced identity map
idenMap = Maps.IdentityMap(nP=nC)
# Create the forward model operator
prob = PF.Magnetics.MagneticIntegral(mesh, mapping=idenMap, actInd=actv)
# Pair the survey and problem
survey.pair(prob)
# Compute linear forward operator and compute some data
d = prob.fields(self.model)
# Add noise and uncertainties (1nT)
data = d + np.random.randn(len(d))
wd = np.ones(len(data)) * 1.0
survey.dobs = data
survey.std = wd
# Create sensitivity weights from our linear forward operator
wr = np.sum(prob.G ** 2.0, axis=0) ** 0.5
wr = wr / np.max(wr)
# Create a regularization
reg = Regularization.Sparse(mesh, indActive=actv, mapping=idenMap)
reg.cell_weights = wr
# Data misfit function
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.Wd = 1 / wd
# Add directives to the inversion
opt = Optimization.ProjectedGNCG(maxIter=100, lower=0.0, upper=1.0, maxIterLS=20, maxIterCG=10, tolCG=1e-3)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
betaest = Directives.BetaEstimate_ByEig()
# Here is where the norms are applied
IRLS = Directives.Update_IRLS(norms=([0, 1, 1, 1]), eps=(1e-3, 1e-3), f_min_change=1e-3, minGNiter=3)
update_Jacobi = Directives.Update_lin_PreCond()
self.inv = Inversion.BaseInversion(invProb, directiveList=[IRLS, betaest, update_Jacobi])
def setUp(self):
# We will assume a vertical inducing field
H0 = (50000., 90., 0.)
# The magnetization is set along a different direction (induced + remanence)
M = np.array([90., 0.])
# Block with an effective susceptibility
chi_e = 0.05
# Create grid of points for topography
# Lets create a simple Gaussian topo and set the active cells
[xx, yy] = np.meshgrid(np.linspace(-200, 200, 50), np.linspace(-200, 200, 50))
b = 100
A = 50
zz = A*np.exp(-0.5*((xx/b)**2. + (yy/b)**2.))
topo = np.c_[Utils.mkvc(xx), Utils.mkvc(yy), Utils.mkvc(zz)]
# Create and array of observation points
xr = np.linspace(-100., 100., 20)
yr = np.linspace(-100., 100., 20)
X, Y = np.meshgrid(xr, yr)
Z = A*np.exp(-0.5*((X/b)**2. + (Y/b)**2.)) + 5
# Create a MAGsurvey
rxLoc = np.c_[Utils.mkvc(X.T), Utils.mkvc(Y.T), Utils.mkvc(Z.T)]
Rx = PF.BaseMag.RxObs(rxLoc)
srcField = PF.BaseMag.SrcField([Rx], param=H0)
survey = PF.BaseMag.LinearSurvey(srcField)
# Create a mesh
h = [5, 5, 5]
padDist = np.ones((3, 2)) * 100
nCpad = [4, 4, 2]
# Get extent of points
limx = np.r_[topo[:, 0].max(), topo[:, 0].min()]
limy = np.r_[topo[:, 1].max(), topo[:, 1].min()]
limz = np.r_[topo[:, 2].max(), topo[:, 2].min()]
# Get center of the mesh
midX = np.mean(limx)
midY = np.mean(limy)
midZ = np.mean(limz)
nCx = int(limx[0]-limx[1]) / h[0]
nCy = int(limy[0]-limy[1]) / h[1]
nCz = int(limz[0]-limz[1]+int(np.min(np.r_[nCx, nCy])/3)) / h[2]
# Figure out full extent required from input
extent = np.max(np.r_[nCx * h[0] + padDist[0, :].sum(),
nCy * h[1] + padDist[1, :].sum(),
nCz * h[2] + padDist[2, :].sum()])
maxLevel = int(np.log2(extent/h[0]))+1
# Number of cells at the small octree level
# For now equal in 3D
nCx, nCy, nCz = 2**(maxLevel), 2**(maxLevel), 2**(maxLevel)
# Define the mesh and origin
mesh = Mesh.TreeMesh([np.ones(nCx)*h[0],
np.ones(nCx)*h[1],
np.ones(nCx)*h[2]])
# Set origin
mesh.x0 = np.r_[
-nCx*h[0]/2.+midX, -nCy*h[1]/2.+midY, -nCz*h[2]/2.+midZ
]
# Refine the mesh around topography
# Get extent of points
F = NearestNDInterpolator(topo[:, :2], topo[:, 2])
zOffset = 0
# Cycle through the first 3 octree levels
for ii in range(3):
dx = mesh.hx.min()*2**ii
nCx = int((limx[0]-limx[1]) / dx)
nCy = int((limy[0]-limy[1]) / dx)
# Create a grid at the octree level in xy
CCx, CCy = np.meshgrid(
np.linspace(limx[1], limx[0], nCx),
np.linspace(limy[1], limy[0], nCy)
)
z = F(mkvc(CCx), mkvc(CCy))
# level means number of layers in current OcTree level
for level in range(int(nCpad[ii])):
mesh.insert_cells(
np.c_[mkvc(CCx), mkvc(CCy), z-zOffset],
np.ones_like(z)*maxLevel-ii,
finalize=False
)
zOffset += dx
mesh.finalize()
# Define an active cells from topo
actv = Utils.surface2ind_topo(mesh, topo)
nC = int(actv.sum())
# Convert the inclination declination to vector in Cartesian
M_xyz = Utils.matutils.dip_azimuth2cartesian(np.ones(nC)*M[0], np.ones(nC)*M[1])
# Get the indicies of the magnetized block
ind = Utils.ModelBuilder.getIndicesBlock(
np.r_[-20, -20, -10], np.r_[20, 20, 25],
mesh.gridCC,
)[0]
# Assign magnetization value, inducing field strength will
# be applied in by the :class:`SimPEG.PF.Magnetics` problem
model = np.zeros(mesh.nC)
model[ind] = chi_e
# Remove air cells
self.model = model[actv]
# Create active map to go from reduce set to full
self.actvPlot = Maps.InjectActiveCells(mesh, actv, np.nan)
# Creat reduced identity map
idenMap = Maps.IdentityMap(nP=nC)
# Create the forward model operator
prob = PF.Magnetics.MagneticIntegral(
mesh, M=M_xyz, chiMap=idenMap, actInd=actv
)
# Pair the survey and problem
survey.pair(prob)
# Compute some data and add some random noise
data = prob.fields(self.model)
# Split the data in components
nD = rxLoc.shape[0]
std = 5 # nT
data += np.random.randn(nD)*std
wd = np.ones(nD)*std
# Assigne data and uncertainties to the survey
survey.dobs = data
survey.std = wd
######################################################################
# Equivalent Source
# Get the active cells for equivalent source is the top only
surf = Utils.modelutils.surface_layer_index(mesh, topo)
# Get the layer of cells directyl below topo
nC = np.count_nonzero(surf) # Number of active cells
# Create active map to go from reduce set to full
surfMap = Maps.InjectActiveCells(mesh, surf, np.nan)
# Create identity map
idenMap = Maps.IdentityMap(nP=nC)
# Create static map
prob = PF.Magnetics.MagneticIntegral(
mesh, chiMap=idenMap, actInd=surf,
parallelized=False, equiSourceLayer=True)
prob.solverOpts['accuracyTol'] = 1e-4
# Pair the survey and problem
if survey.ispaired:
survey.unpair()
survey.pair(prob)
# Create a regularization function, in this case l2l2
reg = Regularization.Sparse(
mesh, indActive=surf, mapping=Maps.IdentityMap(nP=nC),
scaledIRLS=False
)
reg.mref = np.zeros(nC)
# Specify how the optimization will proceed,
# set susceptibility bounds to inf
opt = Optimization.ProjectedGNCG(maxIter=20, lower=-np.inf,
upper=np.inf, maxIterLS=20,
maxIterCG=20, tolCG=1e-3)
# Define misfit function (obs-calc)
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.W = 1./survey.std
# Create the default L2 inverse problem from the above objects
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
# Specify how the initial beta is found
betaest = Directives.BetaEstimate_ByEig()
# Target misfit to stop the inversion,
# try to fit as much as possible of the signal,
# we don't want to lose anything
IRLS = Directives.Update_IRLS(f_min_change=1e-3, minGNiter=1,
beta_tol=1e-1)
update_Jacobi = Directives.UpdatePreconditioner()
# Put all the parts together
inv = Inversion.BaseInversion(
invProb, directiveList=[betaest, IRLS, update_Jacobi]
)
# Run the equivalent source inversion
mstart = np.ones(nC)*1e-4
mrec = inv.run(mstart)
# Won't store the sensitivity and output 'xyz' data.
prob.forwardOnly = True
prob.rx_type = 'xyz'
prob._G = None
prob.modelType = 'amplitude'
prob.model = mrec
pred = prob.fields(mrec)
bx = pred[:nD]
by = pred[nD:2*nD]
bz = pred[2*nD:]
bAmp = (bx**2. + by**2. + bz**2.)**0.5
# AMPLITUDE INVERSION
# Create active map to go from reduce space to full
actvMap = Maps.InjectActiveCells(mesh, actv, -100)
nC = int(actv.sum())
# Create identity map
idenMap = Maps.IdentityMap(nP=nC)
self.mstart = np.ones(nC)*1e-4
# Create the forward model operator
prob = PF.Magnetics.MagneticIntegral(
mesh, chiMap=idenMap, actInd=actv,
modelType='amplitude', rx_type='xyz'
)
prob.model = self.mstart
# Change the survey to xyz components
surveyAmp = PF.BaseMag.LinearSurvey(survey.srcField)
# Pair the survey and problem
surveyAmp.pair(prob)
# Create a regularization function, in this case l2l2
wr = np.sum(prob.G**2., axis=0)**0.5
wr = (wr/np.max(wr))
# Re-set the observations to |B|
surveyAmp.dobs = bAmp
surveyAmp.std = wd
# Create a sparse regularization
reg = Regularization.Sparse(mesh, indActive=actv, mapping=idenMap)
reg.norms = np.c_[0, 0, 0, 0]
reg.mref = np.zeros(nC)
reg.cell_weights = wr
# Data misfit function
dmis = DataMisfit.l2_DataMisfit(surveyAmp)
dmis.W = 1./surveyAmp.std
# Add directives to the inversion
opt = Optimization.ProjectedGNCG(maxIter=30, lower=0., upper=1.,
maxIterLS=20, maxIterCG=20,
tolCG=1e-3)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
# Here is the list of directives
betaest = Directives.BetaEstimate_ByEig()
# Specify the sparse norms
IRLS = Directives.Update_IRLS(f_min_change=1e-3,
minGNiter=1, coolingRate=1,
betaSearch=False)
# The sensitivity weights are update between each iteration.
update_SensWeight = Directives.UpdateSensitivityWeights()
update_Jacobi = Directives.UpdatePreconditioner()
# Put all together
self.inv = Inversion.BaseInversion(
invProb, directiveList=[
betaest, IRLS, update_SensWeight, update_Jacobi
]
)
self.mesh = mesh
z = F(mkvc(CCx), mkvc(CCy))
# level means number of layers in current OcTree level
for level in range(int(nCpad[ii])):
mesh.insert_cells(np.c_[mkvc(CCx), mkvc(CCy), z - zOffset],
np.ones_like(z) * maxLevel - ii,
finalize=False)
zOffset += dx
mesh.finalize()
# Define an active cells from topo
actv = Utils.surface2ind_topo(mesh, topo)
nC = int(actv.sum())
###########################################################################
# A simple function to plot vectors in TreeMesh
#
# Should eventually end up on discretize
#
def plotVectorSectionsOctree(mesh,
m,
normal='X',
ind=0,
vmin=None,
vmax=None,
def set_mesh(self,
topo=None,
dx=None,
dy=None,
dz=None,
n_spacing=None,
corezlength=None,
npad_x=7,
npad_y=7,
npad_z=7,
pad_rate_x=1.3,
pad_rate_y=1.3,
pad_rate_z=1.3,
ncell_per_dipole=4,
mesh_type='TensorMesh',
dimension=2,
method='linear'):
"""
Set up a mesh for a given DC survey
"""
if mesh_type == 'TreeMesh':
raise NotImplementedError()
# 2D or 3D mesh
if dimension in [2, 3]:
if dimension == 2:
z_ind = 1
else:
z_ind = 2
a = abs(np.diff(np.sort(self.electrode_locations[:, 0]))).min()
lineLength = abs(self.electrode_locations[:, 0].max() -
self.electrode_locations[:, 0].min())
dx_ideal = a / ncell_per_dipole
if dx is None:
dx = dx_ideal
warnings.warn(
"dx is set to {} m (samllest electrode spacing ({}) / {})".
format(dx, a, ncell_per_dipole))
if dz is None:
dz = dx * 0.5
warnings.warn("dz ({} m) is set to dx ({} m) / {}".format(
dz, dx, 2))
x0 = self.electrode_locations[:, 0].min()
if topo is None:
locs = self.electrode_locations
else:
locs = np.vstack((topo, self.electrode_locations))
if dx > dx_ideal:
# warnings.warn(
# "Input dx ({}) is greater than expected \n We recommend using {:0.1e} m cells, that is, {} cells per {0.1e} m dipole length".format(dx, dx_ideal, ncell_per_dipole, a)
# )
pass
self.dx = dx
self.dz = dz
self.npad_x = npad_x
self.npad_z = npad_z
self.pad_rate_x = pad_rate_x
self.pad_rate_z = pad_rate_z
self.ncell_per_dipole = ncell_per_dipole
zmax = locs[:, z_ind].max()
zmin = locs[:, z_ind].min()
# 3 cells each for buffer
corexlength = lineLength + dx * 6
if corezlength is None:
corezlength = self.grids[:, z_ind].max()
ncx = np.round(corexlength / dx)
ncz = np.round(corezlength / dz)
hx = [(dx, npad_x, -pad_rate_x), (dx, ncx),
(dx, npad_x, pad_rate_x)]
hz = [(dz, npad_z, -pad_rate_z), (dz, ncz)]
x0_mesh = -(
(dx * pad_rate_x**(np.arange(npad_x) + 1)).sum() + dx * 3 - x0)
z0_mesh = -((dz * pad_rate_z**
(np.arange(npad_z) + 1)).sum() + dz * ncz) + zmax
# For 2D mesh
if dimension == 2:
h = [hx, hz]
x0_for_mesh = [x0_mesh, z0_mesh]
self.xyzlim = np.vstack(
(np.r_[x0, x0 + lineLength], np.r_[zmax - corezlength,
zmax]))
# For 3D mesh
else:
if dy is None:
raise Exception("You must input dy (m)")
self.dy = dy
self.npad_y = npad_y
self.pad_rate_y = pad_rate_y
ylocs = np.unique(self.electrode_locations[:, 1])
ymin, ymax = ylocs.min(), ylocs.max()
# 3 cells each for buffer in y-direction
coreylength = ymax - ymin + dy * 6
ncy = np.round(coreylength / dy)
hy = [(dy, npad_y, -pad_rate_y), (dy, ncy),
(dy, npad_y, pad_rate_y)]
y0 = ylocs.min() - dy / 2.
y0_mesh = -((dy * pad_rate_y**(np.arange(npad_y) + 1)).sum() +
dy * 3 - y0)
h = [hx, hy, hz]
x0_for_mesh = [x0_mesh, y0_mesh, z0_mesh]
self.xyzlim = np.vstack(
(np.r_[x0, x0 + lineLength], np.r_[ymin, ymax],
np.r_[zmax - corezlength, zmax]))
mesh = Mesh.TensorMesh(h, x0=x0_for_mesh)
actind = Utils.surface2ind_topo(mesh, locs, method=method)
else:
raise NotImplementedError()
return mesh, actind
