def createLocalMesh(rxLoc, ind_t):
"""
Function to generate a mesh based on receiver locations
"""
# Create new survey
if input_dict["inversion_type"] == 'grav':
rxLoc_t = PF.BaseGrav.RxObs(rxLoc[ind_t, :])
srcField = PF.BaseGrav.SrcField([rxLoc_t])
local_survey = PF.BaseGrav.LinearSurvey(srcField)
local_survey.dobs = survey.dobs[ind_t]
local_survey.std = survey.std[ind_t]
local_survey.ind = ind_t
elif input_dict["inversion_type"] in ['mag', 'mvi', 'mvis']:
rxLoc_t = PF.BaseMag.RxObs(rxLoc[ind_t, :])
srcField = PF.BaseMag.SrcField([rxLoc_t], param=survey.srcField.param)
local_survey = PF.BaseMag.LinearSurvey(
srcField, components=survey.components
)
dataInd = np.kron(ind_t, np.ones(len(survey.components))).astype('bool')
local_survey.dobs = survey.dobs[dataInd]
local_survey.std = survey.std[dataInd]
local_survey.ind = ind_t
meshLocal = meshutils.mesh_builder_xyz(
topo_elevations_at_data_locs,
core_cell_size,
padding_distance=padding_distance,
mesh_type=inversion_mesh_type,
base_mesh=input_mesh,
depth_core=depth_core
)
if shift_mesh_z0 is not None:
print("In mesh z0")
meshLocal.x0 = np.r_[meshLocal.x0[0], meshLocal.x0[1], shift_mesh_z0]
if inversion_mesh_type.upper() == 'TREE':
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,
)
# Create combo misfit function
return meshLocal, local_survey
def createLocalMesh(rxLoc, ind_t):
"""
Function to generate a mesh based on receiver locations
"""
# Create new survey
if input_dict["inversion_type"].lower() == 'grav':
rxLoc_t = PF.BaseGrav.RxObs(rxLoc[ind_t, :])
srcField = PF.BaseGrav.SrcField([rxLoc_t])
local_survey = PF.BaseGrav.LinearSurvey(srcField)
local_survey.dobs = survey.dobs[ind_t]
local_survey.std = survey.std[ind_t]
local_survey.ind = ind_t
# Utils.io_utils.writeUBCgravityObservations(outDir + "Tile" + str(ind) + '.dat', local_survey, local_survey.dobs)
elif input_dict["inversion_type"].lower() in ['mag', 'mvi', 'mvis']:
rxLoc_t = PF.BaseMag.RxObs(rxLoc[ind_t, :])
srcField = PF.BaseMag.SrcField([rxLoc_t], param=survey.srcField.param)
local_survey = PF.BaseMag.LinearSurvey(srcField,
components=survey.components)
dataInd = np.kron(ind_t,
np.ones(len(survey.components))).astype('bool')
local_survey.dobs = survey.dobs[dataInd]
local_survey.std = survey.std[dataInd]
local_survey.ind = ind_t
# Utils.io_utils.writeUBCmagneticsObservations(outDir + "Tile" + str(ind) + '.dat', local_survey, local_survey.dobs)
meshLocal = meshutils.mesh_builder_xyz(newTopo,
core_cell_size,
padding_distance=padding_distance,
mesh_type='TREE',
base_mesh=meshInput,
depth_core=depth_core)
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,
rxLoc[ind_t, :],
method='surface',
max_distance=max_distance,
octree_levels=octree_levels_obs,
octree_levels_padding=octree_levels_padding,
finalize=True,
)
# Create combo misfit function
return meshLocal, local_survey
def test_box(self):
dx = 0.25
dl = 10
# Create a box 2*dl in width
X, Y, Z = np.meshgrid(np.c_[-dl, dl], np.c_[-dl, dl], np.c_[-dl, dl])
xyz = np.c_[np.ravel(X), np.ravel(Y), np.ravel(Z)]
mesh = meshutils.mesh_builder_xyz(
np.c_[0.01, 0.01, 0.01], [dx, dx, dx],
depth_core=0,
padding_distance=[[0, 20], [0, 20], [0, 20]],
mesh_type='TREE',
)
mesh = meshutils.refine_tree_xyz(
mesh, xyz, octree_levels=[1], method='box', finalize=True
)
# Volume of box
vol = (2*dl)**3
residual = np.abs(
vol -
mesh.vol[
mesh._cell_levels_by_indexes(range(mesh.nC)) == mesh.max_level
].sum()
)/vol * 100
self.assertTrue(residual < 0.5)
def test_surface(self):
dx = 0.1
dl = 20
# Define triangle
xyz = np.r_[
np.c_[-dl/2, -dl/2, 0],
np.c_[dl/2, -dl/2, 0],
np.c_[dl/2, dl/2, 0]
]
mesh = meshutils.mesh_builder_xyz(
np.c_[0.01, 0.01, 0.01], [dx, dx, dx],
depth_core=0,
padding_distance=[[0, 20], [0, 20], [0, 20]],
mesh_type='TREE',
)
mesh = meshutils.refine_tree_xyz(
mesh, xyz, octree_levels=[1], method='surface', finalize=True
)
# Volume of triangle
vol = dl*dl*dx/2
residual = np.abs(
vol -
mesh.vol[
mesh._cell_levels_by_indexes(range(mesh.nC)) == mesh.max_level
].sum()/2
)/vol * 100
self.assertTrue(residual < 5)
def test_radial(self):
dx = 0.25
rad = 10
mesh = meshutils.mesh_builder_xyz(
np.c_[0.01, 0.01, 0.01], [dx, dx, dx],
depth_core=0,
padding_distance=[[0, 20], [0, 20], [0, 20]],
mesh_type='TREE',
)
radCell = int(np.ceil(rad/dx))
mesh = meshutils.refine_tree_xyz(
mesh, np.c_[0, 0, 0],
octree_levels=[radCell], method='radial',
finalize=True
)
# Volume of sphere
vol = 4.*np.pi/3.*rad**3.
residual = np.abs(
vol -
mesh.vol[
mesh._cell_levels_by_indexes(range(mesh.nC)) == mesh.max_level
].sum()
)/vol * 100
self.assertTrue(residual < 3)
def refine_box(mesh):
# Refine for sphere
xp, yp, zp = np.meshgrid([-55.0, 50.0], [-50.0, 50.0], [-40.0, 20.0])
xyz = np.c_[mkvc(xp), mkvc(yp), mkvc(zp)]
mesh = refine_tree_xyz(mesh,
xyz,
octree_levels=[2],
method="box",
finalize=False)
return mesh
def refine_topography(mesh):
# Define topography and refine
[xx, yy] = np.meshgrid(mesh.vectorNx, mesh.vectorNy)
zz = -3 * np.exp((xx**2 + yy**2) / 60**2) + 45.0
topo = np.c_[mkvc(xx), mkvc(yy), mkvc(zz)]
mesh = refine_tree_xyz(mesh,
topo,
octree_levels=[3, 2],
method="surface",
finalize=False)
return mesh
def refine_octree_surface(mesh, f):
"""
Refine an octree mesh around the given surface
:param mesh: TreeMesh instance to refine
:param f: function giving z(x,y) in physical units
:return: TreeMesh instance
"""
xx, yy = np.meshgrid(mesh.vectorNx, mesh.vectorNy)
zz = f(xx, yy)
idx_valid = ~np.isnan(zz)
xx, yy, zz = xx[idx_valid], yy[idx_valid], zz[idx_valid]
surf = np.c_[mkvc(xx), mkvc(yy), mkvc(zz)]
# Play with different octree_levels=[lx,ly,lz] settings below
return refine_tree_xyz(
mesh, surf, octree_levels=[1,1,1], method="surface", finalize=False
)
# Compute number of base mesh cells required in x and y
nbcx = 2**int(np.round(np.log(x_length / dx) / np.log(2.)))
nbcy = 2**int(np.round(np.log(y_length / dy) / np.log(2.)))
# Define the base mesh
hx = [(dx, nbcx)]
hy = [(dy, nbcy)]
M = TreeMesh([hx, hy], x0=['C', -15000])
# definir camada
xx = M.vectorNx
yy = np.zeros(nbcx + 1) #vetor linha(poderia ser uma função ou pontos)
pts = np.c_[matutils.mkvc(xx), matutils.mkvc(yy)]
M = meshutils.refine_tree_xyz(M,
pts,
octree_levels=[1, 1],
method='box',
finalize=False)
#definir um ponto(xc,yc) a ser refinado.
Raio_length = 500
xc = -5000
yc = 2200
xx = M.vectorNx
yy = np.zeros(nbcx + 1) #vetor linha(poderia ser uma função ou pontos)
pts = np.c_[matutils.mkvc(xx), matutils.mkvc(yy)]
def refine(cell):
if np.sqrt(((np.r_[cell.center] + [xc, yc])**2).sum()) < Raio_length:
ind_t = tileIDs == tile_numbers[indMax]
# Create the mesh and refine the same as the global mesh
meshLocal = meshutils.mesh_builder_xyz(
newTopo,
core_cell_size,
padding_distance=padding_distance,
mesh_type='TREE',
base_mesh=meshInput,
depth_core=depth_core)
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,
rxLoc[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)
def run(plotIt=True):
nFreq = 13
freqs = np.logspace(2, -2, nFreq)
# x and y grid parameters
# dh = 10 # minimum cell width (base mesh cell width)
dx = 15 # minimum cell width (base mesh cell width) in x
dy = 15
dz = 10
x_length = 10000. # domain width in x
y_length = 10000.
z_length = 40000.
# Compute number of base mesh cells required in x and y
nbcx = 2**int(np.round(np.log(x_length / dx) / np.log(2.)))
nbcy = 2**int(np.round(np.log(y_length / dy) / np.log(2.)))
nbcz = 2**int(np.round(np.log(z_length / dz) / np.log(2.)))
# Define the base mesh
hx = [(dx, nbcx)]
hy = [(dy, nbcy)]
hz = [(dz, nbcz)]
M = Mesh.TreeMesh([hx, hy, hz], x0=['C', 'C', -15000])
# camadas
xx = M.vectorNx
yy = M.vectorNy
zz = np.zeros(nbcx + 1) #vetor linha(poderia ser uma função ou pontos)
pts = np.c_[matutils.mkvc(xx), matutils.mkvc(yy), matutils.mkvc(zz)]
M = meshutils.refine_tree_xyz(M,
pts,
octree_levels=[1, 1, 1],
method='surface',
finalize=False)
xx = M.vectorNx
yy = M.vectorNy
zz = np.zeros(nbcx +
1) - 150 #vetor linha(poderia ser uma função ou pontos)
pts = np.c_[matutils.mkvc(xx), matutils.mkvc(yy), matutils.mkvc(zz)]
M = meshutils.refine_tree_xyz(M,
pts,
octree_levels=[1, 1, 1],
method='surface',
finalize=False)
xx = M.vectorNx
yy = M.vectorNy
zz = np.zeros(nbcx +
1) - 350 #vetor linha(poderia ser uma função ou pontos)
pts = np.c_[matutils.mkvc(xx), matutils.mkvc(yy), matutils.mkvc(zz)]
M = meshutils.refine_tree_xyz(M,
pts,
octree_levels=[1, 1, 1],
method='surface',
finalize=False)
#
M.finalize()
print("\n the mesh has {} cells".format(M))
ccMesh = M.gridCC
print('indices:', np.size(ccMesh))
###
conds = [1e-2, 1]
sig = simpeg.Utils.ModelBuilder.defineBlock(M.gridCC,
[-15000, 15000, -350],
[15000, 1500, -150], conds)
sig[M.gridCC[:, 2] > 0] = 1e-8
sigBG = np.zeros(M.nC) + conds[1]
sigBG[M.gridCC[:, 2] > 0] = 1e-8
fig = plt.figure('slice: malha + modelo')
ax = fig.add_subplot()
collect_obj, = M.plotSlice(np.log(sig), normal='x', ax=ax, grid=True)
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 createLocalProb(rxLoc, wrGlobal, ind_t, ind):
# createLocalProb(rxLoc, wrGlobal, lims, ind)
# Generate a problem, calculate/store sensitivities for
# given data points
# 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
if input_dict["inversion_type"].lower() == 'grav':
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
Utils.io_utils.writeUBCgravityObservations(outDir + "Tile" + str(ind) + '.dat', survey_t, survey_t.dobs)
elif input_dict["inversion_type"].lower() in ['mag', 'mvi']:
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]
survey_t.ind = ind_t
Utils.io_utils.writeUBCmagneticsObservations(outDir + "Tile" + str(ind) + '.dat', survey_t, survey_t.dobs)
meshLocal = meshutils.mesh_builder_xyz(
newTopo, core_cell_size, padding_distance=padding_distance, mesh_type='TREE', base_mesh=meshInput,
depth_core=depth_core
)
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, rxLoc[ind_t, :], method='surface',
max_distance=max_distance,
octree_levels=octree_levels_obs,
octree_levels_padding=octree_levels_padding,
finalize=True,
)
# Need to find a way to compute sensitivities only for intersecting cells
activeCells_t = np.ones(meshLocal.nC, dtype='bool') # meshUtils.modelutils.activeTopoLayer(meshLocal, topo)
# Create reduced identity map
if input_dict["inversion_type"].lower() == 'mvi':
nBlock = 3
else:
nBlock = 1
tileMap = Maps.Tile((mesh, activeCells), (meshLocal, activeCells_t), nBlock=nBlock)
activeCells_t = tileMap.activeLocal
print(activeCells_t.sum(), meshLocal.nC)
if input_dict["inversion_type"].lower() == 'grav':
prob = PF.Gravity.GravityIntegral(
meshLocal, rhoMap=tileMap, actInd=activeCells_t,
parallelized=parallelized,
Jpath=outDir + "Tile" + str(ind) + ".zarr",
maxRAM=max_ram,
n_cpu=n_cpu,
)
elif input_dict["inversion_type"].lower() == 'mag':
prob = PF.Magnetics.MagneticIntegral(
meshLocal, chiMap=tileMap, actInd=activeCells_t,
parallelized=parallelized,
Jpath=outDir + "Tile" + str(ind) + ".zarr",
maxRAM=max_ram,
n_cpu=n_cpu,
)
elif input_dict["inversion_type"].lower() == 'mvi':
prob = PF.Magnetics.MagneticIntegral(
meshLocal, chiMap=tileMap, actInd=activeCells_t,
parallelized=parallelized,
Jpath=outDir + "Tile" + str(ind) + ".zarr",
maxRAM=max_ram,
modelType='vector',
n_cpu=n_cpu
)
survey_t.pair(prob)
# Write out local active and obs for validation
Mesh.TreeMesh.writeUBC(
meshLocal, outDir + 'Octree_Tile' + str(ind) + '.msh',
models={outDir + 'ActiveGlobal_Tile' + str(ind) + ' .act': activeCells_t}
)
# Data misfit function
dmis = DataMisfit.l2_DataMisfit(survey_t)
dmis.W = 1./survey_t.std
wr = prob.getJtJdiag(np.ones(tileMap.shape[1]), W=dmis.W)
wrGlobal += wr
del meshLocal
# Create combo misfit function
return dmis
h = [40, 40, 20]
pads = [[0, 0], [0, 0],[2000, 0]]
octreeTopo = [0,5,10,10]
octreeObs = [5, 5]
maxDist = 100
depth_core = 2500
mesh = meshutils.mesh_builder_xyz(
topo, h,
padding_distance=pads,
mesh_type='TREE',
depth_core=depth_core,
)
mesh = meshutils.refine_tree_xyz(mesh, topo,
octree_levels=octreeTopo,
method='surface', finalize=False)
mesh = meshutils.refine_tree_xyz(mesh, xyz,
octree_levels=octreeObs,
method='surface',
max_distance=maxDist,
finalize=True)
actv = modelutils.surface2ind_topo(mesh, topo, gridLoc='N')
###############################################################################
def plot_pyvista(mesh, model, actv, interactive=False, use_panel=True, clim=None):
# Convert TreeMesh to VTK
dataset = mesh.toVTK()
def createLocalProb(rxLoc, wrGlobal, lims, ind):
# createLocalProb(rxLoc, wrGlobal, lims, ind)
# Generate a problem, calculate/store sensitivities for
# given data points
# 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
if driver["dataFile"][0] == 'GRAV':
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
Utils.io_utils.writeUBCgravityObservations(
workDir + dsep + outDir + "Tile" + str(ind) + '.dat', survey_t,
survey_t.dobs)
elif driver["dataFile"][0] == 'MAG':
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]
survey_t.ind = ind_t
Utils.io_utils.writeUBCmagneticsObservations(
workDir + dsep + outDir + "Tile" + str(ind) + '.dat', survey_t,
survey_t.dobs)
meshLocal = meshutils.mesh_builder_xyz(
newTopo,
h,
padDist,
mesh_type='TREE',
depth_core=depth_core,
base_mesh=meshInput,
)
if topo is not None:
meshLocal = meshutils.refine_tree_xyz(meshLocal,
topo,
method='surface',
octree_levels=octreeTopo,
finalize=False)
# Refine the mesh around loc
meshLocal = meshutils.refine_tree_xyz(
meshLocal,
newTopo[ind_t, :],
method='surface',
octree_levels=octreeObs,
octree_levels_padding=octree_levels_padding,
finalize=True)
# Need to find a way to compute sensitivities only for intersecting cells
activeCells_t = np.ones(
meshLocal.nC,
dtype='bool') # meshmeshutils.activeTopoLayer(meshLocal, topo)
# Create reduced identity map
tileMap = Maps.Tile((mesh, activeCells), (meshLocal, activeCells_t))
activeCells_t = tileMap.activeLocal
print(activeCells_t.sum(), meshLocal.nC)
if driver["dataFile"][0] == 'GRAV':
prob = PF.Gravity.GravityIntegral(meshLocal,
rhoMap=tileMap,
actInd=activeCells_t,
parallelized=parallelized,
Jpath=workDir + dsep + outDir +
"Tile" + str(ind) + ".zarr",
maxRAM=maxRAM / n_cpu,
n_cpu=n_cpu,
n_chunks=n_chunks)
elif driver["dataFile"][0] == 'MAG':
prob = PF.Magnetics.MagneticIntegral(
meshLocal,
chiMap=tileMap,
actInd=activeCells_t,
parallelized=parallelized,
Jpath=workDir + dsep + outDir + "Tile" + str(ind) + ".zarr",
maxRAM=maxRAM / n_cpu,
n_cpu=n_cpu,
n_chunks=n_chunks)
survey_t.pair(prob)
# Write out local active and obs for validation
Mesh.TreeMesh.writeUBC(
meshLocal,
workDir + dsep + outDir + dsep + 'Octree_Tile' + str(ind) + '.msh',
models={
workDir + dsep + outDir + dsep + 'ActiveGlobal_Tile' + str(ind) + ' .act':
activeCells_t
})
if driver["dataFile"][0] == 'GRAV':
Utils.io_utils.writeUBCgravityObservations(
workDir + dsep + outDir + dsep + 'Tile' + str(ind) + '.dat',
survey_t, survey_t.dobs)
elif driver["dataFile"][0] == 'MAG':
Utils.io_utils.writeUBCmagneticsObservations(
workDir + dsep + outDir + dsep + 'Tile' + str(ind) + '.dat',
survey_t, survey_t.dobs)
# Data misfit function
dmis = DataMisfit.l2_DataMisfit(survey_t)
dmis.W = 1. / survey_t.std
wr = prob.getJtJdiag(np.ones(tileMap.P.shape[1]), W=dmis.W)
wrGlobal += wr
del meshLocal
# Create combo misfit function
return dmis
padDist = np.r_[np.c_[padLen, padLen], np.c_[padLen, padLen], np.c_[padLen, 0]]
print("Creating Global Octree")
mesh = meshutils.mesh_builder_xyz(
newTopo,
h,
padDist,
mesh_type='TREE',
depth_core=depth_core,
base_mesh=meshInput,
)
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)
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 = (50000.0, 90.0, 0.0)
# 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(-200.0, 200.0, 50),
np.linspace(-200.0, 200.0, 50))
b = 100
A = 50
zz = A * np.exp(-0.5 * ((xx / b)**2.0 + (yy / b)**2.0))
# 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(-100.0, 100.0, 20)
yr = np.linspace(-100.0, 100.0, 20)
X, Y = np.meshgrid(xr, yr)
Z = A * np.exp(-0.5 * ((X / b)**2.0 + (Y / b)**2.0)) + 5
# Create a MAGsurvey
xyzLoc = np.c_[utils.mkvc(X.T), utils.mkvc(Y.T), utils.mkvc(Z.T)]
rxLoc = mag.Point(xyzLoc)
srcField = mag.SourceField([rxLoc], parameters=H0)
survey = mag.Survey(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.model_builder.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
sim = mag.Simulation3DIntegral(
self.mesh,
survey=survey,
chiMap=idenMap,
actInd=actv,
store_sensitivities="ram",
)
self.sim = sim
data = sim.make_synthetic_data(self.model,
relative_error=0.0,
noise_floor=1.0,
add_noise=True)
# Create a regularization
reg = regularization.Sparse(self.mesh, indActive=actv, mapping=idenMap)
reg.norms = np.c_[0, 0, 0, 0]
reg.mref = np.zeros(nC)
# Data misfit function
dmis = data_misfit.L2DataMisfit(simulation=sim, data=data)
# Add directives to the inversion
opt = optimization.ProjectedGNCG(
maxIter=10,
lower=0.0,
upper=10.0,
maxIterLS=5,
maxIterCG=5,
tolCG=1e-4,
stepOffBoundsFact=1e-4,
)
invProb = inverse_problem.BaseInvProblem(dmis, reg, opt, beta=1e6)
# 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,
max_irls_iterations=20,
beta_tol=1e-1,
beta_search=False)
update_Jacobi = directives.UpdatePreconditioner()
sensitivity_weights = directives.UpdateSensitivityWeights()
self.inv = inversion.BaseInversion(
invProb, directiveList=[IRLS, sensitivity_weights, update_Jacobi])
if add_data_padding or decimate_to_mesh:
# Scipy.interpolate flags divide-by-zero and invalid value errors when making
# the mesh. They don't affect the result, so we suppress them temporarily.
old_settings = np.seterr(divide='ignore', invalid='ignore')
# Create a quadtree mesh using the same params as the full mesh
decimate_mesh = meshutils.mesh_builder_xyz(
survey.rxLoc[:, :2],
core_cell_size[:2],
padding_distance=padding_distance[:2],
mesh_type='tree'
)
decimate_mesh = meshutils.refine_tree_xyz(
decimate_mesh, survey.rxLoc[:, :2], method='surface',
max_distance=max_distance,
octree_levels=octree_levels_obs,
octree_levels_padding=octree_levels_padding,
finalize=True,
)
np.seterr(**old_settings)
if decimate_to_mesh:
print("Decimating the whole survey to the mesh")
survey, data_trend = decimate_survey_to_mesh(decimate_mesh,
data_trend, survey)
elif add_data_padding:
print("Decimating the padding points to the mesh")
survey, data_trend = decimate_survey_to_mesh(decimate_mesh,
data_trend, survey,
survey)
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
xyzLoc = np.c_[Utils.mkvc(X.T), Utils.mkvc(Y.T), Utils.mkvc(Z.T)]
Rx = PF.BaseMag.RxObs(xyzLoc)
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]
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())
# 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, -15],
np.r_[20, 20, 20],
self.mesh.gridCC,
)[0]
# Assign magnetization value, inducing field strength will
# be applied in by the :class:`SimPEG.PF.Magnetics` problem
model = np.zeros(self.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(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,
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 = xyzLoc.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(self.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(self.mesh, surf, np.nan)
# Create identity map
idenMap = Maps.IdentityMap(nP=nC)
# Create static map
prob = PF.Magnetics.MagneticIntegral(self.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(self.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(self.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(self.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 /= np.max(wr)
# Re-set the observations to |B|
surveyAmp.dobs = bAmp
surveyAmp.std = wd
# Create a sparse regularization
reg = Regularization.Sparse(self.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])
def createLocalProb(rxLoc, wrGlobal, lims, ind):
# 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.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]
survey_t.ind = ind_t
meshLocal = meshutils.mesh_builder_xyz(topo,
h,
padding_distance=padDist,
mesh_type='TREE',
base_mesh=meshInput,
depth_core=depth_core)
if topo is not None:
meshLocal = meshutils.refine_tree_xyz(meshLocal,
topo,
method='surface',
octree_levels=octreeTopo,
finalize=False)
meshLocal = meshutils.refine_tree_xyz(
meshLocal,
rxLoc[ind_t, :],
method='surface',
max_distance=maxDist,
octree_levels=octreeObs,
octree_levels_padding=octreeObs_XY,
finalize=True,
)
actv_t = np.ones(meshLocal.nC, dtype='bool')
# Create reduced identity map
tileMap = Maps.Tile((mesh, actv), (meshLocal, actv_t))
actv_t = tileMap.activeLocal
print(actv_t.sum(), meshLocal.nC)
# Create the forward model operator
prob = PF.Magnetics.MagneticIntegral(meshLocal,
chiMap=tileMap,
actInd=actv_t,
parallelized='dask',
Jpath=work_dir + out_dir +
"Tile" + str(ind) + ".zarr",
store_zarr=True)
survey_t.pair(prob)
# Data misfit function
dmis = DataMisfit.l2_DataMisfit(survey_t)
dmis.W = 1. / survey_t.std
wr = prob.getJtJdiag(np.ones(tileMap.P.shape[1]), W=dmis.W)
localMap = Maps.InjectActiveCells(meshLocal, actv_t, 1e-8)
Mesh.TreeMesh.writeUBC(
mesh,
work_dir + out_dir + 'OctreeMesh' + str(tt) + '.msh',
models={
work_dir + out_dir + 'Wr_' + str(tt) + '.act': actvMap * wr
})
Mesh.TreeMesh.writeUBC(
meshLocal,
work_dir + out_dir + 'OctreeMesh' + str(tt) + '.msh',
models={
work_dir + out_dir + 'Wr_' + str(tt) + '.act':
localMap * tileMap * wr
})
# localMap = Maps.InjectActiveCells(meshLocal, actv_t, 1e-8)
# Mesh.TreeMesh.writeUBC(
# meshLocal, work_dir + out_dir + 'OctreeMesh' + str(tt) + '.msh',
# models={work_dir + out_dir + 'Wr_' + str(tt) + '.act': localMap*wr}
# )
#
wrGlobal += wr
del meshLocal
# Create combo misfit function
return dmis, wrGlobal
