def setUp(self):
url = 'https://storage.googleapis.com/simpeg/tests/potential_fields/'
cloudfiles = [
'MagData.obs', 'Gaussian.topo', 'Mesh_10m.msh', 'ModelStart.sus',
'SimPEG_Mag_Input.inp'
]
self.basePath = io_utils.remoteDownload(url, cloudfiles)
def downloadStoredResults(self):
# download the results from where they are stored on google app engine
return os.path.abspath(
remoteDownload(
self.url, [self.cloudfile], basePath=self.filepath+os.path.sep
)
)
def setUp(self):
url = 'https://storage.googleapis.com/simpeg/tests/potential_fields/'
cloudfiles = ['MagData.obs', 'Gaussian.topo', 'Mesh_10m.msh',
'ModelStart.sus', 'SimPEG_Mag_Input.inp']
self.basePath = io_utils.remoteDownload(url, cloudfiles)
def setUp(self):
url = 'https://storage.googleapis.com/simpeg/tests/em_utils/'
cloudfiles = ['currents.npy']
self.basePath = io_utils.remoteDownload(url, cloudfiles)
def run(plotIt=True):
"""
PF: Gravity: Laguna del Maule Bouguer Gravity
=============================================
This notebook illustrates the SimPEG code used to invert Bouguer
gravity data collected at Laguna del Maule volcanic field, Chile.
Refer to Miller et al 2016 EPSL for full details.
We run the inversion in two steps. Firstly creating a L2 model and
then applying an Lp norm to produce a compact model.
Craig Miller
"""
# Start by downloading files from the remote repository
url = "https://storage.googleapis.com/simpeg/Chile_GRAV_4_Miller/"
cloudfiles = [
'LdM_grav_obs.grv', 'LdM_mesh.mesh', 'LdM_topo.topo',
'LdM_input_file.inp'
]
basePath = os.path.sep.join(
os.path.abspath(os.getenv('HOME')).split(os.path.sep) + ['Downloads'] +
['SimPEGtemp'])
basePath = os.path.abspath(
remoteDownload(url, cloudfiles, basePath=basePath + os.path.sep))
input_file = basePath + os.path.sep + 'LdM_input_file.inp'
# %% User input
# Plotting parameters, max and min densities in g/cc
vmin = -0.6
vmax = 0.6
# weight exponent for default weighting
wgtexp = 3.
# %%
# Read in the input file which included all parameters at once
# (mesh, topo, model, survey, inv param, etc.)
driver = PF.GravityDriver.GravityDriver_Inv(input_file)
# %%
# Now we need to create the survey and model information.
# Access the mesh and survey information
mesh = driver.mesh
survey = driver.survey
# define gravity survey locations
rxLoc = survey.srcField.rxList[0].locs
# define gravity data and errors
d = survey.dobs
wd = survey.std
# Get the active cells
active = driver.activeCells
nC = len(active) # Number of active cells
# Create active map to go from reduce set to full
activeMap = Maps.InjectActiveCells(mesh, active, -100)
# Create static map
static = driver.staticCells
dynamic = driver.dynamicCells
staticCells = Maps.InjectActiveCells(None,
dynamic,
driver.m0[static],
nC=nC)
mstart = driver.m0[dynamic]
# Get index of the center
midx = int(mesh.nCx / 2)
# %%
# Now that we have a model and a survey we can build the linear system ...
# Create the forward model operator
prob = PF.Gravity.GravityIntegral(mesh, rhoMap=staticCells, actInd=active)
prob.solverOpts['accuracyTol'] = 1e-4
# Pair the survey and problem
survey.pair(prob)
# Apply depth weighting
wr = PF.Magnetics.get_dist_wgt(mesh, rxLoc, active, wgtexp,
np.min(mesh.hx) / 4.)
wr = wr**2.
# %% Create inversion objects
reg = Regularization.Sparse(mesh, indActive=active, mapping=staticCells)
reg.mref = driver.mref[dynamic]
reg.cell_weights = wr * mesh.vol[active]
# Specify how the optimization will proceed
opt = Optimization.ProjectedGNCG(maxIter=150,
lower=driver.bounds[0],
upper=driver.bounds[1],
maxIterLS=20,
maxIterCG=20,
tolCG=1e-3)
# Define misfit function (obs-calc)
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.Wd = 1. / wd
# 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()
# IRLS sets up the Lp inversion problem
# Set the eps parameter parameter in Line 11 of the
# input file based on the distribution of model (DEFAULT = 95th %ile)
IRLS = Directives.Update_IRLS(norms=driver.lpnorms,
eps=driver.eps,
f_min_change=1e-2,
maxIRLSiter=20,
minGNiter=5)
# Preconditioning refreshing for each IRLS iteration
update_Jacobi = Directives.Update_lin_PreCond()
# Create combined the L2 and Lp problem
inv = Inversion.BaseInversion(invProb,
directiveList=[IRLS, update_Jacobi, betaest])
# %%
# Run L2 and Lp inversion
mrec = inv.run(mstart)
# %%
if plotIt:
# Plot observed data
PF.Magnetics.plot_obs_2D(rxLoc, d, 'Observed Data')
# %%
# Write output model and data files and print misft stats.
# reconstructing l2 model mesh with air cells and active dynamic cells
L2out = activeMap * reg.l2model
# reconstructing lp model mesh with air cells and active dynamic cells
Lpout = activeMap * mrec
# %%
# Plot out sections and histograms of the smooth l2 model.
# The ind= parameter is the slice of the model from top down.
yslice = midx + 1
L2out[L2out == -100] = np.nan # set "air" to nan
plt.figure(figsize=(10, 7))
plt.suptitle('Smooth Inversion: Depth weight = ' + str(wgtexp))
ax = plt.subplot(221)
dat1 = mesh.plotSlice(L2out,
ax=ax,
normal='Z',
ind=-16,
clim=(vmin, vmax),
pcolorOpts={'cmap': 'bwr'})
plt.plot(np.array([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
np.array([mesh.vectorCCy[yslice], mesh.vectorCCy[yslice]]),
c='gray',
linestyle='--')
plt.scatter(rxLoc[0:, 0], rxLoc[0:, 1], color='k', s=1)
plt.title('Z: ' + str(mesh.vectorCCz[-16]) + ' m')
plt.xlabel('Easting (m)')
plt.ylabel('Northing (m)')
plt.gca().set_aspect('equal', adjustable='box')
cb = plt.colorbar(dat1[0],
orientation="vertical",
ticks=np.linspace(vmin, vmax, 4))
cb.set_label('Density (g/cc$^3$)')
ax = plt.subplot(222)
dat = mesh.plotSlice(L2out,
ax=ax,
normal='Z',
ind=-27,
clim=(vmin, vmax),
pcolorOpts={'cmap': 'bwr'})
plt.plot(np.array([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
np.array([mesh.vectorCCy[yslice], mesh.vectorCCy[yslice]]),
c='gray',
linestyle='--')
plt.scatter(rxLoc[0:, 0], rxLoc[0:, 1], color='k', s=1)
plt.title('Z: ' + str(mesh.vectorCCz[-27]) + ' m')
plt.xlabel('Easting (m)')
plt.ylabel('Northing (m)')
plt.gca().set_aspect('equal', adjustable='box')
cb = plt.colorbar(dat1[0],
orientation="vertical",
ticks=np.linspace(vmin, vmax, 4))
cb.set_label('Density (g/cc$^3$)')
ax = plt.subplot(212)
mesh.plotSlice(L2out,
ax=ax,
normal='Y',
ind=yslice,
clim=(vmin, vmax),
pcolorOpts={'cmap': 'bwr'})
plt.title('Cross Section')
plt.xlabel('Easting(m)')
plt.ylabel('Elevation')
plt.gca().set_aspect('equal', adjustable='box')
cb = plt.colorbar(dat1[0],
orientation="vertical",
ticks=np.linspace(vmin, vmax, 4),
cmap='bwr')
cb.set_label('Density (g/cc$^3$)')
# %%
# Make plots of Lp model
yslice = midx + 1
Lpout[Lpout == -100] = np.nan # set "air" to nan
plt.figure(figsize=(10, 7))
plt.suptitle('Compact Inversion: Depth weight = ' + str(wgtexp) +
': $\epsilon_p$ = ' + str(round(reg.eps_p[0], 1)) +
': $\epsilon_q$ = ' + str(round(reg.eps_q[0], 2)))
ax = plt.subplot(221)
dat = mesh.plotSlice(Lpout,
ax=ax,
normal='Z',
ind=-16,
clim=(vmin, vmax),
pcolorOpts={'cmap': 'bwr'})
plt.plot(np.array([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
np.array([mesh.vectorCCy[yslice], mesh.vectorCCy[yslice]]),
c='gray',
linestyle='--')
plt.scatter(rxLoc[0:, 0], rxLoc[0:, 1], color='k', s=1)
plt.title('Z: ' + str(mesh.vectorCCz[-16]) + ' m')
plt.xlabel('Easting (m)')
plt.ylabel('Northing (m)')
plt.gca().set_aspect('equal', adjustable='box')
cb = plt.colorbar(dat[0],
orientation="vertical",
ticks=np.linspace(vmin, vmax, 4))
cb.set_label('Density (g/cc$^3$)')
ax = plt.subplot(222)
dat = mesh.plotSlice(Lpout,
ax=ax,
normal='Z',
ind=-27,
clim=(vmin, vmax),
pcolorOpts={'cmap': 'bwr'})
plt.plot(np.array([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
np.array([mesh.vectorCCy[yslice], mesh.vectorCCy[yslice]]),
c='gray',
linestyle='--')
plt.scatter(rxLoc[0:, 0], rxLoc[0:, 1], color='k', s=1)
plt.title('Z: ' + str(mesh.vectorCCz[-27]) + ' m')
plt.xlabel('Easting (m)')
plt.ylabel('Northing (m)')
plt.gca().set_aspect('equal', adjustable='box')
cb = plt.colorbar(dat[0],
orientation="vertical",
ticks=np.linspace(vmin, vmax, 4))
cb.set_label('Density (g/cc$^3$)')
ax = plt.subplot(212)
dat = mesh.plotSlice(Lpout,
ax=ax,
normal='Y',
ind=yslice,
clim=(vmin, vmax),
pcolorOpts={'cmap': 'bwr'})
plt.title('Cross Section')
plt.xlabel('Easting (m)')
plt.ylabel('Elevation (m)')
plt.gca().set_aspect('equal', adjustable='box')
cb = plt.colorbar(dat[0],
orientation="vertical",
ticks=np.linspace(vmin, vmax, 4))
cb.set_label('Density (g/cc$^3$)')