def normalize3D(x):
return x / np.kron(np.ones((1, 3)), Utils.mkvc(length3D(x), 2))
def normalize3D(x):
return x/np.kron(np.ones((1, 3)), Utils.mkvc(length3D(x), 2))
from SimPEG import Utils, np
from BaseMesh import BaseRectangularMesh
from DiffOperators import DiffOperators
from InnerProducts import InnerProducts
from View import CurvView
# Some helper functions.
length2D = lambda x: (x[:, 0]**2 + x[:, 1]**2)**0.5
length3D = lambda x: (x[:, 0]**2 + x[:, 1]**2 + x[:, 2]**2)**0.5
normalize2D = lambda x: x/np.kron(np.ones((1, 2)), Utils.mkvc(length2D(x), 2))
normalize3D = lambda x: x/np.kron(np.ones((1, 3)), Utils.mkvc(length3D(x), 2))
class CurvilinearMesh(BaseRectangularMesh, DiffOperators, InnerProducts, CurvView):
"""
CurvilinearMesh is a mesh class that deals with curvilinear meshes.
Example of a curvilinear mesh:
.. plot::
:include-source:
from SimPEG import Mesh, Utils
X, Y = Utils.exampleLrmGrid([3,3],'rotate')
M = Mesh.CurvilinearMesh([X, Y])
M.plotGrid(showIt=True)
"""
__metaclass__ = Utils.SimPEGMetaClass
_meshType = 'Curv'
def run(plotIt=True):
"""
MT: 1D: Inversion
=================
Forward model 1D MT data.
Setup and run a MT 1D inversion.
"""
## Setup the forward modeling
# Setting up 1D mesh and conductivity models to forward model data.
# Frequency
nFreq = 26
freqs = np.logspace(2,-3,nFreq)
# Set mesh parameters
ct = 10
air = simpeg.Utils.meshTensor([(ct,25,1.4)])
core = np.concatenate( ( np.kron(simpeg.Utils.meshTensor([(ct,10,-1.3)]),np.ones((5,))) , simpeg.Utils.meshTensor([(ct,5)]) ) )
bot = simpeg.Utils.meshTensor([(core[0],25,-1.4)])
x0 = -np.array([np.sum(np.concatenate((core,bot)))])
# Make the model
m1d = simpeg.Mesh.TensorMesh([np.concatenate((bot,core,air))], x0=x0)
# Setup model varibles
active = m1d.vectorCCx<0.
layer1 = (m1d.vectorCCx<-500.) & (m1d.vectorCCx>=-800.)
layer2 = (m1d.vectorCCx<-3500.) & (m1d.vectorCCx>=-5000.)
# Set the conductivity values
sig_half = 1e-2
sig_air = 1e-8
sig_layer1 = .2
sig_layer2 = .2
# Make the true model
sigma_true = np.ones(m1d.nCx)*sig_air
sigma_true[active] = sig_half
sigma_true[layer1] = sig_layer1
sigma_true[layer2] = sig_layer2
# Extract the model
m_true = np.log(sigma_true[active])
# Make the background model
sigma_0 = np.ones(m1d.nCx)*sig_air
sigma_0[active] = sig_half
m_0 = np.log(sigma_0[active])
# Set the mapping
actMap = simpeg.Maps.InjectActiveCells(m1d, active, np.log(1e-8), nC=m1d.nCx)
mappingExpAct = simpeg.Maps.ExpMap(m1d) * actMap
## Setup the layout of the survey, set the sources and the connected receivers
# Receivers
rxList = []
rxList.append(NSEM.Rx.Point_impedance1D(simpeg.mkvc(np.array([-0.5]),2).T,'real'))
rxList.append(NSEM.Rx.Point_impedance1D(simpeg.mkvc(np.array([-0.5]),2).T,'imag'))
# Source list
srcList =[]
for freq in freqs:
srcList.append(NSEM.Src.Planewave_xy_1Dprimary(rxList,freq))
# Make the survey
survey = NSEM.Survey(srcList)
survey.mtrue = m_true
## Set the problem
problem = NSEM.Problem1D_ePrimSec(m1d,sigmaPrimary=sigma_0,mapping=mappingExpAct)
problem.pair(survey)
## Forward model data
# Project the data
survey.dtrue = survey.dpred(m_true)
survey.dobs = survey.dtrue + 0.01*abs(survey.dtrue)*np.random.randn(*survey.dtrue.shape)
if plotIt:
fig = NSEM.Utils.dataUtils.plotMT1DModelData(problem,[])
fig.suptitle('Target - smooth true')
# Assign uncertainties
std = 0.05 # 5% std
survey.std = np.abs(survey.dobs*std)
# Assign the data weight
Wd = 1./survey.std
## Setup the inversion proceedure
# Define a counter
C = simpeg.Utils.Counter()
# Set the optimization
opt = simpeg.Optimization.ProjectedGNCG(maxIter = 25)
opt.counter = C
opt.lower = np.log(1e-4)
opt.upper = np.log(5)
opt.LSshorten = 0.1
opt.remember('xc')
# Data misfit
dmis = simpeg.DataMisfit.l2_DataMisfit(survey)
dmis.Wd = Wd
# Regularization - with a regularization mesh
regMesh = simpeg.Mesh.TensorMesh([m1d.hx[active]],m1d.x0)
reg = simpeg.Regularization.Tikhonov(regMesh)
reg.mrefInSmooth = True
reg.alpha_s = 1e-1
reg.alpha_x = 1.
# Inversion problem
invProb = simpeg.InvProblem.BaseInvProblem(dmis, reg, opt)
invProb.counter = C
# Beta cooling
beta = simpeg.Directives.BetaSchedule()
beta.coolingRate = 4.
beta.coolingFactor = 4.
betaest = simpeg.Directives.BetaEstimate_ByEig(beta0_ratio=100.)
betaest.beta0 = 1.
targmis = simpeg.Directives.TargetMisfit()
targmis.target = survey.nD
# Create an inversion object
inv = simpeg.Inversion.BaseInversion(invProb, directiveList=[beta,betaest,targmis])
## Run the inversion
mopt = inv.run(m_0)
if plotIt:
fig = NSEM.Utils.dataUtils.plotMT1DModelData(problem,[mopt])
fig.suptitle('Target - smooth true')
fig.axes[0].set_ylim([-10000,500])
plt.show()
def run(plotIt=True):
"""
MT: 1D: Inversion
=================
Forward model 1D MT data.
Setup and run a MT 1D inversion.
"""
## Setup the forward modeling
# Setting up 1D mesh and conductivity models to forward model data.
# Frequency
nFreq = 26
freqs = np.logspace(2, -3, nFreq)
# Set mesh parameters
ct = 10
air = simpeg.Utils.meshTensor([(ct, 25, 1.4)])
core = np.concatenate(
(np.kron(simpeg.Utils.meshTensor([(ct, 10, -1.3)]), np.ones(
(5, ))), simpeg.Utils.meshTensor([(ct, 5)])))
bot = simpeg.Utils.meshTensor([(core[0], 25, -1.4)])
x0 = -np.array([np.sum(np.concatenate((core, bot)))])
# Make the model
m1d = simpeg.Mesh.TensorMesh([np.concatenate((bot, core, air))], x0=x0)
# Setup model varibles
active = m1d.vectorCCx < 0.
layer1 = (m1d.vectorCCx < -500.) & (m1d.vectorCCx >= -800.)
layer2 = (m1d.vectorCCx < -3500.) & (m1d.vectorCCx >= -5000.)
# Set the conductivity values
sig_half = 1e-2
sig_air = 1e-8
sig_layer1 = .2
sig_layer2 = .2
# Make the true model
sigma_true = np.ones(m1d.nCx) * sig_air
sigma_true[active] = sig_half
sigma_true[layer1] = sig_layer1
sigma_true[layer2] = sig_layer2
# Extract the model
m_true = np.log(sigma_true[active])
# Make the background model
sigma_0 = np.ones(m1d.nCx) * sig_air
sigma_0[active] = sig_half
m_0 = np.log(sigma_0[active])
# Set the mapping
actMap = simpeg.Maps.InjectActiveCells(m1d,
active,
np.log(1e-8),
nC=m1d.nCx)
mappingExpAct = simpeg.Maps.ExpMap(m1d) * actMap
## Setup the layout of the survey, set the sources and the connected receivers
# Receivers
rxList = []
rxList.append(
NSEM.Rx.Point_impedance1D(simpeg.mkvc(np.array([-0.5]), 2).T, 'real'))
rxList.append(
NSEM.Rx.Point_impedance1D(simpeg.mkvc(np.array([-0.5]), 2).T, 'imag'))
# Source list
srcList = []
for freq in freqs:
srcList.append(NSEM.Src.Planewave_xy_1Dprimary(rxList, freq))
# Make the survey
survey = NSEM.Survey(srcList)
survey.mtrue = m_true
## Set the problem
problem = NSEM.Problem1D_ePrimSec(m1d,
sigmaPrimary=sigma_0,
mapping=mappingExpAct)
problem.pair(survey)
## Forward model data
# Project the data
survey.dtrue = survey.dpred(m_true)
survey.dobs = survey.dtrue + 0.01 * abs(
survey.dtrue) * np.random.randn(*survey.dtrue.shape)
if plotIt:
fig = NSEM.Utils.dataUtils.plotMT1DModelData(problem, [])
fig.suptitle('Target - smooth true')
# Assign uncertainties
std = 0.05 # 5% std
survey.std = np.abs(survey.dobs * std)
# Assign the data weight
Wd = 1. / survey.std
## Setup the inversion proceedure
# Define a counter
C = simpeg.Utils.Counter()
# Set the optimization
opt = simpeg.Optimization.ProjectedGNCG(maxIter=25)
opt.counter = C
opt.lower = np.log(1e-4)
opt.upper = np.log(5)
opt.LSshorten = 0.1
opt.remember('xc')
# Data misfit
dmis = simpeg.DataMisfit.l2_DataMisfit(survey)
dmis.Wd = Wd
# Regularization - with a regularization mesh
regMesh = simpeg.Mesh.TensorMesh([m1d.hx[active]], m1d.x0)
reg = simpeg.Regularization.Tikhonov(regMesh)
reg.mrefInSmooth = True
reg.alpha_s = 1e-1
reg.alpha_x = 1.
# Inversion problem
invProb = simpeg.InvProblem.BaseInvProblem(dmis, reg, opt)
invProb.counter = C
# Beta cooling
beta = simpeg.Directives.BetaSchedule()
beta.coolingRate = 4.
beta.coolingFactor = 4.
betaest = simpeg.Directives.BetaEstimate_ByEig(beta0_ratio=100.)
betaest.beta0 = 1.
targmis = simpeg.Directives.TargetMisfit()
targmis.target = survey.nD
# Create an inversion object
inv = simpeg.Inversion.BaseInversion(
invProb, directiveList=[beta, betaest, targmis])
## Run the inversion
mopt = inv.run(m_0)
if plotIt:
fig = NSEM.Utils.dataUtils.plotMT1DModelData(problem, [mopt])
fig.suptitle('Target - smooth true')
fig.axes[0].set_ylim([-10000, 500])
plt.show()
from SimPEG import Utils, np
from BaseMesh import BaseRectangularMesh
from DiffOperators import DiffOperators
from InnerProducts import InnerProducts
# Some helper functions.
length2D = lambda x: (x[:, 0]**2 + x[:, 1]**2)**0.5
length3D = lambda x: (x[:, 0]**2 + x[:, 1]**2 + x[:, 2]**2)**0.5
normalize2D = lambda x: x/np.kron(np.ones((1, 2)), Utils.mkvc(length2D(x), 2))
normalize3D = lambda x: x/np.kron(np.ones((1, 3)), Utils.mkvc(length3D(x), 2))
class CurvilinearMesh(BaseRectangularMesh, DiffOperators, InnerProducts):
"""
CurvilinearMesh is a mesh class that deals with curvilinear meshes.
Example of a curvilinear mesh:
.. plot::
:include-source:
from SimPEG import Mesh, Utils
X, Y = Utils.exampleLrmGrid([3,3],'rotate')
M = Mesh.CurvilinearMesh([X, Y])
M.plotGrid(showIt=True)
"""
__metaclass__ = Utils.SimPEGMetaClass
_meshType = 'Curv'