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import SimPEG as simpeg
import simpegMT as simpegmt
import numpy as np, os
import matplotlib.pyplot as plt
%matplotlib inline
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## Setup the modelling
# Setting up 1D mesh and conductivity models to forward model data.
# Frequency
nFreq = 31
freqs = np.logspace(3,-3,nFreq)
# Set mesh parameters
ct = 20
air = simpeg.Utils.meshTensor([(ct,16,1.4)])
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],10,-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)
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## Make a model
# Some 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 = 2e-3
sig_air = 1e-8
sig_layer1 = .2
sig_layer2 = .2
# Make the true conductivity
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 a background model
sigma_0 = np.ones(m1d.nCx)*sig_air
sigma_0[active] = sig_half
# Define the background model
m_0 = np.log(sigma_0[active])
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## Setup the layout of the survey, set the sources and the connected receivers
# Receivers
rxList = []
for rxType in ['z1dr','z1di']:
rxList.append(simpegmt.SurveyMT.RxMT(simpeg.mkvc(np.array([0.0]),2).T,rxType))
# Source list
srcList =[]
for freq in freqs:
srcList.append(simpegmt.SurveyMT.srcMT_polxy_1Dprimary(rxList,freq))
# Make the survey
survey = simpegmt.SurveyMT.SurveyMT(srcList)
survey.mtrue = m_true
# Set the mapping
actMap = simpeg.Maps.ActiveCells(m1d, active, np.log(1e-8), nC=m1d.nCx)
mappingExpAct = simpeg.Maps.ExpMap(m1d) * actMap
# Set the problem
problem = simpegmt.ProblemMT1D.eForm_psField(m1d,sigmaPrimary=sigma_0,mapping=mappingExpAct)
from pymatsolver import MumpsSolver
problem.solver = MumpsSolver
problem.pair(survey)
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## Forward model observed data
# Project the data
std = 0.05 # 5% std
if os.path.isfile('MT1D_dtrue.npy') and os.path.isfile('MT1D_dobs.npy'):
d_true = np.load('MT1D_dtrue.npy')
d_obs = np.load('MT1D_dobs.npy')
else:
d_true = survey.dpred(m_true)
np.save('MT1D_dtrue.npy',d_true)
d_obs = d_true + std*abs(d_true)*np.random.randn(*d_true.shape)
np.save('MT1D_dobs.npy',d_obs)
# Assign the dobs
survey.dtrue = d_true
survey.dobs = d_obs
survey.std = np.abs(survey.dobs*std) + 0.01*np.linalg.norm(survey.dobs)
# Assign the data weight
survey.Wd = 1/survey.std
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## Setup the inversion proceedure
# Define a counter
C = simpeg.Utils.Counter()
# Set the optimization
opt = simpeg.Optimization.InexactGaussNewton(maxIter = 30)
opt.counter = C
opt.LSshorten = 0.5
opt.remember('xc')
# Data misfit
dmis = simpeg.DataMisfit.l2_DataMisfit(survey)
# Regularization
regMesh = simpeg.Mesh.TensorMesh([m1d.hx[problem.mapping.sigmaMap.maps[-1].indActive]],m1d.x0)
reg = simpeg.Regularization.Tikhonov(regMesh)
reg.smoothModel = False
reg.alpha_s = 1e-7
reg.alpha_x = 1.
# reg.alpha_xx = .001
# Inversion problem
invProb = simpeg.InvProblem.BaseInvProblem(dmis, reg, opt)
invProb.counter = C
# Beta cooling
beta = simpeg.Directives.BetaSchedule()
betaest = simpeg.Directives.BetaEstimate_ByEig(beta0_ratio=0.75)
targmis = simpeg.Directives.TargetMisfit()
targmis.target = .75 * survey.nD
saveModel = simpeg.Directives.SaveModelEveryIteration()
saveModel.fileName = 'Inversion_TargMisEqnDregMesh_smoothFalse'
# Create an inversion object
inv = simpeg.Inversion.BaseInversion(invProb, directiveList=[beta,betaest,targmis,saveModel])
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%%time
simpegmt.Utils.dataUtils.printTime()
mopt = inv.run(m_0)
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%matplotlib inline
simpegmt.Utils.dataUtils.plotMT1DModelData(problem,[m_0,mopt])
plt.suptitle('Target misfit-smooth False')
plt.show()
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reg.alpha_xx = 0.001
saveModel.fileName = 'Inversion_TargMisEqnDregMesh_smoothFalseWxx'
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%%time
simpegmt.Utils.dataUtils.printTime()
moptWxx = inv.run(m_0)
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%matplotlib inline
simpegmt.Utils.dataUtils.plotMT1DModelData(problem,[moptWxx,mopt])
plt.suptitle('Target misfit-smooth False-Wxx included')
plt.show()
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