def run(plotIt=True, nFreq=1):
"""
MT: 3D: Forward
===============
Forward model 3D MT data.
"""
# Make a mesh
M = simpeg.Mesh.TensorMesh([[(100,5,-1.5),(100.,10),(100,5,1.5)],[(100,5,-1.5),(100.,10),(100,5,1.5)],[(100,5,1.6),(100.,10),(100,3,2)]], x0=['C','C',-3529.5360])
# Setup the model
conds = [1e-2,1]
sig = simpeg.Utils.ModelBuilder.defineBlock(M.gridCC,[-1000,-1000,-400],[1000,1000,-200],conds)
sig[M.gridCC[:,2]>0] = 1e-8
sig[M.gridCC[:,2]<-600] = 1e-1
sigBG = np.zeros(M.nC) + conds[0]
sigBG[M.gridCC[:,2]>0] = 1e-8
## Setup the the survey object
# Receiver locations
rx_x, rx_y = np.meshgrid(np.arange(-500,501,50),np.arange(-500,501,50))
rx_loc = np.hstack((simpeg.Utils.mkvc(rx_x,2),simpeg.Utils.mkvc(rx_y,2),np.zeros((np.prod(rx_x.shape),1))))
# Make a receiver list
rxList = []
for loc in rx_loc:
# NOTE: loc has to be a (1,3) np.ndarray otherwise errors accure
for rx_orientation in ['xx','xy','yx','yy']:
rxList.append(NSEM.Rx.Point_impedance3D(simpeg.mkvc(loc,2).T,rx_orientation, 'real'))
rxList.append(NSEM.Rx.Point_impedance3D(simpeg.mkvc(loc,2).T,rx_orientation, 'imag'))
for rx_orientation in ['zx','zy']:
rxList.append(NSEM.Rx.Point_tipper3D(simpeg.mkvc(loc,2).T,rx_orientation, 'real'))
rxList.append(NSEM.Rx.Point_tipper3D(simpeg.mkvc(loc,2).T,rx_orientation, 'imag'))
# Source list
srcList =[]
for freq in np.logspace(3,-3,nFreq):
srcList.append(NSEM.Src.Planewave_xy_1Dprimary(rxList,freq))
# Survey MT
survey = NSEM.Survey(srcList)
## Setup the problem object
problem = NSEM.Problem3D_ePrimSec(M, sigmaPrimary=sigBG)
problem.pair(survey)
problem.Solver = Solver
# Calculate the data
fields = problem.fields(sig)
dataVec = survey.eval(fields)
# Make the data
mtData = NSEM.Data(survey,dataVec)
# Add plots
if plotIt:
pass
def calculateAnalyticSolution(srcList,mesh,model):
surveyAna = NSEM.Survey(srcList)
data1D = NSEM.Data(surveyAna)
for src in surveyAna.srcList:
elev = src.rxList[0].locs[0]
anaEd, anaEu, anaHd, anaHu = NSEM.Utils.MT1Danalytic.getEHfields(mesh,model,src.freq,elev)
anaE = anaEd+anaEu
anaH = anaHd+anaHu
# Scale the solution
# anaE = (anaEtemp/anaEtemp[-1])#.conj()
# anaH = (anaHtemp/anaEtemp[-1])#.conj()
anaZ = anaE/anaH
for rx in src.rxList:
data1D[src,rx] = getattr(anaZ, rx.component)
return data1D
def DerivJvecTest(halfspace_value, freq=False, expMap=True):
survey, sig, sigBG, mesh = NSEM.Utils.testUtils.setup1DSurvey(
halfspace_value, False, structure=True)
problem = NSEM.Problem1D_ePrimSec(mesh,
sigmaPrimary=sigBG,
sigmaMap=simpeg.Maps.IdentityMap(mesh))
problem.pair(survey)
print('Using {0} solver for the problem'.format(problem.Solver))
print(
'Derivative test of Jvec for eForm primary/secondary for 1d comp from {0} to {1} Hz\n'
.format(survey.freqs[0], survey.freqs[-1]))
# problem.mapping = simpeg.Maps.ExpMap(problem.mesh)
# problem.sigmaPrimary = np.log(sigBG)
x0 = sigBG
# cond = sig[0]
# x0 = np.log(np.ones(problem.mesh.nC)*halfspace_value)
# problem.sigmaPrimary = x0
np.random.seed(1983)
# if True:
# x0 = x0 + np.random.randn(problem.mesh.nC)*halfspace_value*1e-1
survey = problem.survey
def fun(x):
return survey.dpred(x), lambda x: problem.Jvec(x0, x)
return simpeg.Tests.checkDerivative(fun, x0, num=4, plotIt=False, eps=FLR)
def dataMis_AnalyticPrimarySecondary(sigmaHalf):
# Make the survey
# Primary secondary
survey, sig, sigBG, mesh = NSEM.Utils.testUtils.setup1DSurvey(sigmaHalf,False,structure=True)
# Analytic data
problem = NSEM.Problem1D_ePrimSec(mesh, sigmaPrimary = sig)
problem.pair(survey)
dataAnaObj = calculateAnalyticSolution(survey.srcList,mesh,sig)
data = survey.dpred(sig)
dataAna = simpeg.mkvc(dataAnaObj)
return np.all((data - dataAna)/dataAna < 2.)
def appRes_psFieldNorm(sigmaHalf):
# Make the survey
survey, sigma, sigBG, mesh = NSEM.Utils.testUtils.setup1DSurvey(sigmaHalf,False)
problem = NSEM.Problem1D_ePrimSec(mesh, sigmaPrimary = sigBG)
problem.pair(survey)
# Get the fields
fields = problem.fields(sigma)
# Project the data
data = survey.eval(fields)
# Calculate the app res and phs
app_r = np.array(NSEM.Utils.testUtils.getAppResPhs(data))[:,0]
return np.linalg.norm(np.abs(np.log(app_r) - np.log(np.ones(survey.nFreq)/sigmaHalf))*np.log(sigmaHalf))
def JvecAdjointTest(sigmaHalf, formulation='PrimSec'):
forType = 'PrimSec' not in formulation
survey, sigma, sigBG, m1d = NSEM.Utils.testUtils.setup1DSurvey(sigmaHalf,tD=forType,structure=False)
print('Adjoint test of e formulation for {:s} comp \n'.format(formulation))
if 'PrimSec' in formulation:
problem = NSEM.Problem1D_ePrimSec(m1d, sigmaPrimary = sigBG)
else:
raise NotImplementedError('Only {} formulations are implemented.'.format(formulation))
problem.pair(survey)
m = sigma
u = problem.fields(m)
np.random.seed(1983)
v = np.random.rand(survey.nD,)
# print problem.PropMap.PropModel.nP
w = np.random.rand(problem.mesh.nC,)
vJw = v.ravel().dot(problem.Jvec(m, w, u))
wJtv = w.ravel().dot(problem.Jtvec(m, v, u))
tol = np.max([TOL*(10**int(np.log10(np.abs(vJw)))),FLR])
print(' vJw wJtv vJw - wJtv tol abs(vJw - wJtv) < tol')
print(vJw, wJtv, vJw - wJtv, tol, np.abs(vJw - wJtv) < tol)
return np.abs(vJw - wJtv) < tol
def run(plotIt=True):
# 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, 15, -1.2)]), np.ones(
(8, ))), simpeg.Utils.meshTensor([(ct, 5)])))
bot = simpeg.Utils.meshTensor([(core[0], 20, -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 variables
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,
sigmaMap=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))
# Assign uncertainties
std = 0.025 # 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()
# Optimization
opt = simpeg.Optimization.InexactGaussNewton(maxIter=25)
opt.counter = C
opt.LSshorten = 0.1
opt.remember('xc')
# Data misfit
dmis = simpeg.DataMisfit.l2_DataMisfit(survey)
dmis.W = 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-2
reg.alpha_x = 1.
reg.mrefInSmooth = True
# Inversion problem
invProb = simpeg.InvProblem.BaseInvProblem(dmis, reg, opt)
invProb.counter = C
# Beta schedule
beta = simpeg.Directives.BetaSchedule()
beta.coolingRate = 4.
beta.coolingFactor = 4.
# Initial estimate of beta
betaest = simpeg.Directives.BetaEstimate_ByEig(beta0_ratio=10.)
# Target misfit stop
targmis = simpeg.Directives.TargetMisfit()
targmis.target = survey.nD
# Create an inversion object
directives = [beta, betaest, targmis]
inv = simpeg.Inversion.BaseInversion(invProb, directiveList=directives)
# 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])
def run(plotIt=True):
# nFreq = 13
# freqs = np.logspace(2, -2, nFreq)
#
# # x and y grid parameters
# ctx = 10 #100
# npadx = 22
# incx = 1.3
# nx = [(ctx,npadx,-incx),(ctx,6),(ctx,npadx,incx)]
#
# # z grid parameters
# ct1 = 10
# npad1 = 21
# inc1 = 1.3
#
# ct = 10
# npad = 20
#
# ct2 = 10
# npad2 = 20
# inc2 = 1.3
nFreq = 13
freqs = np.logspace(2, -2, nFreq)
# x and y grid parameters
ctx = 10 #100
npadx = 16
incx = 1.5
nx = [(ctx,npadx,-incx),(ctx,6),(ctx,npadx,incx)]
# z grid parameters
ct1 = 30
npad1 = 15
inc1 = 1.3
ct = 25
npad = 20
ct2 = 1
npad2 = 27
inc2 = 1.3
nz = [(ct1,npad1,-inc1),(ct,npad),(ct2,npad2,inc2)]
# Origem do sistema de coordenadas da malha
ztop = 0
for i in range(1,npad1+1):
ztop += ct1*inc1**(i)
ztop += 1.*ct*npad #9*ct
# Make a mesh
M = simpeg.Mesh.TensorMesh([nx,nx,nz], x0=['C', 'C', -ztop])
#M = simpeg.Mesh.TensorMesh([nx,nx,nz], x0=['C', 'C', 'C'])
ccMesh=M.gridCC
print(np.size(ccMesh))
#M.setCellGradBC('dirichlet')
#print(inspect.signature(M.setCellGradBC)) # visualize input parameters of functions
# Setup the model
# Profundidade do topo de cada camada (precisa coincidir com a malha!)
ztop = M.vectorNz[-1]
# zh = np.array([ztop,0.,-200.,-350])
# zh = np.array([ztop,0.,-200.,-300])
# conds = np.array([1e-8,1.,0.01,1.])
#sig = simpeg.Utils.ModelBuilder.layeredModel(ccMesh, zh, conds)
conds = [1e-2,1]
sig = simpeg.Utils.ModelBuilder.defineBlock(
M.gridCC, [-15000, -15000, -350], [15000, 15000, -150], conds)
sig[M.gridCC[:, 2] > 0] = 1e-8
#sig[M.gridCC[:, 2] < -1000] = 1 # 1e-1
#sigBG = sig
sigBG = np.zeros(M.nC) + conds[1]
sigBG[M.gridCC[:, 2] > 0] = 1e-8
if plotIt:
fig,axes = plt.subplots(num=1,clear=True)
collect_obj, line_obj = M.plotSlice(np.log(sig), grid=True, normal='y',ax=axes)
plt.colorbar(collect_obj)
plt.show()
#%% Setup the layout of the survey, set the sources and the connected receivers
# Receiver locations
# rx_x, rx_y = np.meshgrid(np.arange(-600, 601, 100), np.arange(-600, 601, 100))
rx_x = np.array([0.])
rx_y = np.array([0.])
#rx_z = np.array([0.])
rx_loc = np.hstack((simpeg.Utils.mkvc(rx_x, 2), simpeg.Utils.mkvc(rx_y, 2), np.zeros((np.prod(rx_x.shape), 1))))
#rx_loc = np.reshape([rx_x,rx_y,rx_z],(1,3))
# Receivers
rxList = []
for rx_orientation in ['xx', 'xy', 'yx', 'yy']:
rxList.append(NSEM.Rx.Point_impedance3D(rx_loc, rx_orientation, 'real'))
rxList.append(NSEM.Rx.Point_impedance3D(rx_loc, rx_orientation, 'imag'))
for rx_orientation in ['zx', 'zy']:
rxList.append(NSEM.Rx.Point_tipper3D(rx_loc, rx_orientation, 'real'))
rxList.append(NSEM.Rx.Point_tipper3D(rx_loc, rx_orientation, '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.Problem3D_ePrimSec(M, sigma=sig, sigmaPrimary=sigBG)
problem.pair(survey)
problem.Solver = Solver
# Calculate the data
fields = problem.fields()
dataVec = survey.eval(fields)
# # Add uncertainty to the data - 10% standard
# # devation and 0 floor
# dataVec.standard_deviation.fromvec(
# np.ones_like(simpeg.mkvc(dataVec)) * 0.0
# )
# dataVec.floor.fromvec(
# np.zeros_like(simpeg.mkvc(dataVec))
# )
if plotIt:
#plotting
# fig,ax1 = plt.subplots(clear=True)
out1 = dataVec.plot_app_res(np.array([0.,0.]),components=['xy','yx'],
comp_plot_dict = {'xy':{'marker':'None','ls':'-'},
'yx':{'marker':'None','ls':'--'} } )
# out1.autoscale(tight=True)
# out1.set_yscale('linear')
# out1.grid(True)
#out1.set_ylim([0.,300.])
mu = 4*math.pi*1E-7; #Magnetic Permeability (H/m)
resistivities = np.array([1.,100.,1.]) #[100,10,200] #[300, 2500, 0.8, 3000, 2500];
thicknesses = [150.,200] #[300,300] #[200, 400, 40, 500];
n = len(resistivities);
nFreq = 13
frequencies = np.logspace(2, -2, nFreq) #[1,5,10,25,50,100] #data[:,0] ##[0.0001,0.005,0.01,0.05,0.1,0.5,1,5,10,50,100,500,10000];
rhoapp = np.zeros(len(frequencies))
#print('freq\tares\t\t\tphase');
for i,frequency in enumerate(frequencies):
w = 2*math.pi*frequency;
impedances = list(range(n));
#compute basement impedance
impedances[n-1] = cmath.sqrt(w*mu*resistivities[n-1]*1j);
for j in range(n-2,-1,-1):
resistivity = resistivities[j];
thickness = thicknesses[j];
# 3. Compute apparent resistivity from top layer impedance
#Step 2. Iterate from bottom layer to top(not the basement)
# Step 2.1 Calculate the intrinsic impedance of current layer
dj = cmath.sqrt((w * mu * (1.0/resistivity))*1j);
wj = dj * resistivity;
# Step 2.2 Calculate Exponential factor from intrinsic impedance
ej = cmath.exp(-2*thickness*dj);
# Step 2.3 Calculate reflection coeficient using current layer
# intrinsic impedance and the below layer impedance
belowImpedance = impedances[j + 1];
rj = (wj - belowImpedance)/(wj + belowImpedance);
re = rj*ej;
Zj = wj * ((1 - re)/(1 + re));
impedances[j] = Zj;
# Step 3. Compute apparent resistivity from top layer impedance
Z = impedances[0];
absZ = abs(Z);
apparentResistivity = (absZ * absZ)/(mu * w);
rhoapp[i] = apparentResistivity
phase = math.atan2(Z.imag, Z.real)
# print(frequency, '\t', apparentResistivity, '\t', phase);
#Plot result
#fig,ax = plt.subplots(num=1,clear=True)
ax = out1
#ax.plot(frequencies,rhoapp,frequencies,data[:,1],'--')
ax.plot(frequencies,rhoapp)
ax.autoscale(tight=True)
ax.legend(('Analytic','Numeric'))
ax.set_xlabel('frequency (Hz)')
ax.set_ylabel('Apparent Resistivity (Rho.m)')
ax.set_xscale('log')
ax.set_yscale('linear')
ax.invert_xaxis()
ax.grid()
out1.autoscale(tight=True)
out1.set_yscale('linear')
out1.grid(True)
# Receivers
rxList = []
for rx_orientation in ['xx', 'xy', 'yx', 'yy']:
rxList.append(NSEM.Rx.Point_impedance3D(rx_loc, rx_orientation, 'real'))
rxList.append(NSEM.Rx.Point_impedance3D(rx_loc, rx_orientation, 'imag'))
for rx_orientation in ['zx', 'zy']:
rxList.append(NSEM.Rx.Point_tipper3D(rx_loc, rx_orientation, 'real'))
rxList.append(NSEM.Rx.Point_tipper3D(rx_loc, rx_orientation, 'imag'))
# Source list,
srcList = []
for freq in freqs:
#srcList.append(NSEM.Src.Planewave_xy_1Dprimary(rxList, freq))
srcList.append(NSEM.Src.Planewave_xy_1Dprimary(rxList, freq, sigBG1d, sigBG))
# Make the survey
survey = NSEM.Survey(srcList)
#survey.mtrue = m_true
# Set the problem
problem = NSEM.Problem3D_ePrimSec(M, sigma=sig, sigmaPrimary=sigBG)
problem.pair(survey)
problem.Solver = Solver
# Calculate the data
fields = problem.fields() # returns secondary field
def run(plotIt=True):
"""
MT: 3D: Forward
===============
Forward model 3D MT data.
"""
# Make a mesh
M = simpeg.Mesh.TensorMesh([[
(100, 9, -1.5), (100., 13), (100, 9, 1.5)
], [(100, 9, -1.5), (100., 13),
(100, 9, 1.5)], [(50, 10, -1.6), (50., 10), (50, 6, 2)]],
x0=['C', 'C', -14926.8217])
# Setup the model
conds = [1, 1e-2]
sig = simpeg.Utils.ModelBuilder.defineBlock(M.gridCC, [-100, -100, -350],
[100, 100, -150], conds)
sig[M.gridCC[:, 2] > 0] = 1e-8
sig[M.gridCC[:, 2] < -1000] = 1e-1
sigBG = np.zeros(M.nC) + conds[1]
sigBG[M.gridCC[:, 2] > 0] = 1e-8
if plotIt:
collect_obj, line_obj = M.plotSlice(np.log10(sig),
grid=True,
normal='X')
color_bar = plt.colorbar(collect_obj)
# Setup the the survey object
# Receiver locations
rx_x, rx_y = np.meshgrid(np.arange(-600, 601, 100),
np.arange(-600, 601, 100))
rx_loc = np.hstack((simpeg.Utils.mkvc(rx_x, 2), simpeg.Utils.mkvc(rx_y, 2),
np.zeros((np.prod(rx_x.shape), 1))))
# Make a receiver list
rxList = []
for rx_orientation in ['xx', 'xy', 'yx', 'yy']:
rxList.append(NSEM.Rx.Point_impedance3D(rx_loc, rx_orientation,
'real'))
rxList.append(NSEM.Rx.Point_impedance3D(rx_loc, rx_orientation,
'imag'))
for rx_orientation in ['zx', 'zy']:
rxList.append(NSEM.Rx.Point_tipper3D(rx_loc, rx_orientation, 'real'))
rxList.append(NSEM.Rx.Point_tipper3D(rx_loc, rx_orientation, 'imag'))
# Source list
srcList = [
NSEM.Src.Planewave_xy_1Dprimary(rxList, freq)
for freq in np.logspace(4, -2, 13)
]
# Survey MT
survey = NSEM.Survey(srcList)
# Setup the problem object
problem = NSEM.Problem3D_ePrimSec(M, sigma=sig, sigmaPrimary=sigBG)
problem.pair(survey)
problem.Solver = Solver
# Calculate the data
fields = problem.fields()
dataVec = survey.eval(fields)
# Add uncertainty to the data - 10% standard
# devation and 0 floor
dataVec.standard_deviation.fromvec(
np.ones_like(simpeg.mkvc(dataVec)) * 0.1)
dataVec.floor.fromvec(np.zeros_like(simpeg.mkvc(dataVec)))
# Add plots
if plotIt:
# Plot the data
# On and off diagonal (on left and right axis, respectively)
fig, axes = plt.subplots(2, 1, figsize=(7, 5))
plt.subplots_adjust(right=0.8)
[(ax.invert_xaxis(), ax.set_xscale('log')) for ax in axes]
ax_r, ax_p = axes
ax_r.set_yscale('log')
ax_r.set_ylabel('Apparent resistivity [xy-yx]')
ax_r_on = ax_r.twinx()
ax_r_on.set_yscale('log')
ax_r_on.set_ylabel('Apparent resistivity [xx-yy]')
ax_p.set_ylabel('Apparent phase')
ax_p.set_xlabel('Frequency [Hz]')
# Start plotting
ax_r = dataVec.plot_app_res(np.array([-200, 0]),
components=['xy', 'yx'],
ax=ax_r,
errorbars=True)
ax_r_on = dataVec.plot_app_res(np.array([-200, 0]),
components=['xx', 'yy'],
ax=ax_r_on,
errorbars=True)
ax_p = dataVec.plot_app_phs(np.array([-200, 0]),
components=['xx', 'xy', 'yx', 'yy'],
ax=ax_p,
errorbars=True)
ax_p.legend(bbox_to_anchor=(1.05, 1), loc=2)