def G(self):
if getattr(self, '_G', None) is None:
#print "Computing G"
# rot = Utils.mkvc(Utils.dipazm_2_xyz(self.prism.pinc, self.prism.pdec))
# rxLoc = Utils.rotatePointsFromNormals(self.survey.rxLoc, rot, np.r_[0., 1., 0.],
# np.r_[0, 0, 0])
xLoc = self.survey.rxLoc[:, 0] - self.prism.xc
yLoc = self.survey.rxLoc[:, 1] - self.prism.yc
zLoc = self.survey.rxLoc[:, 2] - self.prism.zc
R = Utils.rotationMatrix(-self.prism.pinc, -self.prism.pdec, normal=False)
rxLoc = R.dot(np.c_[xLoc, yLoc, zLoc].T).T
rxLoc = np.c_[rxLoc[:, 0] + self.prism.xc, rxLoc[:, 1] + self.prism.yc, rxLoc[:, 2] + self.prism.zc]
# Create the linear forward system
self._G = Intrgl_Fwr_Op(self.prism.xn, self.prism.yn, self.prism.zn, rxLoc)
return self._G
def extractFields(self, bvec):
nD = bvec.shape[0]/3
bvec = np.reshape(bvec, (3, nD))
# rot = Utils.mkvc(Utils.dipazm_2_xyz(-self.prism.pinc, -self.prism.pdec))
# bvec = Utils.rotatePointsFromNormals(bvec.T, rot, np.r_[0., 1., 0.],
# np.r_[0, 0, 0]).T
R = Utils.rotationMatrix(self.prism.pinc, self.prism.pdec)
bvec = R.dot(bvec)
if self.uType == 'bx':
u = Utils.mkvc(bvec[0, :])
if self.uType == 'by':
u = Utils.mkvc(bvec[1, :])
if self.uType == 'bz':
u = Utils.mkvc(bvec[2, :])
if self.uType == 'tf':
# Projection matrix
Ptmi = Utils.dipazm_2_xyz(self.Binc, self.Bdec).T
u = Utils.mkvc(Ptmi.dot(bvec))
return u
def Mind(self):
# Define magnetization direction as sum of induced and remanence
mind = Utils.dipazm_2_xyz(self.Binc, self.Bdec)
R = Utils.rotationMatrix(-self.prism.pinc, -self.prism.pdec, normal=False)
Mind = self.susc*self.Higrf*R.dot(mind)
# Mind = self.susc*self.Higrf*Utils.dipazm_2_xyz(self.Binc - self.prism.pinc,
# self.Bdec - self.prism.pdec)
return Mind
def Mrem(self):
mrem = Utils.dipazm_2_xyz(self.rinc, self.rdec)
R = Utils.rotationMatrix(-self.prism.pinc, -self.prism.pdec, normal=False)
Mrem = self.Q*self.susc*self.Higrf * R.dot(mrem)
# Mrem = self.Q*self.susc*self.Higrf * \
# Utils.dipazm_2_xyz(self.rinc - self.prism.pinc, self.rdec - self.prism.pdec)
return Mrem
def animate(ii):
removePlt()
#ii=1
#inc = 45
#dec = 90
if ii < 18:
dec = 90
inc = 0. + ii * 5.
elif ii < 36:
dec = 270.
inc = 90. - (ii - 18) * 5.
elif ii < 54:
dec = 270.
inc = 0. + (ii - 36) * 5.
else:
dec = 90
inc = 90. - (ii - 54) * 5.
ax1.axis('equal')
block_xyz = np.asarray([[-.2, -.2, .2, .2, 0], [
-.25, -.25, -.25, -.25, 0.5
], [-.2, .2, .2, -.2, 0]]) * 10.
block_xyz[1][:] -= 20.
# rot = Utils.mkvc(Utils.dipazm_2_xyz(pinc, pdec))
# xyz = Utils.rotatePointsFromNormals(block_xyz.T, np.r_[0., 1., 0.], rot,
# np.r_[p.xc, p.yc, p.zc])
R = Utils.rotationMatrix(inc, dec)
xyz = R.dot(block_xyz).T
xyz[:, 2] -= depth + dz / 2.
#print xyz
# Face 1
ax1.add_collection3d(
Poly3DCollection([zip(xyz[:4, 0], xyz[:4, 1], xyz[:4, 2])],
facecolors='b'))
ax1.add_collection3d(
Poly3DCollection(
[zip(xyz[[1, 2, 4], 0], xyz[[1, 2, 4], 1], xyz[[1, 2, 4], 2])],
facecolors='b'))
ax1.add_collection3d(
Poly3DCollection(
[zip(xyz[[0, 1, 4], 0], xyz[[0, 1, 4], 1], xyz[[0, 1, 4], 2])],
facecolors='b'))
ax1.add_collection3d(
Poly3DCollection(
[zip(xyz[[2, 3, 4], 0], xyz[[2, 3, 4], 1], xyz[[2, 3, 4], 2])],
facecolors='b'))
ax1.add_collection3d(
Poly3DCollection(
[zip(xyz[[0, 3, 4], 0], xyz[[0, 3, 4], 1], xyz[[0, 3, 4], 2])],
facecolors='b'))
block_xyz[1][:] += 20.
# rot = Utils.mkvc(Utils.dipazm_2_xyz(pinc, pdec))
# xyz = Utils.rotatePointsFromNormals(block_xyz.T, np.r_[0., 1., 0.], rot,
# np.r_[p.xc, p.yc, p.zc])
R = Utils.rotationMatrix(rinc, rdec)
xyz = R.dot(block_xyz).T
xyz[:, 2] -= depth + dz / 2.
#print xyz
# Face 1
ax1.add_collection3d(
Poly3DCollection([zip(xyz[:4, 0], xyz[:4, 1], xyz[:4, 2])],
facecolors='y'))
ax1.add_collection3d(
Poly3DCollection(
[zip(xyz[[1, 2, 4], 0], xyz[[1, 2, 4], 1], xyz[[1, 2, 4], 2])],
facecolors='y'))
ax1.add_collection3d(
Poly3DCollection(
[zip(xyz[[0, 1, 4], 0], xyz[[0, 1, 4], 1], xyz[[0, 1, 4], 2])],
facecolors='y'))
ax1.add_collection3d(
Poly3DCollection(
[zip(xyz[[2, 3, 4], 0], xyz[[2, 3, 4], 1], xyz[[2, 3, 4], 2])],
facecolors='y'))
ax1.add_collection3d(
Poly3DCollection(
[zip(xyz[[0, 3, 4], 0], xyz[[0, 3, 4], 1], xyz[[0, 3, 4], 2])],
facecolors='y'))
MAG.plotObj3D(p,
rx_h,
View_elev,
View_azim,
npts2D,
xylim,
profile="X",
fig=fig,
axs=ax1,
plotSurvey=False)
ax1.w_yaxis.set_ticklabels('')
ax1.w_yaxis.set_label_text('')
ax1.w_zaxis.set_ticklabels('')
ax1.w_zaxis.set_label_text('')
# Create problem
prob = prismFWR.problem()
prob.prism = p
prob.survey = srvy
prob.Bdec, prob.Binc, prob.Bigrf = dec, inc, Bigrf
prob.Q, prob.rinc, prob.rdec = Q, rinc, rdec
prob.uType, prob.mType = 'tf', 'total'
prob.susc = susc
# Compute fields from prism
b_ind, b_rem = prob.fields()
out = b_ind + b_rem
prob.uType, prob.mType = 'bx', 'total'
b_ind, b_rem = prob.fields()
outx = b_ind + b_rem
prob.uType = 'by'
b_ind, b_rem = prob.fields()
outy = b_ind + b_rem
prob.uType = 'bz'
b_ind, b_rem = prob.fields()
outz = b_ind + b_rem
out_amp = np.sqrt(outx**2. + outy**2. + outz**2.)
#out = plogMagSurvey2D(prob, susc, Einc, Edec, Bigrf, x1, y1, x2, y2, comp, irt, Q, rinc, rdec, fig=fig, axs1=ax2, axs2=ax3)
#dat = axs1.contourf(X,Y, np.reshape(out, (X.shape)).T
global im1
im1 = ax1.contourf(X,
Y,
np.reshape(out, (X.shape)).T,
20,
zdir='z',
offset=rx_h + 5.,
clim=clim,
vmin=clim[0],
vmax=clim[1],
cmap='RdBu_r')
ax5 = fig.add_axes(
[pos.x0, pos.y0 + 0.25, pos.height * 0.02, pos.height * 0.4])
cb = plt.colorbar(im1,
cax=ax5,
orientation="vertical",
ax=ax1,
ticks=np.linspace(im1.vmin, im1.vmax, 4),
format="${%.0f}$")
cb.set_label("$B^{TMI}\;(nT)$", size=12)
cb.ax.yaxis.set_ticks_position('left')
cb.ax.yaxis.set_label_position('left')
global im5
im5 = ax1.text(0,
0,
-60,
'$B_0, I: ' + str(inc) + '^\circ, D: ' + str(dec) +
'^\circ$',
horizontalalignment='center')
#%% Run amplitude inversion
H0 = (Bigrf, 90, 0)
actv = np.ones(mesh.nC) == 1
# Create active map to go from reduce space to full
actvMap = Maps.InjectActiveCells(mesh, actv, -100)
nC = len(actv)
# Create a MAGsurvey
rxLoc = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]
rxLoc = PF.BaseMag.RxObs(rxLoc)
srcField = PF.BaseMag.SrcField([rxLoc], param=H0)
survey = PF.BaseMag.LinearSurvey(srcField)
# We can now create a susceptibility model and generate data
# Lets start with a simple block in half-space
# model = np.zeros((mesh.nCx,mesh.nCy,mesh.nCz))
# model[(midx-2):(midx+2),(midy-2):(midy+2),-6:-2] = 0.02
# model = mkvc(model)
# model = model[actv]
# Create active map to go from reduce set to full
actvMap = Maps.InjectActiveCells(mesh, actv, -100)
# Creat reduced identity map
idenMap = Maps.IdentityMap(nP=nC)
# Create the forward model operator
#probinv = PF.Magnetics.MagneticIntegral(mesh, mapping = idenMap, actInd = actv)
probinv = PF.Magnetics.MagneticAmplitude(mesh,
mapping=idenMap,
actInd=actv)
# Pair the survey and problem
survey.pair(probinv)
# We can now generate data
data = out_amp + np.random.randn(
len(out_amp)) # We add some random Gaussian noise (1nT)
wd = np.ones(len(data)) * 1. # Assign flat uncertainties
# Create distance weights from our linera forward operator
# wr = np.sum(probinv.G**2.,axis=0)**0.5
# wr = ( wr/np.max(wr) )
#survey.makeSyntheticData(data, std=0.01)
survey.dobs = data
survey.std = wd
survey.mtrue = model
# Create a regularization
reg = Regularization.Sparse(mesh, indActive=actv, mapping=idenMap)
# reg.cell_weights = wr
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.Wd = 1 / wd
# Add directives to the inversion
opt = Optimization.ProjectedGNCG(maxIter=100,
lower=0.,
upper=1.,
maxIterLS=20,
maxIterCG=10,
tolCG=1e-3)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
betaest = Directives.BetaEstimate_ByEig()
# Here is where the norms are applied
# Use pick a treshold parameter empirically based on the distribution of model
# parameters (run last cell to see the histogram before and after IRLS)
IRLS = Directives.Update_IRLS(norms=([1, 2, 2, 2]),
eps=(2e-3, 2e-3),
f_min_change=1e-3,
minGNiter=3,
coolingRate=3)
update_Jacobi = Directives.Amplitude_Inv_Iter()
inv = Inversion.BaseInversion(invProb,
directiveList=[update_Jacobi, IRLS, betaest])
m0 = np.ones(nC) * 1e-4
pred0 = probinv.fields(m0)
mrec = inv.run(m0)
mamp = (mrec / mrec.max() + 1e-2)**-1.
#%% Run MVI with constraint
H0 = (Bigrf, inc, dec)
actv = np.ones(mesh.nC) == 1
# Create active map to go from reduce space to full
actvMap = Maps.InjectActiveCells(mesh, actv, -100)
nC = len(actv)
# Create a MAGsurvey
rxLoc = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]
rxLoc = PF.BaseMag.RxObs(rxLoc)
srcField = PF.BaseMag.SrcField([rxLoc], param=H0)
survey = PF.BaseMag.LinearSurvey(srcField)
# Create active map to go from reduce set to full
actvMap = Maps.InjectActiveCells(mesh, actv, -100)
# Creat reduced identity map
idenMap = Maps.IdentityMap(nP=3 * nC)
# Create the forward model operator
#probinv = PF.Magnetics.MagneticIntegral(mesh, mapping = idenMap, actInd = actv)
probinv = PF.Magnetics.MagneticVector(mesh, mapping=idenMap, actInd=actv)
# Pair the survey and problem
survey.pair(probinv)
# We can now generate data
data = out + np.random.randn(
len(out)) # We add some random Gaussian noise (1nT)
wd = np.ones(len(data)) * 1. # Assign flat uncertainties
# Create distance weights from our linera forward operator
wr = np.sum(probinv.G**2., axis=0)**0.5
wr = (wr / np.max(wr)) * np.r_[mamp, mamp, mamp]
#survey.makeSyntheticData(data, std=0.01)
survey.dobs = data
survey.std = wd
survey.mtrue = model
# Create a regularization
reg = Regularization.Sparse(mesh,
indActive=actv,
mapping=idenMap,
nModels=3)
reg.cell_weights = wr
reg.mref = np.zeros(3 * nC)
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.Wd = 1 / wd
# Add directives to the inversion
opt = Optimization.ProjectedGNCG(maxIter=100,
lower=-1,
upper=1.,
maxIterLS=20,
maxIterCG=10,
tolCG=1e-3)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
betaest = Directives.BetaEstimate_ByEig()
# Here is where the norms are applied
# Use pick a treshold parameter empirically based on the distribution of model
# parameters (run last cell to see the histogram before and after IRLS)
IRLS = Directives.Update_IRLS(norms=([2, 2, 2, 2]),
eps=(1e-4, 1e-4),
f_min_change=1e-2,
minGNiter=3,
beta_tol=1e-2)
update_Jacobi = Directives.Update_lin_PreCond()
inv = Inversion.BaseInversion(invProb,
directiveList=[update_Jacobi, IRLS, betaest])
mrec = inv.run(np.ones(3 * len(actv)) * 1e-4)
# Here is the recovered susceptibility model
ypanel = midx
zpanel = -4
m_lpx = actvMap * mrec[0:nC]
m_lpy = actvMap * mrec[nC:2 * nC]
m_lpz = actvMap * -mrec[2 * nC:]
m_lpx[m_lpx == -100] = np.nan
m_lpy[m_lpy == -100] = np.nan
m_lpz[m_lpz == -100] = np.nan
amp = np.sqrt(m_lpx**2. + m_lpy**2. + m_lpz**2.)
m_lpx = (m_lpx / amp).reshape(mesh.vnC, order='F')
m_lpy = (m_lpy / amp).reshape(mesh.vnC, order='F')
m_lpz = (m_lpz / amp).reshape(mesh.vnC, order='F')
amp = amp.reshape(mesh.vnC, order='F')
sub = 2
# m_true = actvMap * model
# m_true[m_true==-100] = np.nan
#Plot L2 model
# global im2
xx, zz = mesh.gridCC[:, 0].reshape(
mesh.vnC, order="F"), mesh.gridCC[:, 2].reshape(mesh.vnC, order="F")
yy = mesh.gridCC[:, 1].reshape(mesh.vnC, order="F")
#ptemp = ma.array(ptemp ,mask=np.isnan(ptemp))
global im2
im2 = ax2.contourf(xx[:, :, zpanel].T,
yy[:, :, zpanel].T,
amp[:, :, zpanel].T,
40,
vmin=vmin,
vmax=vmax,
clim=[vmin, vmax])
global im4
im4 = ax2.quiver(mkvc(xx[::sub, ::sub, zpanel].T),
mkvc(yy[::sub, ::sub, zpanel].T),
mkvc(m_lpx[::sub, ::sub, zpanel].T),
mkvc(m_lpy[::sub, ::sub, zpanel].T),
pivot='mid',
units="xy",
scale=0.2,
linewidths=(1, ),
edgecolors=('k'),
headaxislength=0.1,
headwidth=10,
headlength=30)
ax2.set_aspect('equal')
ax2.xaxis.set_visible(False)
ax2.set_xlim(-60, 60)
ax2.set_ylim(-60, 60)
ax2.set_title('Effective Susceptibility')
ax2.set_ylabel('Northing (m)', size=14)
global im3
im3 = ax3.contourf(xx[:, ypanel, :].T,
zz[:, ypanel, :].T,
amp[:, ypanel, :].T,
40,
vmin=vmin,
vmax=vmax,
clim=[vmin, vmax])
global im6
im6 = ax3.quiver(mkvc(xx[::sub, ypanel, ::sub].T),
mkvc(zz[::sub, ypanel, ::sub].T),
mkvc(m_lpx[::sub, ypanel, ::sub].T),
mkvc(m_lpz[::sub, ypanel, ::sub].T),
pivot='mid',
units="xy",
scale=0.2,
linewidths=(1, ),
edgecolors=('k'),
headaxislength=0.1,
headwidth=10,
headlength=30)
ax3.set_aspect('equal')
ax3.set_xlim(-60, 60)
ax3.set_ylim(-60, 0)
ax3.set_title('EW Section')
ax3.set_xlabel('Easting (m)', size=14)
ax3.set_ylabel('Elevation (m)', size=14)
ax4 = fig.add_axes(
[pos.x0 + 0.75, pos.y0 + 0.25, pos.height * 0.02, pos.height * 0.4])
cb = plt.colorbar(im3,
cax=ax4,
orientation="vertical",
ax=ax1,
ticks=np.linspace(im3.vmin, im3.vmax, 4),
format="${%.3f}$")
cb.set_label("$\kappa_{e}$ (SI)", size=12)
def animate(ii):
removePlt()
#ii=1
if ii<18:
dec = 90
inc = 0. + ii*5.
elif ii < 36:
dec = 270.
inc = 90. - (ii-18)*5.
elif ii < 54:
dec = 270.
inc = 0.+ (ii-36)*5.
else:
dec = 90
inc = 90. - (ii-54)*5.
ax1.axis('equal')
block_xyz = np.asarray([[-.2, -.2, .2, .2, 0],
[-.25, -.25, -.25, -.25, 0.5],
[-.2, .2, .2, -.2, 0]])*10.
block_xyz[1][:] -=20.
# rot = Utils.mkvc(Utils.dipazm_2_xyz(pinc, pdec))
# xyz = Utils.rotatePointsFromNormals(block_xyz.T, np.r_[0., 1., 0.], rot,
# np.r_[p.xc, p.yc, p.zc])
R = Utils.rotationMatrix(inc, dec)
xyz = R.dot(block_xyz).T
xyz[:,2] -= depth + dz/2.
#print xyz
# Face 1
ax1.add_collection3d(Poly3DCollection([zip(xyz[:4, 0],
xyz[:4, 1],
xyz[:4, 2])], facecolors='b'))
ax1.add_collection3d(Poly3DCollection([zip(xyz[[1, 2, 4], 0],
xyz[[1, 2, 4], 1],
xyz[[1, 2, 4], 2])], facecolors='b'))
ax1.add_collection3d(Poly3DCollection([zip(xyz[[0, 1, 4], 0],
xyz[[0, 1, 4], 1],
xyz[[0, 1, 4], 2])], facecolors='b'))
ax1.add_collection3d(Poly3DCollection([zip(xyz[[2, 3, 4], 0],
xyz[[2, 3, 4], 1],
xyz[[2, 3, 4], 2])], facecolors='b'))
ax1.add_collection3d(Poly3DCollection([zip(xyz[[0, 3, 4], 0],
xyz[[0, 3, 4], 1],
xyz[[0, 3, 4], 2])], facecolors='b'))
ax1.w_yaxis.set_ticklabels('')
ax1.w_yaxis.set_label_text('')
ax1.w_zaxis.set_ticklabels('')
ax1.w_zaxis.set_label_text('')
# block_xyz[1][:] +=20.
# # rot = Utils.mkvc(Utils.dipazm_2_xyz(pinc, pdec))
#
# # xyz = Utils.rotatePointsFromNormals(block_xyz.T, np.r_[0., 1., 0.], rot,
# # np.r_[p.xc, p.yc, p.zc])
#
# R = Utils.rotationMatrix(rinc, rdec)
#
# xyz = R.dot(block_xyz).T
# xyz[:,2] -= depth + dz/2.
#
# #print xyz
# # Face 1
# ax1.add_collection3d(Poly3DCollection([zip(xyz[:4, 0],
# xyz[:4, 1],
# xyz[:4, 2])], facecolors='y'))
#
# ax1.add_collection3d(Poly3DCollection([zip(xyz[[1, 2, 4], 0],
# xyz[[1, 2, 4], 1],
# xyz[[1, 2, 4], 2])], facecolors='y'))
#
# ax1.add_collection3d(Poly3DCollection([zip(xyz[[0, 1, 4], 0],
# xyz[[0, 1, 4], 1],
# xyz[[0, 1, 4], 2])], facecolors='y'))
#
# ax1.add_collection3d(Poly3DCollection([zip(xyz[[2, 3, 4], 0],
# xyz[[2, 3, 4], 1],
# xyz[[2, 3, 4], 2])], facecolors='y'))
#
# ax1.add_collection3d(Poly3DCollection([zip(xyz[[0, 3, 4], 0],
# xyz[[0, 3, 4], 1],
# xyz[[0, 3, 4], 2])], facecolors='y'))
MAG.plotObj3D(p, rx_h, View_elev, View_azim, npts2D, xylim, profile="X", fig= fig, axs = ax1, plotSurvey=False)
# Create problem
prob = PFlocal.problem()
prob.prism = p
prob.survey = srvy
prob.Bdec, prob.Binc, prob.Bigrf = dec, inc, Bigrf
prob.Q, prob.rinc, prob.rdec = Q, rinc, rdec
prob.uType, prob.mType = comp, 'total'
prob.susc = susc
# Compute fields from prism
b_ind, b_rem = prob.fields()
if irt == 'total':
out = b_ind + b_rem
elif irt == 'induced':
out = b_ind
else:
out = b_rem
#out = plogMagSurvey2D(prob, susc, Einc, Edec, Bigrf, x1, y1, x2, y2, comp, irt, Q, rinc, rdec, fig=fig, axs1=ax2, axs2=ax3)
#dat = axs1.contourf(X,Y, np.reshape(out, (X.shape)).T
global im1
im1 = ax1.contourf(X,Y,np.reshape(out, (X.shape)).T,20,zdir='z',offset=rx_h+5., clim=clim, vmin=clim[0],vmax=clim[1], cmap = 'RdBu_r')
ax5 = fig.add_axes([pos.x0 , pos.y0+0.25, pos.height*0.02, pos.height*0.4])
cb = plt.colorbar(im1,cax=ax5, orientation="vertical", ax = ax1, ticks=np.linspace(im1.vmin,im1.vmax, 4), format="${%.0f}$")
cb.set_label("$B^{TMI}\;(nT)$",size=12)
cb.ax.yaxis.set_ticks_position('left')
cb.ax.yaxis.set_label_position('left')
global im5
im5 = ax1.text(0,0,-60,'$B_0, I: ' + str(inc) + '^\circ, D: ' + str(dec) + '^\circ$', horizontalalignment='center')
H0 = (Bigrf,inc,dec)
actv = np.ones(mesh.nC)==1
# Create active map to go from reduce space to full
actvMap = Maps.InjectActiveCells(mesh, actv, -100)
nC = len(actv)
# Create a MAGsurvey
rxLoc = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]
rxLoc = PF.BaseMag.RxObs(rxLoc)
srcField = PF.BaseMag.SrcField([rxLoc],param = H0)
survey = PF.BaseMag.LinearSurvey(srcField)
# We can now create a susceptibility model and generate data
# Lets start with a simple block in half-space
# model = np.zeros((mesh.nCx,mesh.nCy,mesh.nCz))
# model[(midx-2):(midx+2),(midy-2):(midy+2),-6:-2] = 0.02
# model = mkvc(model)
# model = model[actv]
# Create active map to go from reduce set to full
actvMap = Maps.InjectActiveCells(mesh, actv, -100)
# Creat reduced identity map
idenMap = Maps.IdentityMap(nP = nC)
# Create the forward model operator
probinv = PF.Magnetics.MagneticIntegral(mesh, mapping = idenMap, actInd = actv)
# Pair the survey and problem
survey.pair(probinv)
# Compute linear forward operator and compute some data
# d = probinv.fields(model)
# Plot the model
# m_true = actvMap * model
# m_true[m_true==-100] = np.nan
#plt.figure()
#ax = plt.subplot(212)
#mesh.plotSlice(m_true, ax = ax, normal = 'Y', ind=midy, grid=True, clim = (0., model.max()/3.), pcolorOpts={'cmap':'viridis'})
#plt.title('A simple block model.')
#plt.xlabel('x'); plt.ylabel('z')
#plt.gca().set_aspect('equal', adjustable='box')
# We can now generate data
data = out + np.random.randn(len(out)) # We add some random Gaussian noise (1nT)
wd = np.ones(len(data))*1. # Assign flat uncertainties
# Create distance weights from our linera forward operator
wr = np.sum(probinv.G**2.,axis=0)**0.5
wr = ( wr/np.max(wr) )
#survey.makeSyntheticData(data, std=0.01)
survey.dobs= data
survey.std = wd
survey.mtrue = model
# Create a regularization
reg = Regularization.Sparse(mesh, indActive=actv, mapping=idenMap)
reg.cell_weights = wr
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.Wd = 1/wd
# Add directives to the inversion
opt = Optimization.ProjectedGNCG(maxIter=100 ,lower=0.,upper=1., maxIterLS = 20, maxIterCG= 10, tolCG = 1e-3)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
betaest = Directives.BetaEstimate_ByEig()
# Here is where the norms are applied
# Use pick a treshold parameter empirically based on the distribution of model
# parameters (run last cell to see the histogram before and after IRLS)
IRLS = Directives.Update_IRLS( norms=([2,2,2,2]), eps=(2e-3,2e-3), f_min_change = 1e-3, minGNiter=3,beta_tol=1e-2)
update_Jacobi = Directives.Update_lin_PreCond()
inv = Inversion.BaseInversion(invProb, directiveList=[IRLS,betaest,update_Jacobi])
m0 = np.ones(nC)*1e-4
mrec = inv.run(m0)
# Here is the recovered susceptibility model
ypanel = midx
zpanel = -4
m_l2 = actvMap * reg.l2model
m_l2[m_l2==-100] = np.nan
m_lp = actvMap * mrec
m_lp[m_lp==-100] = np.nan
# m_true = actvMap * model
# m_true[m_true==-100] = np.nan
#Plot L2 model
#global im2
xx, zz = mesh.gridCC[:,0].reshape(mesh.vnC, order="F"), mesh.gridCC[:,2].reshape(mesh.vnC, order="F")
yy = mesh.gridCC[:,1].reshape(mesh.vnC, order="F")
temp = m_lp.reshape(mesh.vnC, order='F')
ptemp = temp[:,:,indz].T
#ptemp = ma.array(ptemp ,mask=np.isnan(ptemp))
global im2
im2 = ax2.contourf(xx[:,:,indz].T,yy[:,:,indz].T,ptemp,20, vmin = vmin, vmax= vmax, clim=[vmin,vmax])
ax2.plot(([mesh.vectorCCx[0],mesh.vectorCCx[-1]]),([mesh.vectorCCy[indy],mesh.vectorCCy[indy]]),color='w')
ax2.set_aspect('equal')
ax2.xaxis.set_visible(False)
ax2.set_xlim(-60,60)
ax2.set_ylim(-60,60)
ax2.set_title('Induced Model')
ax2.set_ylabel('Northing (m)',size=14)
ptemp = temp[:,indy,:].T
global im3
im3 = ax3.contourf(xx[:,indy,:].T,zz[:,indy,:].T,ptemp,20, vmin = vmin, vmax= vmax, clim=[vmin,vmax])
ax3.set_aspect('equal')
ax3.set_xlim(-60,60)
ax3.set_ylim(-60,0)
ax3.set_title('EW Section')
ax3.set_xlabel('Easting (m)',size=14)
ax3.set_ylabel('Elevation (m)',size=14)
ax4 = fig.add_axes([pos.x0 + 0.75, pos.y0+0.25, pos.height*0.02, pos.height*0.4])
cb = plt.colorbar(im3,cax=ax4, orientation="vertical", ax = ax1, ticks=np.linspace(im3.vmin,im3.vmax, 4), format="${%.3f}$")
cb.set_label("Susceptibility (SI)",size=12)
#
# dec = 90.
# inc = 90. - (ii-19)*10.
MAG.plotObj3D(p, rx_h, View_elev, View_azim, npts2D, xylim, profile="X", fig= fig, axs = ax1, plotSurvey=False)
plt.show()
block_xyz = np.asarray([[-.2, -.2, .2, .2, 0],
[-.25, -.25, -.25, -.25, 0.5],
[-.2, .2, .2, -.2, 0]])
# rot = Utils.mkvc(Utils.dipazm_2_xyz(pinc, pdec))
# xyz = Utils.rotatePointsFromNormals(block_xyz.T, np.r_[0., 1., 0.], rot,
# np.r_[p.xc, p.yc, p.zc])
R = Utils.rotationMatrix(inc, dec)
xyz = R.dot(block_xyz).T
#print xyz
# Face 1
ax1.add_collection3d(Poly3DCollection([zip(xyz[:4, 0]-1,
xyz[:4, 1],
xyz[:4, 2]-4)], facecolors='w'))
ax1.add_collection3d(Poly3DCollection([zip(xyz[[1, 2, 4], 0]-1,
xyz[[1, 2, 4], 1],
xyz[[1, 2, 4], 2]-4)], facecolors='b'))
ax1.add_collection3d(Poly3DCollection([zip(xyz[[0, 1, 4], 0]-1,
xyz[[0, 1, 4], 1],
def plotObj3D(p,
rx_h,
elev,
azim,
npts2D,
xylim,
profile=None,
x0=15.,
y0=0.,
fig=None,
axs=None,
plotSurvey=True,
title=None):
# define the survey area
surveyArea = (-xylim, xylim, -xylim, xylim)
shape = (npts2D, npts2D)
xr = np.linspace(-xylim, xylim, shape[0])
yr = np.linspace(-xylim, xylim, shape[1])
X, Y = np.meshgrid(xr, yr)
Z = np.ones(np.shape(X)) * rx_h
rxLoc = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]
depth = p.z0
x1, x2 = p.xn[0] - p.xc, p.xn[1] - p.xc
y1, y2 = p.yn[0] - p.yc, p.yn[1] - p.yc
z1, z2 = p.zn[0] - p.zc, p.zn[1] - p.zc
pinc, pdec = p.pinc, p.pdec
if fig is None:
fig = plt.figure(figsize=(7, 7))
if axs is None:
axs = fig.add_subplot(111, projection='3d')
if title is not None:
axs.set_title(title)
plt.rcParams.update({'font.size': 13})
axs.set_xlim3d(surveyArea[:2])
axs.set_ylim3d(surveyArea[2:])
# axs.set_zlim3d(depth+np.array(surveyArea[:2]))
axs.set_zlim3d(-surveyArea[-1] * 2, 3)
# Create a rectangular prism, rotate and plot
block_xyz = np.asarray([[x1, x1, x2, x2, x1, x1, x2, x2],
[y1, y2, y2, y1, y1, y2, y2, y1],
[z1, z1, z1, z1, z2, z2, z2, z2]])
# rot = Utils.mkvc(Utils.dipazm_2_xyz(pinc, pdec))
# xyz = Utils.rotatePointsFromNormals(block_xyz.T, np.r_[0., 1., 0.], rot,
# np.r_[p.xc, p.yc, p.zc])
R = Utils.rotationMatrix(pinc, pdec)
xyz = R.dot(block_xyz).T
#print xyz
# Face 1
axs.add_collection3d(
Poly3DCollection(
[zip(xyz[:4, 0] + p.xc, xyz[:4, 1] + p.yc, xyz[:4, 2] + p.zc)],
facecolors='w'))
# Face 2
axs.add_collection3d(
Poly3DCollection(
[zip(xyz[4:, 0] + p.xc, xyz[4:, 1] + p.yc, xyz[4:, 2] + p.zc)],
facecolors='w'))
# Face 3
axs.add_collection3d(
Poly3DCollection([
zip(xyz[[0, 1, 5, 4], 0] + p.xc, xyz[[0, 1, 5, 4], 1] + p.yc,
xyz[[0, 1, 5, 4], 2] + p.zc)
],
facecolors='w'))
# Face 4
axs.add_collection3d(
Poly3DCollection([
zip(xyz[[3, 2, 6, 7], 0] + p.xc, xyz[[3, 2, 6, 7], 1] + p.yc,
xyz[[3, 2, 6, 7], 2] + p.zc)
],
facecolors='w'))
#
# # Face 5
# axs.add_collection3d(Poly3DCollection([zip(xyz[[0, 4, 7, 3], 0]+p.xc,
# xyz[[0, 4, 7, 3], 1]+p.yc,
# xyz[[0, 4, 7, 3], 2]+p.zc)], facecolors='w'))
# # Face 6
# axs.add_collection3d(Poly3DCollection([zip(xyz[[1, 5, 6, 2], 0]+p.xc,
# xyz[[1, 5, 6, 2], 1]+p.yc,
# xyz[[1, 5, 6, 2], 2]+p.zc)], facecolors='w'))
plt.show()
axs.set_xlabel('Easting (X; m)')
axs.set_ylabel('Northing (Y; m)')
axs.set_zlabel('Depth (Z; m)')
# axs.invert_zaxis()
# axs.invert_yaxis()
if plotSurvey:
axs.plot(rxLoc[:, 0], rxLoc[:, 1], rxLoc[:, 2], '.g', alpha=0.5)
if profile == "X":
axs.plot(np.r_[surveyArea[:2]], np.r_[0., 0.], np.r_[rx_h, rx_h], 'r-')
elif profile == "Y":
axs.plot(np.r_[0., 0.], np.r_[surveyArea[2:]], np.r_[rx_h, rx_h], 'r-')
elif profile == "XY":
axs.plot(np.r_[0., 0.], np.r_[surveyArea[:2]], np.r_[rx_h, rx_h], 'r-')
axs.plot(np.r_[surveyArea[2:]], np.r_[0., 0.], np.r_[rx_h, rx_h], 'r-')
axs.view_init(elev, azim)
plt.show()
return True