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