deploy: ce15edf

CNAME

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+gpg.geosci.xyz

_images/EMGeosci_DCR_3DFwr_Sphere_Example.py

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+"""
+        EMGeosci_DCR_3DFwr_Sphere_Example.py
+        Script for the forward modeling of DC resistivity data over a synthetic
+        two-sphere model. The user can define the parameters of the mesh
+        and model, as well as the type of survey ('pdp' | 'dpdp')
+
+        The program outputs a section through the model ("TwoSphere.png") as
+        well as an animation for the current and charge density as a function
+        of source location.
+
+        Dependencies:
+        JSAnimation
+        SimPEG
+
+        Created on Mon December 7th, 2015
+        @author: dominiquef
+
+"""
+
+
+#%%
+from SimPEG import *
+import SimPEG.DCIP as DC
+import pylab as plt
+from pylab import get_current_fig_manager
+import time
+import re
+import scipy.interpolate as interpolation
+from matplotlib import animation
+from JSAnimation import HTMLWriter
+
+# Specify survey type
+stype = 'pdp'
+dtype = 'appc'
+
+# Survey parameters
+a = 20 # Tx-Rx seperation
+b = 10 # Dipole spacing
+n = 1  # Number of Rx per Tx
+
+# Model parameters (background, sphere1, sphere2)
+sig = np.r_[1e-2,1e-1,1e-3]
+
+# Centroid of spheres
+loc = np.c_[[-100.,0.,-100.],[100.,0.,-100.]]
+
+# Radius of spheres
+radi = np.r_[50.,50.]
+
+# Forward solver
+slvr = 'BiCGStab' #'LU'
+
+# Preconditioner
+pcdr = 'Jacobi'#
+
+# Inversion parameter
+pct = 0.01
+flr = 5e-5
+chifact = 100
+ref_mod = 1e-2
+
+# DOI threshold
+cutoff = 0.8
+
+# number of padding cells
+padc = 0
+
+# Plotting param
+xmin, xmax = -200, 200
+zmin, zmax = -200, 0
+vmin = -3.
+vmax = -1.
+depth = 200. # Maximum depth to plot
+dx_in = 5
+
+srvy_end = [(-200.  ,  0.), (200.  ,  0.)]
+#%% SCRIPT STARTS HERE
+# Create mesh
+nx = int(np.abs(srvy_end[0][0] - srvy_end[1][0]) /dx_in)
+ny = int( np.max(radi) /dx_in )
+nz = int( np.abs( np.min(loc[2,:]) - np.max(radi) )  /dx_in )
+
+# Create mesh
+hxind = [(dx_in,13,-1.3), (dx_in, nx), (dx_in,13,1.3)]
+hyind = [(dx_in,13,-1.3), (dx_in, ny), (dx_in,13,1.3)]
+hzind = [(dx_in,13,-1.3),(dx_in, nz)]
+
+mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCN')
+
+# Set background conductivity
+model = np.ones(mesh.nC) * sig[0]
+
+# First anomaly
+ind = Utils.ModelBuilder.getIndicesSphere(loc[:,0],radi[0],mesh.gridCC)
+model[ind] = sig[1]
+
+# Second anomaly
+ind = Utils.ModelBuilder.getIndicesSphere(loc[:,1],radi[1],mesh.gridCC)
+model[ind] = sig[2]
+
+#Set boundary conditions
+mesh.setCellGradBC('neumann')
+
+Div = mesh.faceDiv
+Grad = mesh.cellGrad
+Msig = Utils.sdiag(1./(mesh.aveF2CC.T*(1./model)))
+
+A = Div*Msig*Grad
+
+# Change one corner to deal with nullspace
+A[0,0] = 1
+A = sp.csc_matrix(A)
+
+start_time = time.time()
+
+if re.match(slvr,'BiCGStab'):
+    # Create Jacobi Preconditioner
+    if re.match(pcdr,'Jacobi'):
+        dA = A.diagonal()
+        P = sp.spdiags(1/dA,0,A.shape[0],A.shape[0])
+
+        #LDinv = sp.linalg.splu(LD)
+
+elif re.match(slvr,'LU'):
+    # Factor A matrix
+    Ainv = sp.linalg.splu(A)
+    print("LU DECOMP--- %s seconds ---" % (time.time() - start_time))
+
+#%% Create survey
+# Display top section
+top = int(mesh.nCz)-1
+
+plt.figure()
+ax_prim = plt.subplot(1,1,1)
+dat1 = mesh.plotSlice(model, ind=top, normal='Z', grid=False, pcolorOpts={'alpha':0.5}, ax =ax_prim)
+#==============================================================================
+# plt.xlim([423200,423750])
+# plt.ylim([546350,546650])
+#==============================================================================
+plt.gca().set_aspect('equal', adjustable='box')
+
+plt.show()
+cfm1=get_current_fig_manager().window
+
+# Keep creating sections until returns an empty ginput (press enter on figure)
+#while bool(gin)==True:
+
+# Bring back the plan view figure and pick points
+cfm1.activateWindow()
+plt.sca(ax_prim)
+
+# Takes two points from ginput and create survey
+
+#gin = plt.ginput(2, timeout = 0)
+
+# Add z coordinate to all survey... assume flat
+nz = mesh.vectorNz
+var = np.c_[np.asarray(srvy_end),np.ones(2).T*nz[-1]]
+
+# Snap the endpoints to the grid. Easier to create 2D section.
+indx = Utils.closestPoints(mesh, var )
+endl = np.c_[mesh.gridCC[indx,0],mesh.gridCC[indx,1],np.ones(2).T*nz[-1]]
+
+[survey2D, Tx, Rx] = DC.gen_DCIPsurvey(endl, mesh, stype, a, b, n)
+
+dl_len = np.sqrt( np.sum((endl[0,:] - endl[1,:])**2) )
+dl_x = ( Tx[-1][0,1] - Tx[0][0,0] ) / dl_len
+dl_y = ( Tx[-1][1,1] - Tx[0][1,0]  ) / dl_len
+azm =  np.arctan(dl_y/dl_x)
+
+#%% Create a 2D mesh along axis of Tx end points and keep z-discretization
+dx = np.min( [ np.min(mesh.hx), np.min(mesh.hy), dx_in ])
+ncx = np.ceil(dl_len/dx)+3
+ncz = np.ceil( depth / dx )
+
+padx = dx*np.power(1.4,range(1,padc))
+
+# Creating padding cells
+hx = np.r_[padx[::-1], np.ones(ncx)*dx , padx]
+hz = np.r_[padx[::-1], np.ones(ncz)*dx]
+
+# Create 2D mesh
+x0 = srvy_end[0][0] - np.sum(padx) * np.cos(azm)
+y0 = srvy_end[0][1] - np.sum(padx) * np.sin(azm)
+mesh2d = Mesh.TensorMesh([hx, hz], x0=(x0,mesh.vectorNz[-1] - np.sum(hz) ))
+
+#%% Create array of points for interpolating from 3D to 2D mesh
+xx = x0 + (np.cumsum(mesh2d.hx) - mesh2d.hx/2) * np.cos(azm)
+yy = y0 + (np.cumsum(mesh2d.hx) - mesh2d.hx/2) * np.sin(azm)
+zz = mesh2d.vectorCCy
+
+[XX,ZZ] = np.meshgrid(xx,zz)
+[YY,ZZ] = np.meshgrid(yy,zz)
+
+xyz2d = np.c_[mkvc(XX),mkvc(YY),mkvc(ZZ)]
+
+F = interpolation.NearestNDInterpolator(mesh.gridCC,model)
+m2D = np.reshape(F(xyz2d),[mesh2d.nCx,mesh2d.nCy]).T
+
+#%% Plot a section through the spheres
+fig, axs = plt.subplots(1,1, figsize = (6,4))
+
+plt.tight_layout(pad=0.5)
+
+im1 = axs.pcolormesh(mesh2d.vectorCCx,mesh2d.vectorCCy,np.log10(m2D))
+
+# Add colorbar
+cbar = fig.colorbar(im1, orientation="horizontal", ticks=np.linspace(vmin,vmax, 3), format="$10^{%.1f}$")
+cbar.set_label("Conductivity S/m",size=10)
+
+
+plt.ylim(zz[0],zz[-1]+3*dx)
+plt.xlim(xx[0]-dx,xx[-1]+dx)
+plt.gca().set_aspect('equal', adjustable='box')
+x = np.linspace(xmin,xmax, 5)
+axs.set_xticks(map(int, x))
+axs.set_xticklabels(map(str, map(int, x)),size=12)
+z = np.linspace(zmin,zmax, 5)
+axs.set_yticks(map(int, z))
+axs.set_yticklabels(map(str, map(int, z)),size=12)
+
+circle1=plt.Circle((-98,-98),50,color='w',fill=False, lw=3)
+circle2=plt.Circle((102,-98),50,color='k',fill=False, lw=3)
+axs.add_artist(circle1)
+axs.add_artist(circle2)
+
+for ss in range(survey2D.nSrc):
+    tx = survey2D.srcList[ss].loc[0]
+    axs.scatter(tx[0],tx[2],c='b',s=25)
+
+tx = survey2D.srcList[1].loc[0]
+axs.scatter(tx[0],tx[2],c='r',s=50, marker='v')
+
+fig.savefig('TwoSphere_model.png')
+#%% Forward model data
+fig, axs = plt.subplots(1,1, figsize = (6,4))
+
+plt.tight_layout(pad=0.5)
+
+#pos =  axs.get_position()
+#axs.set_position([pos.x0 , pos.y0+0.2,  pos.width, pos.height])
+
+#im1 = axs.pcolormesh([],[],[], alpha=0.75,extent = (xx[0],xx[-1],yy[-1],yy[0]),interpolation='nearest',vmin=-1e-2, vmax=1e-2)
+#im2 = axs.pcolormesh([],[],[],alpha=0.2,extent = (xx[0],xx[-1],yy[-1],yy[0]),interpolation='nearest',cmap='gray')
+#im1 = axs.pcolormesh(xx,zz,np.zeros((mesh2d.nCy,mesh2d.nCx)), alpha=0.75,vmin=-1e-2, vmax=1e-2)
+im2 = axs.pcolormesh(xx,zz,np.zeros((mesh2d.nCy,mesh2d.nCx)),vmin=-1e-2, vmax=1e-2)
+cbar = plt.colorbar(im2,format="$10^{%.1f}$",fraction=0.04,orientation="horizontal")
+im3 = axs.streamplot(xx, zz, np.zeros((mesh2d.nCy,mesh2d.nCx)), np.zeros((mesh2d.nCy,mesh2d.nCx)),color='k')
+im4 = axs.scatter([],[], c='r', s=200)
+im5 = axs.scatter([],[], c='r', s=200)
+
+circle1=plt.Circle((-98,-98),45,color='w',fill=False, lw=3)
+circle2=plt.Circle((102,-98),45,color='k',fill=False, lw=3)
+axs.add_artist(circle1)
+axs.add_artist(circle2)
+
+problem = DC.ProblemDC_CC(mesh)
+tinf = np.squeeze(Rx[-1][-1,:3]) + np.array([dl_x,dl_y,0])*10*a
+def animate(ii):
+
+
+    removeStream()
+
+
+
+    if not re.match(stype,'pdp'):
+
+        inds = Utils.closestPoints(mesh, np.asarray(Tx[ii]).T )
+        RHS = mesh.getInterpolationMat(np.asarray(Tx[ii]).T, 'CC').T*( [-1,1] / mesh.vol[inds] )
+
+    else:
+
+        # Create an "inifinity" pole
+        tx =  np.squeeze(Tx[ii][:,0:1])
+        #tinf = tx + np.array([dl_x,dl_y,0])*dl_len
+        inds = Utils.closestPoints(mesh, np.c_[tx,tinf].T)
+        RHS = mesh.getInterpolationMat(np.c_[tx,tinf].T, 'CC').T*( [-1,1] / mesh.vol[inds] )
+
+
+    if re.match(slvr,'BiCGStab'):
+
+        if re.match(pcdr,'Jacobi'):
+            dA = A.diagonal()
+            P = sp.spdiags(1/dA,0,A.shape[0],A.shape[0])
+
+            # Iterative Solve
+            Ainvb = sp.linalg.bicgstab(P*A,P*RHS, tol=1e-5)
+
+
+        phi = mkvc(Ainvb[0])
+
+    elif re.match(slvr,'LU'):
+        #Direct Solve
+        phi = Ainv.solve(RHS)
+
+
+    j = -Msig*Grad*phi
+    j_CC = mesh.aveF2CCV*j
+
+    # Compute charge density solving div*grad*phi
+    Q = -mesh.faceDiv*mesh.cellGrad*phi
+
+    jx_CC = j_CC[0:mesh.nC]
+    jy_CC = j_CC[(2.*mesh.nC):]
+
+    #%% Grab only the core for presentation
+    F = interpolation.NearestNDInterpolator(mesh.gridCC,jx_CC)
+    jx_CC_sub =  np.reshape(F(xyz2d),[mesh2d.nCx,mesh2d.nCy]).T
+
+    F = interpolation.NearestNDInterpolator(mesh.gridCC,jy_CC)
+    jy_CC_sub =  np.reshape(F(xyz2d),[mesh2d.nCx,mesh2d.nCy]).T
+
+    F = interpolation.NearestNDInterpolator(mesh.gridCC,Q)
+    Q_sub = np.reshape(F(xyz2d),[mesh2d.nCx,mesh2d.nCy]).T
+
+    J_rho = np.sqrt(jx_CC_sub**2 + jy_CC_sub**2)
+    lw = np.log10(J_rho/J_rho.min())
+
+
+    global im2, cbar
+    #axs.pcolormesh(mesh2d.vectorCCx,mesh2d.vectorCCy,np.log10(m2D), alpha=0.25, cmap = 'gray')
+    im2 = axs.pcolormesh(mesh2d.vectorCCx,mesh2d.vectorCCy,Q_sub, alpha=0.75, vmin=-1e-4,vmax = 1e-4, cmap = 'RdBu')
+
+    # Add colorbar
+    cbar = fig.colorbar(im2, orientation="horizontal",ticks=np.linspace(-1,1, 3))
+    cbar.set_label("Normalized Charge Density",size=10)
+
+
+    global im3
+    im3 = axs.streamplot(xx, zz, jx_CC_sub/J_rho.max(), jy_CC_sub/J_rho.max(),color='k',density=0.5, linewidth = lw)
+
+    global im4
+    im4 = axs.scatter(Tx[ii][0,0],Tx[ii][2,0], c='b', s=100, marker='v' )
+
+    global im5
+    im5 = axs.scatter(Tx[ii][0,1],Tx[ii][2,1], c='r', s=100, marker='v' )
+
+    plt.ylim(zz[0],zz[-1]+3*dx)
+    plt.xlim(xx[0]-dx,xx[-1]+dx)
+    plt.gca().set_aspect('equal', adjustable='box')
+    x = np.linspace(xmin,xmax, 5)
+    axs.set_xticks(map(int, x))
+    axs.set_xticklabels(map(str, map(int, x)),size=12)
+    z = np.linspace(zmin,zmax, 5)
+    axs.set_yticks(map(int, z))
+    axs.set_yticklabels(map(str, map(int, z)),size=12)
+    #axs.set_title("Conductivity (S/m) and Current")
+    #plt.show()
+    #im1.set_array(Q_sub)
+    #im2.set_array(np.log10(model_sub.reshape(mesh2d.nCy,mesh2d.nCx)))
+    #im2.set_array(mesh2d.vectorCCx, mesh2d.vectorCCy,jx_CC_sub.T,jy_CC_sub.T)
+
+    #return [im1] + [im2]
+#%% Create widget
+def removeStream():
+    #global im1
+    #im1.remove()
+
+    global im2, cbar
+    im2.remove()
+    cbar.remove()
+    global im3
+    im3.lines.remove()
+    axs.patches = []
+
+    global im4
+    im4.remove()
+
+    global im5
+    im5.remove()
+#def viewInv(msh,iteration):
+
+
+
+#, linewidth=lw.T
+#%%
+#interact(viewInv,msh = mesh2d, iteration = IntSlider(min=0, max=len(txii)-1 ,step=1, value=0))
+# set embed_frames=True to embed base64-encoded frames directly in the HTML
+anim = animation.FuncAnimation(fig, animate,
+                               frames=survey2D.nSrc, interval=500)
+
+anim.save('TwoSphere_Current_Anim.html', writer=HTMLWriter(embed_frames=True,fps=1))