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Merge branch 'dev' into ex/mt1d
# Conflicts: # SimPEG/Examples/MT_1D_analytic_nlayer_Earth.py # SimPEG/Examples/__init__.py # SimPEG/Examples/sphereElectrostatic_example.py # SimPEG/Optimization.py # docs/examples/DC_PseudoSection_Simulation.rst # docs/examples/Inversion_IRLS.rst # docs/examples/MT_1D_analytic_nlayer_Earth.rst
This commit is contained in:
Lindsey Heagy
@@ -2,19 +2,27 @@ from SimPEG import Mesh, Utils, np, sp
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import SimPEG.DCIP as DC
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import time
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def run(loc=None, sig=None, radi=None, param=None, stype='dpdp', plotIt=True):
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def run(loc=None, sig=None, radi=None, param=None, stype='dpdp', dtype='appc', plotIt=True):
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"""
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DC Forward Simulation
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=====================
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Forward model conductive spheres in a half-space and plot a pseudo-section
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Forward model two conductive spheres in a half-space and plot a
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pseudo-section. Assumes an infinite line source and measures along the
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center of the spheres.
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Created by @fourndo on Mon Feb 01 19:28:06 2016
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INPUT:
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loc = Location of spheres [[x1,y1,z1],[x2,y2,z2]]
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radi = Radius of spheres [r1,r2]
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param = Conductivity of background and two spheres [m0,m1,m2]
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stype = survey type "pdp" (pole dipole) or "dpdp" (dipole dipole)
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dtype = Data type "appr" (app res) | "appc" (app cond) | "volt" (potential)
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Created by @fourndo
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"""
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assert stype in ['pdp', 'dpdp'], "Source type (stype) must be pdp or dpdp (pole dipole or dipole dipole)"
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assert dtype in ['appr', 'appc', 'volt'], "Data type (dtype) must be appr (app res) or appc (app cond) or volt (potential)"
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if loc is None:
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loc = np.c_[[-50.,0.,-50.],[50.,0.,-50.]]
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@@ -27,7 +35,6 @@ def run(loc=None, sig=None, radi=None, param=None, stype='dpdp', plotIt=True):
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# First we need to create a mesh and a model.
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# This is our mesh
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dx = 5.
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@@ -52,14 +59,10 @@ def run(loc=None, sig=None, radi=None, param=None, stype='dpdp', plotIt=True):
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# Get index of the center
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indy = int(mesh.nCy/2)
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# Plot the model for reference
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# Define core mesh extent
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xlim = 200
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zlim = 125
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# Specify the survey type: "pdp" | "dpdp"
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zlim = 100
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# Then specify the end points of the survey. Let's keep it simple for now and survey above the anomalies, top of the mesh
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ends = [(-175,0),(175,0)]
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@@ -77,12 +80,13 @@ def run(loc=None, sig=None, radi=None, param=None, stype='dpdp', plotIt=True):
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dl_len = np.sqrt( np.sum((locs[0,:] - locs[1,:])**2) )
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dl_x = ( Tx[-1][0,1] - Tx[0][0,0] ) / dl_len
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dl_y = ( Tx[-1][1,1] - Tx[0][1,0] ) / dl_len
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azm = np.arctan(dl_y/dl_x)
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#azm = np.arctan(dl_y/dl_x)
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#Set boundary conditions
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mesh.setCellGradBC('neumann')
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# Define the differential operators needed for the DC problem
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# Define the linear system needed for the DC problem. We assume an infitite
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# line source for simplicity.
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Div = mesh.faceDiv
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Grad = mesh.cellGrad
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Msig = Utils.sdiag(1./(mesh.aveF2CC.T*(1./model)))
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@@ -145,16 +149,23 @@ def run(loc=None, sig=None, radi=None, param=None, stype='dpdp', plotIt=True):
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print 'Forward completed'
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# Let's just convert the 3D format into 2D (distance along line) and plot
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# [Tx2d, Rx2d] = DC.convertObs_DC3D_to_2D(survey, np.ones(survey.nSrc))
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survey2D = DC.convertObs_DC3D_to_2D(survey, np.ones(survey.nSrc))
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survey2D = DC.convertObs_DC3D_to_2D(survey, np.ones(survey.nSrc) , 'Xloc')
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survey2D.dobs =np.hstack(data)
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# Here is an example for the first tx-rx array
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if plotIt:
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import matplotlib.pyplot as plt
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fig = plt.figure()
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fig = plt.figure(figsize=(7,7))
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ax = plt.subplot(2,1,1, aspect='equal')
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mesh.plotSlice(np.log10(model), ax =ax, normal = 'Y', ind = indy,grid=True)
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ax.set_title('E-W section at '+str(mesh.vectorCCy[indy])+' m')
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# Plot the location of the spheres for reference
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circle1=plt.Circle((loc[0,0],loc[2,0]),radi[0],color='w',fill=False, lw=3)
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circle2=plt.Circle((loc[0,1],loc[2,1]),radi[1],color='k',fill=False, lw=3)
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ax.add_artist(circle1)
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ax.add_artist(circle2)
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dat = mesh.plotSlice(np.log10(model), ax =ax, normal = 'Y',
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ind = indy,grid=True, clim = np.log10([sig.min(),sig.max()]))
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ax.set_title('3-D model')
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plt.gca().set_aspect('equal', adjustable='box')
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plt.scatter(Tx[0][0,:],Tx[0][2,:],s=40,c='g', marker='v')
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@@ -163,22 +174,34 @@ def run(loc=None, sig=None, radi=None, param=None, stype='dpdp', plotIt=True):
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plt.ylim([-zlim,mesh.vectorNz[-1]+dx])
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ax = plt.subplot(2,1,2, aspect='equal')
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pos = ax.get_position()
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ax.set_position([pos.x0 , pos.y0 + 0.025 , pos.width, pos.height])
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pos = ax.get_position()
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cbarax = fig.add_axes([pos.x0 , pos.y0 + 0.025 , pos.width, pos.height * 0.04]) ## the parameters are the specified position you set
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cb = fig.colorbar(dat[0],cax=cbarax, orientation="horizontal",
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ax = ax, ticks=np.linspace(np.log10(sig.min()),
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np.log10(sig.max()), 3), format="$10^{%.1f}$")
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cb.set_label("Conductivity (S/m)",size=12)
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cb.ax.tick_params(labelsize=12)
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# Second plot for the predicted apparent resistivity data
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ax2 = plt.subplot(2,1,2, aspect='equal')
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# Plot the location of the spheres for reference
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circle1=plt.Circle((loc[0,0]-Tx[0][0,0],loc[2,0]),radi[0],color='w',fill=False, lw=3)
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circle2=plt.Circle((loc[0,1]-Tx[0][0,0],loc[2,1]),radi[1],color='k',fill=False, lw=3)
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ax.add_artist(circle1)
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ax.add_artist(circle2)
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circle1=plt.Circle((loc[0,0],loc[2,0]),radi[0],color='w',fill=False, lw=3)
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circle2=plt.Circle((loc[0,1],loc[2,1]),radi[1],color='k',fill=False, lw=3)
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ax2.add_artist(circle1)
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ax2.add_artist(circle2)
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# Add the speudo section
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DC.plot_pseudoSection(survey2D,ax,stype)
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dat = DC.plot_pseudoSection(survey2D,ax2,stype=stype, dtype = dtype)
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# plt.scatter(Tx2d[0][:],Tx[0][2,:],s=40,c='g', marker='v')
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# plt.scatter(Rx2d[0][:],Rx[0][:,2::3],s=40,c='y')
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# plt.plot(np.r_[Tx2d[0][0],Rx2d[-1][-1,-1]],np.ones(2)*mesh.vectorNz[-1], color='k')
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plt.ylim([-zlim,mesh.vectorNz[-1]+dx])
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ax2.set_title('Apparent Conductivity data')
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plt.ylim([-zlim,mesh.vectorNz[-1]+dx])
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plt.show()
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return fig, ax
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@@ -0,0 +1,132 @@
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from SimPEG import *
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def run(N=200, plotIt=True):
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"""
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Inversion: Linear Problem
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=========================
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Here we go over the basics of creating a linear problem and inversion.
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"""
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np.random.seed(1)
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std_noise = 1e-2
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mesh = Mesh.TensorMesh([N])
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m0 = np.ones(mesh.nC) * 1e-4
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nk = 10
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jk = np.linspace(1.,nk,nk)
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p = -2.
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q = 1.
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g = lambda k: np.exp(p*jk[k]*mesh.vectorCCx)*np.cos(np.pi*q*jk[k]*mesh.vectorCCx)
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G = np.empty((nk, mesh.nC))
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for i in range(nk):
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G[i,:] = g(i)
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mtrue = np.zeros(mesh.nC)
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mtrue[mesh.vectorCCx > 0.3] = 1.
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mtrue[mesh.vectorCCx > 0.45] = -0.5
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mtrue[mesh.vectorCCx > 0.6] = 0
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prob = Problem.LinearProblem(mesh, G)
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survey = Survey.LinearSurvey()
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survey.pair(prob)
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survey.dobs = prob.fields(mtrue) + std_noise * np.random.randn(nk)
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#survey.makeSyntheticData(mtrue, std=std_noise)
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wd = np.ones(nk) * std_noise
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#print survey.std[0]
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#M = prob.mesh
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# Distance weighting
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wr = np.sum(prob.G**2.,axis=0)**0.5
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wr = ( wr/np.max(wr) )
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reg = Regularization.Simple(mesh)
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reg.wght = wr
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dmis = DataMisfit.l2_DataMisfit(survey)
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dmis.Wd = 1./wd
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opt = Optimization.ProjectedGNCG(maxIter=30,lower=-2.,upper=2., maxIterCG= 20, tolCG = 1e-4)
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invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
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invProb.curModel = m0
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beta = Directives.BetaSchedule(coolingFactor=2, coolingRate=1)
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target = Directives.TargetMisfit()
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betaest = Directives.BetaEstimate_ByEig()
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inv = Inversion.BaseInversion(invProb, directiveList=[beta, betaest, target])
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mrec = inv.run(m0)
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ml2 = mrec
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print "Final misfit:" + str(invProb.dmisfit.eval(mrec))
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# Switch regularization to sparse
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phim = invProb.phi_m_last
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phid = invProb.phi_d
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reg = Regularization.Sparse(mesh)
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#==============================================================================
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# fig, axes = plt.subplots(1,2,figsize=(12*1.2,4*1.2))
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# dmdx = reg.mesh.cellDiffxStencil * mrec
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# plt.plot(np.sort(dmdx))
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#==============================================================================
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#reg.recModel = mrec
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reg.wght = np.ones(mesh.nC)
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reg.mref = np.zeros(mesh.nC)
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reg.eps_p = 5e-2
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reg.eps_q = 1e-2
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reg.norms = [0., 0., 2., 2.]
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reg.wght = wr
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opt = Optimization.ProjectedGNCG(maxIter=10 ,lower=-2.,upper=2., maxIterLS = 20, maxIterCG= 20, tolCG = 1e-3)
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invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta = invProb.beta*2.)
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beta = Directives.BetaSchedule(coolingFactor=1, coolingRate=1)
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#betaest = Directives.BetaEstimate_ByEig()
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target = Directives.TargetMisfit()
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IRLS =Directives.Update_IRLS( phi_m_last = phim, phi_d_last = phid )
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inv = Inversion.BaseInversion(invProb, directiveList=[beta,IRLS])
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m0 = mrec
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# Run inversion
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mrec = inv.run(m0)
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print "Final misfit:" + str(invProb.dmisfit.eval(mrec))
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if plotIt:
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import matplotlib.pyplot as plt
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fig, axes = plt.subplots(1,2,figsize=(12*1.2,4*1.2))
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for i in range(prob.G.shape[0]):
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axes[0].plot(prob.G[i,:])
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axes[0].set_title('Columns of matrix G')
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axes[1].plot(mesh.vectorCCx, mtrue, 'b-')
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axes[1].plot(mesh.vectorCCx, ml2, 'r-')
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#axes[1].legend(('True Model', 'Recovered Model'))
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axes[1].set_ylim(-1.0,1.25)
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axes[1].plot(mesh.vectorCCx, mrec, 'k-',lw = 2)
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axes[1].legend(('True Model', 'Smooth l2-l2',
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'Sparse lp:' + str(reg.norms[0]) + ', lqx:' + str(reg.norms[1]) ), fontsize = 12)
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plt.show()
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return prob, survey, mesh, mrec
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if __name__ == '__main__':
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run()
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@@ -100,7 +100,7 @@ def run(plotIt=True):
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# Regularization - with a regularization mesh
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regMesh = simpeg.Mesh.TensorMesh([m1d.hx[problem.mapping.sigmaMap.maps[-1].indActive]],m1d.x0)
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reg = simpeg.Regularization.Tikhonov(regMesh)
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reg.smoothModel = True
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reg.mrefInSmooth = True
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reg.alpha_s = 1e-7
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reg.alpha_x = 1.
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# Inversion problem
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@@ -399,7 +399,7 @@ def PlotAppRes3LayersInteract(h1,h2,sigl1,sigl2,sigl3,mul1,mul2,mul3,epsl1,epsl2
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PlotAppRes(frangn,thick3,sig3,chg3_0,taux3,c3,mu3,eps3,3,F_Envelope,PlotEnvelope)
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def run(n,plotIt=True):
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def run(plotIt=True, n=3):
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# something to make a plot
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F = frange(-5.,5.,20)
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@@ -420,7 +420,7 @@ def run(n,plotIt=True):
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return Res, Phase
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if __name__ == '__main__':
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run(3)
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run(plotIt=True)
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@@ -9,6 +9,7 @@ import EM_Schenkel_Morrison_Casing
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import EM_TDEM_1D_Inversion
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import FLOW_Richards_1D_Celia1990
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import Forward_BasicDirectCurrent
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import Inversion_IRLS
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import Inversion_Linear
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import Mesh_Basic_PlotImage
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import Mesh_Basic_Types
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@@ -22,7 +23,7 @@ import MT_1D_ForwardAndInversion
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import MT_3D_Foward
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import sphereElectrostatic_example
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__examples__ = ["DC_Analytic_Dipole", "DC_Forward_PseudoSection", "EM_FDEM_1D_Inversion", "EM_FDEM_Analytic_MagDipoleWholespace", "EM_Schenkel_Morrison_Casing", "EM_TDEM_1D_Inversion", "FLOW_Richards_1D_Celia1990", "Forward_BasicDirectCurrent", "Inversion_Linear", "Mesh_Basic_PlotImage", "Mesh_Basic_Types", "Mesh_Operators_CahnHilliard", "Mesh_QuadTree_Creation", "Mesh_QuadTree_FaceDiv", "Mesh_QuadTree_HangingNodes", "Mesh_Tensor_Creation", "MT_1D_analytic_nlayer_Earth", "MT_1D_ForwardAndInversion", "MT_3D_Foward", "sphereElectrostatic_example"]
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__examples__ = ["DC_Analytic_Dipole", "DC_Forward_PseudoSection", "EM_FDEM_1D_Inversion", "EM_FDEM_Analytic_MagDipoleWholespace", "EM_Schenkel_Morrison_Casing", "EM_TDEM_1D_Inversion", "FLOW_Richards_1D_Celia1990", "Forward_BasicDirectCurrent", "Inversion_IRLS", "Inversion_Linear", "Mesh_Basic_PlotImage", "Mesh_Basic_Types", "Mesh_Operators_CahnHilliard", "Mesh_QuadTree_Creation", "Mesh_QuadTree_FaceDiv", "Mesh_QuadTree_HangingNodes", "Mesh_Tensor_Creation", "MT_1D_analytic_nlayer_Earth", "MT_1D_ForwardAndInversion", "MT_3D_Foward", "sphereElectrostatic_example"]
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##### AUTOIMPORTS #####
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