def test_nC_residual(self): # x-direction cs, ncx, ncz, npad = 1., 10., 10., 20 hx = [(cs, ncx), (cs, npad, 1.3)] # z direction npad = 12 temp = np.logspace(np.log10(1.), np.log10(12.), 19) temp_pad = temp[-1] * 1.3**np.arange(npad) hz = np.r_[temp_pad[::-1], temp[::-1], temp, temp_pad] mesh = Mesh.CylMesh([hx, 1, hz], '00C') active = mesh.vectorCCz < 0. active = mesh.vectorCCz < 0. actMap = Maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz) mapping = Maps.ExpMap(mesh) * Maps.SurjectVertical1D(mesh) * actMap regMesh = Mesh.TensorMesh([mesh.hz[mapping.maps[-1].indActive]]) reg = Regularization.Simple(regMesh) self.assertTrue(reg._nC_residual == regMesh.nC) self.assertTrue( all([fct._nC_residual == regMesh.nC for fct in reg.objfcts]))
def setUp(self): cs = 10 nc = 20 npad = 10 mesh = Mesh.CylMesh([[(cs, nc), (cs, npad, 1.3)], np.r_[2 * np.pi], [(cs, npad, -1.3), (cs, nc), (cs, npad, 1.3)]]) mesh.x0 = np.r_[0., 0., -mesh.hz[:npad + nc].sum()] # receivers rx_x = np.linspace(10, 200, 20) rx_z = np.r_[-5] rx_locs = Utils.ndgrid([rx_x, np.r_[0], rx_z]) rx_list = [DC.Rx.BaseRx(rx_locs, 'ex')] # sources src_a = np.r_[0., 0., -5.] src_b = np.r_[55., 0., -5.] src_list = [DC.Src.Dipole(rx_list, locA=src_a, locB=src_b)] self.mesh = mesh self.sigma_map = Maps.ExpMap(mesh) * Maps.InjectActiveCells( mesh, mesh.gridCC[:, 2] <= 0, np.log(1e-8)) self.prob = DC.Problem3D_CC(mesh, sigmaMap=self.sigma_map, Solver=Pardiso, bc_type="Dirichlet") self.survey = DC.Survey(src_list) self.prob.pair(self.survey)
def test_getInterpMatCartMesh_Faces(self): Mr = Mesh.TensorMesh([100, 100, 2], x0='CC0') Mc = Mesh.CylMesh([np.ones(10) / 5, 1, 10], x0='0C0', cartesianOrigin=[-0.2, -0.2, 0]) Pf = Mc.getInterpolationMatCartMesh(Mr, 'F') mf = np.ones(Mc.nF) frect = Pf * mf fxcc = Mr.aveFx2CC * Mr.r(frect, 'F', 'Fx') fycc = Mr.aveFy2CC * Mr.r(frect, 'F', 'Fy') fzcc = Mr.r(frect, 'F', 'Fz') indX = Utils.closestPoints(Mr, [0.45, -0.2, 0.5]) indY = Utils.closestPoints(Mr, [-0.2, 0.45, 0.5]) TOL = 1e-2 assert np.abs(float(fxcc[indX]) - 1) < TOL assert np.abs(float(fxcc[indY]) - 0) < TOL assert np.abs(float(fycc[indX]) - 0) < TOL assert np.abs(float(fycc[indY]) - 1) < TOL assert np.abs((fzcc - 1).sum()) < TOL mag = (fxcc**2 + fycc**2)**0.5 dist = ((Mr.gridCC[:, 0] + 0.2)**2 + (Mr.gridCC[:, 1] + 0.2)**2)**0.5 assert np.abs(mag[dist > 0.1].max() - 1) < TOL assert np.abs(mag[dist > 0.1].min() - 1) < TOL
def test_getInterpMatCartMesh_Faces2Edges(self): Mr = Mesh.TensorMesh([100, 100, 2], x0='CC0') Mc = Mesh.CylMesh([np.ones(10) / 5, 1, 10], x0='0C0', cartesianOrigin=[-0.2, -0.2, 0]) Pf2e = Mc.getInterpolationMatCartMesh(Mr, 'F', locTypeTo='E') mf = np.ones(Mc.nF) ecart = Pf2e * mf excc = Mr.aveEx2CC * Mr.r(ecart, 'E', 'Ex') eycc = Mr.aveEy2CC * Mr.r(ecart, 'E', 'Ey') ezcc = Mr.r(ecart, 'E', 'Ez') indX = Utils.closestPoints(Mr, [0.45, -0.2, 0.5]) indY = Utils.closestPoints(Mr, [-0.2, 0.45, 0.5]) TOL = 1e-2 assert np.abs(float(excc[indX]) - 1) < TOL assert np.abs(float(excc[indY]) - 0) < TOL assert np.abs(float(eycc[indX]) - 0) < TOL assert np.abs(float(eycc[indY]) - 1) < TOL assert np.abs((ezcc - 1).sum()) < TOL mag = (excc**2 + eycc**2)**0.5 dist = ((Mr.gridCC[:, 0] + 0.2)**2 + (Mr.gridCC[:, 1] + 0.2)**2)**0.5 assert np.abs(mag[dist > 0.1].max() - 1) < TOL assert np.abs(mag[dist > 0.1].min() - 1) < TOL
def setUp(self): cs = 5. ncx = 20 ncy = 6 npad = 20 hx = [(cs, ncx), (cs, npad, 1.3)] hy = [(cs, npad, -1.3), (cs, ncy), (cs, npad, 1.3)] mesh = Mesh.CylMesh([hx, 1, hy], '00C') active = mesh.vectorCCz < 0. activeMap = Maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz) mapping = Maps.ExpMap(mesh) * Maps.SurjectVertical1D(mesh) * activeMap rxOffset = 40. rx = EM.TDEM.RxTDEM(np.array([[rxOffset, 0., 0.]]), np.logspace(-4, -3, 20), 'bz') src = EM.TDEM.SrcTDEM_VMD_MVP([rx], loc=np.array([0., 0., 0.])) survey = EM.TDEM.SurveyTDEM([src]) self.prb = EM.TDEM.ProblemTDEM_b(mesh, mapping=mapping) # self.prb.timeSteps = [1e-5] self.prb.timeSteps = [(1e-05, 10), (5e-05, 10), (2.5e-4, 10)] # self.prb.timeSteps = [(1e-05, 100)] try: from pymatsolver import MumpsSolver self.prb.Solver = MumpsSolver except ImportError, e: self.prb.Solver = SolverLU
def test_getInterpMatCartMesh_Edges2Faces(self): Mr = Mesh.TensorMesh([100, 100, 2], x0='CC0') Mc = Mesh.CylMesh([np.ones(10) / 5, 1, 10], x0='0C0', cartesianOrigin=[-0.2, -0.2, 0]) Pe2f = Mc.getInterpolationMatCartMesh(Mr, 'E', locTypeTo='F') me = np.ones(Mc.nE) frect = Pe2f * me excc = Mr.aveFx2CC * Mr.r(frect, 'F', 'Fx') eycc = Mr.aveFy2CC * Mr.r(frect, 'F', 'Fy') ezcc = Mr.r(frect, 'F', 'Fz') indX = Utils.closestPoints(Mr, [0.45, -0.2, 0.5]) indY = Utils.closestPoints(Mr, [-0.2, 0.45, 0.5]) TOL = 1e-2 assert np.abs(float(excc[indX]) - 0) < TOL assert np.abs(float(excc[indY]) + 1) < TOL assert np.abs(float(eycc[indX]) - 1) < TOL assert np.abs(float(eycc[indY]) - 0) < TOL assert np.abs(ezcc.sum()) < TOL mag = (excc**2 + eycc**2)**0.5 dist = ((Mr.gridCC[:, 0] + 0.2)**2 + (Mr.gridCC[:, 1] + 0.2)**2)**0.5 assert np.abs(mag[dist > 0.1].max() - 1) < TOL assert np.abs(mag[dist > 0.1].min() - 1) < TOL
def setUp(self): n = 2 self.mesh = Mesh.CylMesh([n, 1, n]) self.face_vec = np.random.rand(self.mesh.nF) self.edge_vec = np.random.rand(self.mesh.nE) # make up a smooth function self.x0 = 2 * self.mesh.gridCC[:, 0]**2 + self.mesh.gridCC[:, 2]**4
def run(plotIt=True): """ EM: FDEM: 1D: Inversion ======================= Here we will create and run a FDEM 1D inversion. """ cs, ncx, ncz, npad = 5., 25, 15, 15 hx = [(cs, ncx), (cs, npad, 1.3)] hz = [(cs, npad, -1.3), (cs, ncz), (cs, npad, 1.3)] mesh = Mesh.CylMesh([hx, 1, hz], '00C') layerz = -100. active = mesh.vectorCCz < 0. layer = (mesh.vectorCCz < 0.) & (mesh.vectorCCz >= layerz) actMap = Maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz) mapping = Maps.ExpMap(mesh) * Maps.SurjectVertical1D(mesh) * actMap sig_half = 2e-2 sig_air = 1e-8 sig_layer = 1e-2 sigma = np.ones(mesh.nCz) * sig_air sigma[active] = sig_half sigma[layer] = sig_layer mtrue = np.log(sigma[active]) if plotIt: import matplotlib.pyplot as plt fig, ax = plt.subplots(1, 1, figsize=(3, 6)) plt.semilogx(sigma[active], mesh.vectorCCz[active]) ax.set_ylim(-500, 0) ax.set_xlim(1e-3, 1e-1) ax.set_xlabel('Conductivity (S/m)', fontsize=14) ax.set_ylabel('Depth (m)', fontsize=14) ax.grid(color='k', alpha=0.5, linestyle='dashed', linewidth=0.5) rxOffset = 10. bzi = EM.FDEM.Rx.Point_b(np.array([[rxOffset, 0., 1e-3]]), orientation='z', component='imag') freqs = np.logspace(1, 3, 10) srcLoc = np.array([0., 0., 10.]) srcList = [ EM.FDEM.Src.MagDipole([bzi], freq, srcLoc, orientation='Z') for freq in freqs ] survey = EM.FDEM.Survey(srcList) prb = EM.FDEM.Problem3D_b(mesh, mapping=mapping) try: from pymatsolver import MumpsSolver prb.Solver = MumpsSolver except ImportError, e: prb.Solver = SolverLU
def genMesh(self, h=0.0, cs=3.0, ncx=15, ncz=30, npad=20): """ Generate cylindrically symmetric mesh """ # TODO: Make it adaptive due to z location hx = [(cs, ncx), (cs, npad, 1.3)] hz = [(cs, npad, -1.3), (cs, ncz), (cs, npad, 1.3)] self.mesh = Mesh.CylMesh([hx, 1, hz], "00C")
def test_simpleInter(self): M = Mesh.CylMesh([4, 1, 1]) locs = np.r_[0, 0, 0.5] fx = np.array([[1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]) self.assertTrue( np.all(fx == M.getInterpolationMat(locs, 'Fx').todense())) fz = np.array([[0., 0., 0., 0., 0.5, 0., 0., 0., 0.5, 0., 0., 0.]]) self.assertTrue( np.all(fz == M.getInterpolationMat(locs, 'Fz').todense()))
def halfSpaceProblemAnaVMDDiff(showIt=False, waveformType="STEPOFF"): cs, ncx, ncz, npad = 20., 25, 25, 15 hx = [(cs, ncx), (cs, npad, 1.3)] hz = [(cs, npad, -1.3), (cs, ncz), (cs, npad, 1.3)] mesh = Mesh.CylMesh([hx, 1, hz], '00C') sighalf = 1e-2 siginf = np.ones(mesh.nC) * 1e-8 siginf[mesh.gridCC[:, -1] < 0.] = sighalf eta = np.ones(mesh.nC) * 0.2 tau = np.ones(mesh.nC) * 0.005 c = np.ones(mesh.nC) * 0.7 m = np.r_[siginf, eta, tau, c] iMap = Maps.IdentityMap(nP=int(mesh.nC)) maps = [('sigmaInf', iMap), ('eta', iMap), ('tau', iMap), ('c', iMap)] prb = ProblemATEMIP_b(mesh, mapping=maps) if waveformType == "GENERAL": # timeon = np.cumsum(np.r_[np.ones(10)*1e-3, np.ones(10)*5e-4, np.ones(10)*1e-4]) timeon = np.cumsum(np.r_[np.ones(10) * 1e-3, np.ones(10) * 5e-4, np.ones(10) * 1e-4]) timeon -= timeon.max() timeoff = np.cumsum(np.r_[np.ones(20) * 1e-5, np.ones(20) * 1e-4, np.ones(20) * 1e-3]) time = np.r_[timeon, timeoff] current_on = np.ones_like(timeon) current_on[[0, -1]] = 0. current = np.r_[current_on, np.zeros_like(timeoff)] wave = np.c_[time, current] prb.waveformType = "GENERAL" prb.currentwaveform(wave) prb.t0 = time.min() elif waveformType == "STEPOFF": prb.timeSteps = [(1e-5, 20), (1e-4, 20), (1e-3, 10)] offset = 20. tobs = np.logspace(-4, -2, 21) rx = EM.TDEM.RxTDEM(np.array([[offset, 0., 0.]]), tobs, "bz") src = EM.TDEM.SrcTDEM_VMD_MVP([rx], np.array([[0., 0., 0.]]), waveformType=waveformType) survey = EM.TDEM.SurveyTDEM([src]) prb.Solver = MumpsSolver prb.pair(survey) out = survey.dpred(m) bz_ana = mu_0 * hzAnalyticDipoleT_CC( offset, rx.times, sigmaInf=sighalf, eta=eta[0], tau=tau[0], c=c[0]) err = np.linalg.norm(bz_ana - out) / np.linalg.norm(bz_ana) print '>> Relative error = ', err if showIt: plt.loglog(rx.times, abs(bz_ana), 'k') plt.loglog(rx.times, abs(out), 'b.') plt.show() return err
def meshp(self): if getattr(self, '_meshp', None) is None: # -------------- Mesh Parameters ------------------ # # x-direction csx1, csx2 = 2.5e-3, 25. # fine cells near well bore pfx1, pfx2 = 1.3, 1.4 # padding factors: fine -> uniform ncx1 = np.ceil(self.casing_b/csx1+2) # number of fine cells # (past casing wall) dx2 = 1000. # uniform mesh out to here npadx2 = 21 # padding out to infinity # z-direction csz = 0.05 # finest z-cells nza = 10 # number of fine cells above air-earth interface pfz = pfx2 # padding factor in z-direction # ------------- Assemble the Cyl Mesh ------------- # # pad nicely to second cell size npadx1 = np.floor(np.log(csx2/csx1) / np.log(pfx1)) hx1a = Utils.meshTensor([(csx1, ncx1)]) hx1b = Utils.meshTensor([(csx1, npadx1, pfx1)]) dx1 = sum(hx1a)+sum(hx1b) dx1 = np.floor(dx1/csx2) hx1b *= (dx1*csx2 - sum(hx1a))/sum(hx1b) # second chunk of mesh ncx2 = np.ceil((dx2 - dx1)/csx2) hx2a = Utils.meshTensor([(csx2, ncx2)]) hx2b = Utils.meshTensor([(csx2, npadx2, pfx2)]) hx = np.hstack([hx1a, hx1b, hx2a, hx2b]) # cell size, number of core cells, number of padding cells in the # x-direction ncz = np.int(np.ceil(np.diff(self.casing_z)[0]/csz))+10 npadzu, npadzd = 43, 43 # vector of cell widths in the z-direction hz = Utils.meshTensor( [(csz, npadzd, -pfz), (csz, ncz), (csz, npadzu, pfz)] ) # primary mesh self._meshp = Mesh.CylMesh( [hx, 1., hz], [0., 0., -np.sum(hz[:npadzu+ncz-nza])] ) print( 'Cyl Mesh Extent xmax: {},: zmin: {}, zmax: {}'.format( self._meshp.vectorCCx.max(), self._meshp.vectorCCz.min(), self._meshp.vectorCCz.max() ) ) return self._meshp
def halfSpaceProblemAnaDiff(meshType, sig_half=1e-2, rxOffset=50., bounds=None, showIt=False): print '\nTesting sig_half = {0}, rxOffset= {1}'.format(sig_half, rxOffset) if bounds is None: bounds = [1e-5, 1e-3] if meshType == 'CYL': cs, ncx, ncz, npad = 5., 30, 10, 20 hx = [(cs, ncx), (cs, npad, 1.3)] hz = [(cs, npad, -1.3), (cs, ncz), (cs, npad, 1.3)] mesh = Mesh.CylMesh([hx, 1, hz], '00C') elif meshType == 'TENSOR': cs, nc, npad = 20., 13, 5 hx = [(cs, npad, -1.3), (cs, nc), (cs, npad, 1.3)] hy = [(cs, npad, -1.3), (cs, nc), (cs, npad, 1.3)] hz = [(cs, npad, -1.3), (cs, nc), (cs, npad, 1.3)] mesh = Mesh.TensorMesh([hx, hy, hz], 'CCC') active = mesh.vectorCCz < 0. actMap = Maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz) mapping = Maps.ExpMap(mesh) * Maps.SurjectVertical1D(mesh) * actMap rx = EM.TDEM.RxTDEM(np.array([[rxOffset, 0., 0.]]), np.logspace(-5, -4, 21), 'bz') src = EM.TDEM.SrcTDEM_VMD_MVP([rx], loc=np.array([0., 0., 0.])) # src = EM.TDEM.SrcTDEM([rx], loc=np.array([0., 0., 0.])) survey = EM.TDEM.SurveyTDEM([src]) prb = EM.TDEM.ProblemTDEM_b(mesh, mapping=mapping) prb.Solver = MumpsSolver prb.timeSteps = [(1e-06, 40), (5e-06, 40), (1e-05, 40), (5e-05, 40), (0.0001, 40), (0.0005, 40)] sigma = np.ones(mesh.nCz)*1e-8 sigma[active] = sig_half sigma = np.log(sigma[active]) prb.pair(survey) bz_ana = mu_0*EM.Analytics.hzAnalyticDipoleT(rx.locs[0][0]+1e-3, rx.times, sig_half) bz_calc = survey.dpred(sigma) ind = np.logical_and(rx.times > bounds[0], rx.times < bounds[1]) log10diff = np.linalg.norm(np.log10(np.abs(bz_calc[ind])) - np.log10(np.abs(bz_ana[ind])))/np.linalg.norm(np.log10(np.abs(bz_ana[ind]))) print 'Difference: ', log10diff if showIt == True: plt.loglog(rx.times[bz_calc>0], bz_calc[bz_calc>0], 'r', rx.times[bz_calc<0], -bz_calc[bz_calc<0], 'r--') plt.loglog(rx.times, abs(bz_ana), 'b*') plt.title('sig_half = {0:e}'.format(sig_half)) plt.show() return log10diff
def setupMeshModel(): cs = 10. nc = 20. npad = 15. hx = [(cs, nc), (cs, npad, 1.3)] hz = [(cs, npad, -1.3), (cs, nc), (cs, npad, 1.3)] mesh = Mesh.CylMesh([hx, 1., hz], '0CC') muMod = 1+MuMax*np.random.randn(mesh.nC) sigmaMod = np.random.randn(mesh.nC) return mesh, muMod, sigmaMod
def setUp(self): # Obtained SE parameters from fitting mopt = self.fit_colecole_with_se() eta, tau, c = mopt[0], np.exp(mopt[1]), mopt[2] # Step2: Set up EMIP problem and Survey csx, csz, ncx, ncz, npadx, npadz = 6.5, 5., 10, 20, 20, 20 hx = [(csx, ncx), (csx, npadx, 1.3)] hz = [(csz, npadz, -1.3), (csz, ncz), (csz, npadz, 1.3)] mesh = Mesh.CylMesh([hx, 1, hz], '00C') sig_half = 0.1 sigmaInf = np.ones(mesh.nC) * sig_half airind = mesh.gridCC[:, 2] > 0. sigmaInf[airind] = 1e-8 etavec = np.ones(mesh.nC) * eta etavec[airind] = 0. tauvec = np.ones(mesh.nC) * tau cvec = np.ones(mesh.nC) * c wiresEM = Maps.Wires(('sigmaInf', mesh.nC), ('eta', mesh.nC), ('tau', mesh.nC), ('c', mesh.nC)) tauvecmap = Maps.ExpMap(nP=mesh.nC) * wiresEM.tau src_z = 30. rxloc = np.array([0., 0., src_z]) srcloc = np.array([0., 0., src_z]) rx = RxEMIP.Point_dbdt( rxloc, np.logspace(np.log10(1e-5), np.log10(0.009), 51), 'z') src = EM.TDEM.Src.CircularLoop([rx], waveform=EM.TDEM.Src.StepOffWaveform(), loc=srcloc, radius=13.) survey = SurveyEMIP([src]) prb_em = Problem3D_e(mesh, sigmaInfMap=wiresEM.sigmaInf, etaMap=wiresEM.eta, tauMap=tauvecmap, cMap=wiresEM.c) prb_em.verbose = False prb_em.timeSteps = [(1e-06, 5), (2.5e-06, 5), (5e-06, 5), (1e-05, 10), (2e-05, 10), (4e-05, 10), (8e-05, 10), (1.6e-04, 10), (3.2e-04, 20)] prb_em.Solver = PardisoSolver prb_em.pair(survey) m = np.r_[sigmaInf, etavec, np.log(tauvec), cvec] self.survey = survey self.src_z = src_z self.m = m self.sig_half = sig_half self.eta = eta self.tau = tau self.c = c self.time = rx.times
def halfSpaceProblemAnaVMDDiff(showIt=False, waveformType="STEPOFF"): cs, ncx, ncz, npad = 20., 25, 25, 15 hx = [(cs, ncx), (cs, npad, 1.3)] hz = [(cs, npad, -1.3), (cs, ncz), (cs, npad, 1.3)] mesh = Mesh.CylMesh([hx, 1, hz], '00C') prb = ProblemATEM_b(mesh) if waveformType == "GENERAL": timeon = np.cumsum(np.r_[np.ones(10) * 1e-3, np.ones(10) * 5e-4, np.ones(10) * 1e-4]) timeon -= timeon.max() timeoff = np.cumsum(np.r_[np.ones(10) * 5e-5, np.ones(10) * 1e-4, np.ones(10) * 5e-4, np.ones(10) * 1e-3, np.ones(10) * 5e-3]) time = np.r_[timeon, timeoff] current_on = np.ones_like(timeon) current_on[[0, -1]] = 0. current = np.r_[current_on, np.zeros_like(timeoff)] wave = np.c_[time, current] prb.waveformType = "GENERAL" prb.currentwaveform(wave) prb.t0 = time.min() elif waveformType == "STEPOFF": prb.timeSteps = [(1e-5, 10), (5e-5, 10), (1e-4, 10), (5e-4, 10), (1e-3, 10), (5e-3, 10)] offset = 20. tobs = np.logspace(-4, -2, 21) rx = EM.TDEM.RxTDEM(np.array([[offset, 0., 0.]]), tobs, "bz") src = EM.TDEM.SrcTDEM_VMD_MVP([rx], np.array([[0., 0., 0.]]), waveformType=waveformType) survey = EM.TDEM.SurveyTDEM([src]) prb.Solver = MumpsSolver sigma = np.ones(mesh.nC) * 1e-8 active = mesh.gridCC[:, 2] < 0. sig_half = 1e-2 sigma[active] = sig_half prb.pair(survey) out = survey.dpred(sigma) bz_ana = mu_0 * hzAnalyticDipoleT(offset, rx.times, sig_half) err = np.linalg.norm(bz_ana - out) / np.linalg.norm(bz_ana) print '>> Relative error = ', err if showIt: plt.loglog(rx.times, bz_ana, 'k') plt.loglog(rx.times, out, 'b.') plt.show() return err
def run(plotIt=True): """ Plot Mirrored Cylindrically Symmetric Model =========================================== Here, we demonstrate plotting a model on a cylindrically symmetric mesh with the plotting symmetric about x=0. """ sig_halfspace = 1e-6 sig_sphere = 1e0 sig_air = 1e-8 sphere_z = -50. sphere_radius = 30. # x-direction cs = 1 nc = np.ceil(2.5 * (-(sphere_z - sphere_radius)) / cs) # cell spacings in the x and z directions h = Utils.meshTensor([(cs, nc)]) # define a mesh mesh = Mesh.CylMesh([h, 1, h], x0='00C') # Put the model on the mesh sigma = sig_air * np.ones(mesh.nC) # start with air cells sigma[mesh.gridCC[:, 2] < 0.] = sig_halfspace # cells below the earth # indices of the sphere sphere_ind = ((mesh.gridCC[:, 0]**2 + (mesh.gridCC[:, 2] - sphere_z)**2) <= sphere_radius**2) sigma[sphere_ind] = sig_sphere # sphere # Plot a cross section through the mesh fig, ax = plt.subplots(2, 1) plt.colorbar(mesh.plotImage(np.log10(sigma), ax=ax[0])[0], ax=ax[0]) ax[0].set_title('mirror = False') ax[0].axis('equal') ax[0].set_xlim([-200., 200.]) plt.colorbar(mesh.plotImage(np.log10(sigma), ax=ax[1], mirror=True)[0], ax=ax[1]) ax[1].set_title('mirror = True') ax[1].axis('equal') ax[1].set_xlim([-200., 200.]) plt.tight_layout()
def test_indActive_nc_residual(self): # x-direction cs, ncx, ncz, npad = 1., 10., 10., 20 hx = [(cs, ncx), (cs, npad, 1.3)] # z direction npad = 12 temp = np.logspace(np.log10(1.), np.log10(12.), 19) temp_pad = temp[-1] * 1.3**np.arange(npad) hz = np.r_[temp_pad[::-1], temp[::-1], temp, temp_pad] mesh = Mesh.CylMesh([hx, 1, hz], '00C') active = mesh.vectorCCz < 0. reg = Regularization.Simple(mesh, indActive=active) self.assertTrue(reg._nC_residual == len(active.nonzero()[0]))
def test_getInterpMatCartMesh_Cells2Nodes(self): Mr = Mesh.TensorMesh([100, 100, 2], x0='CC0') Mc = Mesh.CylMesh([np.ones(10) / 5, 1, 10], x0='0C0', cartesianOrigin=[-0.2, -0.2, 0]) mc = np.arange(Mc.nC) xr = np.linspace(0, 0.4, 50) xc = np.linspace(0, 0.4, 50) + 0.2 Pr = Mr.getInterpolationMat( np.c_[xr, np.ones(50) * -0.2, np.ones(50) * 0.5], 'N') Pc = Mc.getInterpolationMat(np.c_[xc, np.zeros(50), np.ones(50) * 0.5], 'CC') Pc2r = Mc.getInterpolationMatCartMesh(Mr, 'CC', locTypeTo='N') assert np.abs(Pr * (Pc2r * mc) - Pc * mc).max() < 1e-3
def setUp(self): maps2test2D = [M for M in dir(Maps) if M not in MAPS_TO_EXCLUDE_2D] maps2test3D = [M for M in dir(Maps) if M not in MAPS_TO_EXCLUDE_3D] self.maps2test2D = [getattr(Maps, M) for M in maps2test2D if (inspect.isclass(getattr(Maps, M)) and issubclass(getattr(Maps, M), Maps.IdentityMap))] self.maps2test3D = [getattr(Maps, M) for M in maps2test3D if inspect.isclass(getattr(Maps, M)) and issubclass(getattr(Maps, M), Maps.IdentityMap)] a = np.array([1, 1, 1]) b = np.array([1, 2]) self.mesh2 = Mesh.TensorMesh([a, b], x0=np.array([3, 5])) self.mesh3 = Mesh.TensorMesh([a, b, [3, 4]], x0=np.array([3, 5, 2])) self.mesh22 = Mesh.TensorMesh([b, a], x0=np.array([3, 5])) self.meshCyl = Mesh.CylMesh([10.,1.,10.], x0='00C')
def setUp_TDEM(prbtype='b', rxcomp='bz'): cs = 5. ncx = 20 ncy = 15 npad = 20 hx = [(cs, ncx), (cs, npad, 1.3)] hy = [(cs, npad, -1.3), (cs, ncy), (cs, npad, 1.3)] mesh = Mesh.CylMesh([hx, 1, hy], '00C') # active = mesh.vectorCCz < 0. activeMap = Maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz) mapping = Maps.ExpMap(mesh) * Maps.SurjectVertical1D(mesh) * activeMap rxOffset = 10. if prbtype == 'b': prb = EM.TDEM.Problem3D_b(mesh, mapping=mapping) elif prbtype == 'e': prb = EM.TDEM.Problem3D_e(mesh, mapping=mapping) prb.timeSteps = [(1e-3, 5), (1e-4, 5), (5e-5, 10), (5e-5, 10), (1e-4, 10)] out = EM.Utils.VTEMFun(prb.times, 0.00595, 0.006, 100) wavefun = interp1d(prb.times, out) t0 = 0.006 waveform = EM.TDEM.Src.RawWaveform(offTime=t0, waveFct=wavefun) timerx = np.logspace(-4, -3, 20) rx = EM.TDEM.Rx(np.array([[rxOffset, 0., 0.]]), timerx, rxcomp) src = EM.TDEM.Src.MagDipole([rx], waveform= waveform, loc=np.array([0., 0., 0.])) survey = EM.TDEM.Survey([src]) prb.Solver = Solver m = np.log(1e-1)*np.ones(prb.mapping.nP) # + 1e-2*np.random.randn(prb.mapping.nP) prb.pair(survey) mesh = mesh return prb, m, mesh
def setUp_TDEM(self, rxcomp='bz'): cs = 5. ncx = 20 ncy = 6 npad = 20 hx = [(cs, ncx), (cs, npad, 1.3)] hy = [(cs, npad, -1.3), (cs, ncy), (cs, npad, 1.3)] mesh = Mesh.CylMesh([hx, 1, hy], '00C') active = mesh.vectorCCz < 0. activeMap = Maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz) mapping = Maps.ExpMap(mesh) * Maps.SurjectVertical1D(mesh) * activeMap rxOffset = 40. rx = EM.TDEM.Rx(np.array([[rxOffset, 0., 0.]]), np.logspace(-4, -3, 20), rxcomp) src = EM.TDEM.Src.MagDipole([rx], loc=np.array([0., 0., 0.])) rx2 = EM.TDEM.Rx(np.array([[rxOffset-10, 0., 0.]]), np.logspace(-5, -4, 25), rxcomp) src2 = EM.TDEM.Src.MagDipole( [rx2], loc=np.array([0., 0., 0.])) survey = EM.TDEM.Survey([src, src2]) prb = EM.TDEM.Problem3D_b(mesh, mapping=mapping) # prb.timeSteps = [1e-5] prb.timeSteps = [(1e-05, 10), (5e-05, 10), (2.5e-4, 10)] # prb.timeSteps = [(1e-05, 100)] prb.Solver = Solver m = (np.log(1e-1)*np.ones(prb.mapping.nP) + 1e-2*np.random.randn(prb.mapping.nP)) prb.pair(survey) return mesh, prb, m
def setUp_TDEM(prbtype='b', rxcomp='bz'): cs = 5. ncx = 20 ncy = 15 npad = 20 hx = [(cs, ncx), (cs, npad, 1.3)] hy = [(cs, npad, -1.3), (cs, ncy), (cs, npad, 1.3)] mesh = Mesh.CylMesh([hx, 1, hy], '00C') # active = mesh.vectorCCz < 0. activeMap = Maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz) mapping = Maps.ExpMap(mesh) * Maps.SurjectVertical1D(mesh) * activeMap rxOffset = 10. rx = EM.TDEM.Rx(np.array([[rxOffset, 0., -1e-2]]), np.logspace(-4, -3, 20), rxcomp) src = EM.TDEM.Src.MagDipole([rx], loc=np.array([0., 0., 0.])) survey = EM.TDEM.Survey([src]) if prbtype == 'b': prb = EM.TDEM.Problem3D_b(mesh, mapping=mapping) elif prbtype == 'e': prb = EM.TDEM.Problem3D_e(mesh, mapping=mapping) prb.timeSteps = [(1e-05, 10), (5e-05, 10), (2.5e-4, 10)] # prb.timeSteps = [(1e-05, 10), (1e-05, 50), (1e-05, 50) ] #, (2.5e-4, 10)] prb.Solver = Solver m = (np.log(1e-1) * np.ones(prb.mapping.nP) + 1e-3 * np.random.randn(prb.mapping.nP)) prb.pair(survey) mesh = mesh return prb, m, mesh
def getProb(meshType='CYL', rxTypes='bx,bz', nSrc=1): cs = 5. ncx = 20 ncy = 6 npad = 20 hx = [(cs, ncx), (cs, npad, 1.3)] hy = [(cs, npad, -1.3), (cs, ncy), (cs, npad, 1.3)] mesh = Mesh.CylMesh([hx, 1, hy], '00C') active = mesh.vectorCCz < 0. activeMap = Maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz) mapping = Maps.ExpMap(mesh) * Maps.SurjectVertical1D(mesh) * activeMap rxOffset = 40. srcs = [] for ii in range(nSrc): rxs = [ EM.TDEM.RxTDEM(np.array([[rxOffset, 0., 0.]]), np.logspace(-4, -3, 20 + ii), rxType) for rxType in rxTypes.split(',') ] srcs += [EM.TDEM.SrcTDEM_VMD_MVP(rxs, np.array([0., 0., 0.]))] survey = EM.TDEM.SurveyTDEM(srcs) prb = EM.TDEM.ProblemTDEM_b(mesh, mapping=mapping) # prb.timeSteps = [1e-5] prb.timeSteps = [(1e-05, 10), (5e-05, 10), (2.5e-4, 10)] # prb.timeSteps = [(1e-05, 100)] try: from pymatsolver import MumpsSolver prb.Solver = MumpsSolver except ImportError, e: prb.Solver = SolverLU
def run(runIt=False, plotIt=True, saveIt=False, saveFig=False, cleanup=True): """ Run the bookpurnong 1D stitched RESOLVE inversions. :param bool runIt: re-run the inversions? Default downloads and plots saved results :param bool plotIt: show the plots? :param bool saveIt: save the re-inverted results? :param bool saveFig: save the figure :param bool cleanup: remove the downloaded results """ # download the data downloads, directory = download_and_unzip_data() # Load resolve data resolve = h5py.File(os.path.sep.join([directory, "booky_resolve.hdf5"]), "r") river_path = resolve["river_path"][()] # River path nSounding = resolve["data"].shape[0] # the # of soundings # Bird height from surface b_height_resolve = resolve["src_elevation"][()] # fetch the frequencies we are considering cpi_inds = [0, 2, 6, 8, 10] # Indices for HCP in-phase cpq_inds = [1, 3, 7, 9, 11] # Indices for HCP quadrature frequency_cp = resolve["frequency_cp"][()] # build a mesh cs, ncx, ncz, npad = 1., 10., 10., 20 hx = [(cs, ncx), (cs, npad, 1.3)] npad = 12 temp = np.logspace(np.log10(1.), np.log10(12.), 19) temp_pad = temp[-1] * 1.3**np.arange(npad) hz = np.r_[temp_pad[::-1], temp[::-1], temp, temp_pad] mesh = Mesh.CylMesh([hx, 1, hz], '00C') active = mesh.vectorCCz < 0. # survey parameters rxOffset = 7.86 # tx-rx separation bp = -mu_0 / (4 * np.pi * rxOffset**3) # primary magnetic field # re-run the inversion if runIt: # set up the mappings - we are inverting for 1D log conductivity # below the earth's surface. actMap = Maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz) mapping = Maps.ExpMap(mesh) * Maps.SurjectVertical1D(mesh) * actMap # build starting and reference model sig_half = 1e-1 sig_air = 1e-8 sigma = np.ones(mesh.nCz) * sig_air sigma[active] = sig_half m0 = np.log(1e-1) * np.ones(active.sum()) # starting model mref = np.log(1e-1) * np.ones(active.sum()) # reference model # initalize empty lists for storing inversion results mopt_re = [] # recovered model dpred_re = [] # predicted data dobs_re = [] # observed data # downsample the data for the inversion nskip = 40 # set up a noise model # 10% for the 3 lowest frequencies, 15% for the two highest std = np.repeat(np.r_[np.ones(3) * 0.1, np.ones(2) * 0.15], 2) floor = abs(20 * bp * 1e-6) # floor of 20ppm # loop over the soundings and invert each for rxind in range(nSounding): # convert data from ppm to magnetic field (A/m^2) dobs = np.c_[resolve["data"][rxind, :][cpi_inds].astype(float), resolve["data"][rxind, :][cpq_inds]. astype(float)].flatten() * bp * 1e-6 # perform the inversion src_height = b_height_resolve[rxind].astype(float) mopt, dpred, dobs = resolve_1Dinversions(mesh, dobs, src_height, frequency_cp, m0, mref, mapping, std=std, floor=floor) # add results to our list mopt_re.append(mopt) dpred_re.append(dpred) dobs_re.append(dobs) # save results mopt_re = np.vstack(mopt_re) dpred_re = np.vstack(dpred_re) dobs_re = np.vstack(dobs_re) if saveIt: np.save("mopt_re_final", mopt_re) np.save("dobs_re_final", dobs_re) np.save("dpred_re_final", dpred_re) mopt_re = resolve["mopt"][()] dobs_re = resolve["dobs"][()] dpred_re = resolve["dpred"][()] sigma = np.exp(mopt_re) indz = -7 # depth index # so that we can visually compare with literature (eg Viezzoli, 2010) cmap = "jet" # dummy figure for colobar fig = plt.figure() out = plt.scatter(np.ones(3), np.ones(3), c=np.linspace(-2, 1, 3), cmap=cmap) plt.close(fig) # plot from the paper fs = 13 # fontsize # matplotlib.rcParams['font.size'] = fs plt.figure(figsize=(13, 7)) ax0 = plt.subplot2grid((2, 3), (0, 0), rowspan=2, colspan=2) ax1 = plt.subplot2grid((2, 3), (0, 2)) ax2 = plt.subplot2grid((2, 3), (1, 2)) # titles of plots title = [("(a) Recovered model, %.1f m depth") % (-mesh.vectorCCz[active][indz]), "(b) Obs (Real 400 Hz)", "(c) Pred (Real 400 Hz)"] temp = sigma[:, indz] tree = cKDTree(list(zip(resolve["xy"][:, 0], resolve["xy"][:, 1]))) d, d_inds = tree.query(list(zip(resolve["xy"][:, 0], resolve["xy"][:, 1])), k=20) w = 1. / (d + 100.)**2. w = Utils.sdiag(1. / np.sum(w, axis=1)) * (w) xy = resolve["xy"] temp = (temp.flatten()[d_inds] * w).sum(axis=1) Utils.plot2Ddata(xy, temp, ncontour=100, scale="log", dataloc=False, contourOpts={ "cmap": cmap, "vmin": 1e-2, "vmax": 1e1 }, ax=ax0) ax0.plot(resolve["xy"][:, 0], resolve["xy"][:, 1], 'k.', alpha=0.02, ms=1) cb = plt.colorbar(out, ax=ax0, ticks=np.linspace(-2, 1, 4), format="$10^{%.1f}$") cb.set_ticklabels(["0.01", "0.1", "1", "10"]) cb.set_label("Conductivity (S/m)") ax0.plot(river_path[:, 0], river_path[:, 1], 'k-', lw=0.5) # plot observed and predicted data freq_ind = 0 axs = [ax1, ax2] temp_dobs = dobs_re[:, freq_ind].copy() ax1.plot(river_path[:, 0], river_path[:, 1], 'k-', lw=0.5) out = Utils.plot2Ddata(resolve["xy"][()], temp_dobs / abs(bp) * 1e6, ncontour=100, scale="log", dataloc=False, ax=ax1, contourOpts={"cmap": "viridis"}) vmin, vmax = out[0].get_clim() cb = plt.colorbar(out[0], ticks=np.linspace(vmin, vmax, 3), ax=ax1, format="%.1e", fraction=0.046, pad=0.04) cb.set_label("Bz (ppm)") temp_dpred = dpred_re[:, freq_ind].copy() # temp_dpred[mask_:_data] = np.nan ax2.plot(river_path[:, 0], river_path[:, 1], 'k-', lw=0.5) Utils.plot2Ddata(resolve["xy"][()], temp_dpred / abs(bp) * 1e6, ncontour=100, scale="log", dataloc=False, contourOpts={ "vmin": 10**vmin, "vmax": 10**vmax, "cmap": "viridis" }, ax=ax2) cb = plt.colorbar(out[0], ticks=np.linspace(vmin, vmax, 3), ax=ax2, format="%.1e", fraction=0.046, pad=0.04) cb.set_label("Bz (ppm)") for i, ax in enumerate([ax0, ax1, ax2]): xticks = [460000, 463000] yticks = [6195000, 6198000, 6201000] xloc, yloc = 462100.0, 6196500.0 ax.set_xticks(xticks) ax.set_yticks(yticks) # ax.plot(xloc, yloc, 'wo') ax.plot(river_path[:, 0], river_path[:, 1], 'k', lw=0.5) ax.set_aspect("equal") ax.plot(resolve["xy"][:, 0], resolve["xy"][:, 1], 'k.', alpha=0.02, ms=1) ax.set_yticklabels([str(f) for f in yticks]) ax.set_ylabel("Northing (m)") ax.set_xlabel("Easting (m)") ax.set_title(title[i]) plt.tight_layout() if plotIt: plt.show() if saveFig is True: fig.savefig("obspred_resolve.png", dpi=200) resolve.close() if cleanup: os.remove(downloads) shutil.rmtree(directory)
def test_exceptions(self): M = Mesh.CylMesh([4, 1, 1]) locs = np.r_[0, 0, 0.5] self.assertRaises(Exception, lambda: M.getInterpolationMat(locs, 'Fy')) self.assertRaises(Exception, lambda: M.getInterpolationMat(locs, 'Ex')) self.assertRaises(Exception, lambda: M.getInterpolationMat(locs, 'Ez'))
def run(plotIt=True): """ Mesh: Plotting with defining range ================================== When using a large Mesh with the cylindrical code, it is advantageous to define a :code:`range_x` and :code:`range_y` when plotting with vectors. In this case, only the region inside of the range is interpolated. In particular, you often want to ignore padding cells. """ # ## Model Parameters # # We define a # - resistive halfspace and # - conductive sphere # - radius of 30m # - center is 50m below the surface # electrical conductivities in S/m sig_halfspace = 1e-6 sig_sphere = 1e0 sig_air = 1e-8 # depth to center, radius in m sphere_z = -50. sphere_radius = 30. # ## Survey Parameters # # - Transmitter and receiver 20m above the surface # - Receiver offset from transmitter by 8m horizontally # - 25 frequencies, logaritmically between $10$ Hz and $10^5$ Hz boom_height = 20. rx_offset = 8. freqs = np.r_[1e1, 1e5] # source and receiver location in 3D space src_loc = np.r_[0., 0., boom_height] rx_loc = np.atleast_2d(np.r_[rx_offset, 0., boom_height]) # print the min and max skin depths to make sure mesh is fine enough and # extends far enough def skin_depth(sigma, f): return 500. / np.sqrt(sigma * f) print('Minimum skin depth (in sphere): {:.2e} m '.format( skin_depth(sig_sphere, freqs.max()))) print('Maximum skin depth (in background): {:.2e} m '.format( skin_depth(sig_halfspace, freqs.min()))) # ## Mesh # # Here, we define a cylindrically symmetric tensor mesh. # # ### Mesh Parameters # # For the mesh, we will use a cylindrically symmetric tensor mesh. To # construct a tensor mesh, all that is needed is a vector of cell widths in # the x and z-directions. We will define a core mesh region of uniform cell # widths and a padding region where the cell widths expand "to infinity". # x-direction csx = 2 # core mesh cell width in the x-direction ncx = np.ceil( 1.2 * sphere_radius / csx ) # number of core x-cells (uniform mesh slightly beyond sphere radius) npadx = 50 # number of x padding cells # z-direction csz = 1 # core mesh cell width in the z-direction ncz = np.ceil( 1.2 * (boom_height - (sphere_z - sphere_radius)) / csz ) # number of core z-cells (uniform cells slightly below bottom of sphere) npadz = 52 # number of z padding cells # padding factor (expand cells to infinity) pf = 1.3 # cell spacings in the x and z directions hx = Utils.meshTensor([(csx, ncx), (csx, npadx, pf)]) hz = Utils.meshTensor([(csz, npadz, -pf), (csz, ncz), (csz, npadz, pf)]) # define a SimPEG mesh mesh = Mesh.CylMesh([hx, 1, hz], x0=np.r_[0., 0., -hz.sum() / 2. - boom_height]) # ### Plot the mesh # # Below, we plot the mesh. The cyl mesh is rotated around x=0. Ensure that # each dimension extends beyond the maximum skin depth. # # Zoom in by changing the xlim and zlim. # X and Z limits we want to plot to. Try xlim = np.r_[0., 2.5e6] zlim = np.r_[-2.5e6, 2.5e6] fig, ax = plt.subplots(1, 1) mesh.plotGrid(ax=ax) ax.set_title('Simulation Mesh') ax.set_xlim(xlim) ax.set_ylim(zlim) print('The maximum skin depth is (in background): {:.2e} m. ' 'Does the mesh go sufficiently past that?'.format( skin_depth(sig_halfspace, freqs.min()))) # ## Put Model on Mesh # # Now that the model parameters and mesh are defined, we can define # electrical conductivity on the mesh. # # The electrical conductivity is defined at cell centers when using the # finite volume method. So here, we define a vector that contains an # electrical conductivity value for every cell center. # create a vector that has one entry for every cell center sigma = sig_air * np.ones( mesh.nC) # start by defining the conductivity of the air everwhere sigma[mesh.gridCC[:, 2] < 0.] = sig_halfspace # assign halfspace cells below the earth # indices of the sphere (where (x-x0)**2 + (z-z0)**2 <= R**2) sphere_ind = ((mesh.gridCC[:, 0]**2 + (mesh.gridCC[:, 2] - sphere_z)**2) <= sphere_radius**2) sigma[sphere_ind] = sig_sphere # assign the conductivity of the sphere # Plot a cross section of the conductivity model fig, ax = plt.subplots(1, 1) cb = plt.colorbar(mesh.plotImage(np.log10(sigma), ax=ax, mirror=True)[0]) # plot formatting and titles cb.set_label('$\log_{10}\sigma$', fontsize=13) ax.axis('equal') ax.set_xlim([-120., 120.]) ax.set_ylim([-100., 30.]) ax.set_title('Conductivity Model') # ## Set up the Survey # # Here, we define sources and receivers. For this example, the receivers # are magnetic flux recievers, and are only looking at the secondary field # (eg. if a bucking coil were used to cancel the primary). The source is a # vertical magnetic dipole with unit moment. # Define the receivers, we will sample the real secondary magnetic flux # density as well as the imaginary magnetic flux density bz_r = FDEM.Rx.Point_bSecondary( locs=rx_loc, orientation='z', component='real') # vertical real b-secondary bz_i = FDEM.Rx.Point_b( locs=rx_loc, orientation='z', component='imag') # vertical imag b (same as b-secondary) rxList = [bz_r, bz_i] # list of receivers # Define the list of sources - one source for each frequency. The source is # a point dipole oriented in the z-direction srcList = [ FDEM.Src.MagDipole(rxList, f, src_loc, orientation='z') for f in freqs ] print( 'There are {nsrc} sources (same as the number of frequencies - {nfreq}). ' 'Each source has {nrx} receivers sampling the resulting b-fields'. format(nsrc=len(srcList), nfreq=len(freqs), nrx=len(rxList))) # ## Set up Forward Simulation # # A forward simulation consists of a paired SimPEG problem and Survey. # For this example, we use the E-formulation of Maxwell's equations, # solving the second-order system for the electric field, which is defined # on the cell edges of the mesh. This is the `prob` variable below. The # `survey` takes the source list which is used to construct the RHS for the # problem. The source list also contains the receiver information, so the # `survey` knows how to sample fields and fluxes that are produced by # solving the `prob`. # define a problem - the statement of which discrete pde system we want to # solve prob = FDEM.Problem3D_e(mesh, sigmaMap=Maps.IdentityMap(mesh)) prob.solver = Solver survey = FDEM.Survey(srcList) # tell the problem and survey about each other - so the RHS can be # constructed for the problem and the # resulting fields and fluxes can be sampled by the receiver. prob.pair(survey) # ### Solve the forward simulation # # Here, we solve the problem for the fields everywhere on the mesh. fields = prob.fields(sigma) # ### Plot the fields # # Lets look at the physics! # log-scale the colorbar from matplotlib.colors import LogNorm fig, ax = plt.subplots(1, 2, figsize=(12, 6)) def plotMe(field, ax): plt.colorbar(mesh.plotImage(field, vType='F', view='vec', range_x=[-100., 100.], range_y=[-180., 60.], pcolorOpts={ 'norm': LogNorm(), 'cmap': plt.get_cmap('viridis') }, streamOpts={'color': 'k'}, ax=ax, mirror=True)[0], ax=ax) plotMe(fields[srcList[0], 'bSecondary'].real, ax[0]) ax[0].set_title('Real B-Secondary, {}Hz'.format(freqs[0])) plotMe(fields[srcList[1], 'bSecondary'].real, ax[1]) ax[1].set_title('Real B-Secondary, {}Hz'.format(freqs[1])) plt.tight_layout() if plotIt: plt.show()
def run(plotIt=True): """ EM: Schenkel and Morrison Casing Model ====================================== Here we create and run a FDEM forward simulation to calculate the vertical current inside a steel-cased. The model is based on the Schenkel and Morrison Casing Model, and the results are used in a 2016 SEG abstract by Yang et al. .. code-block:: text Schenkel, C.J., and H.F. Morrison, 1990, Effects of well casing on potential field measurements using downhole current sources: Geophysical prospecting, 38, 663-686. The model consists of: - Air: Conductivity 1e-8 S/m, above z = 0 - Background: conductivity 1e-2 S/m, below z = 0 - Casing: conductivity 1e6 S/m - 300m long - radius of 0.1m - thickness of 6e-3m Inside the casing, we take the same conductivity as the background. We are using an EM code to simulate DC, so we use frequency low enough that the skin depth inside the casing is longer than the casing length (f = 1e-6 Hz). The plot produced is of the current inside the casing. These results are shown in the SEG abstract by Yang et al., 2016: 3D DC resistivity modeling of steel casing for reservoir monitoring using equivalent resistor network. The solver used to produce these results and achieve the CPU time of ~30s is Mumps, which was installed using pymatsolver_ .. _pymatsolver: https://github.com/rowanc1/pymatsolver This example is on figshare: https://dx.doi.org/10.6084/m9.figshare.3126961.v1 If you would use this example for a code comparison, or build upon it, a citation would be much appreciated! """ if plotIt: import matplotlib.pylab as plt # ------------------ MODEL ------------------ sigmaair = 1e-8 # air sigmaback = 1e-2 # background sigmacasing = 1e6 # casing sigmainside = sigmaback # inside the casing casing_t = 0.006 # 1cm thickness casing_l = 300 # length of the casing casing_r = 0.1 casing_a = casing_r - casing_t / 2. # inner radius casing_b = casing_r + casing_t / 2. # outer radius casing_z = np.r_[-casing_l, 0.] # ------------------ SURVEY PARAMETERS ------------------ freqs = np.r_[1e-6] # [1e-1, 1, 5] # frequencies dsz = -300 # down-hole z source location src_loc = np.r_[0., 0., dsz] inf_loc = np.r_[0., 0., 1e4] print('Skin Depth: ', [(500. / np.sqrt(sigmaback * _)) for _ in freqs]) # ------------------ MESH ------------------ # fine cells near well bore csx1, csx2 = 2e-3, 60. pfx1, pfx2 = 1.3, 1.3 ncx1 = np.ceil(casing_b / csx1 + 2) # pad nicely to second cell size npadx1 = np.floor(np.log(csx2 / csx1) / np.log(pfx1)) hx1a = Utils.meshTensor([(csx1, ncx1)]) hx1b = Utils.meshTensor([(csx1, npadx1, pfx1)]) dx1 = sum(hx1a) + sum(hx1b) dx1 = np.floor(dx1 / csx2) hx1b *= (dx1 * csx2 - sum(hx1a)) / sum(hx1b) # second chunk of mesh dx2 = 300. # uniform mesh out to here ncx2 = np.ceil((dx2 - dx1) / csx2) npadx2 = 45 hx2a = Utils.meshTensor([(csx2, ncx2)]) hx2b = Utils.meshTensor([(csx2, npadx2, pfx2)]) hx = np.hstack([hx1a, hx1b, hx2a, hx2b]) # z-direction csz = 0.05 nza = 10 # cell size, number of core cells, number of padding cells in the # x-direction ncz, npadzu, npadzd = np.int(np.ceil( np.diff(casing_z)[0] / csz)) + 10, 68, 68 # vector of cell widths in the z-direction hz = Utils.meshTensor([(csz, npadzd, -1.3), (csz, ncz), (csz, npadzu, 1.3)]) # Mesh mesh = Mesh.CylMesh([hx, 1., hz], [0., 0., -np.sum(hz[:npadzu + ncz - nza])]) print('Mesh Extent xmax: {0:f},: zmin: {1:f}, zmax: {2:f}'.format( mesh.vectorCCx.max(), mesh.vectorCCz.min(), mesh.vectorCCz.max())) print('Number of cells', mesh.nC) if plotIt is True: fig, ax = plt.subplots(1, 1, figsize=(6, 4)) ax.set_title('Simulation Mesh') mesh.plotGrid(ax=ax) plt.show() # Put the model on the mesh sigWholespace = sigmaback * np.ones((mesh.nC)) sigBack = sigWholespace.copy() sigBack[mesh.gridCC[:, 2] > 0.] = sigmaair sigCasing = sigBack.copy() iCasingZ = ((mesh.gridCC[:, 2] <= casing_z[1]) & (mesh.gridCC[:, 2] >= casing_z[0])) iCasingX = ((mesh.gridCC[:, 0] >= casing_a) & (mesh.gridCC[:, 0] <= casing_b)) iCasing = iCasingX & iCasingZ sigCasing[iCasing] = sigmacasing if plotIt is True: # plotting parameters xlim = np.r_[0., 0.2] zlim = np.r_[-350., 10.] clim_sig = np.r_[-8, 6] # plot models fig, ax = plt.subplots(1, 1, figsize=(4, 4)) f = plt.colorbar(mesh.plotImage(np.log10(sigCasing), ax=ax)[0], ax=ax) ax.grid(which='both') ax.set_title('Log_10 (Sigma)') ax.set_xlim(xlim) ax.set_ylim(zlim) f.set_clim(clim_sig) plt.show() # -------------- Sources -------------------- # Define Custom Current Sources # surface source sg_x = np.zeros(mesh.vnF[0], dtype=complex) sg_y = np.zeros(mesh.vnF[1], dtype=complex) sg_z = np.zeros(mesh.vnF[2], dtype=complex) nza = 2 # put the wire two cells above the surface ncin = 2 # vertically directed wire # hook it up to casing at the surface sgv_indx = ((mesh.gridFz[:, 0] > casing_a) & (mesh.gridFz[:, 0] < casing_a + csx1)) sgv_indz = ((mesh.gridFz[:, 2] <= +csz * nza) & (mesh.gridFz[:, 2] >= -csz * 2)) sgv_ind = sgv_indx & sgv_indz sg_z[sgv_ind] = -1. # horizontally directed wire sgh_indx = ((mesh.gridFx[:, 0] > casing_a) & (mesh.gridFx[:, 0] <= inf_loc[2])) sgh_indz = ((mesh.gridFx[:, 2] > csz * (nza - 0.5)) & (mesh.gridFx[:, 2] < csz * (nza + 0.5))) sgh_ind = sgh_indx & sgh_indz sg_x[sgh_ind] = -1. # hook it up to casing at the surface sgv2_indx = ((mesh.gridFz[:, 0] >= mesh.gridFx[sgh_ind, 0].max()) & (mesh.gridFz[:, 0] <= inf_loc[2] * 1.2)) sgv2_indz = ((mesh.gridFz[:, 2] <= +csz * nza) & (mesh.gridFz[:, 2] >= -csz * 2)) sgv2_ind = sgv2_indx & sgv2_indz sg_z[sgv2_ind] = 1. # assemble the source sg = np.hstack([sg_x, sg_y, sg_z]) sg_p = [FDEM.Src.RawVec_e([], _, sg / mesh.area) for _ in freqs] # downhole source dg_x = np.zeros(mesh.vnF[0], dtype=complex) dg_y = np.zeros(mesh.vnF[1], dtype=complex) dg_z = np.zeros(mesh.vnF[2], dtype=complex) # vertically directed wire dgv_indx = (mesh.gridFz[:, 0] < csx1) # go through the center of the well dgv_indz = ((mesh.gridFz[:, 2] <= +csz * nza) & (mesh.gridFz[:, 2] > dsz + csz / 2.)) dgv_ind = dgv_indx & dgv_indz dg_z[dgv_ind] = -1. # couple to the casing downhole dgh_indx = mesh.gridFx[:, 0] < casing_a + csx1 dgh_indz = (mesh.gridFx[:, 2] < dsz + csz) & (mesh.gridFx[:, 2] >= dsz) dgh_ind = dgh_indx & dgh_indz dg_x[dgh_ind] = 1. # horizontal part at surface dgh2_indx = mesh.gridFx[:, 0] <= inf_loc[2] * 1.2 dgh2_indz = sgh_indz.copy() dgh2_ind = dgh2_indx & dgh2_indz dg_x[dgh2_ind] = -1. # vertical part at surface dgv2_ind = sgv2_ind.copy() dg_z[dgv2_ind] = 1. # assemble the source dg = np.hstack([dg_x, dg_y, dg_z]) dg_p = [FDEM.Src.RawVec_e([], _, dg / mesh.area) for _ in freqs] # ------------ Problem and Survey --------------- survey = FDEM.Survey(sg_p + dg_p) mapping = [('sigma', Maps.IdentityMap(mesh))] problem = FDEM.Problem3D_h(mesh, mapping=mapping, Solver=solver) problem.pair(survey) # ------------- Solve --------------------------- t0 = time.time() fieldsCasing = problem.fields(sigCasing) print('Time to solve 2 sources', time.time() - t0) # Plot current # current density jn0 = fieldsCasing[dg_p, 'j'] jn1 = fieldsCasing[sg_p, 'j'] # current in0 = [ mesh.area * fieldsCasing[dg_p, 'j'][:, i] for i in range(len(freqs)) ] in1 = [ mesh.area * fieldsCasing[sg_p, 'j'][:, i] for i in range(len(freqs)) ] in0 = np.vstack(in0).T in1 = np.vstack(in1).T # integrate to get z-current inside casing inds_inx = ((mesh.gridFz[:, 0] >= casing_a) & (mesh.gridFz[:, 0] <= casing_b)) inds_inz = (mesh.gridFz[:, 2] >= dsz) & (mesh.gridFz[:, 2] <= 0) inds_fz = inds_inx & inds_inz indsx = [False] * mesh.nFx inds = list(indsx) + list(inds_fz) in0_in = in0[np.r_[inds]] in1_in = in1[np.r_[inds]] z_in = mesh.gridFz[inds_fz, 2] in0_in = in0_in.reshape([in0_in.shape[0] // 3, 3]) in1_in = in1_in.reshape([in1_in.shape[0] // 3, 3]) z_in = z_in.reshape([z_in.shape[0] // 3, 3]) I0 = in0_in.sum(1).real I1 = in1_in.sum(1).real z_in = z_in[:, 0] if plotIt is True: fig, ax = plt.subplots(1, 2, figsize=(12, 4)) ax[0].plot(z_in, np.absolute(I0), z_in, np.absolute(I1)) ax[0].legend(['top casing', 'bottom casing'], loc='best') ax[0].set_title('Magnitude of Vertical Current in Casing') ax[1].semilogy(z_in, np.absolute(I0), z_in, np.absolute(I1)) ax[1].legend(['top casing', 'bottom casing'], loc='best') ax[1].set_title('Magnitude of Vertical Current in Casing') ax[1].set_ylim([1e-2, 1.]) plt.show()
def run(plotIt=True): cs, ncx, ncz, npad = 5., 25, 15, 15 hx = [(cs, ncx), (cs, npad, 1.3)] hz = [(cs, npad, -1.3), (cs, ncz), (cs, npad, 1.3)] mesh = Mesh.CylMesh([hx, 1, hz], '00C') layerz = -100. active = mesh.vectorCCz < 0. layer = (mesh.vectorCCz < 0.) & (mesh.vectorCCz >= layerz) actMap = Maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz) mapping = Maps.ExpMap(mesh) * Maps.SurjectVertical1D(mesh) * actMap sig_half = 2e-2 sig_air = 1e-8 sig_layer = 1e-2 sigma = np.ones(mesh.nCz) * sig_air sigma[active] = sig_half sigma[layer] = sig_layer mtrue = np.log(sigma[active]) if plotIt: fig, ax = plt.subplots(1, 1, figsize=(3, 6)) plt.semilogx(sigma[active], mesh.vectorCCz[active]) ax.set_ylim(-500, 0) ax.set_xlim(1e-3, 1e-1) ax.set_xlabel('Conductivity (S/m)', fontsize=14) ax.set_ylabel('Depth (m)', fontsize=14) ax.grid(color='k', alpha=0.5, linestyle='dashed', linewidth=0.5) rxOffset = 10. bzi = EM.FDEM.Rx.Point_b(np.array([[rxOffset, 0., 1e-3]]), orientation='z', component='imag') freqs = np.logspace(1, 3, 10) srcLoc = np.array([0., 0., 10.]) srcList = [ EM.FDEM.Src.MagDipole([bzi], freq, srcLoc, orientation='Z') for freq in freqs ] survey = EM.FDEM.Survey(srcList) prb = EM.FDEM.Problem3D_b(mesh, sigmaMap=mapping, Solver=Solver) prb.pair(survey) std = 0.05 survey.makeSyntheticData(mtrue, std) survey.std = std survey.eps = np.linalg.norm(survey.dtrue) * 1e-5 if plotIt: fig, ax = plt.subplots(1, 1, figsize=(6, 6)) ax.semilogx(freqs, survey.dtrue[:freqs.size], 'b.-') ax.semilogx(freqs, survey.dobs[:freqs.size], 'r.-') ax.legend(('Noisefree', '$d^{obs}$'), fontsize=16) ax.set_xlabel('Time (s)', fontsize=14) ax.set_ylabel('$B_z$ (T)', fontsize=16) ax.set_xlabel('Time (s)', fontsize=14) ax.grid(color='k', alpha=0.5, linestyle='dashed', linewidth=0.5) dmisfit = DataMisfit.l2_DataMisfit(survey) regMesh = Mesh.TensorMesh([mesh.hz[mapping.maps[-1].indActive]]) reg = Regularization.Tikhonov(regMesh) opt = Optimization.InexactGaussNewton(maxIter=6) invProb = InvProblem.BaseInvProblem(dmisfit, reg, opt) # Create an inversion object beta = Directives.BetaSchedule(coolingFactor=5, coolingRate=2) betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1e0) inv = Inversion.BaseInversion(invProb, directiveList=[beta, betaest]) m0 = np.log(np.ones(mtrue.size) * sig_half) reg.alpha_s = 1e-3 reg.alpha_x = 1. prb.counter = opt.counter = Utils.Counter() opt.LSshorten = 0.5 opt.remember('xc') mopt = inv.run(m0) if plotIt: fig, ax = plt.subplots(1, 1, figsize=(3, 6)) plt.semilogx(sigma[active], mesh.vectorCCz[active]) plt.semilogx(np.exp(mopt), mesh.vectorCCz[active]) ax.set_ylim(-500, 0) ax.set_xlim(1e-3, 1e-1) ax.set_xlabel('Conductivity (S/m)', fontsize=14) ax.set_ylabel('Depth (m)', fontsize=14) ax.grid(color='k', alpha=0.5, linestyle='dashed', linewidth=0.5) plt.legend(['$\sigma_{true}$', '$\sigma_{pred}$'], loc='best')
def test_CylMeshEBDipoles(self): print( "Testing CylMesh Electric and Magnetic Dipoles in a wholespace-" " Analytic: J-formulation") sigmaback = 1. mur = 2. freq = 1. skdpth = 500. / np.sqrt(sigmaback * freq) csx, ncx, npadx = 5, 50, 25 csz, ncz, npadz = 5, 50, 25 hx = Utils.meshTensor([(csx, ncx), (csx, npadx, 1.3)]) hz = Utils.meshTensor([(csz, npadz, -1.3), (csz, ncz), (csz, npadz, 1.3)]) mesh = Mesh.CylMesh( [hx, 1, hz], [0., 0., -hz.sum() / 2]) # define the cylindrical mesh if plotIt: mesh.plotGrid() # make sure mesh is big enough self.assertTrue(mesh.hz.sum() > skdpth * 2.) self.assertTrue(mesh.hx.sum() > skdpth * 2.) SigmaBack = sigmaback * np.ones((mesh.nC)) MuBack = mur * mu_0 * np.ones((mesh.nC)) # set up source # test electric dipole src_loc = np.r_[0., 0., 0.] s_ind = Utils.closestPoints(mesh, src_loc, 'Fz') + mesh.nFx de = np.zeros(mesh.nF, dtype=complex) de[s_ind] = 1. / csz de_p = [EM.FDEM.Src.RawVec_e([], freq, de / mesh.area)] dm_p = [EM.FDEM.Src.MagDipole([], freq, src_loc)] # Pair the problem and survey surveye = EM.FDEM.Survey(de_p) surveym = EM.FDEM.Survey(dm_p) mapping = [('sigma', Maps.IdentityMap(mesh)), ('mu', Maps.IdentityMap(mesh))] prbe = EM.FDEM.Problem3D_h(mesh, mapping=mapping) prbm = EM.FDEM.Problem3D_e(mesh, mapping=mapping) prbe.pair(surveye) # pair problem and survey prbm.pair(surveym) # solve fieldsBackE = prbe.fields(np.r_[SigmaBack, MuBack]) # Done fieldsBackM = prbm.fields(np.r_[SigmaBack, MuBack]) # Done rlim = [20., 500.] lookAtTx = de_p r = mesh.vectorCCx[np.argmin(np.abs(mesh.vectorCCx - rlim[0])):np. argmin(np.abs(mesh.vectorCCx - rlim[1]))] z = 100. # where we choose to measure XYZ = Utils.ndgrid(r, np.r_[0.], np.r_[z]) Pf = mesh.getInterpolationMat(XYZ, 'CC') Zero = sp.csr_matrix(Pf.shape) Pfx, Pfz = sp.hstack([Pf, Zero]), sp.hstack([Zero, Pf]) jn = fieldsBackE[de_p, 'j'] bn = fieldsBackM[dm_p, 'b'] Rho = Utils.sdiag(1. / SigmaBack) Rho = sp.block_diag([Rho, Rho]) en = Rho * mesh.aveF2CCV * jn bn = mesh.aveF2CCV * bn ex, ez = Pfx * en, Pfz * en bx, bz = Pfx * bn, Pfz * bn # get analytic solution exa, eya, eza = EM.Analytics.FDEM.ElectricDipoleWholeSpace( XYZ, src_loc, sigmaback, freq, orientation='Z', mu=mur * mu_0) exa, eya, eza = Utils.mkvc(exa, 2), Utils.mkvc(eya, 2), Utils.mkvc(eza, 2) bxa, bya, bza = EM.Analytics.FDEM.MagneticDipoleWholeSpace( XYZ, src_loc, sigmaback, freq, orientation='Z', mu=mur * mu_0) bxa, bya, bza = Utils.mkvc(bxa, 2), Utils.mkvc(bya, 2), Utils.mkvc(bza, 2) print ' comp, anayltic, numeric, num - ana, (num - ana)/ana' print ' ex:', np.linalg.norm(exa), np.linalg.norm(ex), np.linalg.norm( exa - ex), np.linalg.norm(exa - ex) / np.linalg.norm(exa) print ' ez:', np.linalg.norm(eza), np.linalg.norm(ez), np.linalg.norm( eza - ez), np.linalg.norm(eza - ez) / np.linalg.norm(eza) print ' bx:', np.linalg.norm(bxa), np.linalg.norm(bx), np.linalg.norm( bxa - bx), np.linalg.norm(bxa - bx) / np.linalg.norm(bxa) print ' bz:', np.linalg.norm(bza), np.linalg.norm(bz), np.linalg.norm( bza - bz), np.linalg.norm(bza - bz) / np.linalg.norm(bza) if plotIt is True: # Edipole plt.subplot(221) plt.plot(r, ex.real, 'o', r, exa.real, linewidth=2) plt.grid(which='both') plt.title('Ex Real') plt.xlabel('r (m)') plt.subplot(222) plt.plot(r, ex.imag, 'o', r, exa.imag, linewidth=2) plt.grid(which='both') plt.title('Ex Imag') plt.legend(['Num', 'Ana'], bbox_to_anchor=(1.5, 0.5)) plt.xlabel('r (m)') plt.subplot(223) plt.plot(r, ez.real, 'o', r, eza.real, linewidth=2) plt.grid(which='both') plt.title('Ez Real') plt.xlabel('r (m)') plt.subplot(224) plt.plot(r, ez.imag, 'o', r, eza.imag, linewidth=2) plt.grid(which='both') plt.title('Ez Imag') plt.xlabel('r (m)') plt.tight_layout() # Bdipole plt.subplot(221) plt.plot(r, bx.real, 'o', r, bxa.real, linewidth=2) plt.grid(which='both') plt.title('Bx Real') plt.xlabel('r (m)') plt.subplot(222) plt.plot(r, bx.imag, 'o', r, bxa.imag, linewidth=2) plt.grid(which='both') plt.title('Bx Imag') plt.legend(['Num', 'Ana'], bbox_to_anchor=(1.5, 0.5)) plt.xlabel('r (m)') plt.subplot(223) plt.plot(r, bz.real, 'o', r, bza.real, linewidth=2) plt.grid(which='both') plt.title('Bz Real') plt.xlabel('r (m)') plt.subplot(224) plt.plot(r, bz.imag, 'o', r, bza.imag, linewidth=2) plt.grid(which='both') plt.title('Bz Imag') plt.xlabel('r (m)') plt.tight_layout() self.assertTrue( np.linalg.norm(exa - ex) / np.linalg.norm(exa) < tol_EBdipole) self.assertTrue( np.linalg.norm(eza - ez) / np.linalg.norm(eza) < tol_EBdipole) self.assertTrue( np.linalg.norm(bxa - bx) / np.linalg.norm(bxa) < tol_EBdipole) self.assertTrue( np.linalg.norm(bza - bz) / np.linalg.norm(bza) < tol_EBdipole)