mirror of
https://github.com/wassname/simpeg.git
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Rowan Cockett
be3667b4ab
- Put all examples in same directory - Make a single test - use __init__.py to create the docs automatically
105 lines
3.5 KiB
Python
105 lines
3.5 KiB
Python
from SimPEG import *
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import SimPEG.EM as EM
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from scipy.constants import mu_0
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import matplotlib.pyplot as plt
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def run(plotIt=True):
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"""
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EM: FDEM: 1D: Inversion
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=======================
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Here we will create and run a FDEM 1D inversion.
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"""
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cs, ncx, ncz, npad = 5., 25, 15, 15
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hx = [(cs,ncx), (cs,npad,1.3)]
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hz = [(cs,npad,-1.3), (cs,ncz), (cs,npad,1.3)]
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mesh = Mesh.CylMesh([hx,1,hz], '00C')
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active = mesh.vectorCCz<0.
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layer = (mesh.vectorCCz<0.) & (mesh.vectorCCz>=-100.)
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actMap = Maps.ActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz)
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mapping = Maps.ExpMap(mesh) * Maps.Vertical1DMap(mesh) * actMap
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sig_half = 2e-3
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sig_air = 1e-8
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sig_layer = 1e-3
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sigma = np.ones(mesh.nCz)*sig_air
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sigma[active] = sig_half
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sigma[layer] = sig_layer
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mtrue = np.log(sigma[active])
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if plotIt:
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fig, ax = plt.subplots(1,1, figsize = (3, 6))
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plt.semilogx(sigma[active], mesh.vectorCCz[active])
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ax.set_ylim(-600, 0)
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ax.set_xlim(1e-4, 1e-2)
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ax.set_xlabel('Conductivity (S/m)', fontsize = 14)
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ax.set_ylabel('Depth (m)', fontsize = 14)
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ax.grid(color='k', alpha=0.5, linestyle='dashed', linewidth=0.5)
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rxOffset=1e-3
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rx = EM.TDEM.RxTDEM(np.array([[rxOffset, 0., 30]]), np.logspace(-5,-3, 31), 'bz')
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src = EM.TDEM.SrcTDEM_VMD_MVP([rx], np.array([0., 0., 80]))
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survey = EM.TDEM.SurveyTDEM([src])
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prb = EM.TDEM.ProblemTDEM_b(mesh, mapping=mapping)
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prb.Solver = SolverLU
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prb.timeSteps = [(1e-06, 20),(1e-05, 20), (0.0001, 20)]
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prb.pair(survey)
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dtrue = survey.dpred(mtrue)
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survey.dtrue = dtrue
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std = 0.05
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noise = std*abs(survey.dtrue)*np.random.randn(*survey.dtrue.shape)
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survey.dobs = survey.dtrue+noise
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survey.std = survey.dobs*0 + std
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survey.Wd = 1/(abs(survey.dobs)*std)
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if plotIt:
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fig, ax = plt.subplots(1,1, figsize = (10, 6))
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ax.loglog(rx.times, dtrue, 'b.-')
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ax.loglog(rx.times, survey.dobs, 'r.-')
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ax.legend(('Noisefree', '$d^{obs}$'), fontsize = 16)
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ax.set_xlabel('Time (s)', fontsize = 14)
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ax.set_ylabel('$B_z$ (T)', fontsize = 16)
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ax.set_xlabel('Time (s)', fontsize = 14)
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ax.grid(color='k', alpha=0.5, linestyle='dashed', linewidth=0.5)
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dmisfit = DataMisfit.l2_DataMisfit(survey)
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regMesh = Mesh.TensorMesh([mesh.hz[mapping.maps[-1].indActive]])
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reg = Regularization.Tikhonov(regMesh)
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opt = Optimization.InexactGaussNewton(maxIter = 5)
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invProb = InvProblem.BaseInvProblem(dmisfit, reg, opt)
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# Create an inversion object
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beta = Directives.BetaSchedule(coolingFactor=5, coolingRate=2)
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betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1e0)
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inv = Inversion.BaseInversion(invProb, directiveList=[beta,betaest])
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m0 = np.log(np.ones(mtrue.size)*sig_half)
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reg.alpha_s = 1e-2
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reg.alpha_x = 1.
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prb.counter = opt.counter = Utils.Counter()
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opt.LSshorten = 0.5
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opt.remember('xc')
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mopt = inv.run(m0)
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if plotIt:
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fig, ax = plt.subplots(1,1, figsize = (3, 6))
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plt.semilogx(sigma[active], mesh.vectorCCz[active])
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plt.semilogx(np.exp(mopt), mesh.vectorCCz[active])
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ax.set_ylim(-600, 0)
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ax.set_xlim(1e-4, 1e-2)
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ax.set_xlabel('Conductivity (S/m)', fontsize = 14)
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ax.set_ylabel('Depth (m)', fontsize = 14)
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ax.grid(color='k', alpha=0.5, linestyle='dashed', linewidth=0.5)
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plt.legend(['$\sigma_{true}$', '$\sigma_{pred}$'])
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plt.show()
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if __name__ == '__main__':
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run()
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