srcs, recs = utils.connect_points(src_loc, rec_loc) tts = ttime2d.straight(model, 'vp', srcs, recs) tts, error = utils.contaminate(tts, 0.02, percent=True, return_stddev=True, seed=seed) # Make the mesh mesh = SquareMesh(area, shape) # and run the inversion misfit = srtomo.SRTomo(tts, srcs, recs, mesh) regularization = TotalVariation2D(10**-10, mesh.shape) tomo = misfit + regularization tomo = LCurve(misfit, regularization, [10**i for i in np.arange(-3, 3, 0.5)], jobs=8) # Since Total Variation is a non-linear function, then the tomography becomes # non-linear. So we need to configure fit to use the Levemberg-Marquardt # algorithm, a gradient descent method, that requires an initial estimate tomo.config('levmarq', initial=0.00001*np.ones(mesh.size)).fit() mesh.addprop('vp', tomo.estimate_) # Plot the L-curve annd print the regularization parameter estimated mpl.figure() mpl.title('L-curve: triangle marks the best solution') tomo.plot_lcurve() print "Estimated regularization parameter: %g" % (tomo.regul_param_) # Calculate and print the standard deviation of the residuals # Should be close to the data error if the inversion was able to fit the data residuals = tomo.residuals() print "Assumed error: %f" % (error) print "Standard deviation of residuals: %f" % (np.std(residuals)) mpl.figure(figsize=(14, 5))
depths = (-1e-15*(xs - 50000)**4 + 8000 - 3000*np.exp(-(xs - 70000)**2/(10000**2))) depths -= depths.min() # Reduce depths to zero props = {'density': -300} model = Polygon(np.transpose([xs, depths]), props) x = np.linspace(0, 100000, 100) z = -100*np.ones_like(x) data = utils.contaminate(talwani.gz(x, z, [model]), 0.5, seed=0) # Make the solver and run the inversion misfit = PolygonalBasinGravity(x, z, data, 50, props, top=0) regul = Smoothness1D(misfit.nparams) # Use an L-curve analysis to find the best regularization parameter lc = LCurve(misfit, regul, [10**i for i in np.arange(-10, -5, 0.5)], jobs=4) initial = 3000*np.ones(misfit.nparams) lc.config('levmarq', initial=initial).fit() mpl.figure() mpl.subplot(2, 2, 1) mpl.plot(x, data, 'ok', label='observed') mpl.plot(x, lc.predicted(), '-r', linewidth=2, label='predicted') mpl.legend() ax = mpl.subplot(2, 2, 3) mpl.polygon(model, fill='gray', alpha=0.5) mpl.polygon(lc.estimate_, style='o-r') ax.invert_yaxis() mpl.subplot(1, 2, 2) mpl.title('L-curve') lc.plot_lcurve() mpl.show()