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SeismicInversion.py
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SeismicInversion.py
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#!/usr/bin/env python
# coding: utf-8
# # Pylops - Seismic Inversion with cupy
# In[1]:
import warnings
warnings.filterwarnings('ignore')
import os
import time
import numpy as np
import cupy as cp
import scipy as sp
import cusignal
import matplotlib.pyplot as plt
from scipy.signal import convolve
from pylops.utils import dottest
from pylops.utils.wavelets import *
from pylops.utils.seismicevents import *
from pylops.basicoperators import *
from pylops.signalprocessing import *
from pylops.waveeqprocessing.mdd import *
from pylops.avo.avo import *
from pylops.avo.poststack import *
from pylops.avo.prestack import *
from pylops.optimization.leastsquares import *
dtype = np.float64
plt.style.use('seaborn-dark')
# ## 1D Prestack modelling and inversion
# In[2]:
vp1, vs1, rho1 = 2200., 1300., 2000 # upper medium
vp0, vs0, rho0 = 2300., 1400., 2100 # lower medium
ntheta = 21
thetamin, thetamax = 0, 60
theta = cp.linspace(thetamin, thetamax, ntheta)
# Create composite parameters
ai0, si0, vpvs0 = vp0*rho0, vs0*rho0, vp0/vs0
ai1, si1, vpvs1 = vp1*rho1, vs1*rho1, vp1/vs1
# Zoeppritz
rpp_zoep = zoeppritz_pp(vp1, vs1, rho1, vp0, vs0, rho0, theta)
rpp_zoep_approx = approx_zoeppritz_pp(vp1, vs1, rho1, vp0, vs0, rho0, theta)
print(type(rpp_zoep), type(rpp_zoep_approx), rpp_zoep.dtype, rpp_zoep_approx.dtype)
# Aki Richards
rvp = np.log(vp0) - np.log(vp1)
rvs = np.log(vs0) - np.log(vs1)
rrho = np.log(rho0) - np.log(rho1)
G1, G2, G3 = akirichards(theta, vs1/vp1)
rpp_aki = G1*rvp + G2*rvs + G3*rrho
# Fatti
rai = np.log(ai0) - np.log(ai1)
rsi = np.log(si0) - np.log(si1)
G1, G2, G3 = fatti(theta, vs1/vp1)
rpp_fatti = G1*rai + G2*rsi + G3*rrho
plt.figure(figsize=(4,7))
plt.plot(cp.asnumpy(theta), cp.asnumpy(rpp_zoep), 'k', lw=3, label='Zoeppritz')
plt.plot(cp.asnumpy(theta), cp.asnumpy(rpp_zoep_approx), '--b', lw=3, label='Approx Zoeppritz')
plt.plot(cp.asnumpy(theta), cp.asnumpy(rpp_aki), '--r', lw=3, label='Aki-Richard')
plt.plot(cp.asnumpy(theta), cp.asnumpy(rpp_fatti), '-.g', lw=3, label='Fatti')
plt.xlabel(r'$\Theta$')
plt.title(r'Reflection coefficient $R_{PP}$')
plt.grid()
plt.legend();
# In[3]:
np.random.seed(0)
nt0 = 301
dt0 = 0.004
t0 = np.arange(nt0)*dt0
vp = 1200 + np.arange(nt0) + filtfilt(np.ones(5)/5.,1,np.random.normal(0, 80, nt0))
vs = 600 + vp/2 + filtfilt(np.ones(5)/5.,1,np.random.normal(0, 20, nt0))
rho = 1000 + vp + filtfilt(np.ones(5)/5.,1,np.random.normal(0, 30, nt0))
vp[131:]+=500
vs[131:]+=200
rho[131:]+=100
fig, axs = plt.subplots (1, 3, figsize=(13,7))
axs[0].plot(vp, t0, 'k')
axs[0].set_title('Vp')
axs[0].invert_yaxis()
axs[1].plot(vs, t0, 'k')
axs[1].set_title('Vs')
axs[1].invert_yaxis()
axs[2].plot(rho, t0, 'k')
axs[2].set_title('Rho')
axs[2].invert_yaxis()
vp, vs, rho = cp.asarray(vp).astype(dtype), cp.asarray(vs).astype(dtype), cp.asarray(rho).astype(dtype)
print(vp.dtype, vs.dtype, rho.dtype)
# In[4]:
ntheta = 21
thetamin, thetamax = 0, 40
theta = np.linspace(thetamin, thetamax, ntheta)
ntwav = 41
wav = ricker(t0[:ntwav//2+1], 15)[0]
vsvp = 0.5
vsvp_z = np.linspace(0.4, 0.6, nt0)
m = np.stack((np.log(vp), np.log(vs), np.log(rho)),axis=1)
m = cp.asarray(m).astype(dtype)
# In[5]:
# lop (constant vsvp)
PPop = PrestackLinearModelling(cp.asarray(wav).astype(dtype), cp.asarray(theta).astype(dtype), vsvp=vsvp,
nt0=nt0, linearization='akirich')
dottest(PPop, nt0*ntheta, nt0*3, verb=True, tol=1e-3, backend='cupy')
# dense (constant vsvp)
PPop_dense = PrestackLinearModelling(cp.asarray(wav).astype(dtype), cp.asarray(theta).astype(dtype), vsvp=vsvp,
nt0=nt0, linearization='akirich', explicit=True)
dottest(PPop_dense, nt0*ntheta, nt0*3, verb=True, tol=1e-3, backend='cupy')
print(PPop, PPop_dense)
# lop (depth-variant vsvp)
PPop = PrestackLinearModelling(cp.asarray(wav).astype(dtype), cp.asarray(theta).astype(dtype),
vsvp=cp.asarray(vsvp_z).astype(dtype), linearization='akirich')
dottest(PPop, nt0*ntheta, nt0*3, verb=True, tol=1e-3, backend='cupy')
# dense (depth-variant vsvp)
PPop_dense = PrestackLinearModelling(cp.asarray(wav).astype(dtype), cp.asarray(theta).astype(dtype),
vsvp=cp.asarray(vsvp_z).astype(dtype), linearization='akirich', explicit=True)
dottest(PPop_dense, nt0*ntheta, nt0*3, verb=True, tol=1e-3, backend='cupy')
print(PPop, PPop_dense)
# In[6]:
# lop
dPP = PPop * m.flatten()
dPP = dPP.reshape(nt0,ntheta)
# dense
dPP_dense = PPop_dense * m.T.flatten()
dPP_dense = dPP_dense.reshape(ntheta,nt0).T
dPPn_dense = dPP_dense + cp.random.normal(0, 1e-2, dPP_dense.shape).astype(dtype)
print(dPP.dtype, dPP_dense.dtype)
# In[7]:
fig, axs = plt.subplots(1, 4, figsize=(17,7))
im = axs[0].imshow(cp.asnumpy(dPP), cmap='gray',
extent=(theta[0], theta[-1], t0[-1], t0[0]))
axs[0].set_title('Data - lop');
axs[0].axis('tight');
fig.colorbar(im, ax=axs[0])
im = axs[1].imshow(cp.asnumpy(dPP_dense), cmap='gray',
extent=(theta[0], theta[-1], t0[-1], t0[0]))
axs[1].set_title('Data - dense');
axs[1].axis('tight');
fig.colorbar(im, ax=axs[1])
im = axs[2].imshow(cp.asnumpy(dPP - dPP_dense), cmap='gray',
extent=(theta[0], theta[-1], t0[-1], t0[0]))
axs[2].set_title('Data - error');
axs[2].axis('tight');
fig.colorbar(im, ax=axs[2]);
im = axs[3].imshow(cp.asnumpy(dPPn_dense), cmap='gray',
extent=(theta[0], theta[-1], t0[-1], t0[0]))
axs[3].set_title('Noisy data');
axs[3].axis('tight');
fig.colorbar(im, ax=axs[3]);
# In[8]:
nsmooth = 50
mback = filtfilt(np.ones(nsmooth)/float(nsmooth), 1, cp.asnumpy(m), axis=0)
mback = cp.asarray(mback).astype(dtype)
# lop
dPP_0 = PPop * mback.ravel()
dPP_r = dPP.ravel() - dPP_0
minv = NormalEquationsInversion(PPop, [], dPP_r, epsI=0, **dict(niter=100))
minv = minv.reshape(nt0,3)
# dense
dPP_0_dense = PPop_dense*mback.T.ravel()
dPP_r_dense = dPP_dense.T.ravel() - dPP_0_dense
minv_dense = cp.linalg.lstsq(PPop_dense.A, dPP_r_dense, rcond=1e-5)[0]
minv_dense = minv_dense.reshape(3, nt0).T
minv = mback+minv
minv_dense = mback+minv_dense
print(m.dtype, mback.dtype, minv.dtype, minv_dense.dtype)
# In[9]:
fig, axs = plt.subplots(1, 3, figsize=(10, 8))
axs[0].plot(cp.asnumpy(vp), t0, 'k', lw=4, label='True')
axs[0].plot(np.exp(cp.asnumpy(mback)[:, 0]), t0, '--r', lw=4, label='Back')
axs[0].plot(np.exp(cp.asnumpy(minv)[:, 0]), t0, '--b', lw=2, label='Inv Lop')
axs[0].plot(np.exp(cp.asnumpy(minv_dense)[:, 0]), t0, '--m', lw=2, label='Inv Dense')
axs[0].set_title('Model')
axs[0].invert_yaxis()
axs[1].plot(cp.asnumpy(vs), t0, 'k', lw=4, label='True')
axs[1].plot(np.exp(cp.asnumpy(mback)[:, 1]), t0, '--r', lw=4, label='Back')
axs[1].plot(np.exp(cp.asnumpy(minv)[:, 1]), t0, '--b', lw=2, label='Inv Lop')
axs[1].plot(np.exp(cp.asnumpy(minv_dense)[:, 1]), t0, '--m', lw=2, label='Inv Dense')
#axs[1].plot(np.exp(minv_noise[:, 1]), t0, '--g', lw=2, label='Inv Noisy')
axs[1].set_title('Model')
axs[1].invert_yaxis()
axs[1].axis('tight')
axs[2].plot(cp.asnumpy(rho), t0, 'k', lw=4, label='True')
axs[2].plot(np.exp(cp.asnumpy(mback)[:, 2]), t0, '--r', lw=4, label='Back')
axs[2].plot(np.exp(cp.asnumpy(minv)[:, 2]), t0, '--b', lw=2, label='Inv Lop')
axs[2].plot(np.exp(cp.asnumpy(minv_dense)[:, 2]), t0, '--m', lw=2, label='Inv Dense')
#axs[2].plot(np.exp(minv_noise[:, 2]), t0, '--g', lw=2, label='Inv Noisy')
axs[2].set_title('Model')
axs[2].invert_yaxis()
axs[2].axis('tight')
axs[2].legend();
# In[10]:
minv_dense, dPP_dense_res = PrestackInversion(dPP_dense, cp.asarray(theta).astype(dtype), cp.asarray(wav).astype(dtype), m0=mback, linearization='akirich',
explicit=True, returnres=True, **dict(rcond=1e-5))
minv, dPP_res = PrestackInversion(dPP, cp.asarray(theta).astype(dtype), cp.asarray(wav).astype(dtype), m0=mback, linearization='akirich',
explicit=False, returnres=True, **dict(damp=1e-10, niter=2000))
minv_dense_noise, dPPn_dense_res = PrestackInversion(dPPn_dense, cp.asarray(theta).astype(dtype), cp.asarray(wav).astype(dtype), m0=mback,
linearization='akirich', explicit=True,
simultaneous=False, returnres=True, **dict(rcond=2e-2))
minv_noise, dPPn_res = PrestackInversion(dPPn_dense, cp.asarray(theta).astype(dtype), cp.asarray(wav).astype(dtype), m0=mback,
linearization='akirich', explicit=False,
epsR=5e-1, returnres=True, **dict(damp=1e-1, niter=2000))
print(minv_dense.dtype, minv.dtype, minv_dense_noise.dtype, minv_noise.dtype)
fig, axs = plt.subplots(1, 3, figsize=(10, 8))
axs[0].plot(cp.asnumpy(vp), t0, 'k', lw=4, label='True')
axs[0].plot(np.exp(cp.asnumpy(mback)[:, 0]), t0, '--r', lw=4, label='Back')
axs[0].plot(np.exp(cp.asnumpy(minv)[:, 0]), t0, '--b', lw=2, label='Inv Lop')
axs[0].plot(np.exp(cp.asnumpy(minv_dense)[:, 0]), t0, '--m', lw=2, label='Inv Dense')
axs[0].plot(np.exp(cp.asnumpy(minv_noise)[:, 0]), t0, '--g', lw=2, label='Noisy Lops')
axs[0].plot(np.exp(cp.asnumpy(minv_dense_noise)[:, 0]), t0, '--c', lw=2, label='Noisy Dense')
axs[0].set_title('Model')
axs[0].invert_yaxis()
axs[0].axis('tight')
axs[1].plot(cp.asnumpy(vs), t0, 'k', lw=4, label='True')
axs[1].plot(np.exp(cp.asnumpy(mback)[:, 1]), t0, '--r', lw=4, label='Back')
axs[1].plot(np.exp(cp.asnumpy(minv)[:, 1]), t0, '--b', lw=2, label='Inv Lop')
axs[1].plot(np.exp(cp.asnumpy(minv_dense)[:, 1]), t0, '--m', lw=2, label='Inv Dense')
axs[1].plot(np.exp(cp.asnumpy(minv_noise)[:, 1]), t0, '--g', lw=2, label='Noisy Lops')
axs[1].plot(np.exp(cp.asnumpy(minv_dense_noise)[:, 1]), t0, '--c', lw=2, label='Noisy Dense')
axs[1].set_title('Model')
axs[1].invert_yaxis()
axs[1].axis('tight')
axs[2].plot(cp.asnumpy(rho), t0, 'k', lw=4, label='True')
axs[2].plot(np.exp(cp.asnumpy(mback)[:, 2]), t0, '--r', lw=4, label='Back')
axs[2].plot(np.exp(cp.asnumpy(minv)[:, 2]), t0, '--b', lw=2, label='Inv Lop')
axs[2].plot(np.exp(cp.asnumpy(minv_dense)[:, 2]), t0, '--m', lw=2, label='Inv Dense')
axs[2].plot(np.exp(cp.asnumpy(minv_noise)[:, 2]), t0, '--g', lw=2, label='Noisy Lops')
axs[2].plot(np.exp(cp.asnumpy(minv_dense_noise)[:, 2]), t0, '--c', lw=2, label='Noisy Dense')
axs[2].set_title('Model')
axs[2].invert_yaxis()
axs[2].axis('tight')
axs[2].legend();
fig, axs = plt.subplots(1, 4, figsize=(14,7))
im = axs[0].imshow(cp.asnumpy(dPP_dense_res), cmap='gray',
extent=(theta[0], theta[-1], t0[-1], t0[0]), vmin=-0.1, vmax=0.1)
axs[0].set_title('Residual - dense');
axs[0].axis('tight');
im = axs[1].imshow(cp.asnumpy(dPP_res), cmap='gray',
extent=(theta[0], theta[-1], t0[-1], t0[0]), vmin=-0.1, vmax=0.1)
axs[1].set_title('Residual - lop');
axs[1].axis('tight');
im = axs[2].imshow(cp.asnumpy(dPPn_dense_res), cmap='gray',
extent=(theta[0], theta[-1], t0[-1], t0[0]), vmin=-0.1, vmax=0.1)
axs[2].set_title('Residual - noisy dense');
axs[2].axis('tight');
im = axs[3].imshow(cp.asnumpy(dPPn_res), cmap='gray',
extent=(theta[0], theta[-1], t0[-1], t0[0]), vmin=-0.1, vmax=0.1)
axs[3].set_title('Residual - noisy lop');
axs[3].axis('tight');
# ## Wavelet estimation
# In[11]:
# Create wavelets
ntwav = 41
wavoff=10
wav, twav, wavc = ricker(t0[:ntwav//2+1],20)
wav_phase = np.hstack((wav[wavoff:], np.zeros(wavoff)))
# Create operators
Wavesop = PrestackWaveletModelling(m.astype(dtype), cp.asarray(theta).astype(dtype), nwav=ntwav, wavc=wavc,
vsvp=vsvp, linearization='akirich')
Wavesop_phase = PrestackWaveletModelling(m.astype(dtype), cp.asarray(theta).astype(dtype), nwav=ntwav, wavc=wavc,
vsvp=vsvp, linearization='akirich')
print(Wavesop, Wavesop_phase)
dottest(Wavesop, nt0*ntheta, ntwav, verb=True, backend='cupy')
dottest(Wavesop_phase, nt0*ntheta, ntwav, verb=True, backend='cupy')
# Create data
d = (Wavesop*cp.asarray(wav)).reshape(ntheta,nt0).T
d_phase = (Wavesop_phase*cp.asarray(wav_phase)).reshape(ntheta,nt0).T
print(d.dtype, d_phase.dtype)
fig, axs = plt.subplots(1,2, figsize=(7,7), sharey=True)
axs[0].imshow(cp.asnumpy(d), cmap='gray', extent=(theta[0], theta[-1], t0[-1], t0[0]), vmin=-0.1, vmax=0.1)
axs[0].axis('tight')
axs[0].set_xlabel(r'$\Theta$'), axs[0].set_ylabel(r'$t(s)$')
axs[0].set_title('Data with zero-phase wavelet')
axs[1].imshow(cp.asnumpy(d_phase), cmap='gray',
extent=(theta[0], theta[-1], t0[-1], t0[0]), vmin=-0.1, vmax=0.1)
axs[1].axis('tight')
axs[1].set_title('Data with non-zero-phase wavelet')
axs[1].set_xlabel(r'$\Theta$');
# In[12]:
wav_est = Wavesop / d.T.flatten()
wav_phase_est = Wavesop_phase / d_phase.T.flatten()
print(wav_est.dtype, wav_phase_est.dtype)
fig, axs = plt.subplots(2, 1, sharex=True, figsize=(12,6))
axs[0].plot(wav, 'k', lw=4, label='True')
axs[0].plot(cp.asnumpy(wav_est), '--r', lw=2, label='Estimated')
axs[0].set_title('Zero-phase wavelet')
axs[0].grid()
axs[0].legend(loc='best')
axs[0].axis('tight')
axs[1].plot(wav_phase, 'k', lw=4, label='True')
axs[1].plot(cp.asnumpy(wav_phase_est), '--r', lw=2, label='Estimated')
axs[1].set_title('Wavelet with phase')
axs[1].grid()
axs[1].legend(loc='best')
axs[1].axis('tight');
# In[13]:
#add noise
dn = d + cp.random.normal(0, 1e-2, d.shape).astype(dtype)
# unregularized estimate
wavn_est = Wavesop / dn.T.flatten()
# regularized estimate
# Create regularization operator
D2op = SecondDerivative(ntwav, dtype=dtype)
# Invert for interpolated signal
wavn_reg_est, istop, itn, r1norm, r2norm = RegularizedInversion(Wavesop, [D2op], dn.T.flatten(), epsRs=[np.sqrt(0.1)], returninfo=True,
**dict(damp=np.sqrt(1e-4), niter=200 ,show=0))
print(wavn_est.dtype, wavn_reg_est.dtype)
fig, axs = plt.subplots(1,2, figsize=(7,7), sharey=True)
axs[0].imshow(cp.asnumpy(d), cmap='gray',
extent=(theta[0], theta[-1], t0[-1], t0[0]), vmin=-0.1, vmax=0.1)
axs[0].axis('tight')
axs[0].set_xlabel(r'$\Theta$'), axs[0].set_ylabel(r'$t(s)$')
axs[0].set_title('Data')
axs[1].imshow(cp.asnumpy(dn), cmap='gray',
extent=(theta[0], theta[-1], t0[-1], t0[0]), vmin=-0.1, vmax=0.1)
axs[1].axis('tight')
axs[1].set_title('Noisy Data')
axs[1].set_xlabel(r'$\Theta$');
fig, ax = plt.subplots(1, 1, sharex=True, figsize=(12,6))
ax.plot(wav, 'k', lw=4, label='True')
ax.plot(cp.asnumpy(wavn_est), '--r', lw=2, label='Unregularized estimate')
ax.plot(cp.asnumpy(wavn_reg_est), '--g', lw=2, label='Regularized estimate')
ax.set_title('Zero-phase wavelet from noisy data')
ax.grid()
ax.legend(loc='best')
ax.axis('tight');
# In[14]:
# Create symmetrize operator
Sop = Symmetrize((ntwav+1)//2, dtype=dtype)
# Create smoothing operator
Smop = Smoothing1D(5, dims=((ntwav+1)//2,), dtype=dtype)
# Invert for interpolated signal
wavn_prec_est = PreconditionedInversion(Wavesop, Sop,
dn.T.flatten(),
returninfo=False,
**dict(damp=np.sqrt(1e-4),
niter=200, show=0))
wavn_smooth_est = PreconditionedInversion(Wavesop, Sop*Smop,
dn.T.flatten(),
returninfo=False,
**dict(damp=np.sqrt(1e-4),
niter=200, show=0))
print(wavn_prec_est.dtype, wavn_smooth_est.dtype)
fig, ax = plt.subplots(1, 1, sharex=True, figsize=(8, 6))
ax.plot(wav, 'k', lw=6, label='True')
ax.plot(cp.asnumpy(wav_est), '--r', lw=4, label='Estimated (noise-free)')
ax.plot(cp.asnumpy(wavn_prec_est), '--g', lw=4, label='Estimated (noisy symmetric)')
ax.plot(cp.asnumpy(wavn_smooth_est), '--m', lw=4, label='Estimated (noisy smoothed)')
ax.set_title('Zero-phase wavelet')
ax.grid()
ax.legend(loc='upper right');
# ## 1D Poststack inversion
# In[15]:
m1d = cp.asarray(np.log(vp*rho).flatten()).astype(dtype)
# lop
PPop = PoststackLinearModelling(cp.asarray(wav).astype(dtype), nt0=nt0, explicit=False)
dottest(PPop, nt0, nt0, verb=True, backend='cupy', tol=1e-1)
# dense
PPop_dense = PoststackLinearModelling(cp.asarray(wav).astype(dtype), nt0=nt0, explicit=True)
dottest(PPop_dense, nt0, nt0, verb=True, backend='cupy', tol=1e-1)
print(PPop, PPop_dense, PPop_dense.A.dtype)
# data
d = PPop * m1d
d_dense = PPop_dense * m1d.flatten()
dn_dense = d_dense + cp.random.normal(0, 3e-2, d_dense.shape).astype(dtype)
print(d.dtype, d_dense.dtype)
# In[16]:
nsmooth = 100
m1dback = cp.asarray(filtfilt(np.ones(nsmooth).astype(dtype)/float(nsmooth), 1, cp.asnumpy(m1d))).astype(dtype)
# solve lop
d0 = PPop*m1dback
dr = d - d0
minv = cgls(PPop, dr, cp.zeros_like(m1dback).astype(dtype), niter=600, tol=0)[0]
minv = m1dback + minv
# solve dense
d0_dense = PPop*m1dback
dr_dense = d_dense - d0_dense
minv_dense = cp.linalg.lstsq(PPop_dense.A, dr_dense, rcond=1e-5)[0]
minv_dense = m1dback + minv_dense
print(dr.dtype, dr_dense.dtype, minv.dtype, minv_dense.dtype)
fig, axs = plt.subplots(1, 2, figsize=(10, 12))
axs[0].plot(cp.asnumpy(d), t0, 'k', lw=4, label='Lop')
axs[0].plot(cp.asnumpy(d_dense), t0,'--r', lw=2, label='Dense')
axs[0].set_title('Data')
axs[0].invert_yaxis()
axs[0].axis('tight')
axs[0].legend()
axs[1].plot(cp.asnumpy(m1d), t0, 'k', lw=4, label='True')
axs[1].plot(cp.asnumpy(m1dback), t0, '--r', lw=4, label='Back')
axs[1].plot(cp.asnumpy(minv), t0, '--b', lw=2, label='Inv Lop')
axs[1].plot(cp.asnumpy(minv_dense), t0, '--g', lw=2, label='Inv Dense')
axs[1].set_title('Model')
axs[1].invert_yaxis()
axs[1].axis('tight')
axs[1].legend();
# In[17]:
minv_dense = PoststackInversion(d_dense, cp.asarray(wav).astype(dtype), m0=m1dback,
explicit=True, simultaneous=False, dottest=False, **dict(rcond=1e-5))[0]
minv = PoststackInversion(d_dense, cp.asarray(wav).astype(dtype), m0=m1dback.astype(dtype),
explicit=False, simultaneous=False, dottest=False,
**dict(niter=500, tol=0))[0]
minv_noise = PoststackInversion(dn_dense, cp.asarray(wav).astype(dtype), m0=m1dback.astype(dtype), explicit=True,
epsR=1e0, dottest=False, **dict(damp=1e-1))[0]
print(minv_dense.dtype, minv.dtype, minv_noise.dtype)
fig, axs = plt.subplots(1, 2, figsize=(10, 12))
axs[0].plot(cp.asnumpy(d), t0, 'k', lw=4, label='Lop')
axs[0].plot(cp.asnumpy(d_dense), t0,'--r', lw=2, label='Dense')
axs[0].plot(cp.asnumpy(dn_dense), t0,'--g', lw=2, label='Noisy')
axs[0].set_title('Data')
axs[0].invert_yaxis()
axs[0].axis('tight')
axs[0].legend()
axs[1].plot(cp.asnumpy(m1d), t0, 'k', lw=4, label='True')
axs[1].plot(cp.asnumpy(m1dback), t0, '--r', lw=4, label='Back')
axs[1].plot(cp.asnumpy(minv), t0, '--b', lw=2, label='Inv Lop')
axs[1].plot(cp.asnumpy(minv_dense), t0, '--m', lw=2, label='Inv Dense')
axs[1].plot(cp.asnumpy(minv_noise), t0, '--g', lw=2, label='Inv Noisy')
axs[1].set_title('Model')
axs[1].invert_yaxis()
axs[1].axis('tight')
axs[1].legend();
# ## 2D Poststack inversion
# In[18]:
inputfile = 'poststack_model.npz'
# In[19]:
model = np.load(inputfile)
x, z, m = model['x'], model['z'], cp.asarray(np.log(model['model'])).astype(dtype)
nx, nz = len(x), len(z)
# In[20]:
# lop
PPop = PoststackLinearModelling(cp.asarray(wav).astype(dtype), nt0=nz, spatdims=nx, explicit=False)
dottest(PPop, nz*nx, nz*nx, verb=True, tol=1e-3, backend='cupy')
# dense
PPop_dense = PoststackLinearModelling(cp.asarray(wav).astype(dtype), nt0=nz, spatdims=nx, explicit=True)
dottest(PPop_dense, nz*nx, nz*nx, verb=True, tol=1e-3, backend='cupy')
# data
d = (PPop*m.ravel()).reshape(nz,nx)
d_dense = (PPop_dense*m.flatten()).reshape(nz,nx)
print((d - d_dense).max())
n = cp.random.normal(0, 1e-1, d_dense.shape).astype(dtype)
dn = d + n
dn_dense = d_dense + n
print(d.dtype, d_dense.dtype)
# In[21]:
nsmooth = 60
mback = filtfilt(np.ones(nsmooth)/float(nsmooth), 1, cp.asnumpy(m), axis=0)
mback = cp.asarray(filtfilt(np.ones(nsmooth)/float(nsmooth), 1, mback, axis=1)).astype(dtype)
d_0_dense = PPop_dense*mback.ravel()
d_0_lop = PPop*mback.ravel()
# In[22]:
madj_dense = PPop_dense.H*d_dense.ravel()
madj = PPop.H*d.ravel()
print((madj - madj_dense).max())
# In[23]:
# solve all rows indipendently
d_r_dense = d_dense - d_0_dense.reshape(nz,nx)
minv_dense = get_lstsq(m)(PPop_dense.A, d_r_dense, rcond=1e-5)[0]
minv_dense = mback + minv_dense
# solve all rows together
d_r_dense_iter = d_dense - d_0_dense.reshape(nz,nx)
minv_dense_iter = cgls(PPop_dense, d_r_dense_iter.ravel(), cp.zeros_like(d_r_dense_iter.ravel()), niter=100)[0]
minv_dense_iter = minv_dense_iter.reshape(nz, nx)
minv_dense_iter = mback + minv_dense_iter.reshape(nz, nx)
# solve all rows together with regularization
D2op = Laplacian([nz, nx], dtype=dtype)
print(D2op)
minv_dense_reg = NormalEquationsInversion(PPop_dense, [D2op], d_r_dense.flatten(),
epsRs=[np.sqrt(1e-4)], returninfo=False,
**dict(niter=100))
minv_dense_reg = mback + minv_dense_reg.reshape(nz, nx)
print(minv_dense.dtype, minv_dense_iter.dtype, minv_dense_reg.dtype)
fig, axs = plt.subplots(2, 3, figsize=(15,12))
axs[0][0].imshow(cp.asnumpy(d), cmap='gray', extent = (x[0], x[-1], z[-1], z[0]), vmin=-1, vmax=1)
axs[0][0].set_title('Data')
axs[0][0].axis('tight')
axs[0][1].imshow(cp.asnumpy(m), cmap='gist_rainbow', extent = (x[0], x[-1], z[-1], z[0]),
vmin=m.min(), vmax=m.max())
axs[0][1].set_title('Model')
axs[0][1].axis('tight')
axs[0][2].imshow(cp.asnumpy(mback), cmap='gist_rainbow', extent = (x[0], x[-1], z[-1], z[0]),
vmin=m.min(), vmax=m.max())
axs[0][2].set_title('Smooth Model')
axs[0][2].axis('tight')
axs[1][0].imshow(cp.asnumpy(minv_dense), cmap='gist_rainbow', extent = (x[0], x[-1], z[-1], z[0]),
vmin=m.min(), vmax=m.max())
axs[1][0].set_title('Inverted Model')
axs[1][0].axis('tight')
axs[1][1].imshow(cp.asnumpy(minv_dense_iter), cmap='gist_rainbow', extent = (x[0], x[-1], z[-1], z[0]),
vmin=m.min(), vmax=m.max())
axs[1][1].set_title('Inverted Model iter')
axs[1][1].axis('tight');
axs[1][2].imshow(cp.asnumpy(minv_dense_reg), cmap='gist_rainbow', extent = (x[0], x[-1], z[-1], z[0]),
vmin=m.min(), vmax=m.max())
axs[1][2].set_title('Inverted Model reg')
axs[1][2].axis('tight');
fig, ax = plt.subplots(1, 1, figsize=(5, 12))
ax.plot(cp.asnumpy(m)[:,nx//2], z, 'k', lw=4, label='True')
ax.plot(cp.asnumpy(mback)[:,nx//2], z, '--r', lw=4, label='Back')
ax.plot(cp.asnumpy(minv_dense)[:,nx//2], z, '--b', lw=2, label='Inv Dense')
ax.plot(cp.asnumpy(minv_dense_iter)[:,nx//2], z, '--g', lw=2, label='Inv Dense iter')
ax.plot(cp.asnumpy(minv_dense_reg)[:,nx//2], z, '--m', lw=2, label='Inv Dense reg')
ax.set_title('Model')
ax.invert_yaxis()
ax.axis('tight')
ax.legend();
# In[24]:
wav_cp = cp.asarray(wav).astype(dtype)
minv_dense, dr_dense = PoststackInversion(d_dense, wav_cp, m0=mback, explicit=True, simultaneous=False, **dict(rcond=1e-5))
minv_dense_iter, dr_dense_iter = PoststackInversion(d_dense, wav_cp, m0=mback, explicit=True, simultaneous=True,
**dict(niter=50))
minv_dense_reg, dr_dense_reg = PoststackInversion(d_dense, wav_cp, m0=mback, explicit=True, epsR=np.sqrt(1e-4),
**dict(damp=np.sqrt(1e-4), niter=50))
minv_lop_iter, dr_lop_iter = PoststackInversion(d, wav_cp, m0=mback, explicit=False,
**dict(niter=50))
minv_lop_reg, dr_lop_reg = PoststackInversion(d, wav_cp, m0=mback, explicit=False, epsR=np.sqrt(1e-4),
**dict(damp=np.sqrt(1e-4), niter=50))
print(minv_dense.dtype, minv_dense_iter.dtype, minv_dense_reg.dtype, minv_lop_iter.dtype, minv_lop_reg.dtype)
fig, axs = plt.subplots(2, 3, figsize=(15,12))
axs[0][0].imshow(cp.asnumpy(d), cmap='gray', extent = (x[0], x[-1], z[-1], z[0]), vmin=-1, vmax=1)
axs[0][0].set_title('Data')
axs[0][0].axis('tight')
axs[0][1].imshow(cp.asnumpy(m), cmap='gist_rainbow', extent = (x[0], x[-1], z[-1], z[0]),
vmin=m.min(), vmax=m.max())
axs[0][1].set_title('Model')
axs[0][1].axis('tight')
axs[0][2].imshow(cp.asnumpy(mback), cmap='gist_rainbow', extent = (x[0], x[-1], z[-1], z[0]),
vmin=m.min(), vmax=m.max())
axs[0][2].set_title('Smooth Model')
axs[0][2].axis('tight')
axs[1][0].imshow(cp.asnumpy(minv_dense), cmap='gist_rainbow', extent = (x[0], x[-1], z[-1], z[0]),
vmin=m.min(), vmax=m.max())
axs[1][0].set_title('Inverted Model')
axs[1][0].axis('tight')
axs[1][1].imshow(cp.asnumpy(minv_dense_iter), cmap='gist_rainbow', extent = (x[0], x[-1], z[-1], z[0]),
vmin=m.min(), vmax=m.max())
axs[1][1].set_title('Inverted Model iter')
axs[1][1].axis('tight');
axs[1][2].imshow(cp.asnumpy(minv_dense_reg), cmap='gist_rainbow', extent = (x[0], x[-1], z[-1], z[0]),
vmin=m.min(), vmax=m.max())
axs[1][2].set_title('Inverted Model reg')
axs[1][2].axis('tight');
fig, ax = plt.subplots(1, 1, figsize=(5, 12))
ax.plot(cp.asnumpy(m)[:,nx//2], z, 'k', lw=4, label='True')
ax.plot(cp.asnumpy(mback)[:,nx//2], z, '--r', lw=4, label='Back')
ax.plot(cp.asnumpy(minv_dense)[:,nx//2], z, '--b', lw=2, label='Inv Dense')
ax.plot(cp.asnumpy(minv_dense_iter)[:,nx//2], z, '--g', lw=2, label='Inv Dense iter')
ax.plot(cp.asnumpy(minv_dense_reg)[:,nx//2], z, '--m', lw=2, label='Inv Dense reg')
ax.set_title('Model')
ax.invert_yaxis()
ax.axis('tight')
ax.legend();
# In[25]:
PPop_np = PoststackLinearModelling(wav.astype(dtype), nt0=nz, spatdims=nx, explicit=False)
PPop_dense_np = PoststackLinearModelling(wav.astype(dtype), nt0=nz, spatdims=nx, explicit=True)
# ## 3D Poststack inversion
# In[26]:
ny = 30
y = np.arange(ny)
x, z, m = model['x'], model['z'], np.log(model['model'])
ny, nx, nz = len(y), len(x), len(z)
m3d = np.tile(m[:, :, np.newaxis], (1, 1, ny))
mback3d = np.tile(mback[:, :, np.newaxis], (1, 1, ny))
m3d, mback3d = cp.asarray(m3d).astype(dtype), cp.asarray(mback3d).astype(dtype)
# In[27]:
# lop
PPop = PoststackLinearModelling(wav_cp, nt0=nz, spatdims=(nx, ny))
dottest(PPop, nz*nx*ny, nz*nx*ny, verb=True, tol=1e-3, backend='cupy')
# dense
PPop_dense = PoststackLinearModelling(wav_cp, nt0=nz, spatdims=(nx, ny), explicit=True)
dottest(PPop, nz*nx*ny, nz*nx*ny, verb=True, tol=1e-3, backend='cupy')
# data
d = (PPop*m3d.flatten()).reshape(nz, nx, ny)
d_dense = (PPop_dense*m3d.flatten()).reshape(nz, nx, ny)
n = cp.random.normal(0, 1e-2, d_dense.shape).astype(dtype)
dn = d + n
dn_dense = d_dense + n
print(d.dtype, d_dense.dtype)
# In[28]:
minv_dense_f, dr_dense_f = PoststackInversion(d_dense, wav_cp, m0=mback3d, explicit=True,
simultaneous=False, **dict(rcond=1e-5))
print(minv_dense_f.dtype)
fig, axs = plt.subplots(2, 3, figsize=(15,12))
axs[0][0].imshow(cp.asnumpy(d_dense)[:, :, 5], cmap='gray', extent = (x[0], x[-1], z[-1], z[0]), vmin=-1, vmax=1)
axs[0][0].set_title('Data')
axs[0][0].axis('tight')
axs[0][1].imshow(cp.asnumpy(m3d)[:, :, 5], cmap='gist_rainbow', extent = (x[0], x[-1], z[-1], z[0]),
vmin=m.min(), vmax=m.max())
axs[0][1].set_title('Model')
axs[0][1].axis('tight')
axs[0][2].imshow(cp.asnumpy(mback3d)[:, :, 5], cmap='gist_rainbow', extent = (x[0], x[-1], z[-1], z[0]),
vmin=m.min(), vmax=m.max())
axs[0][2].set_title('Smooth Model')
axs[0][2].axis('tight')
axs[1][0].imshow(cp.asnumpy(minv_dense_f)[:, :, 5], cmap='gist_rainbow', extent = (x[0], x[-1], z[-1], z[0]),
vmin=m.min(), vmax=m.max())
axs[1][0].set_title('Inverted Model')
axs[1][0].axis('tight')
axs[1][1].imshow(cp.asnumpy(minv_dense_f)[:, 50], cmap='gist_rainbow', extent = (x[0], x[-1], z[-1], z[0]),
vmin=m.min(), vmax=m.max())
axs[1][1].set_title('Inverted Model (x slice)')
axs[1][1].axis('tight')
axs[1][2].imshow(cp.asnumpy(minv_dense_f)[200], cmap='gist_rainbow', extent = (x[0], x[-1], z[-1], z[0]),
vmin=m.min(), vmax=m.max())
axs[1][2].set_title('Inverted Model (t slice)')
axs[1][2].axis('tight');
# In[29]:
minv_dense_f, dr_dense_f = PoststackInversion(dn_dense, wav_cp, m0=mback3d, explicit=True, epsI=1e-3,
simultaneous=False, **dict(rcond=1e-5))
dn_dense.dtype, wav_cp.dtype, mback3d.dtype, minv_dense_f.dtype
# In[30]:
minv_dense_f, dr_dense_f = PoststackInversion(dn_dense, wav_cp, m0=mback3d, explicit=True, epsI=1e-3,
simultaneous=False, **dict(rcond=1e-5))
minv_dense_reg_f, dr_dense_reg_f = PoststackInversion(dn_dense, wav_cp, m0=minv_dense_f, explicit=True,
epsR=np.sqrt(1e2),
**dict(damp=np.sqrt(1e-2), niter=50))
minv_lop_reg_f, dr_lop_reg_f = PoststackInversion(dn, wav_cp, m0=minv_dense_f, explicit=False,
epsR=np.sqrt(1e2),
**dict(damp=np.sqrt(1e-2), niter=50))
print(minv_dense_f.dtype, minv_dense_reg_f.dtype, minv_lop_reg_f.dtype)
fig, axs = plt.subplots(2, 3, figsize=(15,12))
axs[0][0].imshow(cp.asnumpy(dn)[:, :, 5], cmap='gray', extent = (x[0], x[-1], z[-1], z[0]), vmin=-1, vmax=1)
axs[0][0].set_title('Data')
axs[0][0].axis('tight')
axs[0][1].imshow(cp.asnumpy(m3d)[:, :, 5], cmap='gist_rainbow', extent = (x[0], x[-1], z[-1], z[0]),
vmin=m.min(), vmax=m.max())
axs[0][1].set_title('Model')
axs[0][1].axis('tight')
axs[0][2].imshow(cp.asnumpy(mback3d)[:, :, 5], cmap='gist_rainbow', extent = (x[0], x[-1], z[-1], z[0]),
vmin=m.min(), vmax=m.max())
axs[0][2].set_title('Smooth Model')
axs[0][2].axis('tight')
axs[1][0].imshow(cp.asnumpy(minv_dense_f)[:, :, 5], cmap='gist_rainbow', extent = (x[0], x[-1], z[-1], z[0]),
vmin=m.min(), vmax=m.max())
axs[1][0].set_title('Inverted Model')
axs[1][0].axis('tight')
axs[1][1].imshow(cp.asnumpy(minv_dense_reg_f)[:, :, 5], cmap='gist_rainbow', extent = (x[0], x[-1], z[-1], z[0]),
vmin=m.min(), vmax=m.max())
axs[1][1].set_title('Inverted Model reg')
axs[1][1].axis('tight');
axs[1][2].imshow(cp.asnumpy(minv_lop_reg_f)[:, :, 5], cmap='gist_rainbow', extent = (x[0], x[-1], z[-1], z[0]),
vmin=m.min(), vmax=m.max())
axs[1][2].set_title('Inverted Model reg - lops')
axs[1][2].axis('tight');
# ### Timings
# In[31]:
def poststack3dmod(wav, nt, nx, ny):
print('3D Poststack modelling with nt=%d, nx=%d, ny=%d....' % (nt, nx, ny))
mempool = cp.get_default_memory_pool()
# Numpy modelling
m = np.random.normal(0, 1, nt*nx*ny).astype(dtype)
PPop = PoststackLinearModelling(wav, nt0=nt, spatdims=(nx, ny))
d = PPop * m
d = d.reshape(nt, nx, ny)
tstart_np = time.time()
PoststackInversion(d, wav, explicit=False,
epsR=np.sqrt(1e2), **dict(damp=np.sqrt(1e-2), iter_lim=5))
telapsed_np = (time.time() - tstart_np)
# Cupy modelling
wav_cp = cp.asarray(wav)
d_cp = cp.asarray(d)
tstart_cp = time.time()
PoststackInversion(d_cp, wav_cp, explicit=False,
epsR=np.sqrt(1e2), **dict(damp=np.sqrt(1e-2), niter=5))
telapsed_cp = (time.time() - tstart_cp)
mempool.free_all_blocks()
return telapsed_np, telapsed_cp
# In[32]:
# Compare timings
nt, nx = 500, 10
nys_post = np.arange(200, 1000, 100).astype(np.int)
telapsed_post = np.vstack([np.array(poststack3dmod(wav, nt, nx, ny)) for ny in nys_post])
print('Speedup poststack inversion', telapsed_post[:, 0]/telapsed_post[:, 1])
plt.figure(figsize=(5, 2))
plt.plot(nys_post, telapsed_post[:, 0], 'k', lw=2, label='Numpy')
plt.plot(nys_post, telapsed_post[:, 1], 'r', lw=2, label='Cupy')
plt.xlabel('ny')
plt.ylabel('t[s]')
plt.title('Elapsed time for 3D PoststackLinearModelling')
plt.legend()
# ## 2D Prestack inversion
# In[33]:
model = np.load(inputfile)
x, z, m = model['x'][::3], model['z'], 1000*model['model'][:, ::3]
nx, nz = len(x), len(z)
mvp = m.copy()
mvs = m/2
mrho = m/3+300
fig, axs = plt.subplots(1, 3, figsize=(15,5))
im=axs[0].imshow(mvp, cmap='gist_rainbow', extent = (x[0], x[-1], z[-1], z[0]),
vmin=mvp.min(), vmax=mvp.max())
axs[0].set_title('VP')
axs[0].axis('tight')
plt.colorbar(im, ax=axs[0])
im=axs[1].imshow(mvs, cmap='gist_rainbow', extent = (x[0], x[-1], z[-1], z[0]),
vmin=mvs.min(), vmax=mvs.max())
axs[1].set_title('VS')
plt.colorbar(im, ax=axs[1])
axs[1].axis('tight')
im=axs[2].imshow(mrho, cmap='gist_rainbow', extent = (x[0], x[-1], z[-1], z[0]),
vmin=mrho.min(), vmax=mrho.max())
axs[2].set_title('Rho')
axs[2].axis('tight');
plt.colorbar(im, ax=axs[2]);
# In[34]:
m = np.log(np.stack((mvp, mvs, mrho),axis=1))
m = cp.asarray(m).astype(dtype)
theta = cp.linspace(thetamin, thetamax, ntheta).astype(dtype)
# lop (constant vsvp)
PPop = PrestackLinearModelling(wav_cp.astype(dtype), theta, vsvp=vsvp, nt0=nz,
spatdims=(nx,), linearization='akirich')
dottest(PPop, nz*ntheta*nx, nz*3*nx, verb=True, backend='cupy', tol=1e-1)
# dense (constant vsvp)
PPop_dense = PrestackLinearModelling(wav_cp.astype(dtype), theta, vsvp=vsvp, nt0=nz,
spatdims=(nx,), linearization='akirich', explicit=True)
dottest(PPop_dense, nz*ntheta*nx, nz*3*nx, verb=True, backend='cupy', tol=1e-1)
# lop
dPP = PPop * m.flatten()
dPP = dPP.reshape(nz,ntheta,nx)
# dense
dPP_dense = PPop_dense*m.swapaxes(0,1).flatten()
dPP_dense = dPP_dense.reshape(ntheta,nz,nx).swapaxes(0,1)
dPPn_dense = dPP_dense + cp.random.normal(0, 5e-2, dPP_dense.shape).astype(dtype)
print(dPP.dtype, dPP_dense.dtype)
# In[35]:
madj_dense = PPop_dense.H*(dPP_dense.swapaxes(0,1).flatten())
madj = PPop.H*dPP.flatten()
madj_dense = madj_dense.reshape(3,nz,nx).swapaxes(0,1)
madj = madj.reshape(nz,3,nx)
print((dPP-dPP_dense).max())
print((madj-madj_dense).max())
# In[36]:
fig, axs = plt.subplots(2, 3, figsize=(15,13))
axs[0][0].imshow(cp.asnumpy(dPP)[:,0,:], cmap='gray')
axs[0][0].axis('tight')
axs[0][1].imshow(cp.asnumpy(dPP_dense)[:,0,:], cmap='gray')
axs[0][1].axis('tight')
axs[0][2].imshow(cp.asnumpy(dPPn_dense)[:,0,:], cmap='gray')
axs[0][2].axis('tight')
axs[1][0].imshow(cp.asnumpy(dPP)[:,:,nx//2], cmap='gray')
axs[1][0].axis('tight')
axs[1][1].imshow(cp.asnumpy(dPP_dense)[:,:,nx//2], cmap='gray')
axs[1][1].axis('tight')
axs[1][2].imshow(cp.asnumpy(dPPn_dense)[:,:,nx//2], cmap='gray')
axs[1][2].axis('tight');
# In[37]: