/
deghosting.py
executable file
·143 lines (118 loc) · 4.43 KB
/
deghosting.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
r"""
13. Deghosting
==============
Single-component seismic data can be decomposed
in their up- and down-going constituents in a model driven fashion.
This task can be achieved by defining an f-k propagator (or ghost model) and
solving an inverse problem as described in
:func:`pylops.waveeqprocessing.Deghosting`.
"""
# sphinx_gallery_thumbnail_number = 3
import numpy as np
import matplotlib.pyplot as plt
from scipy.sparse.linalg import lsqr
import pylops
np.random.seed(0)
plt.close('all')
###############################################################################
# Let's start by loading the input dataset and geometry
inputfile = '../testdata/updown/input.npz'
inputdata = np.load(inputfile)
vel_sep = 2400.0 # velocity at separation level
clip = 1e-1 # plotting clip
# Receivers
r = inputdata['r']
nr = r.shape[1]
dr = r[0, 1]-r[0, 0]
# Sources
s = inputdata['s']
# Model
rho = inputdata['rho']
# Axes
t = inputdata['t']
nt, dt = len(t), t[1]-t[0]
x, z = inputdata['x'], inputdata['z']
dx, dz = x[1] - x[0], z[1] - z[0]
# Data
p = inputdata['p'].T
p /= p.max()
fig = plt.figure(figsize=(9, 4))
ax1 = plt.subplot2grid((1, 5), (0, 0), colspan=4)
ax2 = plt.subplot2grid((1, 5), (0, 4))
ax1.imshow(rho, cmap='gray', extent=(x[0], x[-1], z[-1], z[0]))
ax1.scatter(r[0, ::5], r[1, ::5], marker='v', s=150, c='b', edgecolors='k')
ax1.scatter(s[0], s[1], marker='*', s=250, c='r', edgecolors='k')
ax1.axis('tight')
ax1.set_xlabel('x [m]')
ax1.set_ylabel('y [m]')
ax1.set_title('Model and Geometry')
ax1.set_xlim(x[0], x[-1])
ax1.set_ylim(z[-1], z[0])
ax2.plot(rho[:, len(x)//2], z, 'k', lw=2)
ax2.set_ylim(z[-1], z[0])
ax2.set_yticks([], [])
###############################################################################
# To be able to deghost the input dataset, we need to remove its direct
# arrival. In this example we will create a mask based on the analytical
# traveltime of the direct arrival.
direct = np.sqrt(np.sum((s[:, np.newaxis]-r)**2, axis=0))/vel_sep
# Window
off = 0.035
direct_off = direct + off
win = np.zeros((nt, nr))
iwin = np.round(direct_off/dt).astype(np.int)
for i in range(nr):
win[iwin[i]:, i] = 1
fig, axs = plt.subplots(1, 2, sharey=True, figsize=(8, 7))
axs[0].imshow(p.T, cmap='gray', vmin=-clip*np.abs(p).max(),
vmax=clip*np.abs(p).max(),
extent=(r[0, 0], r[0, -1], t[-1], t[0]))
axs[0].plot(r[0], direct_off, 'r', lw=2)
axs[0].set_title(r'$P$')
axs[0].axis('tight')
axs[1].imshow(win * p.T, cmap='gray', vmin=-clip*np.abs(p).max(),
vmax=clip*np.abs(p).max(),
extent=(r[0, 0], r[0, -1], t[-1], t[0]))
axs[1].set_title(r'Windowed $P$')
axs[1].axis('tight')
axs[1].set_ylim(1, 0)
###############################################################################
# We can now perform deghosting
pup, pdown = \
pylops.waveeqprocessing.Deghosting(p.T, nt, nr, dt, dr, vel_sep,
r[1, 0] + dz, win=win,
npad=5, ntaper=11, solver=lsqr,
dottest=False, dtype='complex128',
**dict(damp=1e-10, iter_lim=60))
fig, axs = plt.subplots(1, 3, sharey=True, figsize=(12, 7))
axs[0].imshow(p.T, cmap='gray', vmin=-clip * np.abs(p).max(),
vmax=clip * np.abs(p).max(),
extent=(r[0, 0], r[0, -1], t[-1], t[0]))
axs[0].set_title(r'$P$')
axs[0].axis('tight')
axs[1].imshow(pup, cmap='gray', vmin=-clip * np.abs(p).max(),
vmax=clip * np.abs(p).max(),
extent=(r[0, 0], r[0, -1], t[-1], t[0]))
axs[1].set_title(r'$P^-$')
axs[1].axis('tight')
axs[2].imshow(pdown, cmap='gray', vmin=-clip * np.abs(p).max(),
vmax=clip * np.abs(p).max(),
extent=(r[0, 0], r[0, -1], t[-1], t[0]))
axs[2].set_title(r'$P^+$')
axs[2].axis('tight')
axs[2].set_ylim(1, 0)
plt.figure(figsize=(14, 3))
plt.plot(t, p[nr // 2], 'k', lw=2, label=r'$p$')
plt.plot(t, pup[:, nr // 2], 'r', lw=2, label=r'$p^-$')
plt.xlim(0, t[200])
plt.ylim(-0.2, 0.2)
plt.legend()
plt.figure(figsize=(14, 3))
plt.plot(t, pdown[:, nr // 2], 'b', lw=2, label=r'$p^+$')
plt.plot(t, pup[:, nr // 2], 'r', lw=2, label=r'$p^-$')
plt.xlim(0, t[200])
plt.ylim(-0.2, 0.2)
plt.legend()
###############################################################################
# To see more examples head over to the following notebook:
# `notebook1 <https://github.com/mrava87/pylops_notebooks/blob/master/developement/WavefieldSeparation-singlecomponent.ipynb>`_.