Blending#

This example shows how to use the pylops.waveeqprocessing.blending.Blending operator to blend seismic data to mimic state-of-the-art simultaneous shooting acquisition systems.

import matplotlib.pyplot as plt
import numpy as np
import scipy as sp

import pylops

plt.close("all")
np.random.seed(0)

Let’s start by considering a streamer seismic dataset and apply blending in so-called continuous blending mode

inputdata = np.load("../testdata/marchenko/input.npz")
data = inputdata["R"]
data = np.pad(data, ((0, 0), (0, 0), (0, 50)))
wav = inputdata["wav"]
wav_c = np.argmax(wav)
ns, nr, nt = data.shape

# time axis
dt = 0.004
t = np.arange(nt) * dt

# convolve with wavelet
data = np.apply_along_axis(sp.signal.convolve, -1, data, wav, mode="full")
data = data[..., wav_c:][..., :nt]

# obc data
data_obc = data[:-1, :-1]
ns_obc, nr_obc, _ = data_obc.shape

# streamer data
nr_streamer = 21
ns_streamer = ns - nr_streamer

data_streamer = np.zeros((ns_streamer, nr_streamer, nt))
for isrc in range(ns_streamer):
    data_streamer[isrc] = data[isrc, isrc : isrc + nr_streamer]

# visualize
isrcplot = [0, ns_obc // 2, ns_obc - 1]
fig, axs = plt.subplots(1, 3, sharey=True, figsize=(12, 8))
fig.suptitle("OBC data")
for i, ax in enumerate(axs):
    ax.imshow(
        data_obc[isrcplot[i]].T,
        cmap="gray",
        vmin=-0.1,
        vmax=0.1,
        extent=(0, nr, t[-1], 0),
        interpolation="none",
    )
    ax.set_title(f"CSG {isrcplot[i]}")
    ax.set_xlabel("#Rec")
    ax.axis("tight")
axs[0].set_ylabel("t [s]")
plt.tight_layout()

isrcplot = [0, ns_streamer // 2, ns_streamer - 1]
fig, axs = plt.subplots(1, 3, sharey=True, figsize=(12, 8))
fig.suptitle("Streamer data")
for i, ax in enumerate(axs):
    ax.imshow(
        data_streamer[isrcplot[i]].T,
        cmap="gray",
        vmin=-0.1,
        vmax=0.1,
        extent=(0, nr_streamer, t[-1], 0),
        interpolation="none",
    )
    ax.set_title(f"CSG {isrcplot[i]}")
    ax.set_xlabel("#Rec")
    ax.axis("tight")
axs[0].set_ylabel("t [s]")
plt.tight_layout()

irecplot = [0, nr_streamer // 2, nr_streamer - 1]
fig, axs = plt.subplots(1, 3, sharey=True, figsize=(12, 8))
fig.suptitle("Streamer data")
for i, ax in enumerate(axs):
    ax.imshow(
        data_streamer[:, irecplot[i]].T,
        cmap="gray",
        vmin=-0.1,
        vmax=0.1,
        extent=(0, ns_streamer, t[-1], 0),
        interpolation="none",
    )
    ax.set_title(f"CRG {irecplot[i]}")
    ax.set_xlabel("#Src")
    ax.axis("tight")
axs[0].set_ylabel("t [s]")
plt.tight_layout()
  • OBC data, CSG 0, CSG 50, CSG 99
  • Streamer data, CSG 0, CSG 40, CSG 79
  • Streamer data, CRG 0, CRG 10, CRG 20

We can now consider the streamer seismic dataset and apply blending in so-called continuous blending mode

overlap = 0.5
ignition_times = np.random.normal(0, 0.6, ns_streamer)
ignition_times += (1 - overlap) * nt * dt
ignition_times[0] = 0.0
ignition_times = np.cumsum(ignition_times)

plt.figure(figsize=(12, 4))
plt.plot(ignition_times, "k")
plt.title("Continuous blending times")

Bop = pylops.waveeqprocessing.BlendingContinuous(
    nt,
    nr_streamer,
    ns_streamer,
    dt,
    ignition_times,
    dtype="complex128",
)
data_blended = Bop * data_streamer
data_pseudo = Bop.H * data_blended

fig, ax = plt.subplots(1, 1, figsize=(4, 19))
ax.imshow(
    data_blended.real.T,
    cmap="gray",
    vmin=-0.1,
    vmax=0.1,
    extent=(0, ns_streamer, Bop.nttot * dt, 0),
    interpolation="none",
)
ax.set_title("Blended CSG")
ax.set_xlabel("#Rec")
ax.set_ylabel("t [s]")
ax.axis("tight")
ax.set_ylim(10, 0)
plt.tight_layout()

fig, axs = plt.subplots(1, 2, sharey=True, figsize=(12, 8))
axs[0].imshow(
    data_streamer[:, 0].real.T,
    cmap="gray",
    vmin=-0.01,
    vmax=0.01,
    extent=(0, ns_streamer, t[-1], 0),
    interpolation="none",
)
axs[0].set_title("Unblended CRG")
axs[0].set_xlabel("#Src")
axs[0].set_ylabel("t [s]")
axs[0].axis("tight")
axs[1].imshow(
    data_pseudo[:, 0].real.T,
    cmap="gray",
    vmin=-0.01,
    vmax=0.01,
    extent=(0, ns_streamer, t[-1], 0),
    interpolation="none",
)
axs[1].set_title("Pseudo-deblended CRG")
axs[1].set_xlabel("#Src")
axs[1].axis("tight")
plt.tight_layout()
  • Continuous blending times
  • Blended CSG
  • Unblended CRG, Pseudo-deblended CRG

Similarly we can consider the OBC data and apply both group and half blending

# Group
group_size = 2
n_groups = ns_obc // 2
ignition_times = np.abs(np.random.normal(0.2, 0.5, ns_obc))  # only positive shifts
ignition_times[0] = 0.0

plt.figure(figsize=(12, 4))
plt.plot(ignition_times.reshape(group_size, n_groups).T, "k")
plt.title("Group blending times")

Bop = pylops.waveeqprocessing.BlendingGroup(
    nt,
    nr_obc,
    ns_obc,
    dt,
    ignition_times.reshape(group_size, n_groups),
    group_size=group_size,
    n_groups=n_groups,
    dtype="complex128",
)
data_blended = Bop * data_obc
data_pseudo = Bop.H * data_blended

fig, ax = plt.subplots(1, 1, figsize=(12, 8))
ax.imshow(
    data_blended[n_groups // 2].real.T,
    cmap="gray",
    vmin=-0.1,
    vmax=0.1,
    extent=(0, ns_streamer, t[-1], 0),
    interpolation="none",
)
ax.set_title("Blended CSG")
ax.set_xlabel("#Rec")
ax.set_ylabel("t [s]")
ax.axis("tight")
plt.tight_layout()

fig, axs = plt.subplots(1, 2, sharey=True, figsize=(12, 8))
axs[0].imshow(
    data_obc[:, 10].real.T,
    cmap="gray",
    vmin=-0.01,
    vmax=0.01,
    extent=(0, ns_streamer, t[-1], 0),
    interpolation="none",
)
axs[0].set_title("Unblended CRG")
axs[0].set_xlabel("#Src")
axs[0].set_ylabel("t [s]")
axs[0].axis("tight")
axs[1].imshow(
    data_pseudo[:, 10].real.T,
    cmap="gray",
    vmin=-0.01,
    vmax=0.01,
    extent=(0, ns_streamer, t[-1], 0),
    interpolation="none",
)
axs[1].set_title("Pseudo-deblended CRG")
axs[1].set_xlabel("#Src")
axs[1].axis("tight")
plt.tight_layout()

# Half
group_size = 2
n_groups = ns_obc // 2
ignition_times = np.abs(np.random.normal(0.1, 0.5, ns_obc))  # only positive shifts
ignition_times[0] = 0.0

plt.figure(figsize=(12, 4))
plt.plot(ignition_times.reshape(group_size, n_groups).T, "k")
plt.title("Half blending times")

Bop = pylops.waveeqprocessing.BlendingHalf(
    nt,
    nr_obc,
    ns_obc,
    dt,
    ignition_times.reshape(group_size, n_groups),
    group_size=group_size,
    n_groups=n_groups,
    dtype="complex128",
    name=None,
)
data_blended = Bop * data_obc
data_pseudo = Bop.H * data_blended

fig, ax = plt.subplots(1, 1, figsize=(12, 8))
ax.imshow(
    data_blended[n_groups // 2].real.T,
    cmap="gray",
    vmin=-0.1,
    vmax=0.1,
    extent=(0, ns_streamer, t[-1], 0),
    interpolation="none",
)
ax.set_title("Blended CSG")
ax.set_xlabel("#Rec")
ax.set_ylabel("t [s]")
ax.axis("tight")
plt.tight_layout()

fig, axs = plt.subplots(1, 2, sharey=True, figsize=(12, 8))
axs[0].imshow(
    data_obc[:, 10].real.T,
    cmap="gray",
    vmin=-0.01,
    vmax=0.01,
    extent=(0, ns_streamer, t[-1], 0),
    interpolation="none",
)
axs[0].set_title("Unblended CRG")
axs[0].set_xlabel("#Src")
axs[0].set_ylabel("t [s]")
axs[0].axis("tight")
axs[1].imshow(
    data_pseudo[:, 10].real.T,
    cmap="gray",
    vmin=-0.01,
    vmax=0.01,
    extent=(0, ns_streamer, t[-1], 0),
    interpolation="none",
)
axs[1].set_title("Pseudo-deblended CRG")
axs[1].set_xlabel("#Src")
axs[1].axis("tight")
plt.tight_layout()
  • Group blending times
  • Blended CSG
  • Unblended CRG, Pseudo-deblended CRG
  • Half blending times
  • Blended CSG
  • Unblended CRG, Pseudo-deblended CRG

Total running time of the script: (0 minutes 6.594 seconds)

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