Wave physics (geobrain.physics.wave)

Wave physics (geobrain.physics.wave)#

Seismic wave propagation, reflectivity, and the wavelets that drive them.

Component

What is there

Time domain

Acoustic2D/3D, Elastic2D/3D, ViscoAcoustic2D, ViscoElastic2D, AnisotropicElastic2D/3D

Frequency domain

Helmholtz2D, with an implicit adjoint

Reflectivity

Zoeppritz, AkiRichards, Shuey, ConvolutionalAVO, Convolutional1D

Wavelets

ricker, GaussianWavelet, OrmsbyWavelet, KlauderWavelet, create_wavelet, shared_wavelet

Surveys

Seismic2DSurvey, Seismic3DSurvey, Helmholtz2DSurvey

Configuration

WaveSimulationConfig, WaveBoundaryConfig, WaveDiscretizationConfig, WaveOutputConfig, WaveMemoryConfig, WaveBackendConfig

A wavelet and a reflectivity kernel. Between them, a convolutional forward model:

import torch
from geobrain.physics.wave import AkiRichards, ricker

wavelet = ricker(64, 0.002, 25.0, dtype=torch.float64)
print("wavelet", tuple(wavelet.shape), "peak at sample", int(wavelet.argmax()))

avo = AkiRichards(angles_deg=[0.0, 15.0, 30.0])
spec = avo.differentiability
print("AkiRichards:", spec.trainable_inputs, "->", spec.output_keys)

wavelet (64,) peak at sample 31
AkiRichards: ('vp', 'vs', 'rho') -> ('reflectivity',)

ricker is zero-phase by default: the peak sits in the middle of the window, not at its start, and causal=True shifts it if that is what your recording convention expects.

Note what the kernel asks for: vp, vs and rho. Put it at the end of a chain that starts from vp alone and the chain’s contract still says vp: the other two are produced upstream by rock physics, and the chain parameterizes on its entry link.

FWI sharpening as the frequency bands are added

Full-waveform inversion climbing the frequency bands, which is the one place in the gallery where time is genuinely the subject. From examples/03_physics/01_seismic_fwi.py.#

The engines#

The time-domain engines take a survey and a wavelet and return a gather. They declare an adjoint rather than taping every timestep, which is what makes FWI on a real model affordable.

Note

Helmholtz2D declares IMPLICIT_VJP: the forward pass solves a linear system, and the gradient comes from an implicit-function adjoint at the price of one extra solve, not a tape through the factorisation.

WaveOutputConfig selects what comes back. Ask for the seismic data and you get the data; asking for wavefield snapshots is a separate, heavier request.

See also#

  • examples/03_physics/01_seismic_fwi.py: multi-scale FWI on Marmousi II, 2 to 11 Hz.

  • examples/00_showcase/02_operator_composition.py: an acoustic chain and a gravity chain as two channels of one bundle, sharing a rock-physics link.

  • examples/01_architecture/03_composition_rules.py: Aki-Richards as the terminal link, and what the chain derives from it.

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