Tutorial 04: Implicit Model Inversion

Tutorial 04: Implicit Model Inversion#

Note

This tutorial is available as a Python script examples/04_implicit_inversion.py and an interactive Jupyter notebook examples/notebooks/04_implicit_inversion.ipynb.

This tutorial demonstrates karst cave detection by inverting post-stack seismic data through a differentiable implicit geological model.

What You Will Learn#

  • Parameterize a cave boundary using surface point z-coordinates

  • Chain implicit modeling with rock physics and seismic convolution

  • Run deterministic inversion with Adam and Adam+L-BFGS optimizers

  • Visualize impedance models, seismic sections, and convergence curves

Key Concepts#

The full forward chain is:

Cave boundary (z-coords)
    -> Implicit Model (soft lithology)
    -> Rock properties (Vp, rho)
    -> Acoustic impedance & reflectivity
    -> Wavelet convolution -> Synthetic seismic

Because every step is differentiable, PyTorch autograd computes gradients of the seismic misfit with respect to the cave boundary coordinates, enabling efficient gradient-based inversion.

Code#

import torch
from geobrain.geomodel.implicit import (
    ImplicitModel, ImplicitModelConfig,
    SeriesDefinition, SurfacePointData, OrientationData,
)
from geobrain.physics.wave import RickerWavelet, create_conv_matrix, normal_incidence_rc
from geobrain.optim import Inverter, bound_constraint

def forward_fn(sp_z):
    coords = torch.stack([SP_X, sp_z], dim=-1)
    sp = SurfacePointData(coords=coords, surface_id=SP_IDS)
    ori = OrientationData(coords=ORI_COORDS, gradients=ORI_GRADS)
    model = ImplicitModel(CONFIG, series=[SeriesDefinition("cave", sp, ori)])
    block = model(soft=True, temperature=50.0)['block'].reshape(NX, NZ)
    # ... rock physics & convolution ...
    return synthetic_seismic

inverter = Inverter.create(
    initial_model=sp_z_init,
    forward_fn=forward_fn,
    constraints=bound_constraint(0.10, 0.90),
)
result = inverter.run(observed_data=seis_obs, max_epochs=500, lr=1e-2)

Results#

../_images/04_seismic.png

Fig. 40 Observed and predicted seismic sections.#

../_images/04_impedance.png

Fig. 41 True vs. inverted acoustic impedance.#

../_images/04_cave_boundary.png

Fig. 42 True vs. inverted cave boundary.#

../_images/04_convergence.png

Fig. 43 Inversion convergence curve.#

Full Example#

See examples/04_implicit_inversion.py.

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