Tutorial 03: Implicit Geological Modeling

Tutorial 03: Implicit Geological Modeling#

Note

This tutorial is available as a Python script examples/03_implicit_modeling.py and an interactive Jupyter notebook examples/notebooks/03_implicit_modeling.ipynb.

This tutorial demonstrates how to build differentiable implicit geological models using Universal Cokriging (Lajaunie et al. 1997).

What You Will Learn#

  • Define surface contact points and orientation data

  • Build single-series models with 1 or 2 surfaces

  • Stack multiple series with ERODE relations

  • Model fault displacement using FaultDefinition

  • Verify end-to-end differentiability with PyTorch autograd

Key Concepts#

Implicit modeling represents geological interfaces as iso-surfaces of a scalar field interpolated from sparse contact points and orientation measurements. The Cokriging formulation jointly honors both data types and supports polynomial drift for regional trends.

Multi-series stacking combines independent interpolations: ERODE lets younger series overwrite older ones, while ONLAP fills only unoccupied regions.

Differentiability means gradients flow from any loss function back through the block model, scalar field, and Cokriging system to the input data — enabling gradient-based inversion of geological parameters.

Code#

import torch
from geobrain.geomodel.implicit import (
    ImplicitModel, ImplicitModelConfig,
    SeriesDefinition, SurfacePointData, OrientationData,
)

config = ImplicitModelConfig(
    extent=(0.0, 1.0, 0.0, 1.0),
    resolution=(80, 80),
    dtype="float64",
)

sp = SurfacePointData(
    coords=torch.tensor([[0.2, 0.55], [0.5, 0.50], [0.8, 0.45]],
                         dtype=torch.float64),
    surface_id=torch.tensor([0, 0, 0]),
)
ori = OrientationData(
    coords=torch.tensor([[0.35, 0.52], [0.65, 0.48]], dtype=torch.float64),
    gradients=torch.tensor([[0.0, 1.0], [0.0, 1.0]], dtype=torch.float64),
)

model = ImplicitModel(config, series=[SeriesDefinition("strata", sp, ori)])
result = model(soft=True, temperature=50.0)
block = result['block']          # (6400,) soft lithology ids
sf = result['scalar_fields'][0]  # (6400,) scalar field

Results#

../_images/03_two_layer.png

Fig. 35 Two-layer implicit model from surface points and orientations.#

../_images/03_three_layer.png

Fig. 36 Three-layer model with two surfaces.#

../_images/03_multi_series.png

Fig. 37 Multi-series stacking with erosion.#

../_images/03_fault.png

Fig. 38 Fault displacement modeling.#

../_images/03_differentiable.png

Fig. 39 Gradient verification: differentiable implicit modeling.#

Full Example#

See examples/03_implicit_modeling.py.

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