Tutorial 02: Advanced Geomodeling

Note

This tutorial is available as a Python script examples/02_geomodel_cosim.py and an interactive Jupyter notebook examples/notebooks/02_geomodel_cosim.ipynb.

This tutorial covers advanced geostatistical techniques: multi-variable co-simulation, Sequential Gaussian Simulation (SGS), and variogram modeling.

What You Will Learn

• Use CoSimConfig to generate correlated multi-variable fields

• Run unconditional SGS with Simple Kriging and Ordinary Kriging

• Perform conditional SGS that honors well data

• Build and visualize variogram models with VariogramModel

Key Concepts

Co-simulation produces multiple spatially correlated fields that respect inter-variable correlations. SGS visits grid nodes in random order, using kriging to estimate the local mean and variance, then drawing from the conditional distribution. Variograms describe how spatial correlation decays with distance.

Code

import torch
from geobrain.geomodel import Simulator, CoSimConfig, SimulationConfig

# Co-simulation
corr = torch.tensor([[1.0, 0.7], [0.7, 1.0]])
config = CoSimConfig(
    shape=(64, 64, 128),
    n_variables=2,
    correlation_matrix=corr,
    field_names=["phi", "vsand"],
    lh=20, lv=5,
    seed=2025,
)
sim = Simulator.create("fft_ma")
fields = sim.simulate(config)

# SGS with conditioning
sim_sgs = Simulator.create("sgs", kriging_type="ok")
sim_sgs.set_conditioning(well_values, well_locations)
fields_cond = sim_sgs.simulate(sgs_config)

Results

Fig. 31 Composite variogram model fitting.

Fig. 32 SGS unconditional simulation with Simple and Ordinary Kriging.

Fig. 33 SGS conditional simulation honoring well data.

Fig. 34 Co-simulated porosity and sand volume fields.

Full Example

See examples/02_geomodel_cosim.py.