Rock physics (geobrain.physics.rock)

Rock physics (geobrain.physics.rock)#

The layer between geology and geophysics: what a rock made of these minerals, with this porosity, saturated with this fluid, does to a wave or a field.

Every model here is differentiable, and the composable ones are PropertyTransforms, so a porosity parameter can drive five rock-physics laws and a wave equation, and the gradient returns through all of them without a hand-written derivative anywhere.

Category

Models

Effective medium

Voigt-Reuss-Hill, Hashin-Shtrikman, SelfConsistent, Hudson, SayersKachanov

Granular media

HertzMindlin, soft sand, stiff sand, contact cement

Fluid substitution

Gassmann, WoodFluidMix, BatzleWangBrine, BiotHighFrequency

Empirical

Gardner, RockPhysicsTemplate

Petrophysics

KozenyCarman permeability, ArchieResistivity

Conversions

VelocitiesFromModuli, ModuliFromVelocities

Two ways in#

The functions are for a one-off calculation:

import torch
from geobrain.physics.rock import velocities_from_moduli

k = torch.tensor(2.0e10, dtype=torch.float64)     # bulk modulus [Pa]
mu = torch.tensor(1.0e10, dtype=torch.float64)    # shear modulus [Pa]
rho = torch.tensor(2300.0, dtype=torch.float64)   # density [kg/m3]
vp, vs = velocities_from_moduli(k, mu, rho)
print(f"vp {float(vp):.0f} m/s, vs {float(vs):.0f} m/s")

vp 3807 m/s, vs 2085 m/s

The operators are for putting in a chain, where they carry a contract:

from geobrain.physics.rock.models import GardnerOperator

spec = GardnerOperator().differentiability
print(spec.trainable_inputs, "->", spec.output_keys, "via", spec.level.value)

('vp',) -> ('rho',) via full_autograd

ROCK_OPERATOR_TYPES and get_rock_operator are the registry, for code that has to pick a model by name.

Two images resolved into rock units

Where rock physics earns its place in an inversion: a petrophysical prior turns two independent images into one set of rock units. From examples/03_physics/04_petrophysical_joint_inversion.py.#

See also#

  • examples/01_architecture/03_composition_rules.py: Gardner and Castagna as chain links feeding Aki-Richards.

  • examples/00_showcase/04_deterministic_bayes_unified.py: porosity driving five rock-physics laws into an AVO gather, inverted both ways.

  • examples/03_physics/04_petrophysical_joint_inversion.py: petrophysics as a coupling term rather than a forward step.

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