Potential fields (geobrain.physics.potential)

Gravity and magnetics: the cheapest data in geophysics, and the least unique.

Operator	Gives
Gravity2D	gz from a 2-D density-contrast section (Talwani)
Gravity3D	gz and the full gradient tensor, from prisms
Magnetic3D	total-field anomaly, with induced and remanent magnetisation
MagneticVector3D	the vector field, component by component

Surveys are PotentialSurvey2D / PotentialSurvey3D. EarthField carries the inducing field’s strength and direction, which is what makes a magnetic anomaly depend on where on the planet you are standing.

import torch
from geobrain.core import ForwardContext, ModelState
from geobrain.mesh import TensorMesh
from geobrain.physics.potential import (Gravity2D, PotentialSurvey2D,
                                        gravity_to_mgal)

mesh = TensorMesh(shape=(10, 20), spacing=(25.0, 25.0))
stations = torch.stack([torch.linspace(0.0, 500.0, 21, dtype=torch.float64),
                        torch.ones(21, dtype=torch.float64)], dim=1)
gravity = Gravity2D(PotentialSurvey2D(stations))

rho = torch.zeros(10, 20, dtype=torch.float64)
rho[3:6, 8:13] = -400.0                      # a light body
gz = gravity(ModelState({"rho": rho}), ForwardContext.of(mesh=mesh)).data["gz"]
print(f"peak anomaly {float(gravity_to_mgal(gz).abs().max()):.3f} mGal")

peak anomaly 0.409 mGal

Warning

These operators are strict about dtype=torch.float64. A float32 survey is rejected rather than quietly losing precision in a kernel that sums a contribution from every cell in the model.

Why gravity needs help

A gravity anomaly does not determine a density distribution: many earths fit the same curve, and the smooth ones fit it best. Depth weighting (geobrain.optim.depth_weighting) stops everything migrating to the surface; an IRLS sparsity pass sharpens the blur; and a second physics, magnetics, with a different sensitivity to the same rock, is what actually breaks the tie. Hence the joint example.

One buried body, four fields: gravity, induced magnetisation at two inclinations, and a remanent case. From examples/03_physics/06_potential_fields.py.

Processing and interpretation

upward_continue, reduce_to_pole, vertical_derivative, horizontal_gradient, tilt_derivative, analytic_signal_amplitude and regional_residual_lowpass are the standard filters. bouguer_slab, bouguer_spherical_cap, free_air_correction and terrain_correction_prism are the reductions. euler_deconvolution estimates source depth from a structural index.

Units are SI inside and converted at the edge: gravity_to_mgal, magnetic_to_nt, gravity_gradient_to_eotvos.

See also

• examples/00_showcase/01_gravity_inversion.py: the whole platform in three objects, on a gravity problem.

• examples/03_physics/06_potential_fields.py: why magnetics answers differently at every latitude and for every remanence.

• examples/03_physics/04_petrophysical_joint_inversion.py: gravity and magnetics together, answering which rock is where rather than how dense it is.