Eigencrust: 3D geophysical inversion

Eigencrust is software for 3D geophysical inversion, developed for large surveys, large meshes and difficult topography.

The project began as a numerical engine for running inversions on GPUs. Waiting hours for each result limits how often the mesh, constraints and other assumptions can be tested. The aim was to shorten that wait so that comparing alternative models and revisiting an interpretation could be part of everyday work.

A browser interface was added to make the engine accessible to more people. Survey data, terrain meshes and inversion results are kept in the same workspace. Supported methods include gravity, magnetics, direct-current (DC) resistivity and induced polarisation (IP).

Inversions run on cloud GPUs. The engine uses GPU parallelism to handle large models without a large CPU cluster, keeping computation times and cloud costs down.

Example: Mount Adams

This magnetic inversion uses 14,007 aeromagnetic stations around Mount Adams in Washington. Two survey blocks, flown at different heights, were fitted together on a terrain mesh. The survey covers roughly 23 by 24 km, with 2.8 km of relief.

Recovered magnetisation model beneath Mount Adams, coloured by depth below the surface, under shaded terrain. — Recovered magnetisation model, coloured by depth below the surface. Vertical exaggeration is 1.8×. The recovered model is one possible interpretation of the magnetic data. Data: USGS, Bracken and Blakely (2024).

Inversion methods

Gravity and gravity gradiometry: Density inversion from gravity components and gravity gradients, including full tensor inversion. The forward calculation uses the closed-form solution for rectangular prisms.
Magnetics and magnetic gradiometry: Susceptibility inversion from total magnetic intensity (TMI), its spatial gradients or magnetic field components. Full tensor inversion fits the magnetic gradient tensor components together.
Magnetisation vector inversion (MVI): MVI recovers three magnetisation components in each active cell, allowing the direction to vary across the model. It can use TMI, magnetic field components or magnetic gradients, including full tensor data. This can represent remanent and reversed magnetisation. The examples include low-latitude TMI inversion without reduction to the pole.
3D DC resistivity: Conductivity inversion for surface electrode surveys, using measured voltages or transfer resistances. Recovered models can be displayed as conductivity or resistivity.
3D induced polarisation: Scalar chargeability inversion with conductivity held fixed, using a recovered DC model or a specified background. DC and IP are separate inversion steps.

Working with data and models

Survey data and topography can be imported from text tables. Meshes are built around the survey, with graded padding and a surface defined by topography. Multiple survey blocks can be fitted on one mesh.

The 3D view shows survey locations, terrain and recovered models. Predicted data and residuals are available for checking the fit. Each result retains the inputs and settings used for that inversion.

Eastern Siliceous IP workspace showing the recovered chargeability model at 4.5 mV/V beneath the survey geometry. — Recovered chargeability at Eastern Siliceous. The surface marks 4.5 mV/V, with survey geometry shown above. Data: GSQ / GBM Resources (CC BY 4.0).

Survey data, meshes, models and results can be saved together in a workspace file. Gravity and magnetic observation files in UBC-GIF format are also supported. Meshes and models can be exported in UBC-GIF or NumPy formats. Models can also be exported as cell-centre CSV.

Access and contact

Access is by invitation. Use the form below to request a free trial or a demo, or to discuss using Eigencrust with a particular survey.

Academic users are especially welcome. Please get in touch to discuss support for research or teaching.