Versatile Surrogate Inversion of Deformation Sources

The amount of geodetic surface displacement observations from GNSS and InSAR has been growing in recent years yet exploring the model space of corresponding sub-surface deformation remains a complicated and computationally expensive exercise. This is especially the case when there is more than one source and is further complicated when there is a variety in source types, such as combinations of on-fault slip and off-fault mantle flow.  While analytical solutions exist for a variety of deformation types within elastic half-spaces (such as fault slip, tensile dislocation, volumetric strain, expansion/contraction) the optimization of source parameters beyond single source models is computationally burdensome due to the need to extensively search with forward passes of the numerical solutions.  In most kinematic modelling exercises, the strategy is to assume geometries of sources and solve for magnitude parameters in inversions or to let a Finite Elements simulation evolve from a starting static displacement.  Furthermore, there is no effective way to blindly discover the number of sources along with their respective modes of deformation.

Here we demonstrate a solution to these problems that uses surrogate cuboid anelastic deformation sources and sparsity. Cuboid surrogates, that are trained on analytical solutions of anelastic deformation in a half-space, provide a versatile parametrization capable of approximating a wide range of deformation styles - from volumes to faults - by collapsing the thickness towards a near-planar geometry.  Once trained, the model can be run in inversion mode so that parameters of the source, such as centroid, length, width, depth, and strain tensor can be optimized by means of a back-propagated loss between the measured surface displacement and surrogate model prediction.  Multiple sources can be added trivially, and a sparse solution found with an approximately sparse optimization strategy.

By replacing repeated forward evaluations with a trained surrogate model, the proposed framework enables rapid optimization directly from observed deformation fields without the need for assuming the types of deformations or number of sources. This combination of a flexible cuboid-based source representation and efficient surrogate modelling offers a practical route towards scalable discovery of sub-surface deformation features.