Inversion of potential fields by interactive optimization of 3D subsurface models using spring-based space warping and evolution strategy

Rapid development of dynamic data-integrative modeling of geological processes and subsurface structures is an important factor for sustainable utilization of natural resources. One of the current gaps is the interactive construction of realistic threedimensional models of the Earth's underground. We present here a methodology of 3-D interactive processing of potential fields - gravity and magnetics - as well as their potentials and derivatives, combining forward and inverse modeling. Forward computations are based on the approximation of geological subsurface structures by polyhedra with triangulated surfaces. Inverse computations for the model geometry are performed by means of Covariance-Matrix-Adaptation Evolution Strategy (CMAES), which is proved to be efficient in case of a strongly non-linear problem and highdimensional parameter space, as in potential field models. The main disadvantage is related to triangulation, as certain algorithmic constraints must be applied during approximation of geological body shapes. To avoid topology distortions we use a concept of warping the space containing the model, rather than the model itself. However, the optimized lengths of grid sides are dependent on each other, which degrades the self-adaptation of the CMA-ES. The elegant solution is to introduce a system of virtual elastic springs connecting the grid nodes. We present a numerical formulation of this system and provide a proof of concept rather than an overview of theoretical concepts of inversion schemes. The new workflow is tested on the 3-D SEAM model and applied to a real case study of salt dome modeling in the Northwest German Basin. In the context of the inversion procedure described here we demonstrate how an interpreter can visually control and influence the quality of the inversion on a timeline.