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

Abstract

The rapid development of dynamic data-integrative modeling of geologic processes and subsurface structures is an important factor for the sustainable utilization of natural resources. One of the current gaps in data-integrative modeling is the interactive construction of realistic 3D models of the earth’s underground. We have developed here a methodology of 3D 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 geologic subsurface structures by polyhedra with triangulated surfaces. Inverse computations for the model geometry are performed by means of the covariance matrix adaptation evolution strategy (CMA-ES), which is proved to be efficient in the case of a strongly nonlinear problem and high-dimensional parameter space, as in potential field models. The main disadvantage is related to triangulation, as certain algorithmic constraints must be applied during the approximation of geologic 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 develop a numerical formulation of this system and provide a proof of the concept rather than an overview of the theoretical concepts of the inversion schemes. The new workflow is tested on the 3D SEG Advanced Modeling Program 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 determine how an interpreter can visually control and influence the quality of the inversion on a timeline.