2D Basement Relief Inversion using Sparse Regularization

TL;DR

This paper compares various regularization techniques and genetic algorithm optimization for 2D basement relief gravimetric inversion, demonstrating their effectiveness in stabilizing solutions and accurately modeling geological structures.

Contribution

It introduces a comprehensive comparison of regularization methods combined with genetic algorithms for basement relief inversion, highlighting the most effective approaches.

Findings

Smoothness constraint yields best results in synthetic models

All methods perform similarly on real data

Genetic algorithms effectively optimize inversion solutions

Abstract

Basement relief gravimetry is crucial in geophysics, especially for oil exploration and mineral prospecting. It involves solving an inverse problem to infer geological model parameters from observed data. The model represents basement relief with constant-density prisms, and the data reflect gravitational anomalies from these prisms. Inverse problems are often ill-posed, meaning small data changes can lead to large solution variations. To mitigate this, regularization techniques like Tikhonov's are used to stabilize solutions. This study compares regularization methods applied to gravimetric inversion, including Smoothness Constraints, Total Variation, Discrete Cosine Transform (DCT), and Discrete Wavelet Transform (DWT) using Daubechies D4 wavelets. Optimization, particularly with Genetic Algorithms (GA), is used to find prism depths that best match observed anomalies. GA, inspired by natural selection, selects the best solutions to minimize the objective function. The results, evaluated through fit metrics and error analysis, show the effectiveness of all regularization methods and GA, with the Smoothness constraint performing best in synthetic models. For the real data model, all methods performed similarly.