An enhanced Genetic Algorithm and its application on two non-linear geophysical problems

Abstract

Since its inception in 1975, Genetics Algorithms (GAs) have been successfully used as a tool for global optimization on non-convex problems in a wide range of real world applications. Its creation was inspired by natural adaptation and selection mechanisms that evolve from one population of chromosomes to a fitter population by means of an artificial natural selection dictated by the operators of elitism, crossover and mutation. An advanced Genetic Algorithm (aGA) was proposed by Sun et al. [2017], and this algorithm seeks the global maximum of n-th dimensional non-convex functions. However, convergence speed is a key factor for the success of a global optimization algorithm when it comes to scalability; in production even a slight efficiency improvement matters as it can easily takes weeks or even months to process a huge data set. Therefore, the goal of this project is to improve the convergence speed of the currently available aGA by simultaneously enhancing both its global and its local search capabilities. To this end, two solutions were proposed. The first is a modified version of the well known Island model GAs and the second was named Self Adaptive Differential Evolution (SADE) fine tuning scheme. After a successful demonstration of its improved performance on several multi-modal test functions, the enhanced Genetic Algorithm (eGA) is used to tackle two common non-linear geophysical problems: static correction and Common Reflection Surface (CRS) stacking. In the former, the near-surface related time-shifts are estimated without resorting to an explicit velocity-depth model; instead, the events of interest are aligned in a data-driven fashion by maximizing the stacking power. The latter is a novel alternative to the traditional Common Midpoint (CMP) stacking that has proven to yield higher quality images, specially when applied to low Signal to Noise Ratio (SNR) data or data with challenging structures like the anomalies encountered in the subsurface. This improvement in the quality of the stacked image is attributed to a non-local mean mentality, which enables using traces from different CMP gathers to the CMP gather being resolved. Owing to the high non-linearity of both problems, they are ideal test beds for global optimization algorithms. The effectiveness of the eGA is demonstrated on synthetic data sets with promising results in these problems.