A comparative study on using metaheuristics for the seismic-ray-tracing problem
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METHODOLOGY ARTICLE
A comparative study on using metaheuristics for the seismic-ray-tracing problem 1,2 ´ Mario A. Aguirre-Lopez
· Roberto Soto-Villalobos3 · Martha-Selene Casas-Ram´ırez1 · F-Javier Almaguer1
Received: 19 March 2020 / Accepted: 29 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper we deal the multi-layer case in the seismic-ray-tracing problem. Each ray is defined by its departure angle, and it spreads according to Snell’s Law; on the other hand, the medium of propagation is characterized by its density, the number of seismic layers, and the deep of these reflectors. Consider the above in the building the models, it allows that the travel time of a ray depends only on one variable but generates an excessive number of degrees of freedom in the system, which restricts the search space and makes it difficult to obtain an optimal solution. The foregoing motivates to solve the problem through a metaheuristic. We propose a solving methodology based on the shooting method immersed in the ray tracing methodology to find a solution to the initial value problem by using some metaheuristics, namely, Spiral Dynamics Inspired Optimization, Gravitational Search Algorithm and Genetic Algorithm. To our knowledge, this methodology has not been reported to solve such problem. There are not analytical solutions for models with two or more layers. A comparative study about the performance of the metaheuristics implemented is presented. The simulation results shows the competitiveness of the proposed algorithms, but in terms of solution quality and consumed time the Spiral Dynamics Inspired Optimization is better, followed by the Genetic Algorithm. Furthermore, the one-layer model was solved with the proposed algorithms and the results agree with the analytical solution reported in literature. In turn, our methodology provides better solutions than the Dix’s equation and a metaheuristic-bending method for all the simulations we present. Keywords Seismic ray tracing · Snell’s law · Spiral optimization · Gravitational search · Genetic algorithm · Computational seismology
Introduction Seismic reflection is one of the geophysical methods most used in hydrocarbons, watersheds and building studies. This is because such method seismic studies bring high precision, resolution and depth of penetration in characterizing lithologies, detecting density anomalies and relating them to subsoil structures, which are known as seismic layers (Stein and Wysession 2003; Kumar and Sharma 2013). The operation of the seismic methods is based on detecting by mean of sensors (geophones) the arrival times at which an emerging elastic wave reaches the surface Communicated by: H. Babaie Mario A. Aguirre-L´opez
[email protected]
Extended author information available on the last page of the article.
at a point of interest. Such wave is originated by a controlled source on the surface, so that the wave spreads into the subsoil throughout one or several seismic layers until it bounces (occur
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