Posterior analysis of particle swarm optimization results applied to gravity inversion in sedimentary basins

J. L. G. Pallero; M. Z. Fernández-Muñiz; J. L. Fernández-Martínez; S. Bonvalot; J. L. G. Pallero; M. Z. Fernández-Muñiz; J. L. Fernández-Martínez; S. Bonvalot

doi:10.3934/math.2024677

AIMS Mathematics

2024, Volume 9, Issue 6: 13927-13943. doi: 10.3934/math.2024677

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Posterior analysis of particle swarm optimization results applied to gravity inversion in sedimentary basins

1.
ETSI en Topografía, Geodesia y Cartografía, Universidad Politécnica de Madrid, Madrid, Spain
2.
Grupo de Problemas Inversos, Optimización y Aprendizaje Automático, Departamento de Matemáticas, Universidad de Oviedo, Oviedo 33007, Spain
3.
Laboratoire GET (Université de Toulouse, CNRS, IRD, CNES), Bureau Gravimétrique International (BGI), Toulouse, France

Received: 19 January 2024 Revised: 09 April 2024 Accepted: 11 April 2024 Published: 16 April 2024
MSC : 86A20, 86A22, 90C26

As is well known, it is impossible to model reality with its true level of detail. Additionally, it is impossible to make an infinite number of observations, which are always contaminated by noise. These circumstances imply that, in an inverse problem, the misfit of the best estimated model will always be less than that of the true one. Therefore, it is not possible to reconstruct the model that actually generated the collected observations. The best way to express the solution of an inverse problem is as a collection of models that explain the observations at a certain misfit level according to a defined cost function. One of the main advantages of global search methods over local ones is that, in addition to not depending on an initial model, they provide a set of generated models with which statistics can be made. In this paper we present a technique for analyzing the results of any global search method, particularized to the particle swarm optimization algorithm applied to the solution of a two-dimensional gravity inverse problem in sedimentary basins. Starting with the set of generated models, we build the equivalence region of a predefined tolerance which contains the best estimated model, i.e., which involves the estimated global minimum of the cost function. The presented algorithm improves the efficiency of the equivalence region detection compared to our previous works.
- global optimization methods,
- particle swarm optimization,
- inverse problems,
- uncertainty analysis,
- gravity inversion
Citation: J. L. G. Pallero, M. Z. Fernández-Muñiz, J. L. Fernández-Martínez, S. Bonvalot. Posterior analysis of particle swarm optimization results applied to gravity inversion in sedimentary basins[J]. AIMS Mathematics, 2024, 9(6): 13927-13943. doi: 10.3934/math.2024677

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Abstract

As is well known, it is impossible to model reality with its true level of detail. Additionally, it is impossible to make an infinite number of observations, which are always contaminated by noise. These circumstances imply that, in an inverse problem, the misfit of the best estimated model will always be less than that of the true one. Therefore, it is not possible to reconstruct the model that actually generated the collected observations. The best way to express the solution of an inverse problem is as a collection of models that explain the observations at a certain misfit level according to a defined cost function. One of the main advantages of global search methods over local ones is that, in addition to not depending on an initial model, they provide a set of generated models with which statistics can be made. In this paper we present a technique for analyzing the results of any global search method, particularized to the particle swarm optimization algorithm applied to the solution of a two-dimensional gravity inverse problem in sedimentary basins. Starting with the set of generated models, we build the equivalence region of a predefined tolerance which contains the best estimated model, i.e., which involves the estimated global minimum of the cost function. The presented algorithm improves the efficiency of the equivalence region detection compared to our previous works.

References

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