GravPSO2D: A Matlab package for 2D gravity inversion in sedimentary basins using the Particle Swarm Optimization algorithm
Introduction
The interface separation between two media having different densities can be estimated in Geophysics using gravity measurements and by posing a nonlinear inverse problem. Gravity inversion in this kind of environments is a tool frequently used in Geophysics in tasks such as prospecting of oil and gas, or in hydrogeology and glaciology studies (Blakely, 1995; Dobrin, 1960; Hinze et al., 2013; Nettleton, 1976; Parker, 1994; Telford et al., 1976). The gravity inverse problem has a non-unique solution, leading to an infinity number of solutions (Al-Chalabi, 1971; Skeels, 1947; Zhdanov, 2015). It is therefore mandatory to introduce some kind of regularization and/or constraint(s) incorporating other geophysical information such as borehole and seismic profile data, contrasted prior models, etc. This will allow to restrict the set of possible solutions and stabilize the inversion.
The problem of the estimation of the basement relief in sedimentary basins using gravity observations is a nonlinear inverse problem, and the most used techniques for its solution are based on local optimization methods, either by the linearization of the problem plus regularization (see Silva et al. (2009) for example), or by the sequential application of the direct formulation (see Bott (1960) or Chen and Zhang (2015) for example). GravPSO2D uses Particle Swarm Optimization (PSO), which is a global search method with excellent capabilities to perform the inverse problem uncertainty analysis and avoiding the weak points of the local optimization procedures, such as the dependency on the prior model and the lack of a proper uncertainty analysis (Fernández-Martínez et al., 2013, 2014b).
GravPSO2D works in two-dimensional environments. This approximation can be used when the dimension of an anomalous body is much larger than the other two dimensions (at least a or factor according to Nettleton (1976)). This situation is common in sedimentary basins, where their horizontal extensions are generally much larger than their depth, so profiles perpendicular to the principal dimensions can be used for the analysis in a 2D formulation (Pick et al., 1973; Telford et al., 1976).
Section snippets
Observations and basin modelization
GravPSO2D works with user-provided complete Bouguer gravity anomalies, , along a profile. The software can also estimate a polynomial regional trend during the inversion, so if this effect exists in it is not necessary to be previously suppressed by the user.
The 2D basin modeling used in GravPSO2D consists in the juxtaposition of rectangles along the profile as it was commonly employed by other authors (see for example Silva et al. (2009) or Ekinci et al. (2020)). As it can be seen in Fig.
Particle Swarm Optimization
The PSO (Particle Swarm Optimization) algorithm (Kennedy and Eberhart, 1995) is a global optimizer based on the behavior of swarms of animals (birds, fish schools) in the nature searching for food. A set of particles (models) explores the parameters' space with the goal of the optimization of a given cost function related to the inverse problem that is considered. As general overview, the algorithm works as follows: (1) in the first step, a set of particles (models) is created with random
Real example
An application of GravPSO2D package for the inversion of observed gravity data is provided in this section. For more reliability with our previous works describing the theoretical aspects of the inversion scheme (Pallero et al., 2015; Fernández-Martínez et al., 2017) we provide here the original data corresponding to the gravity profile already discussed in these papers. In addition, with the aim at giving more replicable examples for users we have also extended this dataset with 3 other
Conclusions
In this paper GravPSO2D, a Matlab software for 2D gravity inversion in sedimentary basins using the Particle Swarm Optimization algorithm has been presented. This software represents the first effort to provide the scientific community with a tool based on the PSO for this particular problem. GravPSO2D is freely available and includes an exhaustive reference manual where all the details related to the input data, file formats, and output results are exposed and analyzed.
It is of particular
Computer code availability
The source code of GravPSO2D will be available free of charge in the BGI's webpage (http://bgi.obs-mip.fr/), and in https://github.com/jgpallero/grav-pso-2d.
Author contributions
J.L.G.P., J.L.F.M., and Z.F.M. designed the methodology, developed the software, processed the data, and wrote the paper. G.G., and T.N. acquired the gravity data. S.B., G.G., and T.N. analyzed, discussed the inversion results corresponding to the real example, and wrote the related part of the paper.
Declaration of competing interest
The authors declare that they have no known competing financial interests nor personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
JLGP acknowledges the support of the GET (Université de Toulouse, CNRS, IRD, CNES), the Bureau Gravimétrique International (BGI), and CNES, that allowed him to develop part of this research in Toulouse during two research stays in 2018 and 2019 (work supported by CNES, CNRS and IRD). He also acknowledges the support of the Universidad Politécnica de Madrid through a Programa Propio de Movilidad grant in 2018.
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