Elsevier

Computers & Geosciences

Volume 146, January 2021, 104653
Computers & Geosciences

GravPSO2D: A Matlab package for 2D gravity inversion in sedimentary basins using the Particle Swarm Optimization algorithm

https://doi.org/10.1016/j.cageo.2020.104653Get rights and content

Highlights

  • A Matlab Package for the 2D gravity inversion in sedimentary basins is presented.

  • The method is based on the Particle Swarm Optimization algorithm.

  • The method uses the advantages of the global search algorithms for a powerful uncertainty analysis.

  • Tests were made using synthetic and real data.

  • The software will be freely available in the Bureau Gravim_etrique Inter-national's web.

Abstract

In this paper GravPSO2D, a Matlab tool for two-dimensional gravity inversion in sedimentary basins using the Particle Swarm Optimization (PSO) algorithm, is presented. The package consists of a collection of functions and scripts that cover the main three parts of the process: (1) the model definition based on the observations, (2) the inversion itself, where the PSO is employed, and (3) the results processing, including best model estimation, uncertainty analysis and plots generation. GravPSO2D is freely available, and represents an effort for providing the scientific community with the first tool based on the PSO algorithm in order perform the inversion and the uncertainty assessment of the sedimentary basin gravity inversion problem, taking into account the gravity regional trend estimation, and vertically and horizontally density contrast variations. Synthetic and real examples are provided in order to show the software capabilities.

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 4× or 6× 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, Δg, along a profile. The software can also estimate a polynomial regional trend during the inversion, so if this effect exists in Δg 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.

References (63)

  • J.L.G. Pallero et al.

    3D gravity inversion and uncertainty assessment of basement relief via Particle Swarm Optimization

    J. Appl. Geophys.

    (2017)
  • L.T. Pham et al.

    GCH_gravinv: a MATLAB-based program for inverting gravity anomalies over sedimentary basins

    Comput. Geosci.

    (2018)
  • M. Al-Chalabi

    Some studies relating to non uniqueness in gravity and magnetic inverse problems

    Geophysics

    (1971)
  • V.C.F. Barbosa et al.

    Generalized compact gravity inversion

    Geophysics

    (1994)
  • V.C.F. Barbosa et al.

    Gravity inversion of basement relief using approximate equality constraints on depths

    Geophysics

    (1997)
  • V.C.F. Barbosa et al.

    Gravity inversion of a discontinuous relief stabilized by weighted smoothness constraints on depth

    Geophysics

    (1999)
  • R.J. Blakely

    Potential Theory in Gravity and Magnetic Applications

    (1995)
  • F. Boschetti et al.

    Inversion of potential field data by genetic algorithms

    Geophys. Prospect.

    (1997)
  • M.H.P. Bott

    The use of rapid digital computing methods for direct gravity interpretation of sedimentary basins

    Geophys. J. Roy. Astron. Soc.

    (1960)
  • T.M. Brocher

    A regional view of urban sedimentary basins in northern California based on oil industry compressional-wave velocity and density logs

    Bull. Seismol. Soc. Am.

    (2005)
  • V. Chakravarthi et al.

    3D gravity inversion of basement relief–A depth-dependent density approach

    Geophysics

    (2007)
  • P. Cornejo et al.

    Estudio Geológico de la región de El Salvador y Potrerillos. Informe Registrado IR 93-1

    (1993)
  • M.B. Dobrin

    Introduction to Geophysical Prospecting

    (1960)
  • Y.L. Ekinci et al.

    Gravity data inversion for the basement relief delineation through global optimization: a case study from the Aegean Graben System, western Anatolia, Turkey

    Geophys. J. Int.

    (2020)
  • K.S. Essa et al.

    PSO (particle swarm optimization) for interpretation of magnetic anomalies caused by simple geometrical structures

    Pure Appl. Geophys.

    (2018)
  • J.P. Fernández-Álvarez et al.

    Application of the particle swarm optimization algorithm to the solution and appraisal of the vertical electrical sounding inverse problem

  • J.L. Fernández-Martínez et al.

    Linear geophysical inversion via the discrete cosine pseudo-inverse: application to potential fields

    Geophys. Prospect.

    (2017)
  • J.L. Fernández-Martínez et al.

    The PSO family: deduction, stochastic analysis and comparison

    Swarm Intelligence

    (2009)
  • J.L. Fernández-Martínez et al.

    Stochastic stability and numerical analysis of two novel algorithms of PSO family: PP-PSO and RR-PSO

    Int. J. Artif. Intell. Tool.

    (2012)
  • J.L. Fernández-Martínez et al.

    Theoretical analysis of particle swarm trajectories through a mechanical analogy

    Int. J. Comput. Intell. Res.

    (2008)
  • J.L. Fernández-Martínez et al.

    Particle swarm optimization applied to solving and appraising the streaming-potential inverse problem

    Geophysics

    (2010)
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