An implementation of differential evolution algorithm for inversion of geoelectrical data (original) (raw)
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Heliyon, 2023
Conventional artifi cial neural networks used to solve electrical resistivity imaging (ERI) inversion problem suffer from overfi tting and local minima. To solve these problems, we propose to use a pruning Bayesian neural network (PBNN) nonlinear inversion method and a sample design method based on the K-medoids clustering algorithm. In the sample design method, the training samples of the neural network are designed according to the prior information provided by the K-medoids clustering results; thus, the training process of the neural network is well guided. The proposed PBNN, based on Bayesian regularization, is used to select the hidden layer structure by assessing the effect of each hidden neuron to the inversion results. Then, the hyperparameter α k , which is based on the generalized mean, is chosen to guide the pruning process according to the prior distribution of the training samples under the small-sample condition. The proposed algorithm is more efficient than other common adaptive regularization methods in geophysics. The inversion of synthetic data and fi eld data suggests that the proposed method suppresses the noise in the neural network training stage and enhances the generalization. The inversion results with the proposed method are better than those of the BPNN, RBFNN, and RRBFNN inversion methods as well as the conventional least squares inversion.
Monte Carlo methods in geophysical inverse problems
Reviews of Geophysics, 2002
1] Monte Carlo inversion techniques were first used by Earth scientists more than 30 years ago. Since that time they have been applied to a wide range of problems, from the inversion of free oscillation data for whole Earth seismic structure to studies at the meter-scale lengths encountered in exploration seismology. This paper traces the development and application of Monte Carlo methods for inverse problems in the Earth sciences and in particular geophysics. The major developments in theory and application are traced from the earliest work of the Russian school and the pioneering studies in the west by Press [1968] to modern importance sampling and ensemble inference methods. The paper is divided into two parts. The first is a literature review, and the second is a summary of Monte Carlo techniques that are currently popular in geophysics. These include simulated annealing, genetic algorithms, and other importance sampling approaches. The objective is to act as both an introduction for newcomers to the field and a comprehensive reference source for researchers already familiar with Monte Carlo inversion. It is our hope that the paper will serve as a timely summary of an expanding and versatile methodology and also encourage applications to new areas of the Earth sciences. INDEX TERMS:3260
Indonesian Journal of Physics, 2019
The purpose of this paper is to present a simulation to the inversion methods applied to geophysical exploration. Anapplication of Monte-Carlo, Metropolis, and Simulated Annealing techniques to 1-Dimensional gravity inversion inBayesian framework has been studied. Differences between these methods are observed in both single parameterinversion and simultaneous multi parameter inversion. After selecting the best inversion strategy from the three methods,a further investigation was investigated. Multi parameter inversion for two anomalies is simultaneously carried out andresults are observed. The synthetical data of GRAV2DC free source were used instead of observed data.
Metaheuristics in Applied Geophysics
Application of four metaheuristic algorithms including particle swarm optimization (PSO), genetic algorithm (GA), differential evolution (DE) and simulated annealing (SA) was presented for the inversion of geophysical data generated by one-, twoand three-dimensional (1D, 2D and 3D) structures. Each algorithm was implemented individually for the anomalies obtained by self-potential (SP), direct current resistivity (DCR), magnetic and crosshole radar methods. Synthetically produced anomalies were used for magnetic and crosshole radar applications while field data sets were considered in SP and DCR cases. PSO was used to determine model parameters (i.e., the electric dipole moment, polarization angle, depth, shape factor and origin of the anomaly) of an SP field anomaly measured in the Ahirwala deposit of the Neem-Ka-Thana copper belt, India. A real-valued GA application was performed for estimating the parameters of a layered subsurface (i.e., resistivity and thickness of each layer) from a vertical electrical sounding (VES) data set collected by DCR method in a karstic environment. A synthetic crosshole radar data set was considered for 2D
7th General Assembly of IUGG Working Group of Electromagnetic Study on Earthquakes and Volcanoes (EMSEV)
This paper describes a 1-D inversion modeling of vertical electrical sounding (VES) data using Schlumberger array. The algorithm employs Markov Chain Monte Carlo (MCMC) previously applied to 1 D inversion of MT data (Grandis et al., 1999). The algorithm was tested to invert synthetic data corresponding to simple three-layer models. The method was also applied to field VES data acquired on a profile. The data were interpolated laterally resulting in denser data coverage and the inverse models were concatenated one to the other to obtain a quasi 2 D model. The model showed satisfactory agreement with 2 D inversion result. The algorithm is quite generic such that it can be used as a template to invert other geo-electromagnetic data (e.g. CSAMT, SNMR etc.) for 1-D modeling.
Application of 2-D inversion with genetic algorithms to magnetotelluric data from geothermal areas
Earth, Planets and Space, 2002
We apply a modified genetic algorithm, the "recombinant genetic analogue" (RGA) to the inversion of magnetotelluric (MT) data from two different geothermal areas, one in El Salvador and another in Japan. An accurate 2-D forward modelling algorithm suitable for very heterogeneous models forms the core of the inverse solver. The forward solution makes use of a gridding algorithm that depends on both model structure and frequency. The RGA represents model parameters as parallel sets of bit strings, and differs from conventional genetic algorithms in the ways in which the bit strings are manipulated in order to increase the probability of convergence to a global minimum objective function model. A synthetic data set was generated from a chessboard model, and the RGA was shown capable of reconstructing the model to an acceptable tolerance. The algorithm was applied to MT data from Ahuachapán geothermal area in El Salvador and compared with other interpretations. Data from the geothermal area of Minamikayabe in Japan served as a second test case. The RGA is highly adaptable and well suited to non-linear hypothesis testing as well as to inverse modelling.
Bayesian inversion of geoelectrical resistivity data
Enormous quantities of geoelectrical data are produced on a daily basis, and often used for large-scale reservoir modelling. Interpretation of these data requires reliable and efficient inversion methods which adequately incorporate prior information and use realistically complex modelling structures. In this paper we use random coloured polygonal models as a powerful and flexible modelling framework for the layered composition of the Earth and we contrast our approach with earlier methods based upon smooth Gaussian fields. We demonstrate how the reconstruction algorithm may be efficiently implemented through the use of multigrid Metropolis-coupled Markov chain Monte Carlo and illustrate the method on a set of field data.
Geophysical inversion with a neighbourhood algorithm-I. Searching a parameter space
Geophysical Journal International, 1999
This paper presents a new derivative-free search method for finding models of acceptable data fit in a multidimensional parameter space. It falls into the same class of method as simulated annealing and genetic algorithms, which are commonly used for global optimization problems. The objective here is to find an ensemble of models that preferentially sample the good datafitting regions of parameter space, rather than seeking a single optimal model. (A related paper deals with the quantitative appraisal of the ensemble.)
2D multi-scale hybrid optimization method for geophysical inversion and its application
Local and global optimization methods are widely used in geophysical inversion but each has its own advantages and disadvantages. The combination of the two methods will make it possible to overcome their weaknesses. Based on the simulated annealing genetic algorithm (SAGA) and the simplex algorithm, an efficient and robust 2-D nonlinear method for seismic travel-time inversion is presented in this paper. First we do a global search over a large range by SAGA and then do a rapid local search using the simplex method. A multi-scale tomography method is adopted in order to reduce non-uniqueness. The velocity field is divided into different spatial scales and velocities at the grid nodes are taken as unknown parameters. The model is parameterized by a bi-cubic spline function. The finite-difference method is used to solve the forward problem while the hybrid method combining multi-scale SAGA and simplex algorithms is applied to the inverse problem. The algorithm has been applied to a numerical test and a travel-time perturbation test using an anomalous low-velocity body. For a practical example, it is used in the study of upper crustal velocity structure of the A'nyemaqen suture zone at the north-east edge of the Qinghai-Tibet Plateau. The model test and practical application both prove that the method is effective and robust.