3D non-linear inversion of magnetic anomalies caused by prismatic bodies using differential evolution algorithm

Balkaya, Çağlayan; Ekinci, Yunus Levent; Göktürkler, Gökhan; Turan, Seçil

doi:10.1016/j.jappgeo.2016.10.040

Cited by 70 publications

(32 citation statements)

References 51 publications

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“…Today, the research field of designing stochastic algorithms is very active. There are many stochastic algorithms such as the Bayesian approach (Minsley 2011;Guo et al 2014;Rosas-Carbajal et al 2014Berube et al 2017;Xiang et al 2018), genetic algorithms (Moorkamp et al 2007;Akca and Basokur 2010;Akca et al 2014), simulated annealing (Prasad 1999;Wang et al 2012), neural networks (El-Qady and Ushijima 2001;Singh et al 2013), evolution algorithms (Balkaya et al 2017; and particle swam optimisation algorithms (Srivastava and Agarwal 2010;Santilano et al 2018;Liu et al 2018a). For their applications in 1D and 2D geo-electromagnetic inversion, please refer to the above references and also a recent review paper (Pankratov and Kuvshinov 2016).…”

Section: Examples Of Nonlinear Model Analysesmentioning

confidence: 99%

Uncertainty and Resolution Analysis of 2D and 3D Inversion Models Computed from Geophysical Electromagnetic Data

Ren

Kalscheuer

2019

Surv Geophys

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A meaningful solution to an inversion problem should be composed of the preferred inversion model and its uncertainty and resolution estimates. The model uncertainty estimate describes an equivalent model domain in which each model generates responses which fit the observed data to within a threshold value. The model resolution matrix measures to what extent the unknown true solution maps into the preferred solution. However, most current geophysical electromagnetic (also gravity, magnetic and seismic) inversion studies only offer the preferred inversion model and ignore model uncertainty and resolution estimates, which makes the reliability of the preferred inversion model questionable. This may be caused by the fact that the computation and analysis of an inversion model depend on multiple factors, such as the misfit or objective function, the accuracy of the forward solvers, data coverage and noise, values of trade-off parameters, the initial model, the reference model and the model constraints. Depending on the particular method selected, large computational costs ensue. In this review, we first try to cover linearised model analysis tools such as the sensitivity matrix, the model resolution matrix and the model covariance matrix also providing a partially nonlinear description of the equivalent model domain based on pseudo-hyperellipsoids. Linearised model analysis tools can offer quantitative measures. In particular, the model resolution and covariance matrices measure how far the preferred inversion model is from the true model and how uncertainty in the measurements maps into model uncertainty. We also cover nonlinear model analysis tools including changes to the preferred inversion model (nonlinear sensitivity tests), modifications of the data set (using bootstrap re-sampling and generalised cross-validation), modifications of data uncertainty, variations of model constraints (including changes to the trade-off parameter, reference model and matrix regularisation operator), the edgehog method, mostsquares inversion and global searching algorithms. These nonlinear model analysis tools try to explore larger parts of the model domain than linearised model analysis and, hence, may assemble a more comprehensive equivalent model domain. Then, to overcome the bottleneck of computational cost in model analysis, we present several practical algorithms to accelerate the computation. Here, we emphasise linearised model analysis, as efficient computation of nonlinear model uncertainty and resolution estimates is mainly determined by fast forward and inversion solvers. In the last part of our review, we present applications of model analysis to models computed from individual and joint inversions of electromagnetic data; we also describe optimal survey design and inversion grid design as important Extended author information available on the last page of the article applications of model analysis. The currently available model uncertainty and resolution analyses are mainly for 1D and 2D problems due to the limitation...

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Section: Examples Of Nonlinear Model Analysesmentioning

confidence: 99%

Uncertainty and Resolution Analysis of 2D and 3D Inversion Models Computed from Geophysical Electromagnetic Data

Ren

Kalscheuer

2019

Surv Geophys

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“…The main objective of geophysical inversion is to apply the same BoltzmannÕs law and to minimize an objective function or the error function in geophysical data modeling. Various optimization methods such as simulated annealing (SA), genetic algorithms (GA), artificial neural networks (ANN), particle swarm optimization (PSO) and differential evolution (DE) (El-Kaliouby and AlGarni 2009;Monteiro Santos 2010;Sharma and Biswas 2011;Sen and Stoffa 2013;Sharma and Biswas 2013;Biswas 2015;Ekinci 2016;Ekinci et al 2016;Balkaya et al 2017) were regularly used to optimize geophysical data and have been applied to derive diverse geophysical information (Rothman 1985(Rothman , 1986Dosso and Oldenburg 1991;Zhao et al 1996;Martínez et al 2010;Li et al 2011;Sharma 2012;Sen and Stoffa 2013). Sen and Stoffa (2013) discussed in detail the SA.…”

Section: Inversionmentioning

confidence: 99%

Inversion of Source Parameters from Magnetic Anomalies for Mineral/Ore Deposits Exploration Using Global Optimization Technique and Analysis of Uncertainty

Biswas

2017

Nat Resour Res

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Global optimization algorithm using very fast simulated annealing has been used for modeling of magnetic anomaly over various idealized geobodies for mineral/ore deposit investigation. The present technique shows that it can match the observed data very well assuming some simple geometrical bodies such as sphere, horizontal cylinder and thin dyke or sheet. Uncertainty associated with the modeling was also studied. It has been found that the obtained source parameters are strongly identical when all the parameters are optimized. The present study shows that amplitude coefficient depends on the shape factor. The relation between them shows a multimodel-type uncertainty. The shape factor modeled from several VFSA runs shows the different kind of subsurface structure. Constraining the shape factor gives reliable results and analysis of histograms and cross-plots also gives the utmost reliable results, which show a unimodel character. Inversion of synthetic noise-free and noisy data shows the worth of the present work. The present algorithm was also tested in five field case studies for mineral/ore exploration. Computation time for this present work is very minimal.

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“…), simulated annealing (SA, Nagihara and Hall ), differential evolution (DE, Balkaya et al . ), neighbourhood algorithm (NA, Basuyau and Tiberi ), and a PSO family (Pallero et al . ).…”

Section: Resultsmentioning

confidence: 99%

“…Wilken and Rabbel (2012) compared the performance of different schemes of PSO with similar stochastic search methods in the context of Scholte-wave inversion. Herein, in order to compare the performance of QPSO with other popular search methods, we have selected a number of recently published studies related to gravity and magnetic inverse problems, which have used ant colony optimisation (ACO, Liu et al 2015), simulated annealing (SA, Nagihara and Hall 2001), differential evolution (DE, Balkaya et al 2017), neighbourhood algorithm (NA, Basuyau and Tiberi 2011), and a PSO family (Pallero et al 2015).…”

Section: Resultsmentioning

confidence: 99%

“…The comparisons are summarised in Table 6 wherein the number of model parameters, the number of particles (or its equivalence for different algorithms), the number of parameters that need tuning, and the number of iterations needed for convergence are included. In most stochastic methods, a (Liu et al 2015) 800 1000 300 375 DE (Balkaya et al 2017) 18 270 70 1.050 PSO family (Pallero et al 2015) 63 250 150 595.24 SA (Nagihara and Hall 2001) 315 50 300 47.62 NA (Basuyau and Tiberi 2011) 768 ß1536 ß15360 30.720 QPSO 2 × 40 250 100 to 150 312.5 to 468.75 number of solutions are tested simultaneously in each iteration. In QPSO/PSO, these place holders for solutions are called particles; in ACO, they are called ants; in evolutionary algorithms, they are referred to as genes and others; therefore, here, we refer to them simply as solution candidates.…”

Section: Resultsmentioning

confidence: 99%

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Non‐linear stochastic inversion of gravity data via quantum‐behaved particle swarm optimisation: application to Eurasia–Arabia collision zone (Zagros, Iran)

Jamasb

Motavalli–Anbaran

Zeyen

2017

Geophysical Prospecting

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Potential field data such as geoid and gravity anomalies are globally available and offer valuable information about the Earth's lithosphere especially in areas where seismic data coverage is sparse. For instance, non‐linear inversion of Bouguer anomalies could be used to estimate the crustal structures including variations of the crustal density and of the depth of the crust–mantle boundary, that is, Moho. However, due to non‐linearity of this inverse problem, classical inversion methods would fail whenever there is no reliable initial model. Swarm intelligence algorithms, such as particle swarm optimisation, are a promising alternative to classical inversion methods because the quality of their solutions does not depend on the initial model; they do not use the derivatives of the objective function, hence allowing the use of L1 norm; and finally, they are global search methods, meaning, the problem could be non‐convex. In this paper, quantum‐behaved particle swarm, a probabilistic swarm intelligence‐like algorithm, is used to solve the non‐linear gravity inverse problem. The method is first successfully tested on a realistic synthetic crustal model with a linear vertical density gradient and lateral density and depth variations at the base of crust in the presence of white Gaussian noise. Then, it is applied to the EIGEN 6c4, a combined global gravity model, to estimate the depth to the base of the crust and the mean density contrast between the crust and the upper‐mantle lithosphere in the Eurasia–Arabia continental collision zone along a 400 km profile crossing the Zagros Mountains (Iran). The results agree well with previously published works including both seismic and potential field studies.

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3D non-linear inversion of magnetic anomalies caused by prismatic bodies using differential evolution algorithm

Cited by 70 publications

References 51 publications

Uncertainty and Resolution Analysis of 2D and 3D Inversion Models Computed from Geophysical Electromagnetic Data

Uncertainty and Resolution Analysis of 2D and 3D Inversion Models Computed from Geophysical Electromagnetic Data

Inversion of Source Parameters from Magnetic Anomalies for Mineral/Ore Deposits Exploration Using Global Optimization Technique and Analysis of Uncertainty

Non‐linear stochastic inversion of gravity data via quantum‐behaved particle swarm optimisation: application to Eurasia–Arabia collision zone (Zagros, Iran)

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