Parameter estimations from gravity and magnetic anomalies due to deep-seated faults: differential evolution versus particle swarm optimization

Estimation of causative source parameters is an essential tool in exploration geophysics and is frequently applied usingpotential field datasets. Naturally inspired metaheuristic optimization algorithms based on some stochastic procedures have attractedmore attention during the last decade due to their capability in finding the optimal solution of the model parameters from the parameterspace via direct search routines. In this study, the solutions obtained through differential evolution algorithm, a rarely used metaheuristicalgorithm in geophysics, and particle swarm optimization, which is one of the most used global optimization algorithms in geophysics,have been compared in terms of robustness, consistency, computational cost, and convergence rate for the first time. Applications havebeen performed using both synthetic and real gravity and magnetic anomalies due to deep-seated fault structures. Before the parameterestimation studies, resolvability of the fault parameters have been examined by producing cost function/error energy topography mapsto understand the suitability of the problem and also the mathematical nature of the inversion procedure. Optimum control parametersof both algorithms have also been determined via some parameter tuning studies performed on synthetic anomalies. Consequently,the tuned parameters clearly improved the effectiveness of both metaheuristics on the solution of the optimization problems underconsideration. Moreover, reliabilities of the obtained solutions and also the possible uncertainties have been investigated using probabilitydensity function analyses. Real data applications have been performed using a residual gravity anomaly observed over the Graber oil field(Oklahoma, USA) and an airborne total field magnetic anomaly observed over the Perth Basin (Australia). Applications have shown thatalthough both algorithms provided close results in both synthetic and real data experiments, the differential evolution algorithm yieldedslightly better solutions in terms of robustness, consistency, computational cost, and convergence rate. Thus, the differential evolutionalgorithm is worth paying more attention to and is suggested as a powerful alternative to particle swarm optimization for the inversionof potential field anomalies.

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Alkan H, Balkaya Ç (2018). Parameter estimation by Differential Search Algorithm from horizontal loop electromagnetic (HLEM) data. Journal of Applied Geophysics 149: 77-94.
Asfahani J, Tlas M (2007). A robust nonlinear inversion for the interpretation of magnetic anomalies caused by faults, thin dikes and spheres like structure using stochastic algorithms. Pure and Applied Geophysics 164: 2023-2042.
Aydemir A, Ates A, Bilim F, Buyuksarac A, Bektas O (2014). Evaluation of gravity and aeromagnetic anomalies for the deep structure and possibility of hydrocarbon potential of the region surrounding Lake Van, eastern Anatolia, Turkey. Surveys in Geophysics 35: 431-448.
Balkaya Ç (2013). An implementation of differential evolution algorithm for inversion of geoelectrical data. Journal of Applied Geophysics 98: 160-175.
Balkaya Ç, Ekinci YL, Göktürkler G, Turan S (2017). 3D non-linear inversion of magnetic anomalies caused by prismatic bodies using differential evolution algorithm. Journal of Applied Geophysics 136: 372-386.
Balkaya Ç, Göktürkler G, Erhan Z, Ekinci YL (2012). Exploration for a cave by magnetic and electrical resistivity surveys: Ayvacık Sinkhole Example, Bozdağ İzmir (Western Turkey). Geophysics 77: B135-B146.
Başokur AT, Akça I, Siyam NWA (2007). Hybrid genetic algorithms in view of the evolution theories with application for the electrical sounding method. Geophysical Prospecting 55: 393- 406.
Biswas A (2015). Interpretation of residual gravity anomaly caused by a simple shaped body using very fast simulated annealing global optimization. Geoscience Frontiers 6: 875-893.
Biswas A (2017). A review on modeling, inversion and interpretation of self-potential in mineral exploration and tracing paleo-shear zones. Ore Geology Reviews 91: 21-56.
Biswas A, Acharya T (2016). A very fast simulated annealing method for inversion of magnetic anomaly over semi-infinite vertical rod-type structure. Modeling Earth System and Environment 2: 198.
Biswas A, Parija MP, Kumar S (2017). Global nonlinear optimization for the interpretation of source parameters from total gradient of gravity and magnetic anomalies caused by thin dyke. Annals of Geophysics 60: G0218.
Biswas A, Sharma SP (2014). Optimization of self-potential interpretation of 2-D inclined sheet-type structures based on very fast simulated annealing and analysis of ambiguity. Journal of Applied Geophysics 105: 235-247.
Boukerbout H, Abtout A, Gibert D, Henry B, Bouyahiaoui B et al. (2018). Identification of deep magnetized structures in the tectonically active Chlef area (Algeria) from aeromagnetic data using wavelet and ridgelet transforms. Journal of Applied Geophysics 154: 167-181.
Büyüksaraç A, Jordanova D, Ateş A, Karloukovski V (2005). Interpretation of the gravity and magnetic anomalies of the Cappadocia Region, Central Turkey. Pure and Applied Geophysics 162: 2197-2213.
Carlisle A, Dozier G (2001). An off-the-shelf PSO. In: Proceedings of the Workshop on Particle Swarm Optimization, Indianapolis, IN, USA, pp. 1-6.
Chen C, Xia J, Liu J, Feng G (2006). Nonlinear inversion of potential field data using a hybrid-encoding genetic algorithm. Computers and Geosciences 32: 230-239.
Chunduru RK, Sen MK, Stoffa PL (1997). Hybrid optimization for geophysical inversion. Geophysics 62: 1196-1207.
Damaceno JG, de Castro DL, Valcácio SN, Souza ZS (2017). Magnetic and gravity modeling of a Paleogene diabase plug in Northeast Brazil. Journal of Applied Geophysics 136: 219-230.
Das S, Abraham A, Konar A (2008). Particle swarm optimization and differential evolution algorithms: technical analysis, applications and hybridization perspectives. Studies in Computational Intelligence 116: 1-38.
Duan HB, Liu SQ (2010). Non-linear dual-mode receding horizon control for multiple unmanned air vehicles formation flight based on chaotic particle swarm optimisation. Control Theory and Applications 4: 2565-2578.
Eberhart RC, Y Shi (2000). Comparing inertia weights and constriction factors in particle swarm optimization. In: Proceedings of the 2000 Congress on Evolutionary Computation. New York, NY, USA: IEEE.
Eiben AE, Smit SK (2011). Parameter tuning for configuring and analyzing evolutionary algorithms. Swarm and Evolutionary Computation 1: 19-31.
Ekinci YL (2008). 2D focusing inversion of gravity data with the use of parameter variation as a stopping criterion. Journal of the Balkan Geophysical Society 11: 1-9.
Ekinci YL (2016). MATLAB-based algorithm to estimate depths of isolated thin dike-like sources using higher-order horizontal derivatives of magnetic anomalies. SpringerPlus 5: 1384.
Ekinci YL, Balkaya Ç, Göktürkler G, Turan S (2016). Model parameter estimations from residual gravity anomalies due to simple-shaped sources using differential evolution algorithm. Journal of Applied Geophysics 129: 133-147.
Ekinci YL, Demirci A (2008). A damped least-squares inversion program for the interpretation of Schlumberger sounding curves. Journal of Applied Sciences 8: 4070-4078.
Ekinci YL, Ertekin C, Yiğitbaş E (2013). On the effectiveness of directional derivative based filters on gravity anomalies for source edge approximation: synthetic simulations and a case study from the Aegean Graben System (Western Anatolia, Turkey). Journal of Geophysics and Engineering 10 (3): 035005.
Ekinci YL, Özyalın Ş, Sındırgı P, Balkaya G, Göktürkler G (2017). Amplitude inversion of 2D analytic signal of magnetic anomalies through differential evolution algorithm. Journal of Geophysics and Engineering 14: 1492-1508.
Ekinci YL, Yiğitbaş EA (2012). Geophysical approach to the igneous rocks in the Biga Peninsula (NW Turkey) based on airborne magnetic anomalies: geological implications. Geodinamica Acta 25: 267-285.
Ekinci YL, Yiğitbaş E (2015). Interpretation of gravity anomalies to delineate some structural features of Biga and Gelibolu peninsulas, and their surroundings (north-west Turkey). Geodinamica Acta 27: 300-319.
Essa KS (2012). A fast interpretation method for inverse modelling of residual gravity anomalies caused by simple geometry. Journal of Geological Research 2012: 327037.
Essa KS, Elhussein M (2018). PSO (Particle Swarm Optimization) for interpretation of magnetic anomalies caused by simple geometric structures. Pure and Applied Geophysics 175: 3539-3553.
Essa KS, Munschy M (2019). Gravity data interpretation using the particle swarm optimization method with application to mineral exploration. Journal of Earth System Science 128: 123.
Fedi M, Rapolla A (1999). 3-D inversion of gravity and magnetic data with depth resolution. Geophysics 64: 452-460.
Ferris C (1987). Gravity anomaly resolution at the Garber field. Geophysics 52: 1570-1579.
Fernández-Martínez JL, García-Gonzalo E, Fernández Álvarez JP, Kuzma HA, Menéndez Pérez CO (2010). PSO: a powerful algorithm to solve geophysical inverse problems. Application to a 1D-DC resistivity case. Journal of Applied Geophysics 71: 13-25.
Gallardo LA, Meju MA (2004). Joint two-dimensional dc resistivity and seismic travel-time inversion with cross-gradients constraints. Journal of Geophysical Research 109: B03311.
Göktürkler G, Balkaya Ç (2012). Inversion of self-potential anomalies caused by simple geometry bodies using global optimization algorithms. Journal of Geophysics and Engineering 9: 498-507.
Grant FS, West GF (1965). Interpretation Theory in Applied Geophysics: New York, NY, USA: McGraw Hill Book Co.
Jiang M, Luo YP, Yang SY (2007). Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm. Information Processing Letters 102 (1): 8-16.
Kaftan İ (2017). Interpretation of magnetic anomalies using a genetic algorithm. Acta Geophysica 65: 627-634.
Kennedy J, Eberhart R (1995). Particle swarm optimization. In: IEEE International Conference on Neural Networks. New York, NY, USA: IEEE, pp. 1942-1948.
Li Y, Oldenburg DW (1996). 3-D inversion of magnetic data. Geophysics 61: 394-408.
Malleswara Rao MM, Ramana Murty TV, Murthy KSR, Vasudeva RY (2003). Application of natural generalised inverse technique in reconstruction of gravity anomalies due to a fault. Indian Journal of Pure and applied Mathematics 34: 31-47.
Maiti S, Gupta G, Erram VC, Tiwari RK (2011). Inversion of Schlumberger resistivity sounding data from the critically dynamic Koyna region using the hybrid Monte Carlo-based neural network approach. Nonlinear Process in Geophysics 18: 179-192.
Mehanee SA (2014). Accurate and efficient regularized inversion approach for the interpretation of isolated gravity anomalies. Pure and Applied Geophysics 171: 1897-1937.
Mehanee S, Essa KS (2015). 2.5D regularized inversion for the interpretation of residual gravity data by a dipping thin sheet: numerical examples and case studies with an insight on sensitivity and non-uniqueness. Earth, Planets and Space 67: 130.
Mehanee S, Essa KS, Smith PD (2011). A rapid technique for estimating the depth and width of a two-dimensional plate from self-potential data. Journal of Geophysics and Engineering 8: 447-456.
Menke W (1989). Geophysical Data Analysis – Discrete Inverse Theory. San Diego, CA, USA: Academic Press.
Montesinos FG, Arnoso J, Viera R (2005). Using a genetic algorithm for 3-D inversion of gravity data in Fuerteventura (Canary Islands). International Journal of Earth Sciences 94: 301-316.
Monteiro Santos FA (2010). Inversion of self-potential of idealized bodies’ anomalies using particle swarm optimization. Computer and Geosciences 36: 1185-1190.
Montesinos FG, Blanco-Montenegro I, Arnoso J (2016). Threedimensional inverse modelling of magnetic anomaly sources based on a genetic algorithm. Physics of the Earth and Planetary Interiors 253: 74-87.
Nagihara S, Hall SA (2001). Three-dimensional gravity inversion using simulated annealing: constraints on the diapiric roots of allochthonous salt structures. Geophysics 66: 1438-1449.
Ogunbo JN (2018). MATLAB code for data-driven initial model of 1D Schlumberger sounding curve. Geophysics 83: F21-F28.
Oruç B, Gomez-Ortiz D, Petit C (2017). Lithospheric flexural strength and effective elastic thickness of the Eastern Anatolian (Turkey) and surrounding region. Journal of Asian Earth Sciences 150: 1-13.
Oruç B, Keskinsezer A (2008). Detection of causative bodies by normalized full gradient of aeromagnetic anomalies from east Marmara region, NW Turkey. Journal of Applied Geophysics 65: 39-49.
Pallero JLG, Fernandez-Martinez JL, Bonvalot S, Fudym O (2015). Gravity inversion and uncertainty assessment of basement relief via particle swarm optimization. Journal of Applied Geophysics 116: 180-191.
Pallero JLG, Fernandez-Martinez JL, Bonvalot S, Fudym O (2017). 3D gravity inversion and uncertainty assessment of basement relief via particle swarm optimization. Journal of Applied Geophysics 139: 338-350.
Pekşen E, Yas T, Kayman AY, Özkan C (2011). Application of particle swarm optimization on self-potential data. Journal of Applied Geophysics 75: 305-318.
Pekşen E, Yas T, Kıyak A (2014). 1-D DC resistivity modeling and interpretation in anisotropic media using particle swarm optimization. Pure and Applied Geophysics 171: 2371-2389.
Qureshi IP, Nalaye AM (1978). A method for direct interpretation of magnetic anomalies caused by 2-d vertical faults. Geophysics 43: 179-188.
Radhakrishna Murthy IV (1998). Gravity and Magnetic Interpretation in Exploration Geophysics. Bangalore, India: Geological Society of India.
Radhakrishna Murthy IV, Krishnamacharyulu SKG (1990). Automatic inversion of gravity anomalies of faults. Computer and Geosciences 16: 539-548.
Radhakrishna Murthy IV, Swamy KV, Jagannadha Rao S (2001). Automatic inversion of magnetic anomalies of faults. Computer and Geosciences 27: 315-325.
Roy L, Sen MK, Blankenship D, Stoffa PL, Richter T (2005). Inversion and uncertainty estimation of gravity data using simulated annealing: an application over Lake Vostok, East Antarctica. Geophysics 70: J1-J12.
Salem A, Ravat D, Mushayandebvu MF, Ushijima K (2004). Linearized least-squares method for interpretation of potential field data from sources of simple geometry. Geophysics 69: 783-788.
Sen M, Stoffa PL (1995). Global Optimization Methods in Geophysical Inversion. Volume 4 of Advances in Exploration Geophysics. Amsterdam, the Netherlands: Elsevier.
Sharma SP, Biswas A (2013). Interpretation of self-potential anomaly over a 2D inclined structure using very fast simulated-annealing global optimization - an insight about ambiguity. Geophysics 78: WB3–WB15.
Shi Y, Eberhart RC (1998). Parameter selection in particle swarm optimization. In: Proceedings of the 7th International Conference on Evolutionary Programming, VII, New York, NY, USA, pp. 591-600.
Sındırgı P, Özyalın Ş (2019). Estimating the location of a causative body from a self-potential anomaly using 2D and 3D normalized full gradient and Euler deconvolution. Turkish Journal of Earth Sciences 28: 640-659.
Singh A, Biswas A (2016). Application of global particle swarm optimization for inversion of residual gravity anomalies over geological bodies with idealized geometries. Natural Resources Research 25: 297-314.
Srivastava S, Agarwal BNP (2010). Inversion of the amplitude of the two-dimensional analytic signal of magnetic anomaly by the particle swarm optimization technique. Geophysical Journal International 182: 652-662.
Storn R (1996). On the usage of differential evolution for function optimization. In: 1996 Biennial Conference North American Fuzzy Information Processing Society, Berkeley, CA, USA, pp. 519-523.
Storn R, Price K (1995). Differential Evolution – A Simple and Efficient Adaptive Scheme for Global Optimization over Continuous Spaces. Technical Report TR-95-012. Berkeley, CA, USA: International Computer Science Institute.
Storn R, Price K (1997). Differential evolution — a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization 11: 341-359.
Tarantola A (2005). Inverse Problem Theory and Methods for Model Parameter Estimation. Philadelphia, PA, USA: Society of Industrial and Applied Mathematics.
Timur E, Kaftan İ, Sarı C, Şalk M (2019). Structure of the Büyük Menderes Graben systems from gravity anomalies. Turkish Journal of Earth Sciences 28: 544-557.
Tlas M, Asfahani J (2011). Fair function minimization for interpretation of magnetic anomalies due to thin dikes, spheres and faults. Journal of Applied Geophysics 75: 237-243.
Toushmalani R (2013). Comparison result of inversion of gravity data of a fault by particle swarm optimization and LevenbergMarquardt methods. SpringerPlus 2: 462.
Trelea IC (2003). The particle swarm optimization algorithm: convergence analysis and parameter selection. Information Processing Letters 85: 317-325.
Xu Y, Hao T, Zhao B, Lihong Z, Zhang L et al. (2011). Investigation of igneous rocks in Huanghua depression, North China, from magnetic derivative methods. Journal of Geophysics and Engineering 8: 74-82.
Yamamoto M, Seama N (2004). Genetic algorithm inversion of geomagnetic vector data using a 2.5-dimensional magnetic structure model. Earth, Planets and Space 56: 217-227.