Uygulamalı jeofizikte metasezgiseller

Year 2016, Volume: 22 Issue: 6, 563 - 580, 20.12.2016

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

Abstract

Bu
çalışmada, parçacık sürü optimizasyonu (PSO), genetik algoritma (GA), farksal
evrim (FE) ve yapay ısıl işlem (YIİ) algoritmalarını kapsayan dört metasezgisel
algoritma jeofiziğin bir, iki ve üç boyutlu (1B, 2B ve 3B) ters çözüm
problemlerinde kullanılmıştır. Doğal uçlaşma (DU), doğru akım özdirenç (DAÖ),
manyetik ve karşılıklı kuyu yer radarı uygulamalarından elde edilen kuramsal
ve/veya alan veri kümeleri yukarıda değinilen metasezgisellerden biriyle
değerlendirilmiştir. PSO, hem sentetik olarak üretilen hem de Güney Bavyera’da
(Almanya) bir grafit yatağında ölçülen DU anomalilerinin model parametrelerinin
(elektrik dipol moment, uçlaşma açısı, derinlik, biçim faktörü ve anomali
orijini) belirlenmesinde kullanılmıştır. Gerçel değer kodlamalı GA, hem
kuramsal hem de Bozdağ, İzmir’de (Türkiye) karstik bir ortamda toplanan düşey
elektrik sondajı veri kümelerinden yatay tabakalı yer modelinin parametrelerini
(tabaka özdirenç ve kalınlıklarını) kestirmek için kullanılmıştır. Sentetik bir
karşılıklı kuyu yer radarı verisinden 2B’lu yeraltı radar hız dağılımının
görüntülenmesi amacıyla YIİ ve yuvarlatma kısıtlı doğrusallaştırılmış en küçük
kareler yönteminin ardışık kullanılmasına dayanan melez bir yaklaşım
uygulanırken; FE algoritması kuramsal olarak üretilen bir toplam alan manyetik
anomali haritasının 3B’lu ters çözümünde kullanılmıştır. Her bir metasezgisel
algoritmanın gerek duyduğu kullanıcı tanımlı parametreler incelenen problemler
dikkate alınarak test çalışmalarıyla belirlenmiştir. Ayrıca, metasezgiseller
tarafından elde edilen sonuçların güvenilirlikleri çeşitli istatistiksel ve
belirsizlik analizleriyle araştırılmıştır. Burada kullanılan metasezgisellerin
çeşitli jeofizik problemlerin model parametrelerinin kestiriminde başarılı
sonuçlar üretmesi bu algoritmaların, jeofiziğin küçük ve görece büyük boyutlu
veri kümelerine uygulanabilirliğini göstermiştir.

Keywords

Metasezgisel, Parçacık sürü optimizasyonu, Genetik algoritma, Farksal evrim, Yapay ısıl işlem, Uygulamalı jeofizik

Metaheuristics in applied geophysics

Abstract

In
this study, four metaheuristic algorithms including particle swarm optimization
(PSO), genetic algorithm (GA), differential evolution (DE) and simulated
annealing (SA) were used for one-, two- and three-dimensional (1D, 2D and 3D) geophysical
inverse problems. Theoretical and/or field data sets obtained by self-potential
(SP), direct current resistivity (DCR), magnetic and crosshole radar
applications were interpreted by one of the above-mentioned metaheuristics. PSO
was used to determine model parameters (i.e., the electric dipole moment,
polarization angle, depth, shape factor and origin of the anomaly) of SP
anomalies which are both synthetically generated and measured over a graphite
deposit in the southern Bavarian woods, Germany. A real-valued GA was used for
estimating the parameters of a horizontally-layered earth model (i.e.,
resistivity and thickness of each layer) from vertical electrical sounding
curves via the data sets based on both theoretical and a field experiment in a
karstic environment in Bozdağ, İzmir (Turkey). A synthetic crosshole radar data
set was considered for 2D imaging of the subsurface radar velocity distribution
by a hybrid approach based on sequential use of SA and a linearized smoothness-constrained
least-squares scheme, and DE algorithm was applied for a 3D inversion of a
synthetically produced total field magnetic anomaly map. User-defined
parameters required by each metaheuristic algorithm were determined by test
studies considering the problems studied. Confidences in the results obtained
by the metaheuristics were also examined by various uncertainty and statistical
analyses. Since the metaheuristics used here produced satisfactory results for
estimating the model parameters of a variety of the geophysical problems, it
can be concluded that these algorithms can be applied to low- and relatively
high-dimensional geophysical data.

Keywords

Metaheuristic, Particle swarm optimization, Genetic algorithm, Differential evolution, Simulated annealing, Applied geophysics

References

• Luke S. Essentials of Metaheuristics. 2nd ed. Lulu Com, 2013. (http://cs.gmu.edu/~sean/book/metaheuristics/).
• Göktürkler G, Balkaya Ç. “Inversion of self-potential anomalies caused by simple-geometry bodies using global optimization algorithms”. Journal of Geophysics and Engineering, 9(5), 498-507, 2012.
• Karaboğa D. Yapay Zekâ Optimizasyon Algoritmaları. 3. baskı. Ankara, Türkiye, Nobel Yayın Dağıtım, 2014.
• Wikipedia.“Metaheuristic”.http://en.wikipedia.org/wiki/Metaheuristic (11.05.2015).
• Corwin RF, Hoover DB. “The self-potential method in geothermal exploration”. Geophysics, 44(2), 226-245, 1979.
• Yüngül S. “Spontaneous potential survey of a copper deposit at Sarıyer, Turkey”. Geophysics, 19(3), 455-458, 1954.
• Bogoslovsky VA, Ogilvy AA. “Geophysical methods for the investigation of landslides”. Geophysics, 42(3), 562-571, 1977.
• Drahor MG, Berge MA. “Geophysical investigation of the Seferihisar geothermal area, Western Anatolia, Turkey”. Geothermics, 35(3), 302-320, 2006.
• Göktürkler G, Balkaya Ç, Erhan Z, Yurdakul A. “Investigation of a shallow alluvial aquifer using geoelectrical methods: a case from Turkey”. Environmental Geology, 54(6), 1283-1290, 2008.
• Bolève A, Janod F, Revil A, Lafon A, Fry J-J. “Localization and quantifiation of leakages in dams using time-lapse self-potential measurements associated with salt tracer injection”. Journal of Hydrology, 403(3-4), 242-252, 2011.
• El-Qady G, Ushijima K, Ahma ES. “Delineation of geothermal reservoir by 2D inversion of resistivity data at Hamam Faraun area, Sinai, Egypt”. Proceedings World Geothermal Congress. Kyushu-Tohoku, Japan, 28 May-10 June, 2000.
• Karlık G, Kaya MA. “Investigation of groundwater contamination using electric and electromagnetic methods at an open waste-disposal site: a case study from Isparta, Turkey”. Environmental Geology, 40(6), 725-731, 2001.
• Hamzah U, Samsudin AR, Malim AP. “Groundwater investigation in Kuala Selangor using vertical electrical sounding (VES) surveys”. Environmental Geology, 51(8), 1349-1359, 2007.
• Kaya MA, Özürlan G, Balkaya Ç. “Geoelectrical investigation of seawater intrusion in the coastal urban area of Çanakkale, NW Turkey”. Environmental Earth Sciences, 73(3), 1151-1160, 2015.
• Quesnel Y, Jrad A, Mocci F, Gattacceca J, Mathe PE, Parisot JC, Hermitte D, Dumas V, Dussouilez P, Walsh K, Miramont C, Bonnet S, Uehara M. “Geophysical signatures of a Roman and early medieval necropolis”. Archaeological Prospecting, 18(2), 105-115, 2011.
• Stampolidis A, Tsokas GN. “Use of edge delineating methods in interpreting magnetic archaeological prospection data”. Archaeological Prospecting, 19(2), 123-140, 2012.
• Ekinci YL, Balkaya Ç, Şeren A, Kaya MA, Lightfoot C. “Geomagnetic and geoelectrical prospection for buried archaeological remains on the Upper City of Amorium, a Byzantine city in midwestern Anatolia, Turkey”. Journal of Geophysics and Engineering, 11(1), 015012, 2014.
• Eventov L. “Applications of magnetic methods in oil and gas exploration”. Leading Edge, 16(5), 489-492, 1997.
• Jallouli C, Mickus K, Turki MM, Rihane C. “Gravity and aeromagnetic constraints on the extent of Cenozoic volcanic rocks within the Nefza-Tabarka region, northwestern Tunisia”. Journal of Volcanology and Geothermal Research, 122(1-2), 51-68, 2003.
• Ekinci YL, Yiğitbaş EA. “A geophysical approach to the igneous rocks in the Biga Peninsula (NW Turkey) based on airborne magnetic anomalies: geological implications”. Geodinamica Acta, 25(3-4), 267-285, 2012.
• Reynolds JM. An Introduction to Applied and Environmental Geophysics. 2nd ed. Chichester, John Wiley and Sons Ltd., 1997.
• Cardimona SJ, Clement WP, Kadinsky-Cade K. “Seismic reflection and ground-penetrating radar imaging of a shallow aquifer”. Geophysics, 63(4), 1310-1317, 1998.
• Knight R. “Ground penetrating radar for environmental applications”. Annual Review of Earth and Planetary Sciences, 29, 229-255, 2001.
• Eisen O, Nixdorf U, Lothar K, Wagenbach D. “Alpine ice cores and ground penetrating radar: combined investigations for glaciological and climatic interpretations of a cold Alpine ice body”. Tellus B, 55(5), 1007-1017, 2003.
• Neal A. “Ground-penetrating radar and its use in sedimentology: principles, problems and progress”. Earth-Science Reviews, 66(3-4), 261-330, 2004.
• Zhou H, Sato M. “Subsurface cavity imaging by crosshole borehole radar measurements”. IEEE Transactions on Geoscience and Remote Sensing, 42(2), 335-341, 2004.
• Göktürkler G, Balkaya Ç. “Traveltime tomography of crosshole radar data without ray tracing”. Journal of Applied Geophysics, 72(4), 213-224, 2010.
• Clement WP, Barrash W. “Crosshole radar tomography in a fluvial aquifer near Boise, Idaho”. Journal of Environmental and Engineering Geophysics, 11(3), 171-184, 2006.
• Ernst JR, Green AG, Maurer H, Holliger K. “Application of a new 2D time-domain full-waveform inversion scheme to crosshole radar data”. Geophysics, 72(5), J53-J64, 2007.
• Kennedy J, Eberhart R. “Particle swarm optimization”. Procedings of IEEE International Conference on Neural Networks”. Piscataway, NJ, 27 November-1 December 1995.
• Holland JH. Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence. Ann Arbor, MI, University of Michigan Press, 1975.
• Storn R, Price KV. “Differential Evolution-A Simple and Efficient Adaptive Scheme for Global Optimization over Continuous Spaces”. International Computer Science Institute, Berkeley, USA, Technical Report, TR-95-012, 1995.
• Kirkpatrick S, Jr Gelatt CD, Vecchi MP. “Optimization by simulated annealing”. Science, 220(4598), 671-680, 1983.
• Sen MK, Stoffa PL. Global Optimization Methods in Geophysical Inversion. 1st ed. The Netherlands, Elsevier Science, 1995.
• Göktürkler G. “A hybrid approach for tomographic inversion of crosshole seismic first-arrival times”. Journal of Geophysics and Engineering, 8(1), 99-108, 2011.
• Eiben AE, Smith JE. Introduction to Evolutionary Computing. Springer-Verlag Berlin Heidelberg GmbH, 2003.
• Storn R, Price K. “Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces”. Journal of Global Optimization, 11(4), 341-359, 1997.
• Monteiro Santos FA. “Inversion of self-potential of idealized bodies’ anomalies using particle swarm optimization”. Computer and Geosciences, 36(9), 1185-1190, 2010.
• Pekşen E, Yas T, Kayman AY, Özkan C. “Application of particle swarm optimization on self-potential data”. Journal of Applied Geophysics, 75(2), 305-318, 2011.
• Biswas A, Sharma SP. “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, 2014.
• Başokur AT, Akça I, Siyam NWA. “Hybrid genetic algorithms in view of the evolution theories with application for the electrical sounding method”. Geophysical Prospecting, 55(3), 393-406, 2007.
• Jha MK, Kumar S, Chowdhury A. “Vertical electrical sounding survey and resistivity inversion using genetic algorithm optimization technique”. Journal of Hydrology, 359(1-2), 71-87, 2008.
• Balkaya Ç, Göktürkler G, Erhan Z, Ekinci YL. “Exploration for a cave by magnetic and electrical resistivity surveys: Ayvacık Sinkhole example, Bozdağ, İzmir (western Turkey)”. Geophysics, 77(3), B135-B146, 2012.
• Göktürkler G. “Karşılıklı kuyu radar verisinin melez ilk varış tomografisi”. Üçüncü Yer Elektrik Çalıştayı, Ilgaz, Türkiye, 24-26 Mayıs 2010.
• Balkaya Ç, Ekinci YL, Göktürkler G. “3D inversion of magnetic data by differential evolution algorithm”. The 20th International Geophysical Congress and Exhibition of Turkey, Antalya, Turkey, 25-27 November 2013.
• Balkaya Ç, Göktürkler G, Ekinci YL, Turan S. “Metaheuristics in applied geophysics”. Proceedings of the 15th EU/ME Workshop, Istanbul, Turkey, 24-25 March 2014.
• Particle Swarm optimization. “Introduction to Particle Swarm Optimization”. http://mnemstudio.org/particle-swarm-introduction.htm (05.08.2015).
• Scrucca L. “GA: A package for genetic algorithms in R”. Journal of Statistical Software, 53(4), 1-37, 2013.
• Zielinski K, Laur, R. Stopping Criteria for Differential Evolution in Constrained Single-Objective Optimization. Editor: Chakraborthy UA. Advances in Differential Evolution, 111-138, Berlin Heidelberg, Springer-Verlag 2008.
• Heaton J. Understanding Simulated Annealing. Editor: Smith K, WordsRU.com. Introduction to Neural Networks with Java, 199-212, Heaton Research, Inc, 2008.
• Shi Y, Eberhart RC. Evolutionary Programming VII. Editors: Porto VW, Saravanan N, Waagen D, Eiben AE. Parameter Selection in Particle Swarm Optimization, 591-600, San Diego, California, USA, Springer Berlin Heidelberg, 1998.
• Poli R, Kennedy J, Blackwell T. “Particle swarm optimization: An overview”. Swarm Intelligence, 1(1), 33-57, 2007.
• Salmon S. “Particle Swarm Optimization in Scilab”. http://forge.scilab.org/index.php/p/pso-toolbox/downloads/ 2011.
• Lee KY, Mohamed PS. “A real-coded genetic algorithm involving a hybrid crossover method for power plant control system design”. Procedings of the 2002 Congress on Evolutionary Computation. Honolulu, HI, USA, 12-17 May 2002.
• Qing A. Differential Evolution: Fundamentals and Applications in Electrical Engineering. 1st ed. New York, USA, John Wiley and Sons, 2009.
• Lin C, Qing A, Feng Q. “A comparative study of crossover in differential evolution”. Journal of Heuristics, 17(6), 675-703, 2011.
• Price KV, Storn RM, Lampinen JA. Differential Evolution: A Practical Approach to Global Optimization. Berlin, Springer-Verlag, 2005.
• Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E. “Equations of state calculations by fast computing machines”. Journal of Chemical Physics, 21(6), 1087-1091, 1953.
• Brooks SP, Morgan BJT. “Optimization using simulated annealing”. Statistician, 44(2), 241-257, 1995.
• Ammon CJ, Vidale JE. “Tomography without rays”. Bulletin of the Seismological Society of America 83(2), 509-528, 1993.
• Yüngül S. “Interpretation of spontaneous polarization anomalies caused by spheroidal orebodies”. Geophysics, 15(2), 237-246, 1950.
• Bhattacharya BB, Roy N. “A note on the use of a nomogram for self-potential anomalies”. Geophysical Prospecting, 29(1), 102-107, 1981.
• Balkaya Ç. “An implementation of differential evolution algorithm for inversion of geoelectrical data”. Journal of Applied Geophysics, 98, 160-175, 2013.
• Meiser P. “A method for quantitative interpretation of selfpotential measurements”. Geophysical Prospecting, 10(2), 203-218, 1962.
• Eberhart RC, Shi Y. “Comparing inertia weights and constriction factors in particle swarm optimization”. Procedings of the Congress on Evolutionary Computation, San Diego, CA, 16-19 July 2000.
• Carlisle A, Dozier G. “An off-the-shelf PSO”. Proceedings of the Workshop on Particle Swarm Optimisation, Indianapolis, IN, January 2001.
• Clerc M, Kennedy J. “The particle swarm-explosion, stability, and convergence in a multidimensional complex space”. IEEE Transactions on Evolutionary Computation, 6(1), 58-73, 2002.
• Trelea IC. “The particle swarm optimization algorithm: convergence analysis and parameter selection”. Information Processing Letters, 85(6), 317-325, 2003.
• Jiang M, Luo YP, Yang SY. Particle Swarm Optimization - Stochastic Trajectory Analysis and Parameter Selection. Editors: Chan FTS, Tiwari MK. Swarm Intelligence, Focus on ant and Particle Swarm Optimization, 179-198, Croatia, I-Tech Education and Publishing, 2007.
• Fernández-Martínez J, García-Gonzalo, E, Naudet V. “Particle swarm optimization applied to the solving and appraisal of the streaming potential inverse problem”. Geophysics, 75(4), WA3–WA15, 2010.
• Fernández Alvarez JP, Fernández Martínez, JL, Menéndez Pérez CO. “Feasibility analysis of the use of binary genetic algorithms as importance samplers application to a 1-D DC resistivity inverse problem”. Mathematical Geosciences, 40(4), 375-408, 2008.
• Fernández Martinez JL, Garcia Gonzalo E, Fernández Álvarez JP, Kuzma HA, Menéndez Pérez CO. “PSO: A powerful algorithm to solve geophysical inverse problems: Application to a 1D-DC resistivity case”. Journal of Applied Geophysics, 71(1), 13-25, 2010.
• Mosegaard K, Tarantola A. “Monte Carlo sampling of solutions to inverse problems”. Journal of Geophysical Research, 100(B7), 12431-12447, 1995.
• Hastings W. “Monte Carlo sampling methods using Markov chains and their applications”. Biometrika, 57(1), 97-109, 1970.
• Chib S, Greenberg E. “Understanding the Metropolis-Hastings algorithm”. American Statistician, 49(4), 327-335, 1995.
• Essa KS. “A new algorithm for gravity or self-potential data interpretation”. Journal of Geophysics and Engineering, 8(3), 434-446, 2011.
• Rao DB, Babu NR. “A rapid method for three-dimensional modeling of magnetic anomalies”. Geophysics, 56(11), 1729-1737, 1991.
• Aldridge DF, Oldenburg DW. “Two-dimensional tomographic inversion with finite-difference traveltimes”. Journal of Seismic Exploration, 2(3), 257-274, 1993.
• Paige CC, Saunders MA. “LSQR: An algorithm for sparse linear equations and sparse least squares”. ACM Transactions on Mathematical Software, 8(1), 43-71, 1982.
• Podvin P, Lecomte I. “Finite difference computation of traveltimes in very contrasted velocity models: a massively parallel approach and its associated tools”. Geophysical Journal International, 105(1), 271-284, 1991.