Uygulamalı jeofizikte metasezgiseller

Öz

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.

Anahtar Kelimeler

• 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

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