Gökhan Göktürkler

Jeofizik verilerinin ters çözümünde günümüzde türev tabanlı optimizasyon yöntemlerinin yerini metasezgisel yöntemler almaya başlamıştır. Arama uzayını kapsamlı taraması, iyi bir başlangıç modeline ihtiyaç duymaması ve her optimizasyon problemine kolay uyarlanabilmesi gibi avantajları nedeniyle doğadan esinlenerek oluşturulan birçok metasezgisel yöntem, jeofizik ters çözüm çalışmalarında kullanılmaktadır. Bu çalışmada, popülasyon tabanlı bir metasezgisel yöntem olan Yarasa Algoritmasının doğal potansiyel verilerinin ters çözümünde kullanımına yönelik incelemeler sunulmuştur. Öncelikle Yarasa Algoritmasının kontrol parametrelerini belirleme çalışmaları yapılmış, elde edilen kontrol parametreleri kullanılarak da gürültüsüz ve gürültü eklenmiş kuramsal doğal potansiyel verilerinin ve iki adet arazi verisinin ters çözümü çalışmaları gerçekleştirilmiştir. Ayrıca, kuramsal ve arazi verilerine ait model parametrelerinin güvenilirliğinin belirlenmesi amacıyla Metropolis-Hasting algoritması kullanılarak, kestirim parametrelerinin olasılık yoğunluğu histogramları, istatistiksel olarak da test edilmiştir. Kuramsal verilerin ters çözüm sonuçları ilgili verilere ait doğru değerlerle, arazi verilerine ait ters çözüm sonuçlarıysa literatürdeki diğer çalışmalarda bulunan sonuçlarla kıyaslanarak Yarasa Algoritmasının doğal potansiyel verilerinin ters çözümünde efektif bir yöntem olarak uygulanabilir olduğu görülmüştür

In this work, we introduce application of a hybrid algorithm (DE/PSO) to estimate the model parameters from residual gravity anomalies due to some simple geometrical bodies. This algorithm combines differential evolution (DE) and particle swarm optimization (PSO). To investigate the performance of the hybrid algorithm, test studies were carried out using synthetic and field data sets. The synthetic data sets include noise-free and noisy synthetic anomalies. Two published gravity anomalies from Cuba and Canada were used as the field data. In the hybrid algorithm, DE and PSO yield [premature] solutions separately and share their best solutions during an iterative process. An openly accessible metaheuristics package (NMOF) in R programming environment was used to implement the hybrid algorithm. Through simulations using synthetic anomalies, DE/PSO algorithm was successful to provide improved results. In comparison to the solutions from the single algorithms (DE and PSO), the DE/PSO algorithm shows more effectiveness in terms of accuracy and convergence. The true model parameters of noise-free and noisy synthetic gravity anomalies were recovered well by the hybrid algorithm. The results of inversion for the field examples are characterized by low residual values between the observed gravity anomalies and the calculated ones.

Fault structure reconstruction is an important aspect of magnetic prospecting as it contributes to understanding tectonic history, hazard assessment, and infrastructure planning. Metaheuristics have proven useful in estimating fault structure parameters from geophysical anomalies. Recently, a modified version of the Backtracking Search Optimization Algorithm (BSA), named mBSA, has been proposed that combines mutation steps of BSA and Differential Evolution (DE) algorithms to achieve a better balance between exploration and exploitation. Here, we present imBSA as an efficient approach that builds on the improvements of mBSA. It uses an adaptive amplitude control factor in the mutation step derived from a normally distributed random number obtained via an exponential function. The performances of these approaches were tested on some widely used benchmark functions such as Rosenbrock, Rastrigin, Griewank, and Himmelblau. Synthetic magnetic fault anomalies were evaluated with and without noise, as well as three real anomalies from the Dehri (India), Perth Basin, and Lachlan Fold Belt (Australia). Prior to the optimizations, the solvability of the model parameters was examined using some error topography images. The obtained solutions in the synthetic cases were evaluated using principal component analysis. In addition, a novel visualization option for high‐dimensional optimization problems was introduced. The experiments showed that imBSA has a faster convergence rate and better optimization statistics compared to BSA and mBSA. Therefore, it is believed to be an efficient and good alternative tool to widely used metaheuristics such as Particle Swarm Optimization and DE in explaining geophysical anomalies and optimization problems in other geoscientific disciplines.

SUMMARY: A gravity inversion procedure using the success-history-based adaptive differential evolution (SHADE) algorithm is presented to reconstruct the 3-D basement relief geometry in sedimentary basins. We introduced exponential population size (number) reduction (EPSR) to reduce the computational cost and used self-adaptive control parameters to solve this highly nonlinear inverse problem. Model parametrization was carried out by discretizing the sedimentary cover via juxtaposed right prisms, each placed below each observation point. Resolvability characteristics of the 3-D inverse problem were revealed through some cost function topography landscapes. The fine-tuned control parameter namely, population number allowed us to get best benefit from the algorithm. Additionally, a stabilizing function as a relative constraint was used to avoid undesired effects originated from the ill-posedness of the problem. In the synthetic data cases, the strategy we propose outperformed the linear population number reduction strategy which has won various IEEE–CEC competitions so far. Thorough uncertainty assessments via probability density function and principal component analysis demonstrated the solidity of the obtained inverse models. In the real data case, residual gravity anomalies of two well-known major grabens of Aegean Graben System (Türkiye), calculated thanks to the finite element method, were inverted. It was determined that the inverse solutions obtained for these basement reliefs, whose depths are still controversial, are statistically reliable. Moreover, these depths were found to be less than the depths reported in most previous studies. We conclude that the SHADE using EPSR strategy that we propose is a powerful alternative inversion tool for highly nonlinear geophysical problems.

SUMMARY: Aegean Graben System is a significant member of the complex geology of western Turkey. The depths to the metamorphic basement reliefs in two major grabens have been reported by many geophysical studies. However, the sediment thicknesses of these graben basins still remain controversial due to the findings differing from each other. Thus, we have inverted the gravity data of the sedimentary cover–metamorphic basement using a stochastic derivative-free vector-based metaheuristic named differential evolution algorithm (DEA). This is the first application of DEA adapted to the basement relief depth problem. Model parametrizations have been achieved by discretizing the basins using a group of juxtaposed vertical blocks. Before the inversion studies, mathematical nature of the inverse problem has been investigated via prediction cost function/error energy maps for some block pairs using a hypothetical basin model. These maps have shown the resolvability characteristic of the block thicknesses on such inversion problem. Parameter tuning studies for the optimum mutation constant/weighting factor have been performed to increase the efficiency of the algorithm. The synthetic data have been successfully inverted via the tuned control parameter and some smoothing operators. Probability density function (PDF) analyses have shown that the best solutions are within the confidence interval limits without uncertainties. In the field data case, long-wavelength anomalies caused by both crustal and deeper effects have been removed from the complete Bouguer anomalies through 2-D finite element method using the element shape functions. Some profiles extracted from the residual gravity anomaly map have been used for the inversion and obtained results have shown that the maximum depths to the metamorphic basement reliefs in the grabens are shallower than the findings of the previous studies. Information obtained from the lithological logs drilled in the grabens has supported our results. Moreover, PDF analyses have indicated the reliability of the obtained solutions without uncertainties.