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 of this system have been reported by many geophysical studies so far. However, the continental sediment thicknesses of these graben basins still remain controversial due to the findings differing from each other. Thus, an attempt has been made here to invert 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 parameterizations 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 by producing prediction cost function/error energy maps for some block pairs using a hypothetical symmetric 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 also 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 of independent runs are within the confidence interval limits without model uncertainties. In the field data case, long-wavelength anomalies originated from both crustal and deeper effects have been removed from the complete Bouguer anomalies through a 2D finite element method (FEM) using the element shape functions (ESFs). 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, probability density function analyses have also indicated the reliability of the obtained sedimentary package thicknesses without uncertainties.

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Recently, Normalized Full Gradient (NFG) method has widespread applications to natural potential fields, especially in gravity and magnetic. In this study, usage of NFG in Self-Potential (SP) data evaluation is tested. Results are compared to other SP interpretation methods. The NFG method is applied to synthetic and field SP data. As a consequence of application of the method to the anomalies of spherical, cylindrical and vertical sheet models, whose theoretical structures are explicit, the structures were found very close to their actual locations. In order to see the capability of the method in detecting the number of sources, NFG method was applied to different spherical models at different depths and locations. The least-squares inverse solution was applied to the same models and NFG method was found more powerful in detecting model structure. Sensitivity of NFG method for application to noisy data is also tested. An anomaly is generated by adding a random noise to two close sphere SP anomalies. The method seems to work for the two close spheres at high S/N ratio. Then, NFG method was applied to two field examples. The first one is the cross section taken from the SP anomaly map of the Ergani-Süleymanköy (Turkey) copper mine. The depth of the mineral deposit at that site was found about 38 m from the ground level. This result is well matched to previous studies. NFG was also applied to SP data from Seferihisar Izmir (Western Turkey) geothermal field and the location of the point source was determined. The field data of this site have already been modeled by the thermoelectric source (coupling) solution method. When these two methods are compared, they seem to support each other. It is concluded that the NFG method works perfectly when the structure model is simple. It is observed that natural potential sources close to earth's surface are identified by the method more accurately at greater harmonics, while deep sources are identified at lesser harmonics. It produces reasonable results for noisy multi-source models than the other parameter identification methods (inverse solution, power spectrum, etc.).

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