A fuzzy logic–based circle method for stable hypocentral estimation of offshore earthquakes: a case study from the Eastern Black Sea

Abstract

Accurate earthquake location in offshore regions presents a fundamental challenge due to large azimuthal gaps and limited station coverage. Under such geometries, standard linearized inversion methods may become weakly constrained, enhancing depth–epicenter trade-offs. This study evaluates a nonlinear fuzzy logic–based circle framework designed to mitigate geometric sensitivity under sparse-network conditions. The method was evaluated using synthetic tests covering both intra-network and extra-network scenarios and applied to 121 shallow events in the eastern Black Sea region. Unlike traditional approaches that minimize travel-time residuals via partial derivatives, this framework maps Pg arrival-time uncertainties into a bounded three-dimensional compatibility space defined over the discretized hypocentral search grid. To ensure unbiased validation, results were benchmarked against routine catalog solutions provided by national seismological agencies. Results indicate that while epicentral estimates are largely consistent between methods (median difference ~ 4.26 km), the fuzzy logic approach demonstrates enhanced stability in depth behavior, reflected by more spatially confined compatibility maxima. Occasional shallow depth clustering observed in linearized inversion under offshore conditions reflects geometric limitations rather than systematic mislocation. These differences reflect alternative algorithmic responses under identical structural assumptions rather than absolute mislocation.