A bi-hyperbolic tilt method for robust edge detection in gravity and magnetic data

Abstract Structural edge detection in gravity and magnetic data is fundamental for constraining subsurface architecture in complex tectonic settings. Yet widely used derivative- and phase-based filters still face a trade-off between resolution, stability, and noise sensitivity. In this study, we introduce a new edge-enhancement operator, the Bi-Hyperbolic Tilt (BiHT) filter, which combines directional derivatives of the Total Horizontal Derivative (THDR) with a bidirectional hyperbolic tangent transformation. The method applies dual $$\tanh$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>tanh</mml:mo> </mml:math> functions to the x and y components of the THDR, and uses a $$\beta$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> -Vertical Derivative ( $$\beta$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> -VDR) stabilization step to sharpen lateral contrasts while suppressing noise-induced artifacts. We evaluate the performance of BiHT through four synthetic experiments designed to span both gravity and magnetic data and to represent noise-free and noisy survey conditions. Comparative analyses against seven established filters (THDR, AS, TDR, TDX, TDTH, THSTDR, THiTDX) show that BiHT consistently produces sharper, more geologically coherent edges with reduced false boundary generation and improved depth continuity, particularly in noisy datasets. The method is further tested on aeromagnetic data from the Seattle Uplift region in western Washington, USA. Here, BiHT delineates the main structural trends associated with the Seattle Fault Zone and the Tacoma Fault more clearly than conventional filters do. When combined with tilt-angle depth estimation, it yields source depths that are consistent with previous geophysical interpretations. These results indicate that BiHT is a robust and adaptable tool for structural interpretation of potential-field data. It offers a practical balance between edge resolution and complements existing derivative- and phase-based approaches.