Fluid-filled cracks sustain a slow guided wave (Krauklis wave or crack wave) whose resonant frequencies are widely used for interpreting long period (LP) and very long period (VLP) seismic signals at active volcanoes. Significant efforts have been made to model this process using analytical developments along an infinite crack or numerical methods on simple crack geometries. In this work, we develop an efficient hybrid numerical method for computing resonant frequencies of complex-shaped fluid-filled cracks and networks of cracks and apply it to explain the ratio of spectral peaks in the VLP signals from the Fani Maoré submarine volcano that formed in Mayotte in 2018. By coupling triangular boundary elements and the finite volume method, we successfully handle complex geometries and achieve computational efficiency by discretizing solely the crack surfaces. The resonant frequencies are directly determined through eigenvalue analysis. After proper verification, we systematically analyze the resonant frequencies of rectangular and elliptical cracks, quantifying the effect of aspect ratio and crack stiffness ratio. We then discuss theoretically the contribution of fluid viscosity and seismic radiation to energy dissipation. Finally, we obtain a crack geometry that successfully explains the characteristic ratio between the first two modes of the VLP seismic signals from the Fani Maoré submarine volcano in Mayotte. Our work not only reveals rich eigenmodes in complex-shaped cracks but also contributes to illuminating the subsurface plumbing system of active volcanoes. The developed model is readily applicable to crack wave resonances in other geological settings, such as glacier hydrology and hydrocarbon reservoirs.

Supershear earthquakes are rare compared to their subshear counterparts, but the cause for their paucity remains to be understood. We investigate for the first time the prevalence of supershear ruptures across multiple earthquake cycles on long faults using rate-and-state friction and a 2.5D approximation that accounts for the finite seismogenic width W. We find supershear events occur only in a narrow range of friction parameters that is not commonly observed in laboratory experiments, which may explain its rarity in nature. Particularly, the ratio between direct and evolution effects of rate-and-state friction needs to be low (a/b<0.4) and the nucleation length has to be sufficiently large compared to W, but not too large that it causes a transition from seismic to aseismic slip. Our numerical and analytical developments contribute fundamentally to understanding the state of stress on long faults over multiple earthquake cycles and their potential for hosting supershear earthquakes.