Resonances of Fluid-Filled Cracks With Complex Geometry and Application to Very Long Period (VLP) Seismic Signals at Mayotte Submarine Volcano

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 Maore 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. 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 Maore 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. Just as sound trapped in organ pipes, vibrating waves in fluid-filled cracks produce different tunes, called resonant frequencies, which are useful for inferring crack geometries and fluid properties as a larger and narrower crack produces a lower tune. Previous works have primarily studied simple crack geometries while cracks in the natural world normally have complex shapes. In this study, we develop a new method to compute the resonant frequencies of fluid-filled cracks of complex geometry. This method relies on solving equations only on the crack surface and thus very efficient. We then study vibrations in rectangular and elliptical cracks and evaluate the effect of crack aspect ratio and stiffness. Rich vibrational patterns exist in a crack network, some isolated in a single segment and others involving the entire network. We then discuss the effect of fluid friction and seismic waves on the energy loss of these vibrations. Finally, we show that the crack in Fani Maore submarine volcano in Mayotte that produced the seismic signal may be dumbbell-shaped. Overall, our method is applicable for simulating fluid-filled cracks in wide geological environments, such as active volcanos, glaciers, and oil reservoirs. Hybrid boundary element and finite volume method efficiently computes resonant frequencies of complex-shaped fluid-filled cracks Elliptical crack shares similar modes with rectangular crack but a crack network produces more complex resonances A dumbbell-shaped crack explains ratio of first two modes (similar to 2.5) in the very long period seismic signal at Mayotte submarine volcano