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. 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.

中文翻译：

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具有复杂几何形状的流体填充裂缝的共振及其在马约特海底火山超长周期 (VLP) 地震信号中的应用

充满流体的裂缝维持着慢导波（Krauklis 波或裂缝波），其共振频率广泛用于解释活火山的长周期 (LP) 和超长周期 (VLP) 地震信号。人们已经做出了巨大的努力，利用无限裂纹的分析发展或简单裂纹几何形状的数值方法来模拟这一过程。在这项工作中，我们开发了一种有效的混合数值方法，用于计算复杂形状的流体填充裂缝和裂缝网络的共振频率，并将其应用于解释法尼毛雷海底火山 VLP 信号中的光谱峰值比率。马约特岛，2018 年。通过耦合三角形边界元和有限体积法，我们成功处理了复杂的几何形状，并通过仅离散裂纹表面来实现计算效率。通过特征值分析直接确定谐振频率。经过适当的验证，我们系统地分析了矩形和椭圆形裂纹的共振频率，量化了纵横比和裂纹刚度的影响。然后我们从理论上讨论流体粘度和地震辐射对能量耗散的贡献。最后，我们获得了裂缝几何形状，成功地解释了来自马约特岛法尼毛雷海底火山的 VLP 地震信号前两种模式之间的特征比率。我们的工作不仅揭示了复杂形状裂缝中丰富的本征模态，而且还有助于阐明活火山的地下管道系统。开发的模型很容易适用于其他地质环境中的裂纹波共振，例如冰川水文和油气藏。