Elastic Wave Propagation Through Cylinders with Fluid-Filled Fractures Using the Discontinuous Galerkin Method

Ana L. Ramos-Barreto, Jonas D. De Basabe () and Raul U. Silva-Avalos
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Ana L. Ramos-Barreto: Seismology Department, Earth Science Division, CICESE, Ensenada 22860, Mexico
Jonas D. De Basabe: Seismology Department, Earth Science Division, CICESE, Ensenada 22860, Mexico
Raul U. Silva-Avalos: Unidad Académica de Ciencia y Tecnología de la Luz y la Materia, Universidad Autónoma de Zacatecas, Campus Siglo XXI, Zacatecas 98160, Mexico

Mathematics, 2025, vol. 13, issue 10, 1-18

Abstract: Accurately modeling fractures in wave-propagation simulations is challenging due to their small scale relative to other features. While equivalent-media models can approximate fracture-induced anisotropy, they fail to capture their discrete influence on wave propagation. To address this limitation, the Interior-Penalty Discontinuous Galerkin Method (IP-DGM) can be adapted to incorporate the Linear-Slip Model (LSM) to represent fractures explicitly. In this study, we apply IP-DGM to elastic wave propagation in fractured cylindrical domains using realistic fracture compliances obtained from laboratory experiments (using ultrasonic-pulse transmission) to simulate the effects of fluid-filled fractures. We analyze how fracture spacing and fluid type influence P- and S-wave behavior, focusing on amplitude attenuation and wave-front delays. Our numerical results align with experimental and theoretical predictions, demonstrating that higher-density fluids enhance wave transmission, reducing the impedance contrast and improving coupling across fracture surfaces. These findings highlight the capability of IP-DGM to accurately model wave propagation in realistic fractured and saturated media, providing a valuable tool for seismic monitoring in fractured reservoirs and other applications where fluid-filled fractures are prevalent.

Keywords: discontinuous Galerkin method; wave propagation; fluid-filled fractured media; fracture compliance; linear slip model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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