2D full-waveform modeling of seismic waves in layered karstic media

Abstract

We have developed a new propagator-matrix scheme to simulate seismic-wave propagation and scattering in a multilayered medium containing karstic voids. The propagator matrices can be found using the boundary element method. The model can have irregular boundaries, including arbitrary free-surface topography. Any number of karsts can be included in the model, and each karst can be of arbitrary geometric shape. We have used the Burton-Miller formulation to tackle the numerical instability caused by the fictitious resonance due to the finite size of a karstic void. Our method was implemented in the frequency-space domain, so frequency-dependent Q can be readily incorporated. We have validated our calculation by comparing it with the analytical solution for a cylindrical void and to the spectral element method for a more complex model. This new modeling capability is useful in many important applications in seismic inverse theory, such as imaging karsts, caves, sinkholes, and clandestine tunnels.

Rapid falling of an orbiting moon to its parent planet due to tidal-seismic resonance

“…The change of figure of the planet can change the planet gravitational field to exert a net torque on the moon. To compute this torque, we need to compute the tidal-force induced seismic wavefield and we use the boundary element integral equation approach (Zheng et al, 2016a) to do so (see Appendix C). The advantage of this computational method is that it is implemented in the frequency domain and can model long-term seismic field evolution (i.e., can avoid numerical dispersion in many time-domain methods) and can also handle planet topography.…”

“…We apply the Boundary Element Method (BEM) (Zheng et al, 2016b) to numerically model the seismic field in the planet excited by tidal force. This method can solve the problem with arbitrary boundary shape in the frequency domain, which reduces the computational cost in this study.…”

Extending Esh3D Code to Solve Interacting Eshelby's Inhomogeneity Problems

“…Therefore, a whole space problem does not require any numerical grid. Zheng et al () apply similar formalism to waveform modeling in layered 2‐D medium that contains multiple elliptical voids.…”

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

“…However, similar to FDM, FEM needs to discretize the volume, which results in a large number of elements and high computational cost. On the other hand, the boundary element method (BEM) reduces the simulation space from a domain to boundary surfaces, drastically decreasing the number of degrees of freedom, and has been used to study waves in fluid‐filled cracks (Jin et al., 2022; Pointer et al., 1998; Yamamoto & Kawakatsu, 2008) and other inclusions (Sun et al., 2020; Zheng et al., 2016). However, previous BEM simulations are either in two dimensions or focus on the wave diffraction instead of analyzing the resonant frequencies.…”