Multiple Scattering of Elastic Waves by Subsurface Fractures and Cavities

Abstract

Comprehensive studies in geophysics and seismology have dealt with scattering phenomena in unbounded elastic domains containing fractures or cavities. Other studies have been carried out to investigate scattering by discontinuities located near a free surface. In this last case, the presence of fractures and cavities significantly affects wave motion and, in some cases, large resonant peaks may appear. To study these resonant peaks and describe how they can be affected by the presence of other near-free-surface fractures or cavities we propose the use of the indirect boundary element method to simulate 2D scattering of elastic P and SV waves. The geometries considered are planar and elliptic cracks and cavities. This method establishes a system of integral equations that allows us to compute the diffracted displacement and traction fields. We present our results in both frequency and time domains. In the planar cracks located near the free surface, we validate the method by comparing results with those of a previously published study. We develop several examples of various fractures and cavities to show resonance effects and total scattered displacement fields, where one can observe conspicuous peaks in the frequency domain and important wave interactions in the time domain. Finally, we show how our dimensionless graphs can be used to deal with materials like clay, sand, or gravel and compare the response with finite-element analysis of elastic beams.

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

“…However, ½I∕2 þ A −1 does not exist if the frequency ω is an eigenfrequency of the interior problem with a rigid boundary condition on S (Martin, 2006;Rodriguez-Castellanos et al, 2006). In the eigenstate, there are nonzero eigenfunctions v k s that satisfy the following equation:…”

“…When the imaginary part of the frequency is small (i.e., slow decay), the integral operator can still be close to singular. Another solution is the multiregion concept proposed by Rodriguez-Castellanos et al (2006), which splits an inclusion into three regions with overlapping boundaries extending to infinity. However, this technique may not be numerically straightforward when dealing with multiple cavities.…”

Improved Holistic Analysis of Rayleigh Waves for Single- and Multi-Offset Data: Joint Inversion of Rayleigh-Wave Particle Motion and Vertical- and Radial-Component Velocity Spectra

“…To reduce the physical effort related to the hammer work and source re-location, the stack adopted for each singleoffset is then often small and, consequently, the signal-to-noise ratio risks to be poor. This can be significant in some cases, especially for the radial Figure 4 Concise representation of the Full Velocity Spectrum (FVS) analysis: a phase velocity spectrum of a field dataset; b phase velocity spectrum of the synthetic model identified by means of the FVS optimization procedure presented in Dal Moro et al ( , 2016 and Dal Moro (2014); c compact representation of the two previous velocity spectra (the background colors represent the velocity spectrum of the field data, while the overlaying black contour lines pertain to the synthetic data); d same data as in the previous plot but from a different (3D) perspective component, which is often more sensitive to heterogeneities between the source and the receivers (e.g., Rodríguez-Castellanos et al 2006). …”

“…In fact, data always and necessarily contain some noise (both coherent and incoherent) that can reflect differently on the considered components and objective functions. Rodríguez-Castellanos et al (2006) showed for instance that, with respect to the vertical component, the radial component of Rayleigh waves is more affected by possible cracks in the medium.…”

Dynamic interaction of twin vertically overlapping lined tunnels in an elastic half space subjected to incident plane waves

“…Kattis et al (2003) used the BEM to study the harmonic body waves scattering by lined and unlined tunnels in an infinite poroelastic saturated soil. Rodriguez-Castellanos et al (2006) studied the scattering of P and SV waves by cracks and underground cavities using the indirect boundary element method (IBEM). Esmaeili et al (2006) analyzed the dynamic response of plane harmonic waves by a lined circular tunnel using the hybrid boundary and FEM.…”