Numerical simulation of multiple scattering of P and SV waves caused by near-surface parallel cracks

Abstract

Scattering and diffraction of P and SV waves caused by parallel oriented cracks located near to a free surface are investigated in this work. The Indirect Boundary Element Method (IBEM) was applied for studying the wave propagation phenomena in a half-plane model that contain the cracks. Various incidence angles of P and SV waves are considered. Sometime before it has been reported that a near free-surface crack generates scattered surface waves whose amplitude spectra show conspicuous resonance peaks. Such effect has been attributed to local resonances originated in a virtual layer between the shallowest crack and the free surface. For our case of two parallel crack system, where cracks are located at different depths, the amplitude spectra show additional peaks, which can be associated with the presence of the second crack. Given similar sizes between these two cracks, the characteristic resonance frequency observed at the free surface corresponds mainly to the equivalent layer formed by the shallowest crack and the free surface. However, when the deepest crack becomes sufficiently large with respect to the shallow crack, two resonance characteristic frequency peaks appear in the measured spectra at the free surface. Some examples including a three crack system are also illustrated in our work. The identification and characterization of the seismic response for the scattered field generated by the second and third crack has been an intricate task and, the time domain interpretation of traces becomes quite complicated. The results in this paper have been validated against some other reported from classic papers. In order to show the seismic response and multiple scattering effects due to the presence of systems of cracks, calculations in frequency and time domain are provided.

Insight into the modeling of seismic waves for detection of underground cavities

“…For very simple cases the propagation of seismic waves can be described analytically [28,1,2,10]. For more complex cases, seismic waves with a significantly smaller or larger wave length than the characteristic size of the obstacle can be approximated by ray tracing methods [13] or effective medium methods [24,44,37], respectively. However, we are interested in the scattered wave patterns when the wavelengths of the propagating waves and the characteristic size of heterogeneities are comparable and here numerical methods become essential.…”