Seismic diffracted waves from topography using 3-D discrete wavenumber-boundary integral equation simulation
Sylvette Durand, Stéphane Gaffet, Jean Virieux, 2016. "Seismic diffracted waves from topography using 3-D discrete wavenumber-boundary integral equation simulation", Seismic Diffraction, Kamil Klem-Musatov, Henning Hoeber, Michael Pelissier, Tijmen Jan Moser
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Compressional (P) and shear (S) wave diffraction by free-surface topography plays a prominent part in the prediction of site responses for seismic risk estimation. Wave propagation modeling in 3-D media is required for an accurate estimation of these diffractions. We have extended the discrete wavenumber-indirect boundary integral equation method for a 3-D geometry in the case of irregular topography. The Green’s functions are expressed as finite sums of analytical density functions over the horizontal wavenumbers using the spatial periodicity of the topography and a discretization of the surface. We show that the evaluation over vertical wavenumber kz of the analytical integral is possible because a new factor in 1/ £2 exists. When the force point and the receiver point are at the same vertical position, we develop a numerical strategy to choose the sign of the exponential factor, which is not given by the analytical formulation. The free-streSs boundary conditions at the topography lead to a large linear system that can be solved to obtain the source density functions. Knowing these source density functions, we can compute the diffracted wave-field anywhere inside the medium. We have determined a useful optimal, imaginary frequency to obtain the displacement directly in the frequency domain, avoiding the necessity of returning to the time domain. We have then applied this method to investigate the effect of topography on the ground motion produced by a vertical incident P- or S-wavefield. Waveforms obtained for various topographic steepnesses and shapes show deterministic correlations between the maximum amplitude zone, the geometry of the 3-D topography, and the P- or 5-wave incident field characteristics. The maximum amplitude of the diffracted displacement is found near topographic zones that have horizontal or vertical dimensions closely related to the wavelength of the incident field. The predicted ground motion maximal amplifications are twice those calculated in the case of a flat topography.
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The use of diffraction imaging to complement the seismic reflection method is rapidly gaining momentum in the oil and gas industry. As the industry moves toward exploiting smaller and more complex conventional reservoirs and extensive new unconventional resource plays, the application of the seismic diffraction method to image sub-wavelength features such as small-scale faults, fractures and stratigraphic pinchouts is expected to increase dramatically over the next few years. “Seismic Diffraction” covers seismic diffraction theory, modeling, observation, and imaging. Papers and discussion include an overview of seismic diffractions, including classic papers which introduced the potential of diffraction phenomena in seismic processing; papers on the forward modeling of seismic diffractions, with an emphasis on the theoretical principles; papers which describe techniques for diffraction mathematical modeling as well as laboratory experiments for the physical modeling of diffractions; key papers dealing with the observation of seismic diffractions, in near-surface-, reservoir-, as well as crustal studies; and key papers on diffraction imaging.