Exact Time-Domain Solutions for Acoustic Diffraction by a Half Plane
David R. Dalton, Matthew J. Yedlin, 2016. "Exact Time-Domain Solutions for Acoustic Diffraction by a Half Plane", Seismic Diffraction, Kamil Klem-Musatov, Henning Hoeber, Michael Pelissier, Tijmen Jan Moser
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We derive exact time-domain solutions for scattering of acoustic waves by a half plane by inverse Fourier transforming the frequency-domainintegral solutions. The solutions consist of a direct term, a reflected term and two diffraction terms. The diffracting edge induces step functiondiscontinuities in the direct and reflected terms at two shadow boundrics. At each boundary, the associated diffraction term reaches a maximumamplitude of half the geometrical optics term and has a signum function discontinuity so that the total field remains continuous. Wc evaluatesolutions for practical point source configurations by numerically convolving the impulse diffraction responses with a wavelet. We solve theassociated problems of convolution with a singular, truncated diffraction operator by analytically derived correction techniques, Wc produce a zerooffset section and compare it to a Kirchhoff integral solution. Our exact diffraction hyperbola exhibits noticeable asymmetry, with higheramplitudes on the reflector side of the edge. Near the apex of the hyperbola (he Kirchhoff solution approximates the exact diffraction termsymmetric in amplitude about the reflection shadow boundary, bui omits the other low amplitude term necessary to ensure continuity at the directshadow boundary.
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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.