ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
This paper considers the effects of multiples, generated at plane bed interfaces, on the characteristics of a mean seismic wave propagating at an angle to the bedding plane. It is found that(a) the multiples produce frequency- and angle-dependent phase shifts to the coherent wave as well as providing an effective attenuation, which is also frequency and angle dependent; (b) a slim angular pencil of monochromatic waves rapidly loses information about its original angular width due to the multiples as the pencil propagates; (c) a seismic pulse, initially traveling at a fixed angle, has both its envelope amplitude and its phase distorted by multiples, and after a short distance of transmission into the medium, the wave shape is nearly completely determined by the generated multiples and is only slightly beholden to the initial pulse shape; (d) the phase and group directions of the mean seismic wave are different than the incident wave's direction and are canted closer to the horizontal with the group direction being the most highly canted; and (e) lateral spreading information of the mean seismic wave is contained in the cross-correlated response of separated geophones and, in principle, can be extracted from cross-correlated measurements. How the generic response depends on the power spectrum of the reflectivity sequence is illustrated by comparing and contrasting results for a transitional sedimentation pattern with those from a cyclic sedimentation pattern; the former produces both a frequency-dependent time delay and attenuation while the latter produces a pure time delay except in the local vicinity of isolated, but periodic frequencies. Numerical estimates, using parameters believed representative of typical seismic conditions, indicate that all of the effects uncovered are large—in the sense that they fall squarely in the regime where they can be expected to have a significant impact both on the subsurface evolution of seismic waves and on interpretations of subsurface conditions made using surface-received signals.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.527121
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