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Changes in Seismic Pulse Forms Due to Diffraction Effects

  • Odd Løvhaugen
  • Jakob J. Stamnes
Part of the Acoustical Imaging book series (ACIM, volume 14)

Abstract

It is known that diffraction gives rise to dispersive effects on the seismic signal (Trorey, 1977). To examine these effects, we have developed a computer program that includes diffraction in the simulation of acoustic pulse propagation in complex 3D media (Sandvin, Pedersen, Gjøystdal, 1984). The programs are based on a generalized Kirchhoff approximation of the diffraction integral for inhomogeneous media. The approximation utilizes a dynamic ray tracing solution both for the Green’s function and the boundary values in the Kirchhoff integral. Thus the full solution of the diffraction integral will consist of a sum over reflected and refracted rays representing the boundary values and a sum of reflected and refracted rays representing the Green’s function.

By using an asymptotic solution to this integral we get contributions only from rays with stationary points in surfaces (geometrical reflections) or stationary points on edge curves (edge diffraction contribution). (Stamnes, 1982, 1983). Each contribution to the diffraction integral can thus be identified as a seismic event, for instance a reflection of the seismic pulse at a surface, or a diffraction contribution associated with an edge. Depending on the type of event and the position of the source and receiver, the seismic pulse form and spectrum will suffer a various degree of change. For a reflection-event contribution the pulse form will be maintained, but for an edge-diffraction event the pulse form will change with the detector/source geometry and the shape of the diffracting surface and edge.

An expression for the differaction frequency response for edge diffraction has been found. On the basis of this expression we discuss the possibility of using the dispersion effect to discriminate between reflection and diffraction events. Results of simple model simulations are presented, which illustrate the possibility of identifying diffractors by this method.

Keywords

Stationary Point Seismic Event Inhomogeneous Medium Seismic Signal Full Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Sandvin, 0., Pedersen, H.M., Gjøystdal, H., 1984, “Diffraction modelling in Complex 3D-media”, Expanded abstracts of the 54th Meeting of the Society of Exploration Geophysisists, Atlanta, 395–397.Google Scholar
  2. Stamnes, J.J., 1982, “Diffraction, asymptotics and catastrophes”, Opt. Acta, 29, 823–842.MathSciNetADSGoogle Scholar
  3. Stamnes, J.J., 1983, “Uniform asymptotic theory of diffraction by apertures”, J. Opt. Soc. Am. 73, 96 – 109.MathSciNetADSCrossRefGoogle Scholar
  4. Trorey, A.W., 1977, “Diffraction for arbitrary source receiver location”, Geophysics, 42, 1177 – 1182.ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1985

Authors and Affiliations

  • Odd Løvhaugen
    • 1
  • Jakob J. Stamnes
    • 1
  1. 1.Senter for Industriforskning (Center for Industrial Research)Oslo 3Norway

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