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The Banlimited Pulse from a Dynamite Source in an Elastic Medium

  • Anton Ziolkowski
Part of the Acoustical Imaging book series (ACIM, volume 14)

Abstract

In exploration seismology it is usual to describe the response xj(t) received at the jth geophone station as the convolution of the impulse response of the earth gij (t) with a seismic wavelet si(t), plus some uncorrelated noise nij(t):
$${x_j}(t) = \mathop \smallint \limits_o^\infty {g_{ij}}(\tau ){s_i}(t - \tau )d\tau + {n_{ij}}(t)$$
(1)
In this equation gij(t) is regarded as the response the jth geophone station would measure in the absence of any noise, if a perfect impulse were emitted at the ith source position at time t = 0. It contains all possible arrivals, including the direct arrival, primary and multiple reflections, refractions and diffractions. The response gij(t) clearly depends on both the source and receiver position relative to the geology.

Keywords

Seismic Response Seismic Source Spherical Symmetry Direct Arrival Receiver Position 
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.

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References

  1. Blake, F.G., 1952, Spherical wave propagation in solid media, Journal of the Acoustical Society of America, Vol 24, No 2, pp 211 – 215.ADSCrossRefGoogle Scholar
  2. Bracewell, R., 1965, The Fourier Transform and its Applications, McGraw-Hill.Google Scholar
  3. Ziolkowski, A. and Lerwill, W.E., 1979, A Simple Approach to High Resolution Seismic Profiling for Coal, Geophysical Prospecting, Vol 27, No 2, pp 360 – 393.ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1985

Authors and Affiliations

  • Anton Ziolkowski
    • 1
  1. 1.Department of Mining EngineeringUniversity of TechnologyDelftThe Netherlands

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