Seismic inversion for geophysical prospecting

  • Avner Friedman
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 83)


For the purposes of oil exploration impulses of seismic waves are generated by a source at the ground surface and the backscattered vibrations are received by an array of geophones laid out also on the ground surface. The signal from each receiver as a function of time is recorded digitally for later processing. Typically a seismic `survey’ consists of many such `source gathers’ for many different positions of the source and receiver array. Treating the earth as an elastic medium the problem is to deduce the elastic parameters of the subsurface material and its density as functions of position from the data recorded at the surface. Mathematically this is an inverse problem in elastic wave scattering. On January 6, 1995 Robert Burridge from Schlumberger-Doll Research described the inverse problem and some steps towards its solution.


Inverse Problem Ground Surface Static Correction Data Plane Rock Stratum 
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    G. Beylkin and R. BurridgeLinearized inverse scattering problems in acoustics and elasticityWave Motion, 12 (1990), 15–22.MathSciNetMATHCrossRefGoogle Scholar
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    J.B. Keller, R.M. Lewis and B.D. Seckler, Asymptoticsolution of some diffraction problemsCommunications on Pure and Applied Mathematics, 9 (1956), 207–264.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Avner Friedman
    • 1
  1. 1.Institute for Mathematics and its ApplicationsUniversity of MinnesotaMinneapolisUSA

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