Mathematical Geosciences

, Volume 41, Issue 7, pp 761–777 | Cite as

Estimation of Vertical Continuous Stochastic Parameters from Seismic Reflection Data



This paper presents a scheme to invert reflected seismic wave fields for vertical spatial statistics of the Earth’s continuous stochastic velocity distribution. The forward model is based on a single scattering theory, where a seismogram is modeled as a convolution of a source wavelet and stochastic reflectivity, which obeys a von Kármán autocorrelation function. Tests with synthetic data indicate that the method presented here recovers vertical characteristic length from seismic reflection data that is similar to that of the original velocity model; however, the inversion does not reliably recover the Hurst exponent, ν. The input wavelet’s power spectrum is a free parameter in the inversion and is estimated as well, but is band-limited relative to the original source wavelet. Noise degrades the quality of the estimates of the stochastic parameters such that the recovered stochastic parameters are biased according to the power spectrum of the noise.


Stochastic earth Reflection seismology Stochastic inversion Characteristic length Hurst exponent 


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Copyright information

© International Association for Mathematical Geosciences 2008

Authors and Affiliations

  1. 1.Dept. of Chemistry and PhysicsAugustaUSA

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