2-D random media with ellipsoidal autocorrelation functions

The integration of surface seismic data with borehole seismic data and well‐log data requires a model of the earth which can explain all these measurements. We have chosen a model that consists of large and small scale inhomogeneities: the large scale inhomogeneities are the mean characteristics of the earth while the small scale inhomogeneities are fluctuations from these mean values. In this paper, we consider a two‐dimensional (2-D) model where the large scale inhomogeneities are represented by a homogeneous medium and small scale inhomogeneities are randomly distributed inside the homogeneous medium. The random distribution is characterized by an ellipsoidal autocorrelation function in the medium properties. The ellipsoidal autocorrelation function allows the parameterization of small scale inhomogeneities by two independent autocorrelation lengths a and b in the horizontal and the vertical Cartesian directions, respectively. Thus we can describe media in which the inhomogeneities are isotropic (a = b...

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