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We revisit geophysical diffraction tomography (GDT) and cast it into a stochastic framework, in which the geophysical formation to be imaged is modeled as a realization of a two-dimensional stationary random process. it is shown that the optimum reconstruction algorithm, in both the cases of offset vertical seismic profiling and well-to-well probing, attains a modified filtered backpropagation form. [ABSTRACT FROM AUTHOR]

We address the problem of reconstructing the directional derivative and/or the Laplacian of an object function f characterizing a weakly inhomogeneous scatterer directly from data collected in a set of scattering experiments. We employ the Rytov approximation to model the complex phase of the scattered wavefields and show that a minimum-norm least-squares solution can be obtained from the well known filtered backpropagation algorithm of diffraction tomography with appropriate modification of the tomographic filters employed on the filtering step of the algorithm. The procedure is illustrated by a computer simulation study. [ABSTRACT FROM AUTHOR]