Generalized acoustic diffraction tomogra phy1

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Abstract
A generalized diffraction tomography algorithm is developed, which in principle can handle irregularly spaced data, curved acquisition lines and non‐uniform background models. By direct comparison with medical diffraction tomography, it is shown that the generalized method involves the same two processing steps: data filtering and back‐propagation. The filter handles the irregular sampling of the model space and the uneven energy coverage, while the back‐propagation operator removes the wave propagation effects. Paraxial ray‐tracing techniques are employed to compute both these quantities.In medical diffraction tomography, the resolution vector (i.e. the Fourier vector of the model space) is defined by the incident and scattered plane‐wave directions. It is shown here that a similar relationship exists for a non‐uniform background, where the resolution vector at a particular image point is defined by the incident and scattered ray directions. Consequently, the impulse response of the generalized algorithm becomes space variant.Finally, a general processing procedure for transmission mode seismic data, based on this generalized algorithm, is proposed. The potential of the method is demonstrated using synthetic cross‐hole data.