Seismic reconstruction using a 3D tau-p transform

Maria S. Donati and Nicolas W. Martin


The present paper introduces a τ-p transform algorithm for 3D seismic data which not require any geometrical symmetry on the wavefield contained in the seismic data. It only requires to have the data regularly spaced. This algorithm express the τ-p transform by a four-fold sequence of 1D Fourier transforms in time, and spatial coordinates as indicated by McCowan and Brysk (1989) for a point source in an arbitrary medium.

In other words, the 3D τ-p transform is considered as an integration process of different two-dimensional τ-p transforms, each one representing a particular picture of the propagating wave field, along inline and crossline directions. The two-dimensional τ-p transform (back and forward) is performed in the k-w domain using the algorithm published by Wade and Gardner (1988) and Gardner and Lu (1991) based on the "Fourier slice theorem" or "projection slice theorem" (Kak and Rosenfeld, 1982).

The 3D τ-p transform algorithm is tested on synthetic data simulating a shot acquired on an horizontally layered earth model. The results are shown for P and converted data using two different S/N ratios (free-noise and 15% of random noise) showing the robustness of the algorithm for recovering the original shot gathers in the presence of noise.

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