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  Geo-X 5D Interpolation  

The Geo-X proprietary 5D interpolation is ASFT (Arbitrarily Sampled Fourier Transform). It works in the corresponding frequency/wave number domains of inline, x-line, offset, azimuth and time, or inline, x-line, offset_x, offset_y and time. The recorded data is composed of the seismic wave field and the irregular sampled geometry. The algorithm attempts to reconstruct the wave field by solving one Fourier coefficient at a time starting from the strongest wave number first, working all the way down based on the strength of each wave number above a pre-set threshold, with the assumption that the strength of the wave numbers representing the seismic signal are stronger than those representing the noise/alias introduced by the irregular acquisition geometry. Other frequency/wave number domain methods (MWNI and POCS) have the same assumption.

Unlike MWNI and POCS, ASFT does not snap the input traces into the bin centres of a regular grid in order to use Fast Fourier Transform (FFT) for speed. ASFT uses the original spatial coordinates and offset/azimuth of the input traces. It does not restrict the wave numbers in a grid system, in other words, it solves the Fourier coefficients in a continuous wave number domain for accurate representation of the recorded seismic data. Therefore it does not smear the geological structure, and does not compromise AVO effect of the data. With the optimized algorithm, the run time of ASFT is comparable to MWNI.

The advantage of doing interpolation in CDP (inline/xline) domain, not in shot/receiver domain, is that it allows us to localize the interpolation operator to preserve rapid changes of geological structures. It also helps to preserve small scale lithology anomalies.