This paper presents a new idea for designing a matching filter for processing time-lapse seismic data in a surface-consistent manner. We extend the surface-consistent data model to the case of designing matching filters to equalize two seismic surveys in the least-squares sense. The frequency-domain surface-consistent design equations are similar to those for surface-consistent deconvolution except that the data term is the spectral ratio of two surveys. Since taking spectral ratios poses a challenge, we design the matching filter in a least-squares sense in the time domain and Fourier transform the result. We decompose the result into four surface-consistent components: source, receiver, offset, and midpoint. Each of these components collects unique effects, thus providing us with freedom on how to utilize them.
We discuss two examples that demonstrate how the matching filters are constructed and implemented. In the first example, we apply all four-components to the first monitoring survey to match it to the baseline survey, whose subsurface (the reservoir) is unchanging but shows surface-consistent variability. In the operator window, the residual between the matched survey and the baseline survey is extremely small.
The second example is between the first monitoring survey and second the monitoring survey where the reservoir is variable and shows surface-consistent variability as well. In this case, the residual is close to zero in the matching filter window (Figure 1).
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