We introduce the concept of surface-consistent matching ﬁlters for processing time- lapse seismic data, where matching ﬁlters are convolutional ﬁlters that minimize the sum- squared error between two signals. Since in the Fourier domain, a matching ﬁlter is the spectral ratio of the two signals, we extend the well known surface-consistent hypothesis such that the data term is a trace-by-trace spectral ratio of two data sets instead of only one (i.e. surface-consistent deconvolution). To avoid unstable division of spectra, we compute the spectral ratios in the time domain by ﬁrst designing trace-sequential, least-squares matching ﬁlters, then Fourier transforming them. A subsequent least-squares solution then factors the trace-sequential matching ﬁlters into four operators : two surface-consistent (source and receiver), and two subsurface-consistent (offset and midpoint).
We present a time-lapse synthetic data set with nonrepeatable acquisition parameters, complex near surface geology, and a variable subsurface reservoir layer. We compute the four-operator surface-consistent matching ﬁlters from two surveys, baseline and monitor, then apply these matching ﬁlters to the monitor survey to match it to the baseline survey over a temporal window where changes are not expected. This algorithm signiﬁcantly reduces the effect of most of the nonrepeatable parameters, such as differences in source strength, receiver coupling, wavelet bandwidth and phase, and static shifts. We compute the NRMS (normalized root mean square difference) on raw stacked data (baseline and monitor) and obtained a mean value of 70%. This value was signiﬁcantly reduced after applying the four-component surface-consistent matching ﬁlters to about 15%.
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