Abstract
In this paper, we show that an aligned J-channel deconvolution can be converted into an equivalent single-channel deconvolution. For unaligned two-channel seismic data, we model channel 1 as a convolutional model and channel 2 as a cascade of a time-varying delay system and a convolutional model. We then provide a three-step alignment procedure. The first step includes single-channel deconvolution. The second step includes time-varying delay system identification; it uses the single-channel deconvolved results obtained in the first step. The third step is one of alignment, and is based on the time-varying delay information obtained in step 2. For an unaligned. J-channel system, we choose a reference channel so as to make the other channels aligned with it using our two-channel alignment procedure. After we have completed the alignment on the unaligned. J-channel system, we are then able to convert unaligned J-channel deconvolution into an equivalent single-channel deconvolution. The 3-step alignment algorithm proposed in this paper provides a method to accomplish stacking prior to velocity analysis. Velocity analysis can be performed after maximum-likelihood deconvolution by fitting hyperbolas to the matched spikes, because our algorithm is based on a multichannel model that incorporates elements of velocity analysis.