Principle phase decomposition: a new concept in blind seismic deconvolution

This paper outlines an exciting new approach for carrying out blind seismic deconvolution. In this algorithm, overlapping source wavelets are modeled as amplitude-modulated sinusoids, and blind deconvolution is carried out by initially determining the seismogram's principle phase components. Once the principle phases are determined, a Rao-Blackwellized particle filter (RBPF) is utilized to separate the corresponding overlapping source wavelets. This deconvolution technique is referred to as principle phase decomposition (PPD). The PPD technique makes use of the fact that in reflection seismology the discrete convolution operation can be represented as the summation of several source wavelets of differing arrival times. In this algorithm, a jump Markov linear Gaussian system (JMLGS) is defined where changes (jumps) in the state-space system and measurement equations are due to the occurrences and losses of overlapping source wavelet events. The RBPF obtains optimal estimates of the possible overlapping source wavelets by individually weighting and subsequently summing a bank of Kalman filters (KFs). These KFs are specified and updated by samples drawn from a Markov chain distribution that defines the probability of the overlapping source wavelets that compose the JMLGS. In addition, hidden Markov model filters are utilized for refining the principle phase estimates.