Incorporation of Iterative Forward Modeling Into the Principle Phase Decomposition Algorithm for Accurate Source Wave and Reflection Series Estimation

This paper outlines a more powerful formulation of a previously published new concept in blind seismic deconvolution, referred to as principle phase decomposition (PPD). In this new PPD filter formulation, an iterative forward modeling (IFM) algorithm is incorporated, which facilitates the estimation of parameters defining the source wave (i.e., dominant frequency, phase, and decay) and the overlapping source waves (i.e., reflection coefficients' corresponding arrival times and amplitudes). This IFM integrated PPD algorithm allows for a significantly more accurate approach in estimating the source wave and corresponding reflection series compared to the previously published technique of sequentially estimating the source wave and overlapping source waves utilizing a Rao–Blackwellized particle filter. In general terms, the source wave is modeled as an amplitude-modulated sinusoid, and the overlapping source waves are treated as known inputs within the Kalman filter formulation based on the current source wave and reflection series IFM parameter estimates. The source wave and reflection series parameters are obtained by iteratively minimizing a cost function defined to be the rms difference between the measured seismogram and the synthesized seismogram within the IFM algorithm.