Sparse reflectivity inversion of processed reflection seismic data is intended to produce reflection coefficients that represent boundaries between geologic layers. However, the objective function for sparse inversion is usually dominated by large reflection coefficients, which may result in unstable inversion for weak events, especially those interfering with strong reflections. We have determined that any seismogram can be decomposed according to the characteristics of the inverted reflection coefficients that can be sorted and subset by magnitude, sign, and sequence, and new seismic traces can be created from only reflection coefficients that pass the sorting criteria. We call this process reflectivity decomposition. For example, original inverted reflection coefficients can be decomposed by magnitude, large ones removed, the remaining reflection coefficients reconvolved with the wavelet, and this residual reinverted, thereby stabilizing inversions for the remaining weak events. As compared with inverting an original seismic trace, subtle impedance variations occurring in the vicinity of nearby strong reflections can be better revealed and characterized when only the events caused by small reflection coefficients are passed and reinverted. When we apply reflectivity decomposition to a 3D seismic data set in the Midland Basin, seismic inversion for weak events is stabilized such that previously obscured porous intervals in the original inversion can be detected and mapped, with a good correlation to the actual well logs.

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