Band-controlled sparse deconvolution

Sparse-spike deconvolution is widely applied for improving the resolution of stacked seismogram. However, the method frequently suffers from instability and low accuracy owing to the nonuniqueness of the inverse problem. A traditional alternative is linear deconvolution, but its processing result is band limited to the effective band of raw data. We developed a band-controlled sparse deconvolution (BCSD) algorithm that inverts for seismic data with suitable bandwidth to guarantee resolution and accuracy simultaneously. Besides, BCSD is able to rebuild reflectivity and in this case it turns into sparse-spike inversion. The new algorithm was implemented through minimizing a cost function including three terms: a data misfit term that is applicable for reconstructing high-resolution seismic data, a sparse constraint term bringing in high-frequency constituents, and a high-pass-filtered term controlling the retrieved bandwidth. A 1D synthetic series example illustrated the potential benefits of retrieving band-controlled seismic response, and the inability of the existing approach in recovering such a seismic data. Two 2D model and a field data examples demonstrate that BCSD can provide a better seismogram than linear deconvolution in term of broadening the frequency band of data and meanwhile guaranteeing the stability and reliability.