Multichannel sparse spike deconvolution based on dynamic time warping

Seismic sparse spike deconvolution is commonly used to invert for subsurface reflectivity series and is usually implemented as an inversion scheme. Conventional sparse spike deconvolution method does not utilize the relationships among adjacent traces resulting in instability and poor lateral continuity of the inverted result. We propose a multichannel sparse spike deconvolution method with a sparsity-promoting constraint and an extra lateral constraint exploiting the spatial relationships among adjacent seismic traces. Firstly, the dynamic time warping (DTW) is performed between any two adjoining seismic traces to obtain the warping path (a series of estimated time shifts of one seismic trace relative to the other). Based on the assumption that if the inverted reflectivity series is convolved with the same wavelet used for inversion, the newly constructed adjoining seismic traces shall also be conformable to the relationships exploited among the original seismic traces by DTW. A difference operator is constructed with the estimated time shifts to guarantee the difference operation is performed between corresponding time samples on adjoining seismic traces and the inversion is regularized with this difference operator as the lateral constraint. Synthetic and real data case studies confirm that inverted result obtained by the proposed method is superior to those obtained by single-channel sparse spike deconvolution method and another multichannel deconvolution method based on horizontal first-order derivative constraint in both signal-to-noise ratio and lateral continuity.