A New Bi-directional Sparse/Spike Deconvolution Method that Overcomes the Minimum Phase Assumption

Traditionally blind deconvolution makes the assumption that the spectrum of the reflectivity series is white. Earlier we dropped that assumption and adopted the assumption that the output spike series is sparse under a hyperbolic penalty function. This approach now allows us to take a step further and drop the assumption of minimum phase. In this new method (what we called Bidirectional Sparse Deconvolution), We solve explicitly for the maximum phase part of the source wavelet. This method is simple in theory (a small modification on the old theory), easy to implement, robust to apply and requires slightly more manual tuning. Results on both synthetic data and field data show clear improvements. Especially the field data result demonstrated the potential of this method to uncover the subsurface impedence directly from deconvolution output.