A log spectral approach to bidirectional deconvolution

INTRODUCTION

We three have been impressed by the excellent field data results of Zhang and Claerbout (2010), making us feel that proper blind deconvolution will give much more reliable presentation of seismogram polarity, and hopefully impedance. Additionally Fu et al. (2011) have estimated a field-data shot waveform of remarkable plausibility. Exploring with programs similar to Zhang and Claerbout (2010), however, we discovered a variety of unexpected irregularities that have sent us back to many investigations with synthetic data. Indeed, we now have three quite independent approaches. We believe the heart of the problem lies in the fundamental non-linearity of the basis of the formulation. We are not aware of any realistic linear formulation of it. To allieviate the difficulties we have (1) come up with a much improved starting solution in the form of Ricker wavelet inverses, (2) come up with a smooth ``simultaneous'' descent method, and (3) come up with a log spectral formulation. Unfortunately, we are not out of the woods yet. Hopefully, adding preconditioning to our codes will guide us away from spurious solutions enabling us to make more firm conclusions about the theory which would then allow us to plunge confidently into many field data investigations.

A log spectral approach to bidirectional deconvolution