Focused blind deconvolution of interferometric Green’s functions

Abstract

We detail a novel multichannel blind deconvolution (BD) algorithm that extracts the cross-correlated or interferometric Green's functions from the records due to a single noisy source. In this framework, we perform a least-squares fit of the cross-correlated records, rather than the raw records, which greatly reduces the indeterminacy inherent to traditional BD methods. To resolve the remaining degrees of freedom, we seek a first approximation where the Green's functions are “maximally white”, and relax this requirement as the iterations progress. This requirement is encoded as the focusing near zero lag of the energy of the auto-correlated Green's functions, hence we call the method focused blind deconvolution (FBD). We demonstrate the benefits of FBD using synthetic seismic-while-drilling experiments to look around and ahead of a bore-hole. Here, the noise due to the operation of the drill bit is not directly usable for reflection imaging, but FBD can provide the processing needed to extract the noise signature without unrealistically assuming the drill noise to be uncorrelated. The interferometric Green's functions obtained from FBD can either be directly imaged or further processed to output the usual subsurface Green's functions. Note that FBD is designed for an acquisition where the noise is recorded for a longer time period than the propagation time of the seismic waves e.g., as could be done during normal drilling operations. Traditional seismic imaging may now be augmented by added information around and ahead of the drill bit, potentially allowing less frequent traditional surveys.