Imaging P-to-S conversions with broad-band seismic arrays using multichannel time-domain deconvolution

This paper describes a series of innovations in the problem of deconvolving forward scattered P-to-S conversions. We introduce a theoretical foundatio n for a recently developed Multichannel stacking technique and show that th is process is equivalent to a spatial convolution of the incident wavefield with the discretely sampled set of station locations. We then show that de convolution of the stacked data is a form of multi-channel deconvolution wi th a spatially variable set of weights equal to those used in stacking. Thi s result is independent of the particular deconvolution method that is used . A second innovation focuses on the design of deconvolution operators that correctly account for the loss of high frequency components of P-to-S conv ersions caused by differential attenuation of P and S waves. We describe tw o complimentary methods to implement this: (1) through the use of a regular ization operator that penalizes high frequencies and increases with P-to-S lag time, or (2) through the use of a quelling operator. For the latter, we introduce the use of a t* operator that is applied to the deconvolution ma trix operator. The t* operator progressively filters the vertical component seismogram with increasing P-to-S lag time and is based on an earth model of body wave attenuation. Both techniques produce progressively smoother so lutions for increasing P-to-S lag times. The quelling approach has two adva ntages: (1) it is based on the physical principle that this solution is des igned to address, and (2) it provides a unified inversion framework for the combination of stacking and deconvolution. This combination may be interpr eted as a three-dimensional quelling (smoothing) operator that is applied t o the full wavefield to stabilize the inversion. Application of this proced ure to synthetic data shows that while the addition of a time dependent com ponent to the deconvolution tends to decrease the frequency content of the solution, the amplitude of background ringing is reduced and the input mode l is reliably recovered. Further tests with data from the Lodore broad-band array in Colorado and Wyoming show significant improvement over convention al time domain methods. We image lateral variations in Moho continuity and reflectivity across the array, with significant improvement in resolution i n the first 10 seconds of data.