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 foundation for a recently developed multichannel stacking technique and show that this process is equivalent to a spatial convolution of the incident wavefield with the discretely sampled set of station locations. We then show that deconvolution of the stacked data is a form of multichannel deconvolution with a spatially variable set of weights equal to those used in stacking. This 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 conversions caused by differential attenuation of P and S waves. We describe two complimentary methods to implement this: (1) through the use of a regularization 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 matrix 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 solutions for increasing P-to-S lag times. The quelling approach has two advantages: (1) it is based on the physical principle that this solution is designed to address, and (2) it provides a unified inversion framework for the combination of stacking and deconvolution. This combination may be interpreted as a three-dimensional quelling (smoothing) operator that is applied to the full wavefield to stabilize the inversion. Application of this procedure to synthetic data shows that while the addition of a time dependent component to the deconvolution tends to decrease the frequency content of the solution, the amplitude of background ringing is reduced and the input model is reliably recovered. Further tests with data from the Lodore broad-band array in Colorado and Wyoming show significant improvement over conventional time domain methods. We image lateral variations in Moho continuity and reflectivity across the array, with significant improvement in resolution in the first 10 seconds of data.