Deconvolution of 3-component Teleseismic P-waves using the Autocorrelation of the P to SV Scattered Waves

We investigate the deconvolution of 3-component teleseismic P-waves using the autocorrelation of the P to SV scattered waves. We first estimate the SV component of the P waveform by rotating the 3-component data to the P-SV-SH frame and also take into account the free surface. This removes the direct P-wave from the SV component leaving only the scattered P to SV waves. Assuming that the transmission P to SV scatterers are random and white, then the autocorrelation of the SV component provides an estimate of the autocorrelation of the source-time function. This is analogous to the use of the autocorrelation of a reflection seismogram in exploration seismology to estimate the source pulse, where for this case, the P-wave reflectivity is assumed to be random and white. The autocorrelation of the SV component can be used to deconvolve the autocorrelation of the unrotated radial and Z components, which include the direct P-wave, in order to estimate the transmission and reflection coefficients. Alternatively, a Aminimum phase source-time function estimated from the autocorrelation of the SV component can be used to deconvolve the unrotated radial and Z components that have been processed to be minimum phase. In either case, a minimum phase source pulse is not required, but the direct P-wave must be larger than the scattered waves on the unrotated components. These procedures are first tested on 1-D synthetics. They are then applied to observed data from the 1993 Cascadia experiment where both P-wave and SV-wave images of the earth structure are estimated from the data which have been deconvolved using the autocorrelation of the SV component.