Signal restoration through deconvolution applied to deep mantle seismic probes

We present a method of signal restoration to improve the signal-to-noise ratio, sharpen seismic arrival onset, and act as an empirical source deconvolution of specific seismic arrivals. Observed time-series g_i are modelled as a convolution of a simpler time-series f_i, and an invariant point spread function (PSF) h that attempts to account for the earthquake source process. The method is used on the shear wave time window containing SKS and S, whereby using a Gaussian PSF produces more impulsive, narrower, signals in the wave train. The resulting restored time-series facilitates more accurate and objective relative traveltime estimation of the individual seismic arrivals. We demonstrate the accuracy of the reconstruction method on synthetic seismograms generated by the reflectivity method. Clean and sharp reconstructions are obtained with real data, even for signals with relatively high noise content. Reconstructed signals are simpler, more impulsive, and narrower, which allows highlighting of some details of arrivals that are not readily apparent in raw waveforms. In particular, phases nearly coincident in time can be separately identified after processing. This is demonstrated for two seismic wave pairs used to probe deep mantle and core-mantle boundary structure: (1) the S_ab and S_cd arrivals, which travel above and within, respectively, a 200-300-km-thick, higher than average shear wave velocity layer at the base of the mantle, observable in the 88-92 deg epicentral distance range and (2) SKS and SP_diffKS, which are core waves with the latter having short arcs of P-wave diffraction, and are nearly identical in timing near 108-110 deg in distance. A Java/ Matlab algorithm was developed for the signal restoration, which can be downloaded from the authors web page, along with example data and synthetic seismograms.