recfunk_estack.f -- an event-stacking algorithm for RF with long delay times

Click the title to access the Fortran code recfunk_estack.f in

recfunk_estack is a version of the multiple taper correlation receiver-function estimator that allows the time-domain RF to extend to times longer than (roughly) T/10, where T is the duration of the analysis window. Recfunk_estack does NOT apply a moveout or migration correction, so the ability to resolve Ps from deeper interfaces is limited. Other codes to be posted soon will have these properties.

The major shortcoming of the MTC RF estimator of Park & Levin (2000) is its difficulty retrieving Ps conversions at long delay times. Receiver function studies of upper mantle structure at the base of the lithosphere and the transition zone involve Ps converted phases with delay times between 20 and 70 seconds (e.g., Bostock, 1998; Sheehan et al 2000), but the frequency averaging properties of the Slepian data tapers with time-bandwidth product p\ge 2 tends to limit typical RFs to delay times \tau<20 br="" s.="">
Frequency averaging affords the MTC algorithm desirable statistical properties, especially for single-event RF estimates. We can achieve a narrower frequency average for the retrieval of Ps from interfaces deeper than 100 km if we sum single spectral estimates over K seismic events, rather than K eigenspectra from one event, in the RF cross-correlation formulas (2) and(3). Using only one spectrum estimate per component for each P wave, we estimate the spectra with a Slepian taper of time-bandwidth p=1, that is, the "one-\pi-prolate" taper. This taper averages local frequency information over a central bandwidth similar to the simple boxcar taper, but is optimized for spectral leakage resistance.