Q for short‐period P‐waves: is it frequency dependent?

Abstract

Two types of anelastic attenuation model have been derived for short‐period P‐waves for teleseismic ray paths out of the Shagan River Test Site (STS), USSR and the Nevada Test Site (NTS) USA. One type assumes that the specific quality factor Q and hence t* (the ratio of traveltime to Q) is independent of frequency and the other that Q increases (and hence t* decreases) with frequency in the SP band. Evidence for the frequency‐independent t* comes from the observed rate of fall‐off of explosion spectra to high frequencies, whereas a frequency‐dependent t* is required to bring the amplitudes at 1 Hz predicted from widely accepted source models, such as the Muellar‐Murphy (M‐M) model derived from close‐in observations at the NTS, into agreement with observed amplitudes. It has also been claimed that the P spectra for STS explosions show evidence of the frequency‐dependence of t*. In this paper results are presented derived by deconvolving observed P seismograms using each of the two types of attenuation model, in an attempt to determine which best describes the attenuation. Evidence from spectra for frequency‐dependent t* models is also reassessed. The results of the deconvolution of STS seismograms show that neither the frequency‐dependent nor the frequency‐independent models produce deconvolved seismograms that can be interpreted as a series of pulses of the M‐M type. Such M‐M pulses should show a positive initial motion followed by a negative overshoot with amplitude less than about a third of that of the positive motion; the leading edge of the main pulse being sharper than the trailing edge. Use of the frequency‐dependent t* leads to pulses apparently with overshoot. The amplitude of the overshoot however, is larger than predicted by the theoretical source model and appears to be an artefact of the processing rather than a property of the source pulse itself. With t* independent of frequency the estimated pulses have the form of symmetrical trapezia. Reassessment of the evidence from observed P spectra for frequency‐dependent t* is shown to be at best inconclusive and it turns out that the spectra of symmetrical trapezia have a fall‐off that can account for those features of explosion spectra that have been attributed to the effects of frequency‐dependent t*. It is concluded that the frequency‐independent t* model is the better attenuation model for paths from the STS. The results obtained from deconvolution of the P seismograms of NTS explosions are similar to those obtained for STS explosions and again suggest that t* is independent of frequency. As with the STS results, use of frequency‐dependent t* sometimes leads to pulses with overshoots that appear to be artefacts of the processing and not part of the source pulse. Further, deconvolution using the frequency‐independent t* leads to a more systematic variation of pulse duration with depth (and hence presumably yield) than is found using the frequency‐dependent models. Use of the frequency‐independent t* again leads to pulses which have the rough form of symmetrical trapezia. On the interpretation given here, amplitudes predicted using a M—M source and assuming t* is independent of frequency are much larger than observed because it is the source model rather than the attenuation model that is incorrect. At low frequencies the differences between the observed amplitudes and those predicted from the M‐M model may be significantly less than a factor of 2. However at around 1 Hz the amplitudes for the M‐M source model are much larger than those of source models derived here by deconvolution, mainly because of the overshoot in the M‐M model which produces a peak in the spectrum at around 1 Hz. The results support the suggestion that the M‐M model is incorrect because it is based on observations made in the non‐linear zone, and that non‐linear attenuation within the zone eliminates overshoot from the pulses radiated into the linear zone. Copyright © 1992, Wiley Blackwell. All rights reserved