Source effects on surface wave group travel times and group velocity maps
Introduction
Surface wave tomographic studies are commonly based on phase and group velocity dispersion measurements (e.g., Zhang and Tanimoto, 1993; Wu and Levshin, 1994; Trampert and Woodhouse, 1995; Laske and Masters, 1996; Curtis and Woodhouse, 1997; Ekström et al., 1997; Wu et al., 1997; Ritzwoller and Levshin, 1998; Ritzwoller et al., 1998). Two distinct approaches to such measurements are in practice today. The first is based on direct measurements of surface wave functionals such as phase and group velocities, particle motion (ellipticity, polarization), and amplitudes as functions of period (e.g., Knopoff, 1972). The second is based on waveform fitting (e.g., Woodhouse and Dziewonski, 1984; Nolet, 1987; Snieder, 1988) in which phase velocity curves, phase velocity maps, or seismic models of the Earth are iteratively improved by comparing synthetic waveforms to observations.
In the first, and more traditional, approach apparent surface wave velocities may be distorted by the effect of the so-called `source phase' (e.g., Knopoff and Schwab, 1968). The source phase is the phase of a complex excitation function produced by convolving the components of the strain tensor carried by a given surface wave and evaluated at the source depth with the elements of the moment tensor. This function is one of several factors that define the surface wave spectrum (e.g., Gilbert, 1976; Aki and Richards, 1980). The nature of this excitation function, and consequently its phase, depends on frequency, source mechanism, depth, and the seismic structure of the medium near to the source. Source phase is an initial phase that introduces a temporal shift in the measurement of a phase time and, hence, a perturbation in phase velocity. We call this shift the `source phase time' (SPT) shift. In addition, there is an associated shift in group time which produces a perturbation in group velocity. `Source group time (SGT)' shift is related to the frequency derivative of source phase. If source phase is nearly frequency-independent, SGT is very small.
It is commonly reported (e.g., Knopoff and Schwab, 1968) that at periods below about 50 s, source phase depends only weakly on frequency and, hence, SGT shifts at these periods are usually neglected in most group velocity studies. This is, in fact, one of the features that commends the use of group velocity measurements over phase velocities at relatively short periods. Group velocity measurements are not as strongly contaminated by source effects and it is believed that group velocity measurements can be made and used without a knowledge of the source mechanism.
In contrast, the need to introduce SPT corrections into phase velocity measurements has long been recognized (e.g., Knopoff and Schwab, 1968; Panza et al., 1973) and is now a part of most processing routines. If the source mechanism and a regional model of the medium near to the source are known, it is possible to compute the necessary phase corrections and to remove them from phase measurements leaving only perturbations in phase produced during the propagation of the wave. The main difficulty in applying source phase corrections is the inherent inaccuracy of estimates of the source depth and mechanism. This information is commonly taken from global catalogs such as the Harvard Centroid Moment Tensor (CMT) catalog (e.g., Dziewonski et al., 1981). The accuracy of depth and moment tensor estimates presented in such catalogs depends strongly on the magnitude, spatial location, and depth of an event. The relative accuracy of depth estimates is particularly poor for crustal events in coarsely instrumented regions. Muyzert and Snieder (1996)analyzed the effect of uncertainties in source depth and source mechanism on phase velocity corrections and found that this effect is significant, especially for Rayleigh waves.
Although group velocities probably remain somewhat less used than phase velocities, they are commonly utilized in the analysis of small regional events, in seismic verification research (e.g., Stevens and Day, 1985), and, recently, at long periods for the study of the crust and upper mantle (e.g., Ritzwoller and Levshin, 1998). There are several different techniques for obtaining such measurements; all involve direct measurements made on the observed seismogram and use some kind of windowing of the observed signals in the time, frequency, or a time–frequency domains to suppress interference from unwanted signals (e.g., Cara, 1973; Dziewonski et al., 1969; Landisman et al., 1969; Knopoff, 1972; Levshin et al., 1972Levshin et al., 1989Levshin et al., 1992; Russell et al., 1988; Ritzwoller et al., 1995). No a priori model of the medium of propagation is needed for such measurements, and most of these methods do not include any model fitting procedures. Source corrections for group velocity measurements are commonly considered to be negligibly small and have not been applied to observed group velocities in most of related studies. Exceptions are Cara and Hatzfeld (1976)who noted that SGT is zero only for particular source mechanisms and Jimenez et al. (1989)in which the authors analyzed the importance of such corrections in determining selected source mechanisms. Calcagnile et al. (1982)and Vdovin et al. (1999)applied SGT corrections in their structural studies. However, taking into account the growing use of broadband group velocity data in modern surface wave tomographic studies aimed at obtaining detailed and reliable 3D structure of the Earth's lithosphere, we believe that it would be useful to investigate the accuracy of the approach neglecting SGT corrections. We will limit our discussion to Rayleigh waves, as our calculations have shown that for Love waves the SGT is negligible in the period band (10–200 s) and source depth range (0–200 km). We also ignore here effects caused by the finite duration and finite size of earthquake sources. These effects are usually strongly diminished by using CMT centroid estimates (Dziewonski et al., 1981) as the source time and spatial coordinates instead of hypocenter determinations. The estimates of possible bias in group velocity tomographic maps introduced by errors in event locations were presented earlier in the work of Ritzwoller and Levshin (1998).
The goal of this paper is to evaluate the possible effects of SGT on group velocity measurements and tomographic maps constructed by inverting Rayleigh wave group velocity data. We will estimate the range of periods and source depths for which corrections due to SGT are negligible or practically non-essential in comparison with the inherent inaccuracy of the group velocity measurements and CMT solutions.
Section snippets
Theoretical background
The asymptotic formalisms defining surface wave waveforms and spectra in laterally homogeneous media and smoothly laterally inhomogeneous media are summarized briefly in Appendix A. The expressions for the source phase and the SGT shift for a given surface mode in a laterally homogeneous half-space are given by formulas (A16, A17, A22, A23). In the case of a smooth laterally inhomogeneous medium, these functions are described by similar formulas.
To estimate the validity of these asymptotic
Effects of source mechanism and depth on SGT delays of Rayleigh waves
As shown in Appendix A, SGT depends on several factors. For a given model of a laterally homogeneous or smooth laterally inhomogeneous medium, SGT is a function of the period T, the source depth h, the source mechanism (i.e., seismic moment tensor M), and the source–receiver geometry; namely, the angle ψ between the strike of the fault and the direction from the epicenter to a station. Because the last factor varies widely from station-to-station and from event-to-event, we will consider the
Distortions of tomographic images due to neglecting SGT
As we have shown in Section 3, SGT corrections are appreciable, especially at periods more than 75 s and for source depths more than 25 km. As they are usually neglected in tomographic studies, it is important to understand the level of bias produced in tomographic group velocity maps by neglecting SGT corrections. We performed several synthetic tests to estimate this bias. In these tests, we used the same set of Rayleigh wave paths as in the tomographic inversion performed by Ritzwoller and
Sensitivity of SGT corrections to source characteristics
As shown at Section 3, the magnitude of SGT can easily be above 10–15 s for periods above 75 s and source depths larger than 25 km. This means that some of observed group velocities uncorrected for SGT may be appreciably distorted. At the same time, the tomographic experiment based on the Eurasian tomographic data set discussed in Section 4demonstrated the existence of appreciable bias due to uncorrected SGT at the rim of the continent. These results imply that it may be advisable to apply SGT
Conclusions
In this study, we estimated the possible effect of SGT on group velocity measurements for fundamental Rayleigh waves generated by double-couple type seismic events. We have studied the dependence of this effect on period (10–100 s), source mechanism, and depth (15–100 km). We found that there is a great variability in azimuthal patterns and magnitude of SGT depending on these three factors. Statistics of certain salient functionals that characterize the dependence of SGT on different factors
Acknowledgements
We thank Michel Cara, an anonymous reviewer, and Barbara Romanowicz (Ed.) for critical comments on this paper which substantially improved its content. We are very grateful to Alexander Lander for his help in the triangular representation of source mechanisms. This work was supported by the US National Science Foundation Grants NSF-OPP-9615139 and NSF-EAR-9706188, and the US Department of Defense Contract DSWA01-97-C-0157.
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