Do earthquakes scale self-similarly or are large earthquakes dynamically different than small ones? This question is important from a seismic hazard prediction point of view, as well as for understanding basic rupture dynamics for earthquakes. We test the extent to which narrowband coda envelopes can improve upon the traditional spectral ratio using direct phases, allowing a better comparison with theoretical models to investigate similarity. The motivation for using the coda is its stability relative to direct waves and its unique property of spatially homogenizing its energy (*Mayeda et al.*, 2003). Based on prior work on local and regional coda, we hypothesize that amplitude ratios of the same event-pair will be much more stable for coda than for direct S-waves. We tested this hypothesis by forming narrowband amplitude ratios for both wave types and compared their standard deviations for many event pairs. In practice, direct wave empirical Greens function studies have limited their data to co-located events with the same source mechanism. This, however, severely limits the useable amount of data, and if proven feasible, the coda's stability and minimal move-out will allow inclusion of more events that are separated in distance and not necessarily of the same focal mechanism.
For both the coda and direct S-waves, we formed amplitude ratios for event pairs by simply subtracting the log10 amplitudes for each station that recorded the event pair. Since the site and path are the same for both events, the ratio should reflect the source differences in the frequency band. Figure 2.11 shows an example of direct wave amplitude ratios and coda wave ratios. Both events are roughly the same size and, as expected, the log10 average of the ratios is close to 0; however, the direct wave results are significantly more scattered.
Using all available ratios, such as the example shown in Figure 2.11, we plot the amplitude ratio standard deviation versus event-pair offset for each frequency band (2.12). The coda amplitude ratios are roughly a factor of 3 smaller and do not show any appreciable increase with event separation, in contrast to the direct waves. This means that the use of the coda will allow for the inclusion of many more events in spectral ratios studies, whereas in direct wave studies, only those events that are virtually co-located are used. Equally important, the coda spectral ratios are significantly less scattered and thus source parameters, such as corner frequency, will be better constrained when we fit the observed data with theoretical source models, such as the commonly used omega-square model (*Aki*, 1967; *Brune*, 1970).

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