SUMMARY If an earthquake has a primarily unilateral rupture, the pulse width observed on seismograms will vary depending on the angle between the rupture direction and the takeoff vector to the station. We have developed a method to estimate the amount of pulse broadening from the spectrum and apply it to a long-period database of large, globally distributed earthquakes that occurred between 1988 and 2000. We select vertical-component P-waves at epicentral distances of 20 ◦ ‐98 ◦ .W ecompute the spectrum from a 64-s-long window around each P-wave arrival. Each spectrum is the product of source, receiver and propagation response functions as well as local source- and receiver-side effects. Since there are multiple receivers for each source and multiple sources for each receiver, we can estimate and remove the source- and receiverside terms by stacking the appropriate P log spectra. For earthquakes deeper than ∼200 km, source effects dominate the residual spectra. We use our pulse-width estimates to determine the best rupture direction and to identify which nodal plane of the Harvard centroid moment tensor (CMT) solution is most consistent with this rupture direction for 66 events. In about 30 per cent of the cases, one of the two nodal planes produces a much better fit to the data and can be identified as the true fault plane. When results from previous studies are available for comparison, our rupture directions are usually consistent with their results, particularly for earthquakes with simple rupture histories.
We study the frequency dependence of and lateral variations in P-wave attenuation in the mantle by analyzing the spectra from >18,000 P and >14,000 PP arrivals. We select seismograms from the IRIS FARM database from large, shallow earthquakes at epicentral distances of 40°-80° for P waves and 80°-160° for PP waves and compute the spectrum for a 12.8-s-long window around each arrival. Each spectrum is the product of source, receiver, and propagation response functions as well as local sourceand receiver-side effects, and we use a stacking procedure to isolate the propagation effects. Using separate absorption bands in the upper and lower mantles, we model the average depth and frequency dependence of mantle Q by combining measurements of the amplitude decay of the propagation log spectra between 0.16 and 0.86 Hz with long-period Qβ values of other workers. We fi nd that the upper mantle is more attenuating than the lower mantle and that this contrast is greater at higher frequencies. At 1 Hz, the top 220 km of the mantle is ~6 times more attenuating than the lower mantle. In addition, our results indicate that the up-
We respond to the comments by Douglas regarding our earlier paper by emphasizing that our automated method was intended to distinguish between the primary and auxiliary fault planes in earthquake focal mechanisms and does not always produce reliable results for rupture velocity and rupture length.
The directivity method of Warren and Silver (2006) has been used to distinguish the fault planes of deep earthquakes in the Tonga and Middle America subduction zones. These studies identified exclusively subhorizontal fault planes between 100 and 300 km depth, raising the question of whether the observations represent new constraints on the physical mechanism of the earthquakes or a bias in the methodology. Here, the strengths, weaknesses, and biases of the method are investigated through the comprehensive analysis of 120 synthetic earthquakes with varying depth, rupture vector orientation, rupture complexity, signal‐to‐noise ratio, and station distribution. These synthetic tests, which allow the evaluation of the effect of each of the varied parameters on the rupture vector determination, show that fault planes can be identified for a wide variety of conditions. The method underestimates rupture velocities by 76%–94%, but this does not affect the determination of the orientation of the rupture vector. The most important parameter for determining the orientation of the rupture vector, and thereby allowing identification of the fault plane, is the distribution of stations recording the earthquake; better coverage around the earthquakes results in tighter constraints on the rupture vector. The broader distribution of recording stations for deeper earthquakes results in tighter constraints on the rupture vectors for deeper earthquakes and, therefore, more ease in identifying the fault plane. However, the difference in resolution does not systematically prohibit the identification of certain orientations of fault planes at shallower depths and suggests that previous observations of exclusively subhorizontal fault planes between 100 and 300 km depth are not the result of systematic bias in the methodology. Instead, the observed dominance of subhorizontal fault planes provides important constraints on the physical mechanism of intermediate‐depth earthquakes. The observed subhorizontal fault orientation is inconsistent with the reactivation of the dominant trenchward‐dipping outer rise normal faults.
