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Sahakian, V, Baltay A, Hanks T, Buehler J, Vernon F, Kilb D, Abrahamson N.  2018.  Decomposing leftovers: Event, path, and site residuals for a small‐magnitude Anza region GMPE. Bulletin of the Seismological Society of America.   10.1785/0120170376   Abstract

Ground‐motion prediction equations (GMPEs) are critical elements of probabilistic seismic hazard analysis (PSHA), as well as for other applications of ground motions. To isolate the path component for the purpose of building nonergodic GMPEs, we compute a regional GMPE using a large dataset of peak ground accelerations (PGAs) from small‐magnitude earthquakes ( 0.5≤M≤4.5 with >10,000 events, yielding ∼120,000 recordings) that occurred in 2013 centered around the ANZA seismic network (hypocentral distances ≤180km ) in southern California. We examine two separate methods of obtaining residuals from the observed and predicted ground motions: a pooled ordinary least‐squares model and a mixed‐effects maximum‐likelihood model. Whereas the former is often used by the broader seismological community, the latter is widely used by the ground‐motion and engineering seismology community. We confirm that mixed‐effects models are the preferred and most statistically robust method to obtain event, path, and site residuals and discuss the reasoning behind this. Our results show that these methods yield different consequences for the uncertainty of the residuals, particularly for the event residuals. Finally, our results show no correlation (correlation coefficient [CC] <0.03 ) between site residuals and the classic site‐characterization term VS30 , the time‐averaged shear‐wave velocity in the top 30 m at a site. We propose that this is due to the relative homogeneity of the site response in the region and perhaps due to shortcomings in the formulation of VS30 and suggest applying the provided PGA site correction terms to future ground‐motion studies for increased accuracy.

Mellors, RJ, Vernon FL, Thomson DJ.  1998.  Detection of dispersive signals using multitaper dual-frequency coherence. Geophysical Journal International. 135:146-154. AbstractWebsite

We demonstrate the use of 'dual-frequency' coherence in defecting and characterizing dispersive waves, Using a multitaper method. we calculate the coherence between different frequencies of one or multiple signals, We test the algorithm both on a variety of synthetic signals and on broad-band seismic data. Dispersive waves such as seismic surface waves are easily identified, and we show that the method is robust in the presence of noise. Phase relationships between different frequencies can be extracted, allowing reconstruction of the original phase function. 'Dual-frequency' coherence is useful in identifying overtones and frequency shifts between signals, features that are undetectable by standard coherence measures. We construct a filter to extract only the coherent frequencies from a waveform, and show that it significantly increases the signal-to-noise ratio for dispersive waveforms.

Martynov, VG, Vernon FL, Kilb DL, Roecker SW.  2004.  Directional variations in travel-time residuals of teleseismic P waves in the crust and mantle beneath northern Tien Shan. Bulletin of the Seismological Society of America. 94:650-664.   10.1785/0120030015   AbstractWebsite

We study the directional variation in travel-time residuals using 13,820 P-wave arrivals from 1,998 teleseismic events (15degrees less than or equal to Delta less than or equal to 98degrees, 4.1 less than or equal to m(b) less than or equal to 7.3) recorded in 1991-1997 by the Kyrgyz Digital Seismic Network (KNET). Based on a modified version of the iasp91 model that accounts for the Kyrgyz crustal thickness beneath KNET, we convert P-wave travel times to travel-time residuals deltat. The dependence of deltat on backazimuth is modeled as one-, two-, and four-lobed variations in a horizontal plane (Backus, 1965). A least-squares fit of the azimuthal variation of deltat indicates that the crust in the northern Tien Shan is about 11-15 km thicker than it is in the Kazakh Shield and the Chu Depression. From nine KNET stations, the one-lobe model estimates that the slowest P-wave travel-time direction is - 5.0degrees +/- 4.8degrees (almost directly north) and the magnitude of variation is 1.71 +/- 0.13 sec. This result is consistent with an upwelling lower mantle plume. For the two-lobe model, the slowest P-wave travel-time directions (anisotropy term) are 89.7degrees and 269.7degrees +/- 4.7degrees (i.e., trending east-west). We find P-wave velocity anisotropy of 2.0%-2.9% associated with a layer with a thickness of 440 km at the top of the lower mantle. The fast direction of the P-wave travel-time (north-south) azimuthal anisotropy at the top of the lower mantle is (1) parallel to the absolute motion of the India plate and (2) close to the direction of the upwelling hot mantle flow. The last result suggests that the azimuthal anisotropy of the travel-time residuals is due to the shape-preferred orientation of middle-mantle material that results from plume intrusion. Shear-wave splitting studies (Makeyeva et al., 1992; Wolfe and Vernon, 1998) estimated the fast polarization direction to be parallel to the strike of the geological structures of the northern Tien Shan (71degrees +/- 29degrees). Thus, the fast polarization direction determined from these shear-wave splitting studies using KNET data contradicts (differs by >90degrees) the fast travel-time direction (-0.3degrees and 179.7degrees +/- 4.7degrees) we determine here using P-wave travel-time residuals using KNET data. This suggests that the azimuthal anisotropy determined from P-wave travel-time variations and from shear-wave splitting in SKS and SKKS have different sources.