Upper Mantle Surprises derived from the recent
Virginia Earthquake waveform data
Risheng Chu, Don Helmberger, and Michael Gurnis
Supplement Material
Data and Method
Explosions are particularly useful for studying 1D earth structure because of the relatively simple waveforms. Although small explosions are still popular in crustal studies, large explosions are less common. Here we rely on the relatively low seismicity of the stable craton and exploit the dense wide-aperture receiver coverage provided by TA.
Before we can study the P wave propagation of the Virginia earthquake, we need to determine the source parameters using our preferred Cut-and-Paste (CAP) method (Fig. S1). This technique fits Pnl and surface wave segments between observed and synthetics that are allowed to shift independently in timing for alignment [Zhu and Helmberger, 1996]. Thus, the procedure automatically determines the travel-time delays along each path. We also invert the focal mechanism of the earthquake using a teleseismic version (CAPt) [Chu et al., 2011], obtaining a slightly different solution (Fig. S2). Because the West Coast stations are at the same azimuths as the TA, we have used the teleseismic solution although using the regional solutions produces similar results. Synthetics for possible models were generated both in 1D and 2D using the methods discussed in Chu et al. (2012). An example of a 2D calculation is given in Fig. S3 along with ray-paths computed by the WKM code, Ni et al. (2003). These analytical codes are routinely checked against 2D finite-difference codes to insure accuracy.
It proves difficult to fit both travel time and amplitudes without more data constraints, which will hopefully be provided by the migration of the TA eastward. We follow a forward modeling approach with a trial-and-error procedure in fitting waveform data. The fits are measured by computing the cross-correlations of synthetics compared with data. As in our recent modeling in the CR paper, we also conducted some grid searches as displayed in Fig. S4. We use the WKM code with ray paths to define the depths of significant boundaries. The best 1D fit is given in Fig. 4D, see Fig. S4 for more details. All the models display sudden velocity increases near 300 km, but its sharpness is not well resolved as well as the layer thickness because of the likelihood of a LVZ before the 410 transition onset and the absence of recordings at larger distances. However, there is strong evidence for a LVZ above the 410 near the edge of this anomalous structure, as displayed in profile III.
The details of the construction of synthetics for model III is given in Fig. S5. Here we generate the responses at 14° and 16° to highlight the effect of adding the low-velocity zone just above the 410 discontinuity. We have included the corresponding analysis for synthetics predicted by the CR model without this LVZ. Note that the low-velocity zones near the depths of 160 km produces the dotted AB branch (start of diffractions) and again near the depth of 375 km (off-set in BC branch as given in Fig. S5B). The role of changes in the p-t plots (Fig. S5C) controls the synthetic where the numerical derivative δp/δt rules (Ni et al., 2003; Chapman, 2004). Example ray plots are presented in Fig. S5D along with p-t plots in Fig. S5C. Note that there are two arrivals, one early A and one late C. Adding the lower LVZ produces more of a flat portion strengthening the second arrival (large δp/δt) as displayed in Fig. S5 for model III. The accuracy of the WKM method is discussed in Ni et al. (2003) and Chu et al. (2012). We have not attempted to fit the observed waveform in detail because the structure is probably 3D, but have tested the sensitivity along the 410 region to enhance the CD branch as displayed. Some of their amplitudes are very strong (Fig. 5) and are probably produced by 3D focusing.
Reference:
Chapman, C., Fundamentals of Seismic Wave Propagation, Cambridge Univ. Press, New York, (2004).
Chu, R., B. Schmandt, and D. V. Helmberger, Juan de Fuca subduction zone from a mixture of tomography and waveform modeling, J. Geophys. Res., doi:10.1029/2012JB009146, 2012.
Hartzell, S. and D. V. Helmberger, Strong-motion modeling of the Imperial Valley earthquake of 1979, Bull. Seismol. Soc. Am., 72, 571-596, 1982.
Herrmann, R. B., Surface wave focal mechanisms for eastern North American earthquakes with tectonic implications, J. Geophys. Res., 84 (B7), 3543–3552, 1979.
Ni, S., V. F. Cormier, and D. V. Helmberger, A comparison of synthetic seismograms for 2D structures: Semianalytical versus numerical, Bull. Seismol. Soc. Am., 93(6), 2752–2757, doi:10.1785/0120030011, 2003.
Zhu, L., and D. V. Helmberger (1996), Advancement in source estimation techniques using broadband regional seismograms, Bulletin of the Seismological Society of America, 86(5), 1634-1641,
Figure Captions:
Figure S1. Cut-and-Paste (CAP) inversion of the Virginia earthquake determined by modeling regional broadband waveforms, which are arranged according to their azimuths. The Pn waves are filtered using frequencies 5-50s and surface waves are filtered using frequencies 10-50s. The best-fitting mechanism is a thrust event at the depth of 6 km. The crust velocity model used here is taken from Herrmann [1979]. (A) Observed velocity data is shown as black traces, and red traces are the corresponding synthetic velocity seismograms. The two numbers beneath each trace are its time shift relative to the synthetic segments generated from the 1D model to match the data and the cross-correlation coefficient (CC). Green traces denote bad data with low CCs. The control on depth is produced by the separation between Pn and the depth phases pPn and sPn, see Zhu and Helmberger [1996]. (B) The misfit is plotted against depth. (C) Map of the regional stations (triangles) and the travel-time residuals of Love waves.
Figure S2. Inversion of global waveform data in P and SH to define the mechanism of the Virginia earthquake. The cross-correlation coefficients for P- and S-waves are shown in (A) and (B), respectively, with some sample waveform fits displayed. Because of the thrust mechanism, fits of P waves have larger CCs than SH waves because of the weak nature of SH relative to SV which causes contamination (Hartzell and Helmberger, 1982), and (C) The misfit is plotted against depth yield.
Figure S3. (A) Ray path sampling of the lithosphere and upper mantle for stations between 8o and 18o. The red and blue box denote low-velocity zone (~-3%) in the lithosphere and X-discontinuity (~2.5%), respectively. (B) Comparison of the data (black) and synthetics (red).
Figure S4. (A) Velocity models constructed in the grid search (red dashed lines). The black and red lines are the initial and final 1D models, respectively. Waveform fits for model M1 and M2 are shown in (B) and (C), respectively. Note that M2 fit is quite good, i.e., about as good as given in Fig. 4D except the synthetic CD branch is too weak. This issue can be readdressed when there are receiver function data available beneath the X-phase position.
Figure S5. Display of WKM synthetic generation involving ray paths, triplications, and ray parameter (p) versus travel time (t) plots. The P-velocity models are given in (A). The triplications are displayed in (B) with dashed lines indicating shadow zones where only diffracted arrivals are observed. Note that the C tip occurs between 14° and 16° for both models (dotted lines). Plots of p-t curves for the CR (black) and model III (red) at ranges 14° (diffracted) and 16° (geometry) are included in (C). Note that δp/δt does not have the classical square-root singularity at 14° for either model although the red trace is closer. The ray paths are given in (D) showing the shallow A branch reaching the shadow zone. Near 400 km we can see the rays in red bending at the LVZ boundary, indicated by the arrow.
Figure S6. (A) Data of the Quebec earthquake along profile IV shows clear arrival of CD branch. The AB branch, however, is distorted. (B) Synthetics generated using CR (black) and model II (red) at distance larger than 22o show distorted AB branch.
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