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