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Shear-Wave Splitting in NE Appalachians

Figure 7 shows the pattern of SKS shear-wave splitting for two earthquakes with different back azimuths (westerly and northwesterly), observed at all available seismic stations in the NE Appalachian region. The observed shear-wave fast directions differ for the two back azimuths. The event with westerly back azimuth has a northeasterly fast direction, while the event with the northwesterly back azimuth has an easterly fast direction. The fast direction appears to be a rapidly-varying function of back azimuth. Variability is also seen across the region for each event, indicating that some lateral heterogeneity is present. This heterogeneity was characterized by Levin et al. [1996] in terms of differences between "Appalachian" and "Grenvillian" provinces.

We compiled SKS splitting data for the two longest-running of these stations, HRV (Harvard, MA) and PAL (Palisades, NY) (Figure 8). We used observations of SKS, SKKS and PKS phases, as well as a few tex2html_wrap_inline585 and S phases from deep-focus events. Core phases (SKS and the like) are SV-polarized by the P-S conversion at the core-mantle boundary, and are useful for the study of the seismic anisotropy in the upper mantle and lithosphere. In the interest of broadening the azimuthal coverage of our dataset we also used S and tex2html_wrap_inline585 phases from medium-sized events with hypocenters deeper then 500 km. We assume that these phases encounter anisotropy only in the "receiver-side" upper mantle and the lithosphere. We also note that splitting parameters obtained for tex2html_wrap_inline585 phases (two observations for HRV, three observations for PAL) closely match splitting parameters obtained for SKS phases from same events. Thus potential contamination of the tex2html_wrap_inline585 signal by the D'' anisotropy [Garnero and Lay, 1997] does not seem strong along these particular paths.

The data for these two stations are quite similar (Figure 9). Fast direction azimuths tend to fall into the northeasterly and easterly populations discussed above, resulting in a bimodal distribution of the azimuthal angle between pairs of measurements (iFigure 10). The assumption of two populations (with mean azimuths of tex2html_wrap_inline427 and tex2html_wrap_inline429 ) is statistically superior to the assumption of only one population (with mean azimuth of tex2html_wrap_inline609 ) at the 99.9% significance level (computed via the F-test). The means of these two populations are also different at the 99.9% significance level (computed via the t-test). We have examined the SKS seismograms that were used as input to the splitting parameter estimation procedure (Figure 11). No anomalies that might cause spurious parameter estimates are apparent, giving us confidence that observed variation of splitting parameters is real.

Barruol et al. [1997] measured shear-wave splitting at HRV using several of the earthquakes in our data set. They report tex2html_wrap_inline615 (values given for two different processing techniques). This result is quite similar to our "single population" mean of tex2html_wrap_inline617 . It is interesting to note that the plot of all HRV data in Barruol et al. [1997] (their Figure 5) and the table listing individual values (electronic supplement table 2) contain members of both populations of fast directions. Another analysis of HRV data was done by Fouch and Fischer [1995] to compare with data from the MOMA portable array, but included only those events that occurred while the array was active (1995 through early 1996). They reported an average tex2html_wrap_inline619 s, similar to our mean over easterly back-azimuths ( tex2html_wrap_inline621 ). In both cases the measured average value is biased by the event distribution, which is dominated by northwesterly events from NW Pacific earthquakes. The discrepancy in reported sets of splitting parameters most likely reflects differences in the distribution of data with back azimuth. Although of dubious value given the systematic fluctuations of the data, the mean value of the splitting direction (calculated as a model result, and discussed below) is tex2html_wrap_inline623 , which matches the tex2html_wrap_inline465 value reported by Barruol et al. [1997].

We modeled the seismic data using splitting parameters derived from synthetic seismograms of SKS phases. We compared two different algorithms for computing the synthetic seismograms in vertically stratified, anisotropic media: a propagator matrix method [Levin and Park, 1997b], and a ray method. Both give near-identical results. We use a grid-search over anisotropic parameters to find a best-fitting earth model, where the goodness-of-fit criteria minimizes the misfit

displaymath627

Here tex2html_wrap_inline629 and tex2html_wrap_inline631 are the standard deviations of the delay time tex2html_wrap_inline469 and fast azimuth tex2html_wrap_inline465 , respectively. We have examined two classes of earth models: one or two anisotropic mantle layers placed between an isotropic crustal layer and an isotropic mantle halfspace. We search only for the thickness of the layers and the orientation of the anisotropic tensors. The anisotropic medium is constrained to consist of 30% orthorhombic olivine and 70% isotropic olivine, a mixture that is about 6% anisotropic for shear waves. The best-fitting one-layer model has an anisotropic layer that is 58 km thick, and the two layer model has top and bottom layers that are 60 and 90 km thick, respectively. Parameters for our preferred hexagonally symmetric model are indicated in Table 1. Tensor orientations for our preferred orthorhombic model are indicated in Table 2 and Figure 12. Both hexagonal and orthorhombic two-layer models correctly capture the variation of splitting parameters with back azimuth, while the one-layer models do not. Figure 13 compares results for the 1- and 2-layer orthorhombic models. The variance reduction of the two-layer model is roughly three times greater than the one-layer model, an amount that is statistically significant to the 99% level (computed via the F-test). The two-layer orthorhombic model gives fast-axis azimuths of tex2html_wrap_inline433 and tex2html_wrap_inline435 for the bottom and top layers, respectively, which are close to the means of the two observed azimuthal populations. The fast-axis strikes for hexagonal symmetry are only slightly different, at tex2html_wrap_inline437 and tex2html_wrap_inline645 for the bottom and top layers, respectively. However, the symmetry axes are tilted: only tex2html_wrap_inline647 above the horizontal in the top mantle layer, but tex2html_wrap_inline649 below the horizontal in the lower layer.

To test whether the symmetry-axis tilts are significant we compare the observed back-azimuth pattern of the apparent fast direction with those predicted by our hexagonal and orthorhombic models, and also by the 2-layer splitting operator of Silver and Savage [1994] (Figure 14). To construct the operators, we computed the delays tex2html_wrap_inline651 a vertically-incident shear phase would experience in each layer of the orthorhombic and hexagonal models, and used respective fast directions. Predicted patterns are quite similar although, as one would expect, the approximation and synthetics show greatest difference at discontinuities in the pattern, where waveform complexity is the greatest. Also, patterns from forward modeling are only approximately periodic because of the tilts of the anisotropy axes. These violations of tex2html_wrap_inline441 periodicity may possibly serve as diagnostic traits in choosing the preferred model. Our present collection of data is too limited to uniquely resolve the tilt of the symmetry axes, though they seem to prefer some deviation from the horizontal.

The broad spatial coherence of shear-wave directions throughout the NE Appalachians (as evidenced in Figure 5) suggest that there is a strong vertical stratification of the anisotropy in the upper mantle beneath that region. Earth models with two anisotropic upper-mantle layers can fit the observed SKS splitting data well. More complicated vertically-stratified models cannot be ruled out, but are not required by the data. Some lateral heterogeneity is also present in the splitting data. We note, however, that even large heterogeneity in the splitting data does not necessarily translate into large heterogeneity in structure. Given the quick variation of the parameters with back azimuth, just a few degrees rotation of either the earth model or the incoming shear wave can lead to widely different values of the splitting parameters. A complete characterization of any 3-D "anisotropic domains" responsible for the observed lateral heterogeneity will require extensive back-azimuth coverage at many stations.

We interpret the top anisotropic layer to represent the continental lithosphere associated with the Appalachian orogen, and the bottom layer to represent the asthenosphere. A conceptual model of layered anisotropy under HRV is presented on Figure 15. Alignment of the fast axes of olivine in the upper layer is near-normal to the strike of geomorphological features in New England, where the trend of the Appalachians rotates from northeast to north. The alignment in the lower layer of the model is more in line with the overall strike of the Appalachian Orogen, as well as the hypothetical "edge" of the North American cratonic keel.


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Next: Shear Wave Splitting at Up: Shear-Wave Splitting in the Previous: Splitting Parameters and Their

vadim levin
Mon Mar 22 11:12:08 EST 1999