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 
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 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 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
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 
and 
) is statistically superior to the
assumption of only one population (with mean azimuth of 
) 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 
(values given for two different processing techniques).
This result is quite similar to our "single population" mean of 
.
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 
s, similar to our mean over easterly back-azimuths
( 
). 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
, which matches the 
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
Here 
and 
are
the standard deviations of the delay time 
and fast azimuth
, 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 
and 
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 
and 
for the bottom and top
layers, respectively.
However, the symmetry axes are tilted: only 
above the
horizontal in the top mantle layer, but 
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 
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 
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.