Geophysical Research Letters
Supporting Information for
Seismic anisotropy in the lowermost mantle near the Perm Anomaly
Maureen D. Long and Colton Lynner
Department of Geology and Geophysics, Yale University, New Haven, CT USA
Contents of this file
Text describing the SKS-SKKS splitting discrepancy method in detail
Captions for Supplementary Figures S1 to S5
Captions for Supplementary Tables S1 to S3
Additional Supporting Information (Files uploaded separately)
Figures S1 to S5
Tables S1 to S3
Introduction
Supplementary information to this article includes a description of the SKS-SKKS
splitting discrepancy method, captions for the supplementary figures and tables, a list of
supplementary references, supplementary Figures S1-S5, and supporting Tables S1-S3.
SKS-SKKS splitting discrepancies: Assumptions, limitations, and interpretation
Clear discrepancies between the measured shear wave splitting parameters for SKS and
SKKS phases measured for the same event-station pair were first documented in the literature
by James and Assumpçao [1996] and first exploited to constrain anisotropy in the lower mantle
by Niu and Perez [2004]. The splitting of SK(K)S phases is very commonly used to constrain
anisotropy in the upper mantle beneath the seismic station; several lines of evidence suggest
that the upper mantle makes the major contribution to the splitting of core-refracted phases,
including the generally good agreement between SK(K)S splitting and models of upper mantle
anisotropy derived from surface waves [e.g., Becker et al., 2012]. A number of recent papers
have used the SKS-SKKS discrepancy technique to study anisotropy in the lower mantle [e.g.,
Niu and Perez, 2004; Hall et al., 2004; Restivo and Helffrich, 2006; Long, 2009; He and Long,
2011; Lynner and Long, 2012, 2014a; Roy et al., 2014; Ford et al., 2015]. Here we provide a
description of the assumptions and limitations of this measurement technique, along with the
limitations inherent in the interpretation of discrepant SKS-SKKS splitting data.
1
The SKS-SKKS splitting discrepancy technique exploits the similarity in the ray
propagation paths for SKS and SKKS phases in the upper mantle to look for a signal from
anisotropy in the lowermost mantle. If the transverse component waveforms for an SKS phase
and an SKKS phase from the same seismogram are significantly different (and therefore the
waves exhibit different shear wave splitting), then the difference can be attributed to
anisotropy in the lowermost mantle. The reason for this is that the two phases sample the
upper mantle in a nearly identical way, while they sample different portions of the lowermost
mantle (and have a modest difference in propagation angle just above the core-mantle
boundary, or CMB). Therefore, large differences in the estimated splitting parameters for the
two phases implies a contribution from anisotropy in the lower mantle; such differences cannot
be easily explained in terms of anisotropy in the upper mantle [e.g., Niu and Perez, 2004; Hall et
al., 2004; Restivo and Helffrich, 2006; Long, 2009]. It is important to keep in mind, however, that
in the vast majority of cases (approximately 95%), lowermost mantle anisotropy does not cause
significant splitting of SK(K)S phases [Niu and Perez, 2004; Restivo and Helffrich, 2006; Nowacki
et al., 2011]. Therefore, lowermost mantle anisotropy is not the first-order contributor to
SK(K)S splitting at the stations examined in this study (or in any other study of lowermost
mantle anisotropy) Rather, the SKS-SKKS splitting discrepancy method seeks to identify subtle,
intermittent, and localized contributions from the lowermost mantle to the splitting of a small
minority of SK(K)S arrivals at a given station (or set of stations).
While the observation of strong SKS-SKKS splitting discrepancies is a straightforward
indicator of a contribution from anisotropy in the lower mantle, the interpretation of discrepant
measurements in terms of actual structure is somewhat complicated. One assumption that is
usually made in SKS-SKKS splitting discrepancy studies is that the most likely source of the
anisotropy is the D” region at the base of the mantle, as there is abundant evidence from other
types of seismic data that the D” region often has strong anisotropy [Nowacki et al., 2011, and
references therein], while the bulk of the lower mantle is generally thought to be isotropic [e.g.,
Meade et al., 1995; Visser et al., 2008]. However, a contribution to discrepant SKS-SKKS
splitting from elsewhere in the lower mantle cannot generally be ruled out [e.g., Niu and Perez,
2004]. Another inference that is generally made from discrepant SKS-SKKS splitting
observations is that strongly discrepant measurements typically reflect lateral variability in
seismic anisotropy at the base of the mantle. That is, because SKS and SKKS phases sample
slightly different regions of the lower mantle (see, e.g., the maps in Figures 3 and 4 of the
paper), the simplest possibility is that there is a difference in anisotropic structure between the
portion of D” being sampled by the SKS phase, and that sampled by the SKKS phase. An
alternative explanation invokes an anisotropic geometry at the base of the mantle that would
cause different splitting for SKS and SKKS phases, given the difference in propagation angle
(about 15° at the base of the mantle). For an arbitrary anisotropic symmetry, differences in
predicted splitting would be expected for different propagation directions. However, for most
realistic anisotropic geometries expected for D” (e.g., crystallographic preferred orientation of
post-perovskite or ferropericlase, or shape preferred orientation of aligned melt), the splitting
parameters vary fairly smoothly as a function of propagation direction, except at a few distinct
directions [e.g., Nowacki et al., 2011; Ford et al., 2015]. Such smooth variations would not be
expected to cause significant discrepancies under most conditions, even taking into account
the difference in propagation direction and path length for SKS vs. SKKS phases. In either case,
however, significant discrepancies in splitting between the phases implies a contribution from
anisotropy in the lower mantle near either the SKS exit point near the CMB, the SKKS exit
point, or both.
2
Another nuance in the interpretation of SKS-SKKS splitting discrepancies is the fact
that while clearly discrepant SKS-SKKS splitting requires a contribution from anisotropy in the
lower mantle, the observation of non-discrepant SKS-SKKS splitting for any given pair does not
necessarily rule out a contribution from the lowermost mantle. Globally, in about 95% of cases,
splitting parameters measured for the two phases agree (within errors) [Niu and Perez, 2004].
This observation is used to argue against a first-order contribution to the global SK(K)S splitting
database from lower mantle anisotropy, along with other observations [e.g., Niu and Perez,
2004; Long, 2009; Becker et al., 2012; Nowacki et al., 2011]. However, for any given nondiscrepant SKS-SKKS pair, it is possible that lowermost mantle anisotropy is contributing to the
splitting of both phases in a similar way, or that both phases are sampling anisotropy in the
lowermost mantle, but in a raypath geometry that does not cause splitting (that is, along the
“null directions” of lowermost mantle anisotropy). When examining maps of non-discrepant
and discrepant SKS-SKKS pairs, therefore, it is important to remember that an observation of
non-discrepant splitting does not necessarily imply a lack of anisotropy in that region; it may be
that both phases are sampling the same anisotropy, or that they are propagating at a direction
that does not cause splitting. Indeed, in most studies of SKS-SKKS splitting discrepancies it is
common to see discrepant observations interspersed with non-discrepant observations with
only slightly different propagation paths [e.g., Long, 2009; He and Long, 2011; Lynner and Long,
2014a]. This may be due to small-scale variations in anisotropic structure, variability in the
propagation direction for different SKS-SKKS pairs, or natural variability in noisy seismic data.
While strong SKS-SKKS discrepancies are a straightforward indicator of a contribution
from lowermost mantle anisotropy, in general they cannot be interpreted directly in terms of
lowermost mantle structure, unless the anisotropic signal in the upper mantle beneath the
seismic station is well known. If the upper mantle signal is not well known, then it is impossible
to isolate the portion of the splitting of the SKS and SKKS phases due to lowermost mantle
anisotropy; instead, one can only say that one or both of the phases has been affected by the
lowermost mantle. For this reason, in some studies of SKS-SKKS splitting discrepancies,
stations are selected such that the upper mantle anisotropy is well understood and simple; if
this is the case, then the waveforms can be corrected for the effect of the upper mantle and the
portion of the signal due to D” anisotropy can be isolated. We take this approach in the present
study. The downside of this approach is that there are fewer stations to work with; however, it
has a major advantage in that we can directly isolate the portion of the splitting signal due to
the lowermost mantle in many cases. Furthermore, in this situation we can then make use of
observations of non-discrepant pairs to rule out a contribution from the lowermost mantle in
many cases. For cases where there is no contribution to splitting from the upper mantle (that is,
either the station overlies apparently isotropic upper mantle, or the waves are polarized close
to a fast or slow direction of upper mantle anisotropic symmetry), a non-discrepant observation
of null splitting for both SKS and SKKS implies a lack of contribution from the lower mantle as
well.
Our approach to selecting statins in this study, therefore, is to use long-running stations
at which we have already examined SKS splitting parameters as a function of backazimuth, and
to only use stations that exhibit simple upper mantle splitting patterns whose waveforms can
be easily corrected for the effect of upper mantle anisotropy. We use two types of stations in
this study: 1) stations for which we observe null SKS arrivals over a wide backazimuthal range,
which suggests that to first order, the upper mantle does not cause significant splitting at the
periods used (~8-50 sec), or 2) stations for which we measure consistent SKS splitting
3
parameters in several backazimuthal quadrants, suggesting that the upper mantle can be
approximated with a single, horizontal layer of anisotropy. (Examples of SKS splitting patterns
for stations used in this study are shown in Figure S1.) For either of these two cases, it is
straightforward to correct the waveforms for the effect of upper mantle anisotropy (by rotating
and time-shifting the horizontal components appropriately) and isolate the contribution from
the lowermost mantle. We do not use stations that exhibit systematic variations in measured
SKS splitting patterns with backazimuth, as that suggests multiple layers of upper mantle
anisotropy beneath the station and it is difficult to make an accurate correction for the upper
mantle in these cases. We also do not use stations for which the backazimuthal coverage for
SKS is poor, as this means we cannot distinguish between simple and complex upper mantle
anisotropy patterns. We emphasize, again, that at the stations selected for use in this study, the
lowermost mantle does not make the first-order contribution to the splitting of SK(K)S phases;
the first-order aspects of the SK(K)S splitting patterns are controlled by the upper mantle.
Rather, our analysis technique aims to isolate infrequent, localized contributions from the
lowermost mantle to the splitting of a small number of SK(K)S arrivals in our dataset. Of course,
for the small minority of cases for which we observe significant SKS-SKKS splitting
discrepancies, this contribution from the lower mantle will cause a small amount of variability in
the overall splitting patterns that reflects a contribution from D” for certain SK(K)S arrivals.
These subtle deviations from the “simple” upper mantle splitting patterns, identified by
searching for SKS-SKKS splitting discrepancies in this study, reflect localized contributions from
lowermost mantle anisotropy.
As discussed in the main text, it is important to rule out alternative explanations for
differences in transverse component waveforms (and thus discrepant splitting measurements)
for SKS and SKKS phases before attributing the discrepancies to lowermost mantle anisotropy.
The possible effects of finite-frequency wave propagation, small-scale isotropic heterogeneity
in the upper or lowermost mantle, interference from other seismic phases, and difference in
propagation direction between the two phases are discussed in the main text and in a previous
study [Lynner and Long, 2014a]. Another possible explanation for discrepant SKS-SKKS splitting
is topography on the CMB, or other dipping structures at the base of the mantle, which might
modify the polarizations of SKS and SKKS phases differently. This scenario was explored in
detail by Restivo and Helffrich [2006], who suggested that anomalies in the polarization of
SK(K)S phases upon (or shortly after) their exit from the CMB may be imparted by strong CMB
topography, dipping interfaces within D”, or significant lateral velocity heterogeneity at the
base of the mantle. In any of these cases, the polarization of the converted wave may deviate
(up to ~20° in the Restivo and Helffrich [2006] study) from the purely SV polarization predicted
by ray theory for homogeneous, non-dipping layers. While we considered this possibility, it is
unlikely to be the primary explanation for the observations in our dataset, as we examined the
polarizations (using algorithms built in to SplitLab) of the SKS and SKKS phases in our study
both before and after correction for any splitting, as part of our normal processing routine. We
did not observe any systematic deviations in initial polarizations from the prediction of SV
polarized waves in our dataset, which suggests that in general, the differences in the observed
transverse components for discrepant pairs were imparted by anisotropy, and not by dipping
interfaces at the base of the mantle. We note, however, that Restivo and Helffrich (2006)
documented a small number of anomalous SK(K)S polarizations beneath out study area, so it is
possible that this effect makes a small contribution to our dataset.
4
Supplementary Figure Captions
Figure S1. Examples of SKS splitting patterns as a function of backazimuth for selected stations
used in this study. Top row: Stereoplots of SKS splitting measurements measured at stations
(HGN and ITHO) at which we infer a negligible contribution from upper mantle anisotropy to
the SKS splitting patterns. Circles indicate null (that is, non-split) SKS arrivals, while the
orientation and length of the bars indicate the fast direction and delay time, respectively, of
split arrivals. All measurements are plotted as a function of backazimuth (azimuth around
circle) and incidence angle in the upper mantle (distance from center). Bottom row: Stereoplots
of SKS splitting measurements measured at stations (ARU and VTS) at which we infer a
“simple” contribution from upper mantle anisotropy; that is, the upper mantle anisotropy can
be represented with a single, homogeneous, horizontal anisotropic layer. Plotting conventions
are as in the top row. SKS splitting patterns and upper mantle anisotropy for the stations used
in this study are documented in detail in Lynner and Long [2013, 2014b] and Ford et al. [2015].
Figure S2. Histogram of the number of measurements obtained as a function of epicentral
distance. Histogram shows the number of non-discrepant pairs (blue) along with discrepant
pairs (red, yellow, and black, as indicated by the legend). There are no systematic differences in
the number of observed discrepant pairs as a function of distance.
Figure S3. Plot of the measured delay times for splitting due to anisotropy in the lowermost
mantle as a function of epicentral distance. These measurements correspond to the
measurements in Figure 4 of the paper and have been corrected for the effect of anisotropy in
the upper mantle. There is no systematic change in measured fast direction as a function of
epicentral distance, although the number of measurements is small (10).
Figure S4. Plot of splitting as a function of distance from the center of the Perm Anomaly (top
panel) and from the edge of the African LLSVP (bottom panel). For the top figure, we have
taken the subset of measurements which lie closer to the Perm Anomaly than to the edge of
the African LLSVP, as delineated by the cluster analysis of Lekic et al. [2012], and plotted delay
time measurements of D”-associated anisotropy (corresponding to Figure 4 of the paper) as a
function of distance from the center of the anomaly. Null measurements are represented as
zero delay time with error bars that extend up to delay times of 0.5 sec, which represents the
approximate detection limit for shear wave splitting at the periods under study here. For the
bottom figure, we have combined our measurements of D”-associated splitting along the
northern border of the African LLSVP (western portion of Figure 4) with the dataset presented
in Lynner and Long [2014a] that samples a larger geographical region surrounding the LLSVP.
Non-null measurements of lowermost mantle anisotropy from this study are shown with blue
diamonds; measurements from Lynner and Long [2014a] are shown in red.
Figure S5. Similar to the left panel of Figure 3, except the background map shows lateral
gradients in shear wavespeed at the base of the mantle, from Lekic et al. [2012]. These
gradients are represented by the median range of Vs (m/s) over a distance of 5° in the five
tomographic models considered by Lekic et al. [2012].
Supplementary Table Captions
5
Table S1. List of stations used in this study. Columns indicate the station name, network code,
station latitude, station longitude, upper mantle delay time (sec), and upper mantle fast
direction (degrees). For those columns marked NULL, no upper mantle correction is needed.
Table S2. Measured shear wave splitting parameters obtained using the transverse component
minimization method for SKS-SKKS pairs, measured before upper mantle corrections. Columns
indicate the station name, event date, julian day of event, station latitude (degrees), station
longitude (degrees), event latitude (degrees), event longitude (degrees), event depth (km),
phase type (SKS vs. SKKS), 95% confidence region lower bound for fast direction (degrees), fast
direction (degrees), upper bound on fast direction (degrees), lower bound for delay time (sec),
delay time (sec), upper bound for delay time (sec), null flag (yes for null, no for non-null),
agreement flag (3 for discrepant pairs, 2 for non-discrepant pairs).
Table S3. Estimates of shear wave splitting parameters due to lowermost mantle anisotropy,
obtained using the transverse component minimization method. Where needed, corrections
have been applied to account for any contributions to splitting from upper mantle anisotropy
beneath the station. Columns indicate the station name, event date, event day of year, station
latitude (degrees), station longitude (degrees), event latitude (degrees), event longitude
(degrees), event depth (km), phase type (SKS vs. SKKS), 95% confidence region lower bound
for fast direction (degrees), fast direction (degrees), upper bound on fast direction (degrees),
lower bound for delay time (sec), delay time (sec), upper bound for delay time (sec), null flag
(yes for null, no for non-null).
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