Introduction

The dependence of seismic wave velocities on the propagation and/or polarization direction of the wave (seismic anisotropy) is typically an indicator of deformation in Earth's interior (e.g., Long & Becker, 2010;Romanowicz & Wenk, 2017;Wolf, Li, Long, & Garnero, 2024). Shear-wave splitting measurements (e.g., Asplet et al., 2023;Hansen et al., 2021;Liu et al., 2014;Meade et al., 2005;Niu & Perez, 2004;Wolf, Long, Li, & Garnero, 2023) and seismic tomography (e.g., Chang et al., 2015;French & Romanowicz, 2014;Panning & Romanowicz, 2006) reveal that strong seismic anisotropy can be found in Earth's upper mantle and crust, the bulk of the lower mantle is almost isotropic, and the lowermost few 100 km of the mantle (the D ′′ layer) exhibit seismic anisotropy of (on average) moderate strength (Figure 1a). This observation can be explained if upper and lowermost mantle materials deform via dislocation creep, which causes the alignment of mineral crystals and thus seismic anisotropy, while the bulk of the lower mantle is dominated by diffusion creep, which generally does not lead to anisotropy (e.g., Karato et al., 2008;Kocks et al., 2000;Montagner, 1998;Wenk & Houtte, 2004). D ′′ anisotropy has been detected in many regional studies (e.g., Asplet et al., 2020Asplet et al., , 2023;;Lay & Young, 1991;Nowacki et al., 2010;Wolf, Long, & Frost, 2024), which usually have lateral resolution capabilities of 100s of kilometers, as well as via global inversions for radially anisotropic structure (Chang et • The influence of the deepest mantle on SKS (usually used to infer upper mantle anisotropy) is non-negligible in some regions

Supporting Information:

Supporting Information may be found in the online version of this article. Romanowicz, 2014), which reliably resolve large-scale structures. The regional studies published to date use a variety of different techniques, some of which are more sensitive to lowermost mantle anisotropy than others (Wolf, Li, Long, & Garnero, 2024). Only a few of these studies (e.g., Reiss et al., 2019;Suzuki et al., 2021) investigate seismic anisotropy in relatively large geographic regions using a comprehensive methodology, thereby enabling detailed inferences on seismic anisotropy over a broad region. Such uniform investigations are important to infer how widespread seismic anisotropy in D ′′ is, and how strongly it can affect the splitting of seismic waveforms, including phases that are often used to study upper mantle anisotropy.

For measurements of upper mantle shear-wave splitting from *KS waves, which travel through the outer core as P waves and then convert to S upon re-entry in the mantle from the core (e.g., SKS, S2KS or PKS; see Figure 1b, inset), it is typically assumed that the lowermost mantle anisotropy contribution can be neglected (e.g., Liu et al., 2014;Savage, 1999;Silver & Chan, 1991;Wolf & Long, 2023;Yang et al., 2017). This is because D ′′ anisotropy is, on average, weaker than upper mantle anisotropy (Figure 1a); furthermore, *KS waves may have stronger sensitivity to upper mantle anisotropy (e.g., Sieminski et al., 2008). At the same time, differential splitting between pairs of *KS waves is often attributed to D ′′ anisotropy because the raypaths of *KS phases sample different portions of the lowermost mantle, while they are almost identical in the upper mantle (e.g., Niu & Perez, 2004;Tesoniero et al., 2020;Wang & Wen, 2004). This technique does have some challenges, because moderate differences in shear wave splitting can also be due to the slightly different upper mantle raypaths (e.g., Lin et al., 2014;Tesoniero et al., 2020) or to seismic noise (Wolf, Frost, et al., 2023). However, if certain precautions are followed (such as only interpreting splitting intensity differences >0.4), discrepant *KS splitting has been shown to be generally reliable as a tool for detecting lowermost mantle anisotropy (Tesoniero et al., 2020;Wolf et al., 2022).

One novel method that has been shown to reduce noise while averaging single-station splitting parameters involves a beamforming approach (Frost et al., 2024;Wolf, Frost, et al., 2023). Beamforming (e.g., Frost et al., 2020;Rost & Thomas, 2002, 2009) stacks seismograms of a seismic phase across neighboring seismic stations, taking into account the differential travel times to stations with different locations. The increased signalto-noise ratios (SNRs) of beamformed data can enable the measurement of shear wave splitting from seismic phases that are not usually used for this purpose due to their typically low amplitudes in single-station seismograms, such as S3KS (Wolf, Frost, et al., 2023). Additionally, by suppressing uncorrelated noise, beamforming diminishes the effects of scattering due to small-scale structure close to the receiver, leading to a substantial reduction of overall measurement scattering (due to noise) for many commonly used *KS seismic phases (e.g., SKS, S2KS). Therefore, the measurement of *KS differential splitting using a beamforming approach is wellsuited to both (a) provide constraints on lowermost mantle anisotropy in a broad region and (b) allow inferences on the influence of this lowermost mantle anisotropy on upper mantle measurements. Wolf, Frost, et al. (2023) developed the *KS beam splitting technique and presented a proof-of-concept application to a limited data set from North America; however, the technique has yet to be widely applied to study deep mantle anisotropy. Here we expand on the work of Wolf, Frost, et al. (2023) and apply differential *KS beam splitting to array data throughout North America, with the goal of providing a comprehensive view of D ′′ anisotropy beneath the region.

Methods

Data Selection and Beamforming

The lowermost mantle beneath North America and the northeastern Pacific Ocean represents an ideal application for differential *KS beam splitting measurements. This region features excellent data coverage, with the past installation of the dense Transportable Array (IRIS Transportable Array, 2003) across parts of this region and the good ray coverage for *KS waves from subduction zone earthquakes in the southwestern Pacific Ocean and South America (Figure 1b). Using single-station SKS-S2KS data, the presence of seismic anisotropy has been previously suggested for parts of this region, in particular beneath the northeastern Pacific Ocean (e.g., Asplet et al., 2020Asplet et al., , 2023;;Long, 2009;Wolf & Long, 2022) and the western United States (e.g., Lutz et al., 2020;Nowacki et al., 2010;Wolf, Li, Haws, & Long, 2024). However, these single-station measurements often showed different measurement results for adjacent raypaths, likely due to noise.

We focus on events over magnitude 6 within 100-140°from stations in Central America and North America. Events observed at 60 or more stations in either region are retained, resulting in 214 events. These data are instrument deconvolved, horizontal components are rotated to radial and transverse directions, and seismograms are filtered between 0.02 and 0.25 Hz. Record sections of the radial component of each event are then manually inspected and events with clear *KS energy are retained, leaving 61 events (Table S1 in Supporting Information S1).

We apply the beamforming method of Frost et al. (2024) to this data. For each event, a 1 × 1 degree grid is set up across Central America and Alaska and at each grid point the nearest 5-20 stations are selected, forming a subarray (Figure 2). Subarrays with fewer than 5 stations are skipped. We attempt to form stacks for each of the following phases predicted to exist at that subarray according to PREM (Dziewonski & Anderson, 1981): SKS, S2KS, S3KS, and PKS. If more than one PKS wave arrives due to triplication, we analyze the first arriving wave.

Separately for the radial and transverse seismograms, and for each phase, data are windowed 40 s before and 40 s after the PREM-predicted arrival time. The optimal slowness and backazimuth for each phase is determined using gridsearch approach. We construct F-vespagrams (Frost et al., 2024) from individual F-traces (Blandford, 1974;Selby, 2008) themselves constructed for slownesses between 0 and 9 in 0.1 s/deg increments and backazimuths between -20 and 20°in 1°increments, measured relative to the great circle path. The optimal slowness and backazimuth are selected using the maximum F-value (coherence) in the vicinity of the predicted arrival of each phase. These optimal values are then used to construct linearly stacked beams so as to minimize waveform distortions, and enhance coherent signal, allowing the beams to be used for anisotropy calculations. This beam signal processing procedure is shown in Figure 2 using example S2KS seismograms recorded in southern Alaska (Figure 2a). In this example, the SNR of the beams (blue) is clearly enhanced compared to the single-station data (black; Figures 2b and 2c).

Shear-Wave Splitting Measurements

*KS seismic waves are SV-polarized upon their conversion from P-to-S as they re-enter the mantle from the core. If these waves are split due to seismic anisotropy, energy will be visible on the transverse component. The transverse component T(t) has the shape of the radial component time derivative R′(t) if the wave is split due to seismic anisotropy (e.g., Silver & Chan, 1991;Vinnik et al., 1989). Furthermore, the transverse component amplitude reflects the strength of splitting affecting a particular waveform. Therefore, a quantity that characterizes shear-wave splitting of *KS waves is the splitting intensity (SI; Chevrot, 2000), which can be expressed as:

Previous work has shown that splitting intensity is a particularly convenient measurement for *KS splitting discrepancy studies (e.g., Deng et al., 2017;Reiss et al., 2019). We determine the splitting intensity of SKS, S2KS, S3KS, and PKS (Figure 1b, inset) beams using SplitRacer (Reiss & Rümpker, 2017), a MATLAB toolkit to compute shear-wave splitting. To ensure the robustness of our SI measurements, we repeat them for 30 randomly selected time windows for most phases and only include results that are consistent across all time windows. For S3KS, we manually select the time window because this phase often arrives shortly after S2KS, which renders the automatic time window selection impractical. We always bandpass-filter our beams to retain periods between 6 and 25 s, and only include measurements for beam waveforms with amplitudes at least twice as large as the noise level.

Example S2KS, S3KS, and PKS waveforms and SI measurements are shown in Figure 3. In this case, PKS is split only slightly (SI ≈ 0.3), whereas S2KS and S3KS are split strongly (SI ≥ 0.9). This differential splitting is likely due to the different raypaths of PKS compared to S2KS/S3KS through D ′′ , while S2KS and S3KS are relatively similar (Figure 1b, inset). In general, differentially split *KS phase pairs with δSI > 0.4 indicate the presence of D ′′ anisotropy influencing shear-wave splitting of one phase more strongly than the other. In contrast, nondiscrepant splitting may often be due to weak or absent D ′′ anisotropy, although it can also be consistent with certain D ′′ anisotropy configurations (Tesoniero et al., 2020;Wolf et al., 2022).

In this study, we specifically focus on SKS-S2KS, SKS-S3KS, and PKS-S2KS differential beam splitting (e.g., the difference of SI values in Figure 3). The reason that we do not focus on differential beam splitting between S2KS-S3KS and PKS-SKS pairs is their similar raypaths at certain epicentral distances (Figure 1b, inset; Figure 4b). Figure 4 shows differential S2KS-S3KS and PKS-SKS beam splitting as a function of source-receiver distance and deep mantle raypath separation. For larger distances, receiver-side mantle raypaths of PKS and SKS become more similar (Figure 4a). Accordingly, absolute δSI-values tend to be lower at large distances, while the opposite is true for S2KS-S3KS (Figure 4b). This test is made possible by the use of beamformed data, which enables us to measure shear-wave splitting for many different *KS phases from the same seismogram.

Results and Discussion

Lowermost Mantle Anisotropy

We obtain ∼2500 measurements of differential SKS-S2KS splitting, ∼400 measurements of differential SKS-S3KS splitting, and ∼250 measurements of differential PKS-S2KS splitting. Binned differential splitting intensities (bin size 1.5°× 1.5°) between *KS pairs are presented in Figure 5, while Figure S1 in Supporting Information S1 shows individual measurements. The plotting convention is such that SI differences are projected laterally to the middle of the horizontal distance (viewed from above) between *KS pierce points (Figure 5a, inset) at the CMB and the top of the D ′′ layer. SKS-S2KS pairs, for example, can be affected by seismic anisotropy in D ′′ anywhere between the point where SKS pierces through the CMB and the point where S2KS leaves D ′′ , which we assume is 250 km above the CMB for the purpose of this plotting convention. The line in between these two pierce points, viewed from above, we will refer to as the pierce point connecting segment (cyan line in Figure 5a, inset). We document large *KS splitting intensity differences, indicating the presence of D ′′ anisotropy, beneath the Bering Sea, the northeastern Pacific Ocean, the western/central United States, and western Canada.

For ∼ 60 % of the beams, S2KS and/or S3KS are more strongly split than SKS or PKS; however, the opposite is true for some regions, including for SKS waves that sample the lowermost mantle beneath the northeastern Pacific Ocean and parts of the Bering Sea.

For each bin, we calculate differential SI averages considering all pierce point connecting segments crossing the bin (Figure 6a). We undertake this exercise because the (commonly used) plotting convention in Figure 5 can be misleading, as it only projects splitting intensity differences to a single point and does not consider the lengths of the pierce point connecting segments. For each bin, we expect a certain spread of values, because (a) the start/end points of different connecting segments differ, (b) shear wave splitting depends on the sampling angle of the seismic anisotropy, and (c) SKS and S2KS waves have different propagation directions through D ′′ . Maximum standard deviations of the mean can be relatively high (up to ∼0.8

) for some portions of our study area (Figure 6c). Elevated standard deviations in these areas are likely explained by different sampling angles of the seismic anisotropy and the presence of small-scale heterogeneity. We also calculate the percentage of connecting segments crossing each bin for which |δSI| measurements >0.4 (Figure 6d).

We select a threshold of |δSI| > 0.4 (Figure 6d), in line with previous work suggesting that for individual splitting measurements this threshold can distinguish effects from lowermost mantle anisotropy from other influences, such as the upper mantle contributions due to slightly different raypaths (Tesoniero et al., 2020). However, it is worth emphasizing that this threshold applies to individual measurements, implying that when measurements are binned and averaged, even smaller |δSI| values may be indicative of lowermost mantle anisotropy. The main Note that for S3KS the analysis time window is manually selected to avoid interference with S2KS, which arrives just before S3KS. S2KS and S3KS SI measurements are similar (likely due to their similar raypaths through the mantle) and discrepant with PKS. For this example, we do not obtain a high-quality SKS beam.

Journal of Geophysical Research: Solid Earth

10.1029/2024JB029516

reason is that for every lowermost mantle bin, |δSI| values are recorded across different stations above a variably anisotropic (or isotropic) upper mantle. Therefore, effects from upper mantle anisotropy contributions may be unsystematic. Any averaged, unsystematic effects from upper mantle anisotropy contributions will have a lesser influence on the measurements as the number of contributing measurements in the bin increases.

Our view of data in Figure 6d helps us to distinguish four broad anisotropic regions. Region #1 covers the lowermost mantle beneath the Bering Sea, where seismic anisotropy has been identified in several previous shearwave splitting studies (e.g., Garnero & Lay, 1997;Lay & Young, 1991;Matzel et al., 1996;Wysession et al., 1999). These previous studies all used ScS or S diff waves that are sensitive to D ′′ anisotropy along long raypaths through D ′′ . Our results using SKS-S2KS differential splitting confirm these findings with an independent method that is better suited to determine the lateral boundaries of the anisotropy due to the more nearly vertical raypaths of *KS phases through D ′′ . The most detailed previous lateral and depth resolution of seismic anisotropy in Region #1 has been obtained by Suzuki et al. (2021). These authors inverted waveforms around the ScS arrivals for radially anisotropic structure, which is hard to explicitly compare with our shear-wave splitting measurements Journal of Geophysical Research: Solid Earth 10.1029/2024JB029516

crystallographic preferred orientation of post-perovskite crystals (Asplet et al., 2020(Asplet et al., , 2023)), perhaps induced by slab-driven mantle flow (Wolf, Li, & Long, 2024;Wolf & Long, 2022).

Region #3 (Figure 6d) covers parts of the northeastern Pacific Ocean and large portions of the western and central United States. Previous studies that have found seismic anisotropy in parts of this region (e.g., Asplet et al., 2020Asplet et al., , 2023;;Lutz et al., 2020;Nowacki et al., 2010;Wolf, Li, Haws, & Long, 2024) have connected their findings to, for example, approximately horizontal flow along the CMB in large parts of Region #3 (e.g., Asplet et al., 2020;Nowacki et al., 2010), or to vertical flow at the Yellowstone plume root (Nelson & Grand, 2018) beneath Baja California (Wolf, Li, Haws, & Long, 2024). None of these studies, however, imaged the full broad extent of the anisotropic region that is shown in Figure 6d.

Seismic anisotropy in Region #4, to the west of the Mexican coast, has previously been inferred by Long (2009) through differential SKS-S2KS measurements. The precise lateral extent of this anisotropic region, however, remains unclear because it is located at the edge of our study region. Apart from the prominent Regions #1-4 that we highlight, the presence of seismic anisotropy is indicated in several places at the edge our study region. Due to the unknown spatial extent of these regions and the limited ray coverage within them (Figure 6b), we do not Journal of Geophysical Research: Solid Earth 10.1029/2024JB029516

interpret seismic anisotropy in these regions more closely. However, our results appear to be an ideal starting point for more detailed future investigations.

Our results provide a comprehensive picture of *KS splitting discrepancies due to D ′′ anisotropy beneath North America and the northeastern Pacific Ocean. Many previous studies of D ′′ anisotropy in our study region have linked their observations to mantle flow driven by slab remnants (e.g., Asplet et al., 2020Asplet et al., , 2023;;Long, 2009;Nowacki et al., 2010;Suzuki et al., 2021;Wolf & Long, 2022) or to smaller-scale regional upwellings in the lowermost mantle (Suzuki et al., 2021;Wolf, Li, Haws, & Long, 2024). Considering that remnants of several slabs (e.g., the Beaufort, Wichita, Izanagi, Farallon, and Telkhina slabs) likely reside in the lowermost mantle beneath North America and parts of the Pacific Ocean (Suzuki et al., 2021;van der Meer et al., 2018), it is plausible that some of the anisotropy we observe is due to the deformation induced by them. On the other hand, not all regions with higher than average velocities in D ′′ necessarily represent remnants of material that has been subducted (geologically) recently. More generally, the overall patterns of seismic anisotropy represent evidence for widespread strain-induced seismic anisotropy at the base of the mantle, with deformation accommodated in the dislocation creep regime. This strain in turn can be due to gradients in flow at the mantle's lower horizontal boundary layer. The reason is that upper mantle anisotropy is, on average, stronger than lowermost mantle anisotropy (Figure 1a); therefore, studies of upper mantle anisotropy typically assume that sufficiently accurate measurements of upper mantle splitting can be obtained without explicit consideration of the lowermost mantle splitting contribution. However, such an approach may not lead to precise results in all regions. The results of our study, based on high-SNR beamformed seismograms, enable an investigation of the potential influence of lowermost mantle anisotropy on *KS splitting measurements (which are typically interpreted as evidence for upper mantle anisotropy) across North and Central America. 2012) that are often interpreted as being due to (mostly) upper mantle anisotropy. This database primarily relies on SKS splitting data. However, our differential *KS splitting results indicate that-in certain regions-the measured splitting may also be influenced by the lowermost mantle. It is worth noting that SKS-S2KS splitting intensity differences do not necessarily imply that, for example, SKS is influenced by D ′′ anisotropy and S2KS is not-and that the SKS splitting measurements, therefore, partially reflect D ′′ anisotropy. More likely, in most cases, both SKS and S2KS splitting measurements are influenced by seismic anisotropy in the lowermost mantle. However, discrepant SKS-S2KS splitting in a particular station region implies that, without further information, measured splitting parameters cannot be confidently attributed to (only) upper mantle anisotropy. In some regions, in which SKS splitting is nearly null but SKKS is split, it is likely that a small number of SKS shear-wave splitting measurements have been previously reported in the literature. Such regions, with weak or absent SKS splitting, may have been implicitly excluded from previous upper mantle anisotropy analysis.

Implications for Upper Mantle Anisotropy Studies

Averaged, binned SI differences across our station region can be as high as 0.8 (Figure 7). Given that delay times δt are mostly between 0.5 and 2 s across the United States (Liu et al., 2014;Yang et al., 2017) and the splitting intensity behaves approximately as δt sin[2(bϕ)] (b = backazimuth; ϕ = fast polarization direction), this implies that the D ′′ contribution to *KS splitting is likely not negligible in all regions, as typically assumed. For example, Wolf, Li, Haws, and Long (2024) showed that SKS seismic waves recorded in southern California are strongly influenced by lowermost mantle anisotropy, likely accumulating absolute splitting intensities of ∼1.0 in D ′′ , while S2KS likely is much less affected by seismic anisotropy in the deepest mantle in this region. Our results shown in Figure 7 are consistent with this finding, and indicate that more than half of the measured SI magnitudes in southern California, dependent on backazimuth, may be due to a D ′′ contribution. Additionally, in Montana, Wyoming and Colorado, *KS splitting measurements may be substantially affected by lowermost mantle seismic anisotropy (Figure 7). It has been argued that in this region effects of lowermost mantle anisotropy on S2KS are stronger than on SKS (Wolf & Long, 2022). However, the interpretations of upper mantle anisotropy in Montana, Wyoming and Colorado partly rely on S2KS splitting measurements (e.g., Yang et al., 2014), which may explain some of the inconsistent measurements of different previous studies (e.g., IRIS DMC, 2012;Liu et al., 2014). In addition to these two regions, *KS splitting recorded in parts of Ontario, Canada, and parts of Central America may be affected by a lowermost mantle anisotropy contribution (Figure 7). However, we obtain fewer measurements in these regions, which may mean that these results are less robust. Importantly, differential *KS splitting approach can reveal the backazimuthal directions from which the influence of lowermost mantle anisotropy may have to be considered. Our measurements in this study were mainly made using paths at backazimuths between -120°(Central America) and -30°(North America) (Figure 1b).

Our results in this study are based on measured splitting intensities. In studies of shear wave splitting due to upper mantle anisotropy, however, (ϕ, δt) measurements are used most frequently. If non-negligible lowermost mantle anisotropy is present and affecting shear-wave splitting measurements, which we have shown is the case in certain regions, (ϕ, δt) values used to infer upper mantle anisotropy will be affected in a non-trivial manner. To explicitly solve for the upper mantle contribution to splitting, essentially an inversion assuming two anisotropic layers is necessary (e.g., Bonnin et al., 2012;Silver & Savage, 1994). This issue may become even more challenging in cases in which more than one layer of seismic anisotropy may be present in the upper mantle.

Overall, our results indicate that the D ′′ contribution to *KS shear-wave splitting measurements is likely more important than often assumed, at least for some of the stations under study across the United States. There are several approaches that may be taken to ensure that splitting in studies of upper mantle anisotropy is indeed mainly due to an upper mantle anisotropy contribution. For example, nondiscrepant *KS splitting indicates that lowermost mantle anisotropy is unlikely to strongly influence splitting (although it could play a role for some specific anisotropy configurations). Moreover, our results reinforce the importance of measuring upper mantle shear-wave splitting for a range of backazimuths, as is often used to distinguish between simple or complex (e.g., Chen et al., 2018;Silver & Savage, 1994) seismic anisotropy. For example, if SI values as a function of backazimuth behave like a sin[2(bϕ)]-curve, splitting is likely due to upper mantle anisotropy. If there are deviations from such a pattern in a small backazimuthal window, a possible influence from D ′′ anisotropy on these measurements should be considered (e.g., Lynner & Long, 2012;Wolf, Li, Haws, & Long, 2024). Whether *KS differential splitting, backazimuthally varying splitting, or a combination of both approaches are used to distinguish effects from upper versus lowermost mantle anisotropy, beam splitting measurements are particularly helpful, as beamforming, by increasing SNRs, enables shear-wave splitting measurements for more phases and over larger backazimuthal and epicentral distance swaths than possible for single-station seismograms.

Journal of Geophysical Research: Solid Earth 10.1029/2024JB029516

Conclusions

Using a large and comprehensive set of differential shear-wave splitting measurements from beamformed *KS data, we have identified evidence for widespread seismic anisotropy in four broad regions in the lowermost mantle beneath North America and the surrounding area. These regions encompass the base of the mantle beneath parts of the northern and eastern Pacific Ocean, the Bering Sea, western Canada, the United States, and part of Central America. The detected anisotropy is likely caused by mantle convection induced deformation, potentially linked in some larger regions to remnant slabs, and in more spatially restricted areas to upwelling flow. The detected D ′′ anisotropy likely has non-negligible effects on SKS splitting measurements for stations located in some regions across North and Central America, including southern California, Montana, Wyoming and Colorado as well as southeastern Ontario, Canada. Studies of upper mantle anisotropy using *KS waves should explicitly consider D ′′ contributions to shear-wave splitting, particularly for waves that travel through the lowermost mantle in regions that have previously been shown to be anisotropic, including our study region beneath North America.

is publicly available at https://www.geophysik.uni-frankfurt.de/64002762/Software. All other codes/software used in this study are available at https://doi.org/10.5281/zenodo.12739753 (Wolf, Frost, et al., 2024).