Effects of upper mantle structure beneath Alaska on core-sensitive seismic wave absolute and differential measurements: implications for estimates of inner core anisotropy

Authors: Daniel A. Frost1*, Barbara Romanowicz123

Affiliations:1Department of Earth & Planetary Science, University of California, Berkeley, CA, USA.2 Collège de France, Paris, France. 3 Université de Paris, Institut de Physique du Globe de Paris, Paris, France.

*Correspondence to: dafrost@berkeley.edu

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AbstractInner core anisotropy is often studied using differential travel times between the inner core phase, PKPdf, and one of two outer core phases, either PKPbc or PKPab, to eliminate contamination by crust and upper mantle structure. In particular, given the similarity of the two ray paths in the shallow Earth, the PKPbc-df differential travel time is assumed to robustly reflect the structure of the inner core, and not be influenced by mantle structure. Measurements of PKPab-df and PKPbc-df differential times reveal that the inner core is anisotropic: PKPdf rays travel through the inner core ~3% faster along polar paths than along equatorial paths. Even so, measurements of both PKPbc-df and PKPab-df differential travel times on quasi-polar paths between sources in the South Sandwich Islands and stations in Alaska present greater scatter (6 seconds spread) than other equivalent quasi-polar paths from other parts of the globe (2 seconds spread). While the South Sandwich Islands to Alaska data help increase spatial sampling of the inner core, including these data in inner core models significantly increases estimates of average global inner core anisotropy strength, by more than 1%. Whether this reflects real spatial variability in the strength of inner core anisotropy or else results from complexity outside of the inner core is uncertain but is crucial for constraining the inner core composition and growth history. Using a regional tomographic model of the Alaskan upper mantle to predict upper mantle effects on PKP travel times, we show that the signature of the Alaska slab is present in trends of observed absolute PKPbc, ab, and df travel times, both as a function of distance and azimuth. Moreover, we demonstrate that the effect of the slab is not fully cancelled by differential measurements. This implies that past models of the inner core are biased towards too strong average anisotropy. In order to better constrain inner core anisotropy in future, differential measurements of core-phase travel times need to be more accurately corrected for upper mantle three-dimensional structure, which in turns requires the construction of higher resolution tomographic models.

IntroductionStudies of the inner core (IC) rely heavily on measuring travel times of PKPdf, the most readily observed body wave that is sensitive to its structure. Absolute PKPdf travel time anomalies measured relative to predictions from a 1D reference velocity model can also be used to infer IC velocity structure and anisotropy (e.g. Creager, 1992; Morelli et al., 1986; Shearer, 1994), but differential measurements with respect to the outer core phases PKPbc and/or PKPab are preferred (e.g. Irving and Deuss, 2011; Shearer and Toy, 1991), as they should account for errors due to source mislocation and upper-mantle structure that are common to both measurements. The paths of the pair of phases PKPdf and PKPbc are more similar in the entire mantle than those of the pair PKPdf and PKPab (Figure 1a), thus the differential time of PKPbc-df is assumed to better represent IC structure than PKPab-df. However, PKPbc is only detectable up to source-receiver distances of ~155° before it starts diffracting along the IC boundary, while PKPab is detectable out to antipodal distances. Since depth of propagation of PKPdf into the IC increases with source-receiver distance, PKPab-df can be used to study structure down to the centre of the IC, while PKPbc-df is limited to studying the upper ~350 km of the IC.

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Figure 1: (a) PKP rays from a source (star) to receiver (triangle) showing how, for PKPdf waves, the angle ξ is measured relative to the Earth’s rotation axis (dashed red vertical line). The dashed box beneath the receiver indicates where the tomography model is used. (b) Slice through the Alaskan upper mantle tomography model of Roecker et al. (2018) at 200 km depth. Black contour marks +0.8% dlnVp, outlining the slab. Green line marks the section used in Figures 4 and 7.

A combination of differential and absolute travel times have revealed the global patterns of IC seismic structure (see Deuss, 2014 for a review). The IC is cylindrically anisotropic, as measured by variations in the PKPdf travel time anomaly as a function of the angle relative to the rotation axis, ξ (Frost & Romanowicz, 2019; Irving & Deuss, 2011; Morelli & Dziewonski, 1987; Shearer & Toy, 1991). PKPdf is up to 10 s faster than the 1D reference model ak135 (Kennett et al., 1995) for paths near-parallel to the rotation axis than for equatorial paths (Frost et al., accepted; Lythgoe et al., 2014). The anisotropy likely results from preferred alignment of intrinsically anisotropic iron crystals in the IC during growth (Jeanloz and Wenk, 1988). Interpreting IC growth history from PKPdf travel times requires accurately separating the IC contribution from mantle contributions.

Differential measurements should remove the effect of the mantle from PKP travel times, but equatorial IC paths (where the travel time anomaly due to IC anisotropy should be close to zero, according to models) still show anomalies with respect to a 1D reference model of ±1 s for PKPbc-df and 2 s for PKPab-df (Bréger et al, 2000; Tkalčić et al., 2002; Romanowicz et al., 2003). Additional corrections for mantle structure using global tomographic models can reduce this scatter, especially when scaling up the strength of velocity anomalies (Song and Helmberger, 1997; Bréger et al., 2000). However, these corrections are still insufficient, particularly on paths from sources in the South Sandwich Islands (SSI) to stations in Alaska. These data present a larger spread than IC data sampling other regions of the Earth (6 s compared with 2 s), implying some significant remaining contribution either from unmodelled

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complexity in IC anisotropy or unmodelled mantle structure (Romanowicz et al., 2003; Garcia et al., 2006; Tkalčić, 2010b; Frost et al., 2020). Explaining the SSI-Alaska anomaly has been a longstanding challenge for IC studies. Including this data likely led to overestimating the strength of anisotropy in the outer ~500 km of the IC in past studies.

Most studies on the source of the spread of South Sandwich Islands (SSI) to Alaska travel times focus on the effects of lower mantle structure on differential travel times, where the paths of the two phases diverge most, and where heterogeneity is strong, relative to the mid-mantle. Long et al., (2018) implicated the lower mantle beneath Alaska. However, their model requires a thick, high velocity block at the core-mantle boundary under Alaska (either 650 km tall with dlnVp≤3%, where dlnVp=1-(dVp/Vp0), or 200 km tall with dVp≤10%), which is inconsistent with the velocity structure in regional (Suzuki et al., 2016) and global tomographic models (Simmons et al., 2012) and as resolved by PcP-P body waves sampling this region (Ventosa and Romanowicz, 2015). Therefore, we must look somewhere else for the source of the SSI-Alaska anomaly.

Meanwhile, the upper mantle beneath Alaska is complex, owing to the tectonic setting, with the Pacific plate subducting along the Aleutian arc from ~55 Ma to present (Scholl et al., 1986). Seismic studies of Alaska have revealed the complexities of the crust and mantle (Feng and Ritzwoller, 2019; Jiang et al., 2018; Martin-Short et al., 2016; Miller et al., 2018). From inversion of regional and teleseismic P and S travel times recorded at the USArray stations, we recently obtained a high-resolution image of the upper 400 km beneath Alaska (Roecker et al., 2018), observing the sharp 100 km thick slab with dlnVp +3% dipping ~55° to the north-west and the Yakutat terrain with dlnVp -3% in the south-east (Figures 1b, S1). In Frost et al., (2020), we demonstrated that the Alaskan upper mantle contributed significantly to the large range in absolute PKPdf travel time and wave direction anomalies observed across USArray from SSI events.

The effect of upper mantle structure on differential travel times is thought to be much smaller since the paths of the 3 core phases are very close there. However, 3D ray tracing has shown that the strong seismic heterogeneity at shallow depths can affect the paths of deep traveling waves significantly (Simmons et al., 2012; Vidale, 1987) causing systematic effects on both absolute and differential travel times (Helffrich and Sacks, 1994). In addition, seismic heterogeneity can refract waves (Figure S1), distorting wavepaths and thus perturbing path length (contributing to travel time anomalies). Moreover, distorting the wave path also perturbs the wave’s incident direction, which can be used as a diagnostic for the source of travel time anomalies.

To isolate the source of the spread of SSI to Alaska PKP differential travel times, here we evaluate the effect of upper mantle structure beneath Alaska on PKP waves from SSI sources. Firstly, we analyse absolute PKPab and PKPbc travel time and directional anomalies, which should not be affected by IC structure, and then differential PKPbc-df and PKPab-df measurements. We compare this with predictions of the impact of the Alaskan upper mantle using high resolution regional tomography (Roecker et al., 2018). We then investigate trade-offs

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between the strength of upper mantle heterogeneity and IC anisotropy and finally, we estimate the maximum strength of globally averaged IC anisotropy accounting for these trade-offs.

MethodWe collect vertical component PKP waveforms from USArray stations and other seismic networks in Alaska and Canada (AK, AV, CN, II, IM, IU, TA, and US) from 6 SSI events from 2016 to 2018 (Table S1). For each event, we use between 293 and 402 stations, depending on the number deployed at the time. We remove the linear trend and mean, and deconvolve the instrument response. Data are bandpass filtered between 0.3-4.0 Hz, a range found to best enhance the clarity of PKP waves relative to the noise.

Measuring PKP wavesWe construct subarrays of the USArray and use beam-forming to measure the travel time, slowness, and back-azimuth of PKPab and PKPbc at each location, following the method of Frost et al. (2020), initially developed for PKPdf. We construct subarrays in a grid across Alaska with 1°×1° spacing, and for every grid point select the closest station and the next closest 5 to 8 stations around it, within a region ±120 km of the grid point. The final number of stations used in the subarray depends on the number of stations proximal to the grid point. We construct between 74 and 177 subarrays per event, again depending on how much of the USArray had been deployed at the time of the event. We discard subarrays with fewer than 6 stations or with a non-unique collection of stations. The minimum station number ensures high slowness and back-azimuth resolution, while a maximum of 9 stations is chosen to minimise the sampling region of each subarray, thus increasing spatial resolution between subarrays. The beam point is set to the average location of all stations in the subarray.

Data are windowed 20 s prior to and 20 s after the predicted arrival times of PKPdf and PKPab, respectively, using 1D reference model ak135 (Kennett et al., 1995). We simultaneously grid search over slownesses from 0 to 6 s/deg, and back-azimuths of ±20° relative to the great-circle path and construct vespagrams (Davies et al., 1971) for PKPbc and for PKPab (the latter after Hilbert transformation). Next, we apply a coherence measure called the F-statistic (Selby, 2008; Frost et al., 2013) to suppress aliasing and sharpen the slowness and back-azimuth resolution. Coherence, F, is computed as the ratio of the sum of the energy in the beam, b, to the sum of the differences between the beam and each trace used to form the beam, xi, in a time window, M, normalized by the number of traces in the beam, N:

F=N−1N

∑t=1

M

b(t )2

∑t=1

M

∑i=1

N

( xi ( t )−b ( t ))2 (1)

F-vespagrams are visually inspected and we select the best fitting slowness, back-azimuth, and travel times for PKPbc and PKPab using the untransformed and Hilbert transformed data, respectively (Figure S2). Subarrays where PKPbc or PKPab is absent or poorly resolved are discarded. Residual PKPbc and PKPab back-azimuths are measured relative to the great-circle

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path from source to receiver; travel time and slowness anomalies are measured relative to predictions from ak135, and travel times are corrected for ellipticity (Kennett and Gudmundsson, 1996). We pick arrival times by cross-correlation of the beams with empirical PKPbc and PKPab wavelets, constructed by adaptively stacking the beams that show the target phase from each event (Rawlinson and Kennett, 2004). We subtract the median travel time anomaly for each event and phase to highlight the variation across Alaska. We transform slowness (U) and back-azimuth (θ) to Ux and Uy, respectively the east-west and north-south components of slowness on the horizontal plane (Rost and Thomas, 2002). This allows for direct comparison of the incoming direction between the different PKP phases that have distinctly different incidence angles, which would otherwise bias lower slowness phases towards larger back-azimuth variability.

We estimate the resolution of our subarray measurements of slowness, back-azimuth, and arrival time. Our subarray method collapses the finite sampling volume of the rays used to form the beam onto the single beam point, thereby smearing the effects of larger structure. Taking the width of the subarrays of ~2° and the first Fresnel zone of a 1 Hz wave, our minimum spatial resolution is ~220km, Therefore, we cannot interpret patterns that are smaller than 2°, which is 2 circles north-south and 4 circles east-west in Figure 2. We estimate the precision of the resolved slowness and travel time for an example subarray. We take a synthetic signal with real, uncorrelated noise and shift the traces in time to simulate the moveout across the subarray of a wave coming from a range of incoming directions. We then apply the same vespagram and cross-correlation method described above and measure the resolved time and slowness of the synthetic signal, which we compare to the input slowness, and time. Across the range of directions tested, we determine the resolution to be ±0.1 s in dT and ±0.1 s/deg in dUx and ±0.05 s/deg in dUy. We vary the number of stations in the subarray (between 6 and 9, as used in our method, with random resampling of stations) and find that the slowness is resolved accurately for all subarray sizes. Therefore, we are able to accurately resolve signals of the magnitude that we observe, that is up to ±1 s and up to ±0.8 s/deg in time and slowness, respectively.

Predicting the effect of the mantleUsing our Alaskan tomography model, we can predict the effect of the upper mantle on incoming wave direction and time. We use a 3D ray-tracer (Roecker et al., 2010; Comte et al., 2016) to trace PKPab and PKPbc ray paths through our tomographic model of the upper 400 km beneath Alaska (Roecker et al., 2018). For PKPdf, we use the values calculated in Frost et al. (2020). This method computes travel times in ak135 from the source up to the bottom edge of the regional tomographic model, then finds the fastest path through the box to the receiver using an eikonal equation solver (Zhiwei et al., 2009). At each subarray, we fit a plane to the travel time anomalies as a function of station location, representing the moveout of a plane wavefront, decomposing the slope into Ux and Uy and calculating a single travel time as the average of the predicted times. We compute travel time (dT) and slowness (dUx and dUy) anomalies resulting from the 3D mantle structure relative to a purely 1D model. It is important to note that absolute travel time anomalies will be biased by uncertainties in source location and origin time, but that these will cancel in the differential times.

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Correcting for the effect of the inner coreIn what follows, we remove the effect of IC anisotropy on PKPdf data. To do so we construct a model of inner core western hemisphere anisotropy (with hemisphere boundaries at 167° W and 40° E) using the PKPab-df and PKPbc-df measurements used in Frost and Romanowicz, (2019) and Frost et al. (in press). We attribute the entire PKPdf travel time anomaly to structure in the

IC and convert travel times to relative velocity anomalies as: dtt=−dvv0

, where t and v0 are

reference travel times and velocities in the IC, respectively, calculated in model ak135. This accounts for the difference in path length between the shallow and more deeply travelling waves. We construct cylindrically symmetric models of anisotropy, in which the perturbation to a spherically symmetric model, after Song (1997), is expressed as:

δvv0

=α+ε cos2 ξ+γ sin22ξ (1)

where v0 and δv represent the reference velocity and velocity perturbations, respectively, and ξ the IC paths make with the rotation axis. We take subsets of our data (using both lateral and depth limits) and construct several models of IC anisotropy. We construct models that exclude either the SSI-Alaska data or all measurements made in Alaska and use data sensitive to different depths in the inner core (Table S2). For reference, the PKPdf waves travelling on the SSI-Alaska path turn within the upper 500 km of the inner core (up to 500 km below the inner core boundary). Our preferred model includes data sampling between the ICB and 500 km below the ICB in the western hemisphere, matching the turning depth range of SSI-Alaska data, but not using SSI-Alaska data (model 7 in Table S2). This model is described by coefficients α, ε, and γ to be: 0.013, 2.974, and -0.5, respectively, with a maximum velocity anomaly of 2.9%. Predicted travel time corrections for IC anisotropy for the SSI-Alaska data vary smoothly, primarily as a function of source-receiver distance (Figure S3), and minimally with azimuth, ranging between 2.25 and 3.7 s. In the discussion we examine the trade-off between inner core anisotropy and scaling of the tomographic model.

ResultsFor both PKPab and PKPbc, which do not traverse the IC, we observe patterns of absolute travel time, slowness, and back-azimuth anomalies that vary systematically across Alaska (Figure 2). Patterns are consistent across the 6 events, in spite of their different locations and depths; spatial averages of anomalies across the events have small standard deviations demonstrating that there is little difference in observations between events (Figure S4). We measure travel time, dUx, and dUy anomalies for PKPbc of ±0.8 s and ±0.8 s/deg PKPab of ±1.0 s and ±0.8 s/deg, respectively. Similar to the patterns observed for PKPdf in (Frost et al., 2020; Figure 2a-c), we observe three robust features for both PKPab and PKPbc:

1. Negative travel time anomalies over the Alaskan slab and positive travel time anomalies to the east, west, and north.

2. Negative dUx over the slab with sharply contrasting positive anomalies to the north-west.3. Positive dUy over the slab with negative anomalies surrounding it.

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Compared to the PKPdf absolute anomalies, the PKPab and PKPbc absolute anomalies show some robust differences (Figures 2):

1. Weaker travel time anomalies for both PKPab and PKPbc.2. Negative PKPab travel time anomalies over the slab that extend further to the north-west

compared with PKPdf.3. Positive PKPab and PKPbc dUx anomalies to the northeast of the slab.

The spatial patterns of PKPab and PKPbc travel time anomalies best match those of PKPdf when shifted by 0.75° to the south and to the east. Differences in anomalies and their spatial distribution between the PKP phases reflect the contrast in incidence angle between the phases, exacerbated by the 3D geometry of the structure under Alaska.

Figure 2: (a, d, g) Absolute travel times, (b, e, h) slowness dUx, and (c, f, i) slowness dUy

anomalies spatially averaged at 1×1° grid points across all 6 events for (a-c) PKPdf, (d-f) PKPbc, and (g-i) PKPab. The median travel time anomaly is removed from each event before averaging across all events. See Figure S4 for standard deviations of the mean. PKPdf travel times have been corrected for inner core velocity anisotropy. Green line in a marks the section used in Figures 4 and 7. Distances from the average source are labelled on the dashed lines in

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(a). Numbers on the left in a relate to Figures S5-6. Black contour marks +0.8% dlnVp in the model of Roecker et al. (2018) at 200 km depth, outlining the slab.

Travel time, dUx, and dUy anomalies predicted by 3D ray-tracing through the upper mantle model show good correlation with both the absolute travel time and slowness observations particularly for PKPbc and PKPdf, and to a lesser degree, but still significantly for PKPab (Figures 3). As a function of distance parallel to the dip of the slab, there is a clear spatial correlation between these patterns and the location of the slab, that is replicated by ray-tracing (Figure 4). Because PKPab and PKPbc do not travel through the IC, this gives us confidence in ascribing an important part of the systematic variations in dUx, dUx, and travel time to mantle structure beneath Alaska.

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Figure 3: Observations versus upper mantle predictions after spatial averaging for (a ,d, g) absolute travel times, (b, e, h) slowness, and (c, f, i) back-azimuth anomalies for (a-c) PKPdf, (d-f) PKPbc, and (g-i) PKPab. Median travel time anomalies for each event are removed prior to averaging. PKPdf travel times have been corrected for inner core anisotropy. Data are fit with a least-squares regression, for which the R2 fit and gradient, m, are shown in the top left corner, while the purple dashed line shows a 1-to-1 relationship. The overall apparent saturation of the predicted travel time anomalies (both positive and negative) for PKPdf and PKPab results from limitations of the tomographic model.

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Figure 4: Comparison of observed (blue) and upper mantle predicted (red) absolute (a, b, c) travel time and (d, e, f) dUx and (g, h, i) dUy anomalies, as a function of source-receiver distance for (a, d, g) PKPdf, (b, e, h) PKPbc, and (c, f, i) PKPab by sampling data shown in Figure 2 within ±1° of green section line, chosen to best demonstrate the slab contribution. Location of the slab along the section at 200 km depth shown in grey. PKPdf travel times have been corrected for IC anisotropy. RMS misfit between the observations and predictions are shown in each panel.

Comparing observed absolute travel time and slowness anomalies between phases, we see significant correlation between PKPdf and PKPbc or PKPab (Figure 5). The observed PKPdf travel time and slowness anomalies are more similar to those of PKPbc than to those of PKPab, supporting the assumption that the PKPbc-df differential time better accounts for crustal and mantle structure. However, the significant deviations from a one-to-one correlation of travel times and slownesses imply that the upper mantle contributes to the PKPdf travel times.

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Figure 5: Phase to phase comparison after spatial averaging of observed (a-c) absolute travel time, (d-f) dUx, and (g-i) dUy anomalies for (a, d, g) PKPdf and PKPbc, (b, e, h) PKPdf and PKPab, and (c, f, i) PKPab and PKPbc. Median travel time anomalies for each event are removed prior to averaging. PKPdf travel times have been corrected for inner core anisotropy. Data are fit with a least-squares regression, for which the R2 fit and gradient, m, are shown in the top left corner.

From the observed absolute travel time and slowness anomalies (Figures 2 and 4) we calculate differential anomalies (Figures 6 and 7). Differential travel time anomalies are smaller than the absolute anomalies and vary by ±0.5 s, ±1.0 s for PKPbc-df, PKPab-df, respectively. Their spatial distribution correlates with the slab location and show systematic variations as a function

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of distance for particular azimuth sections (Figure 6 and 7a-c). These patterns, as well as those of differential slowness anomalies (Figure 7d-i; Figure S5-6) are well-predicted by our 3D regional upper mantle model, except for the apparent trend with distance for PKPbc-df travel time anomalies (Fig. 7a), part of which may be due to an under-prediction of the strength of the velocity perturbation due to the lithospheric Yakutat terrain, and short wavelength fluctuations of dUx (Figure 7d). We note that PKPbc-df and PKPab-df travel time anomalies are underpredicted in the grey band that corresponds to the slab location at 200 km depth (Figure 7ab). These observations indicate that much of the differential anomaly can be explained by upper mantle rather than IC structure.

Figure 6: (a, d, g) Differential travel times, (b, e, h) slowness dUx, and (c, f, i) slowness dUy

anomalies spatially averaged at 1×1° grid points across all 6 events for (a-c) PKPbc-df, (d-f) PKPab-df, and (g-i) PKPbc-ab. The median travel time anomaly is removed from each event before averaging across all events. Each phase has the median travel time anomaly removed before comparison and PKPdf travel times have been corrected for inner core velocity anisotropy. Green line in a marks the section used in Figures 4 and 7. Distances from the average source are labelled on the dashed lines in a. Black contour marks +0.8% dlnVp in the model of Roecker et al. (2018) at 200 km depth, outlining the slab.

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Figure 7: Comparison of observed (blue) and upper mantle predicted (red) differential (a, b, c) travel time and (d, e, f) dUx and (g, h, i) dUy anomalies as a function of source-receiver distance for (a, d, g) PKPbc-df, (b, e, h) PKPab-df, and (c, f, i) PKPbc-ab by sampling spatially averaged data shown in Figure 1 within ±1° of section line. Grey shading marks the slab. PKPdf travel times have been corrected for IC anisotropy. RMS misfit between the observations and predictions are shown in each panel.

DiscussionOur analysis of PKP waves from sources in the SSI observed across Alaska shows that upper mantle structure can influence the differential travel times by up to ±1 s for PKPab-df and ±0.5 s for PKPbc-df, and slownesses by ±0.75 s/deg for PKPab-df and ±0.5 s/deg for PKPbc-df. The observed patterns, corrected for an average IC anisotropy model, can be matched fairly well by predictions from our upper mantle tomographic model (RMS=0.355 and 0.222 for PKPbc-df and PKPab-df, respectively, as in Figure 7a-c), a model which was derived without any PKP data. Here, we discuss the trade-offs between IC anisotropy and upper mantle structure, the effect of heterogeneity in the rest of the mantle on our measurements, and the implications for IC anisotropy inferred using these measurements.

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While PKPdf absolute, PKPbc-df and PKPab-df differential travel times across Alaska have previously been attributed to IC anisotropy, the patterns of travel time and slowness anomalies observed here, which vary systematically with both epicentral distance and azimuth, are unlikely to result from IC structure. Indeed, the match between the observed patterns and those predicted by our upper mantle tomography model indicates the importance of the contribution of the Alaskan upper mantle (Figures 3-4,7). However, in these comparisons, we corrected the PKPdf data for an assumed simple IC anisotropy model, constrained by data outside of Alaska. Figure S7 shows the correction from the IC anisotropy model, and the effect of this correction on PKPdf absolute travel times. The correction helps explain the general trend of the anomalies with distance, but not the smaller-scale variations (Figure S8), which correlate with the predictions from the slab model. Still, there are likely trade-offs between the IC anisotropy model and upper mantle structure.

Here, we evaluate the trade-offs between the IC anisotropy model and upper mantle structure by modifying the mantle and IC models in a simple way, to improve fit between the predicted and observed travel times. We uniformly scale velocities in the tomography model by factors of 0.5, 0.625, 0.75, 0.875, 1, 1.125, 1.25, 1.375, 1.5, 2.0, and also non-uniformly to (model A) strengthen the velocity anomaly of the Yakutat by scaling up the model south-east of the slab by a factor of 2.5, and 1.0 everywhere else as in Frost et al., (2020), and to (model B) strengthen the velocity anomaly of the slab by saturating velocities inside the slab to +5%. We use a range of IC anisotropy models derived from global PKP data but excluding the SSI-Alaska data (Table S2). To test the alternative hypothesis that the patterns in Alaska are best explained by the inner core we and also construct one model including the SSI-Alaska data and use a model from the literature that includes SSI-Alaska data, note that these two models do not fit the global PKP data well due to the addition of the SSI-Alaska data. Since IC anisotropy primarily affects dT (and to an insignificant degree, dUx and dUy) we seek the lowest combined RMS misfit between observations and predictions for differential PKPbc-df, PKPab-df, and PKPbc-ab travel times (Figure 8). We find that the IC model introduced earlier with 2.9% anisotropy and a mantle scaling factor of 1.125 minimises misfit, with model A also performing well. This result demonstrates the need for increasing the strength of the mantle model. In particular, the tomography model under-predicts anomalies at lower azimuths, and over-predicts anomalies at higher azimuths (top and bottom rows in Figures S5-6). Model A fits well since it has stronger anomalies in the south-east.

Our modelling demonstrates that the misfit depends more strongly on mantle scaling than on IC anisotropy model. Nonetheless, the IC model preferred by the SSI-Alaska data falls within the range capable of matching global measurements of anisotropy for this range of depths in the west hemisphere (in shaded region in Figure 8). Other models that are within 90% of the best fit include models with weaker IC anisotropy, but with relatively low dependence of dT on ξ, i.e., a flatter anisotropy curve in Figure S3a. Also, when including both travel time and slowness anomalies in the misfit, we find a best scaling factor of 0.625. Looking more closely at this surprising result, we see that none of the scaled mantle models are able to fit the small wavelength variations of dUx with distance for PKPbc-df (Figures S9-11b,e,h). This indicates that the velocity gradients in our tomographic model need improvement. Overall, our analysis

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demonstrates that the IC, sampled along SSI-Alaska paths (in the western hemisphere), doesn’t require anisotropy greater than 3% in the top 500 km of the IC, in contrast to ≥4.5% from previous studies such as Irving and Deuss (2011). Moreover, to explain the azimuthal patterns we require a weaker dependence of dV on ξ than past IC models, which translates to weaker maximum anisotropy.

In addition to Alaska, the PKP waves in this study may be influenced by the Scotia slab beneath the South Sandwich Islands on the source side. The Scotia slab is not well-resolved shallower than 800km in global P-wave tomography models GAP_P4 and LLNL-G3Dv3 (Fukao and Obayashi, 2013; Simmons et al., 2012), but these models suggest that it is underlain by faster than average P velocities down to the core-mantle boundary. In the slab geometry model Slab2 (Hayes et al., 2018), the Scotia slab is mapped to 300 km depth due to limited seismic coverage and seismicity. While we cannot predict the effects of the Scotia slab on the PKP waves considered here, we argue that the slab itself likely has little impact on the travel times observed in Alaska since the patterns are consistent for both shallow and deep SSI events (see also Romanowicz et al., 2003; Tkalčić, 2010a).

Figure 8: Trade-off between inner core anisotropy and scaled tomographic models (see discussion section in main text) in fitting the observed PKPbc-df and PKPab-df travel time anomalies. The best model with a mantle scaling factor of 1.125 is marked by the light red circle and models with misfit within 90% of the best are marked by dark red circles, while model A (cyan circle) also performs well. Inner core anisotropy models used in this figure are numbered on the right axis, corresponding to Table S2. The shaded region below the dashed line represents inner core models compatible with global inner core data.

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We also consider the effects of velocity anomalies along the rest of the path in the mantle below 400 km. Using the global LLNL-G3Dv3 model and the associated 3D ray-tracer (Simmons et al., 2012) we compute predicted PKP travel time and slowness anomalies. The resolution of the global model is poorer than our regional model: the Alaskan slab is broader and weaker. However, high velocity anomalies associated with the Alaskan slab exist down to ~1000 km depth in the global model. The pattern of travel time anomalies predicted using this model is generally similar to that predicted by the upper mantle model, with early travel times over the slab (Figure 9), albeit significantly weaker. We then modify the region of the global model beneath Alaska in two ways by removing lateral heterogeneity either (1) above 410 km or (2) above 1070 km depth, fixing velocities to the 1D average velocity in these regions. In (1) we no longer see the effects of the slab and in (2) we barely see any variation of travel time anomalies. We conclude that most of the travel time and slowness anomaly patterns observed across Alaska result from the Alaskan upper mantle, that global models do not have sufficient resolution to provide meaningful corrections, and the rest of the mantle (as resolved in current tomographic models) has a limited impact on the observed spatial patterns.

Figure 9: (left) Map of the LLNL_G3D velocity anomalies at 220 km depth (Simmons et al., 2012), with spatially averaged station locations shown as black circles. Azimuth sections shown on the right are labelled 1-4. (right) Absolute observed and predicted PKPdf travel time

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anomalies as a function of distance and for different sections through the slab, spatially averaged at 1×1° grid points across the events. PKPdf travel times anomalies corrected for inner core anisotropy (blue) and predictions from 3D ray tracing through the upper mantle model of Roecker et al. (2018) (red), standard whole mantle LLNL_G3D model (black), LLNL_G3D with no lateral velocity anomalies in the upper 410 km (green), and LLNL_G3D with no lateral velocity anomalies in the upper 1070 km of the region (purple). Note that decreasing distance means moving across section from northwest to southeast.

Of the global PKP differential travel time catalogues, at present, only the SSI-Alaska data is seen to exhibit such a large spread of PKP differential travel times over such a small range in polar angle, ξ. This may result from Alaska’s unique geometry where a shallow slab underlies seismic stations on land, combined with the particular azimuth of paths from the SSI relative to the slab dip direction. Prior to the deployment of the TA in Alaska, most seismic stations were located in the central and southern part of the state. Using the whole of the TA (Figure 6ad), we can now see that the upper mantle imparts both positive differential PKPbc-df and PKPab-df travel time anomalies relative to the median in the southern part of the state, and negative differential PKPbc-df and PKPab-df travel time anomalies in the rest of the state. The upper mantle under Alaska, therefore, significantly contributes to the spread of PKP differential travel times. Without further work we cannot rule out that other slabs may have similar effects on differential travel times. We caution that PKP differential travel times may still retain some signature of the upper mantle, thus the strength of IC anisotropy in such models may be impacted. Corrections from global models appear insufficient to remove the effect of the upper mantle, while using high resolution regional tomography models may better serve to address this issue.

ConclusionWe have shown that upper mantle heterogeneity beneath Alaska significantly affects the travel times and paths of all three PKP branches from sources in the SSI observed at stations of the USArray. In particular, at least 1 s of the PKPab-df differential travel time anomaly that was previously attributed to the IC should instead be attributed to upper mantle structure beneath Alaska. Correcting the PKP differential travel time anomalies for the effect of the mantle model also reduces the spread and brings the data better in line with datasets from other quasi-polar paths in the western hemisphere, for which the average IC anisotropy strength is no more than 3%. Global tomographic models are not of sufficient resolution to correct for the effects of the upper mantle, and regional models of upper mantle structure could be further improved to allow more accurate corrections of PKP travel times on the SSI to Alaska path. More generally, caution should be used when assuming that PKP differential travel time measurements accurately account for upper mantle contributions in regions of strong heterogeneity. Therefore, it should be understood that models of inner core anisotropy constructed using differential travel times may be imperfect.

Acknowledgements We thank Steve Roecker at Renselaer Polytechnic Institute for providing the regional tomographic model and 3D regional ray tracer. We thank the International Seismological Centre

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(ISC) for access to the EHB and On-line Bulletins, http://www.isc.ac.uk, Internatl. Seismol. Cent., Thatcham, United Kingdom, 2015. The facilities of IRIS Data Services, and specifically the IRIS Data Management Center, were used for access to waveforms, related metadata, and/or derived products used in this study. IRIS Data Services are funded through the Seismological Facilities for the Advancement of Geoscience and EarthScope (SAGE) Proposal of the National Science Foundation under Cooperative Agreement EAR-1261681. This work was supported by NSF grants EAR-1135452 NSF, EAR-1829283, and EAR-2027181.

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