# Upper mantle slab under Alaska: contribution to anomalous core-phase observations on south-Sandwich to Alaska paths

Daniel A. Frost, Barbara Romanowicz, Steve Roecker

► To cite this version:

Daniel A. Frost, Barbara Romanowicz, Steve Roecker. Upper mantle slab under Alaska: contribution to anomalous core-phase observations on south-Sandwich to Alaska paths. Physics of the Earth and Planetary Interiors, 2020, 299, 18 pp. 10.1016/j.pepi.2020.106427. insu-03584801

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Distributed under a Creative Commons Attribution 4.0 International License
**Title**

Upper mantle slab under Alaska: contribution to anomalous core-phase observations on south-Sandwich to Alaska paths

**Permalink**

https://escholarship.org/uc/item/1mt480tz

**Author**

Frost, Daniel Andrew

**Publication Date**

2020-01-12

Peer reviewed
1 Upper mantle slab under Alaska: contribution to anomalous

2 core-phase observations on south-Sandwich to Alaska paths

3

4 Authors: Daniel A. Frost¹*, Barbara Romanowicz¹,²,³, Steve Roecker⁴

5

6 Affiliations:

7 ¹Earth & Planetary Science, University of California, Berkeley, CA, USA

8 ²Institut de Physique du Globe de Paris, Paris, France

9 ³College de France, Paris, France

10 ⁴Rensselaer Polytechnic Institute, Troy, NY, USA

11

12 *Correspondence to: dafrost@berkeley.edu

13

14 Abstract

15 Observations of travel time anomalies of inner core-sensitive PKPdf
16 seismic body waves, as a function of path orientation with respect to
17 the earth's rotation axis, have been interpreted as evidence of
18 anisotropy in the inner core. Paths from earthquakes in the South
19 Sandwich Islands to stations in Alaska show strongly anomalous travel
times, with a large spread that is not compatible with simple models of
21 anisotropy. Here we assess the impact of strong velocity heterogeneity
22 under Alaska on the travel times, directions of arrival and amplitudes
23 of PKPdf. We use 3D ray-tracing and 2.5D waveform modelling through
24 a new, high-resolution tomography model of the upper mantle beneath
25 Alaska. We find that the structure beneath Alaska, notably the
26 subducting slab, is reflected in the patterns of these PKPdf
27 observations, and this can be replicated by our model. We also find
28 similar patterns in observed teleseismic P waves that can likewise be
29 explained by our slab model. We conclude that at least 2 s of the travel
30 time anomaly often attributed to inner core anisotropy is due to slab
31 effects in the upper mantle beneath Alaska.

32

33 **Introduction**

34 The observation of directionally dependent travel time anomalies of
35 inner-core sensitive body waves, combined with anomalous splitting of
36 core-sensitive normal modes, have been interpreted as evidence of
37 cylindrical velocity anisotropy within the inner core (IC) (Morelli et al.,
38 1986; Woodhouse et al., 1986). The fast axis of anisotropy is within
39 several degrees of the rotation axis, while the slow direction migrates
40 from in the plane of the equator to within 55° of the rotation axis with
41 increasing depth in the IC (e.g. Ishii and Dziewonski, 2002; Lythgoe et
42 al., 2014; Frost and Romanowicz, 2019). This anisotropy has been
43 interpreted as resulting from preferred alignment of anisotropic iron
44 crystals within the inner core (Stixrude and Cohen, 1995). The
45 magnitude of anisotropy has been shown to vary between 0 and 8%,
46 dependent on depth of sampling (e.g. Vinnik et al., 1994; Lythgoe et
al., 2014). Meanwhile, its dependence on the longitude of sampling has been interpreted as evidence of a hemispherical dichotomy, where the quasi-western hemisphere shows stronger anisotropy of around 4% in most models, while the quasi-eastern hemisphere show weaker anisotropy of 1-2% (Creager, 1999; Irving and Deuss, 2011; Tanaka and Hamaguchi, 1997)

53

Inner core anisotropy is investigated using the core-sensitive body wave, PKP, which comprises two branches sensitive only to the outer core, PKPbc and PKPab, and one branch sensitive to both the outer and inner cores, PKPdf. The PKPab and PKPbc branches are often used as references, in order to reduce the influence of source and origin time errors, as well as upper mantle velocity heterogeneity, on the recorded differential travel times. Residual travel times of PKPdf relative to a 1D reference model show a dependence on the angle of the inner core portion of the ray relative to the rotation axis, ξ (Morelli et al., 1986).

Rays with ξ<35° are referred to as polar and are roughly aligned with the fast axis of anisotropy. These rays show negative PKPdf travel time anomalies of up to 10 seconds (Morelli, Dziewonski and Woodhouse, 1986; Shearer, 1994; Su and Dziewonski, 1995; Li and Cormier, 2002; Cao and Romanowicz, 2007; Lythgoe et al., 2014; Romanowicz et al., 2015, Frost et al., in revision). Here, we use observed PKPdf travel
69 times measured relative to predictions from a 1D reference model,
70 referred to as absolute PKPdf travel time anomalies.

71

72 Resolution of the global pattern of inner core anisotropy is limited by
73 spatially heterogeneous sampling of the IC on polar paths. Previous
74 studies have noted the strongly anomalous character of travel times
75 on polar paths from sources in the South Sandwich Islands (SSI) to
76 stations Alaska, where rays with a range in ξ of only 6° (26<ξ<32°)
77 show a range of 6 s in travel time anomaly, in contrast with ~3 s for
78 the global data in the same ξ range, (Romanowicz et al., 2003; Garcia
79 et al., 2006; Leykam et al., 2010; Tkalčić, 2010; Tkalčić et al., 2015;
80 Frost and Romanowicz, 2017). This behaviour is seen for both PKPdf
81 absolute and PKPbc-df and PKPab-df relative travel times
82 (Supplementary Figure 1). This SSI-Alaska path may also show
83 variations in the amplitude of PKPdf (Long et al., 2018). The SSI-Alaska
84 anomaly has led to complications in the interpretation of inner core
85 structure (Tkalčić, 2010).

86

87 Notably, given the frequent seismicity in the SSI, data from this source
88 region to stations in Alaska are often over-represented in catalogues of
89 IC travel time anomalies (e.g. Tkalčić et al., 2002). Previous studies
90 have attempted to explain the discrepant SSI-Alaska PKP data by
91 invoking regional variations in the strength of IC anisotropy (Tkalčić,
92 2010). Other studies have argued for a source outside of the IC,
93 specifically velocity anomalies in the tangent cylinder of the outer core
94 (Romanowicz et al., 2003), or polar caps with higher concentration of
95 light elements (Romanowicz and Bréger, 2000).

96

97 Other explanations have invoked the effect of lower mantle structure
98 where the paths of PKPdf and outer core reference phases PKPbc and
99 PKPab most diverge. Tkalčić et al. (2002) showed that fitting the SSI-
100 Alaska anomaly requires rapid lateral variations in the D" layer.
101 Recently, Long et al. (2018) proposed a model with a 3% velocity
102 increase in the lowermost mantle under Alaska, in addition to uniform
103 inner core anisotropy, to explain the SSI-Alaska anomaly. However, to
104 explain the entire pattern of travel time and amplitude anomalies with
105 lower mantle structure alone requires a rather extreme distribution of
106 heterogeneity near the CMB. Accounting for trade-offs requires either a
107 thickness up to 650 km with a velocity perturbation of +3%, or P
108 velocity increases of 9.75% over a thickness of 200 km, which is far in
109 excess of that seen in tomography: 4 times stronger than that
110 observed in the regional model of Suzuki et al., (2016) and over 10
111 times stronger than observed in the global model of Simmons et al.,
112 (2011). In particular, fitting the variation of the anomaly from the
113 southwest to the northeast across Alaska requires an increasingly thick
114 fast D" layer in the lowermost mantle, in contrast with mineral physics
considerations which predict that the D" discontinuity height decreases towards the northeast (Sun et al., 2016). Moreover, while PcP-P travel time measurements do indicate higher than average wavespeeds in the lower mantle beneath Alaska, the models of Long et al., (2018) predict PcP-P travel time anomalies 3 times greater than observed (Ventosa and Romanowicz, 2015). Thus, while models of D" heterogeneity can explain the SSI-Alaska anomaly, the parameters required are hard to reconcile with independent observations. On the other hand, Helffrich and Sacks (1994) suggested that upper mantle structure could be responsible for some portion of PKP travel time anomalies. Indeed, in addition to lower mantle heterogeneity, global tomographic models show strong velocity heterogeneity in the upper 1000 km of the mantle in the vicinity of subduction zones (e.g. Fukao and Obayashi, 2013), resulting from active tectonic processes near the surface.

Here we investigate the source of the SSI-Alaska anomaly, using data from the USArray deployment in Alaska, which offers high spatial resolution of PKPdf travel times. We observe and model the effects of strong upper mantle structure in our recent 3D upper mantle tomography model of Alaska (Roecker et al., 2018) on the direction, slowness and travel time of PKP waves. We show that the complex upper mantle structure under Alaska is likely responsible for much of
138 the SSI-Alaska anomalous PKPdf observations. Observation and
139 modelling of similar behaviour in P waves (that do not sample the core)
140 supports this conclusion.

141

142 **Upper mantle structure beneath Alaska and 3D effects on PKP**
143 **propagation**

144 Alaska has been subject to multiple episodes of subduction, collision,
145 and accretion since the mid-Jurassic (Plafker et al., 1994). The present-
146 day subduction of the Pacific plate along the Aleutian arc began at
147 ~55Ma (e.g. Scholl et al., 1986) and manifests as steep subduction in
148 the west, and flat slab subduction in the east, where the Yakutat
149 terrane, an oceanic plateau with a thick, low-density crust, is currently
150 being accreted. The structure of Alaska has been extensively studied
151 using a range of methodologies: receiver functions (e.g. Miller et al.,
152 2018), surface waves (e.g., Feng et al., 2018), arrival time
153 tomography (e.g. Martin-Short et al., 2016), and joint interpretations of
154 body and surface waves (e.g. Jiang et al., 2018). These models show
155 strong and multi-scale velocity heterogeneity throughout the
156 uppermost 800 km of the mantle.

157

158 The most recent models take advantage of the newly deployed
159 USArray in Alaska which offers instrumentation with a station spacing
160 of ~85 km. In a separate study, we obtained a high-resolution model of
161 the upper 400 km of the Alaskan mantle using a joint inversion of
162 regional and teleseismic P and S travel times from 7 months of data in
163 2017 (Roecker et al., 2018). The main features of this model are
164 (Figure 1): a sharply resolved slab of ~100 km thickness with dVp~
165 3%, the Yakutat terrain visible down to 120 km depth with dVp~ -3%,
166 and regions of low velocities on either side of the slab. We note that
167 the slab structure is both stronger and sharper than in previous models
168 (Jiang et al., 2018; Martin-Short et al., 2018, 2016).

169

170 Interpretation of PKP travel time anomalies is generally based on the
171 infinite frequency approximation in a 1D mantle, where seismic waves
172 are only affected by velocities along the infinitesimal ray path and
173 where structure only changes with depth. When such corrections for
174 the tomographically resolved structure are applied, they do not fully
175 remove scatter in travel times (Bréger et al., 2000). Moreover, it has
176 been shown that considering the 3D effects of strong velocity
177 heterogeneity on ray paths improves the fit of tomographic models to
178 data (Simmons et al., 2012). Finally, when finite frequency effects are
179 considered, strong heterogeneities, such as a subducting slab, can
180 affect the travel time, waveform, and frequency content of seismic
181 waves that intersect it (Helffrich and Sacks, 1994; Vidale, 1987). Of
182 particular importance for slabs is that the magnitude of the effect is
183 strongly dependent on the incident direction of the wave relative to the
184 dip of the heterogeneity.

185

186 Seismic heterogeneity can distort an incident wave front, leading to
187 travel time and directional anomalies. Using an array of multiple
188 stations, the delay time of a wave across the array, or moveout, can be
189 measured. This moveout is characteristic of the direction from which
190 the wave arrives in terms of direction on the surface, or back-azimuth
191 (θ), and the incidence angle, or slowness (u). The residual of the travel
192 time, slowness, and back-azimuth, relative to a 1D reference model,
193 thus demonstrates the effect that the 3D velocity structure has on the
194 wavefield (e.g. Durand et al., 2018). Using sub-arrays of the USArray
195 (e.g. Ventosa and Romanowicz, 2015), now deployed in Alaska, we can
196 measure the local effects of the structure of the Alaskan mantle.

197

<figure><img src="image_2.png" /><figcaption>b</figcaption></figure>

<figure><img src="image_3.png" /></figure>

198
**Figure 1:** (a) Cross-section of the Vp model of Roecker et al. (2018) along a representative path from event 6 (Suppl. Table 1) to USAarray stations displayed as per cent deviation from a 1D reference model. (b) Slice through the model at 200 km depth showing the cross-section path as the green line. Contour marks 0.8% dVp.

204

## Methods

We determine the variation of travel time, slowness, and back-azimuth anomalies across Alaska using a sub-array measurement technique. We use 6 events in the South Sandwich Islands from 2016 to 2018 (Supplementary table 1) recorded at the USAarray and associated networks in Alaska and Canada (AK, AV, CN, II, IM, IU, TA, and US). We collect vertical component seismograms, remove the linear trend and mean from the data, and deconvolve the instrument response. Data are bandpass filtered between 0.4-2.0 Hz, a range which is found to best enhance the clarity of PKPdf relative to the noise.

215

For each event, we construct sub-arrays of the USAarray to measure the travel time, slowness, and back-azimuth of PKPdf at each location. We construct a 1°×1° grid across Alaska, and at each grid point we find the closest station and select an additional 5 to 8 stations around it. Sub-arrays with fewer than 6 stations in total are excluded, and sub-arrays with a non-unique station list are not repeated. The minimum
222 number of stations is chosen to ensure high slowness and back-azimuth resolution. Meanwhile, the maximum number of stations of 9 223 is chosen to minimise the sampling region of each subarray, thus 224 increasing spatial resolution between subarrays. At each sub-array we 225 window the data 20 s prior to and 40 s after the predicted arrival times 226 of PKPdf and PKPab, respectively according to the 1D reference model 227 ak135 (Kennett et al., 1995). We set the beampoint to the average 228 location of all stations in the subarray. We simultaneously grid search 229 over slownesses from 0 to 8 s/deg, and back-azimuths of ±20° relative 230 to the great-circle path and construct linear stacks, or vespagrams 231 (Davies et al., 1971). We then apply the F-statistic, a coherence 232 measure, which effectively suppresses aliasing, thus sharpening 233 resolution of slowness and back-azimuth (Frost et al., 2013; Selby, 234 2008). The coherence, F, is computed from the ratio of the sum of the 235 energy in the beam, b, to the summed differences between the beam 236 and each trace used to form the beam, xᵢ, in a time window, M, 237 normalized by the number of traces in the beam, N: 238

239
$$F = \frac{N-1}{N} \frac{\sum_{t=1}^{M} b(t)^2}{\sum_{t=1}^{M} \sum_{i=1}^{N} (x_i(t) - b(t))^2} \quad (1)$$

241 We visually inspect the F-vespagrams and select the best fitting 242 slowness, back-azimuth, and travel time for PKPdf (Figure 2). We 243 display vespagrams calculated for a range of slownesses (Figure 2c)
244 and back-azimuths (Figure 2d) with the other parameter (back-azimuth
245 and slowness for Figures 2c and 2d, respectively) allowed to vary
246 depending on the maximum F-value. Thus these 2D time-slowness and
247 time-back-azimuth vespagrams effectively display a 3D space.
248 Residual PKPdf travel time and slowness anomalies are measured
249 relative to predictions from ak135, and travel times are corrected for
250 ellipticity (Kennett and Gudmundsson, 1996). Back-azimuth residuals
251 are measured relative to the great-circle path from source to receiver.
252 Sub-arrays for which PKPdf is absent or not clearly resolved are
discarded. To improve accuracy of the travel time anomaly
253 measurement, we cross-correlate beams with an empirical PKPdf
254 wavelet. The wavelet is constructed for each event by adaptively
stacking (Rawlinson and Kennett, 2004) all selected beams from that
256 event. We then cross correlate each beam with the empirical wavelet
257 and measure the time shift. To account for errors in origin time and
258 source location inherent in using PKPdf absolute measurements, we
259 subtract the median observed travel time from all residual times in the
260 array (corrections are listed in Supplementary Table 1). We correct
261 data for a model of inner core anisotropy in the upper 450 km of the
262 western hemisphere, constructed without using data from the SSI-
263 Alaska path (model details are given below). This correction accounts
264 for 1.4 to 2.6 s of travel time anomaly, depending on ξ and path length
265
266 in the inner core. A weaker or stronger anisotropy model would remove

267 less or more of the observed travel time anomaly, respectively.

268

269

<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

270

271 **Figure 2:** Waveform data, station locations, and resultant F-

272 vespagrams for an example sub-array constructed for event 5 on

273 2018-08-14 (Suppl. Table 1). (a) PKP wavetrain with PKPdf moveout

274 marked by the blue line, and 1D predictions for PKPdf, PKPbc, and

275 PKPab marked by purple broken lines. Individual stations are shown in

276 black and the filtered beam is shown in green. (b) Map of stations in

277 the subarray (red) and the beam point (yellow) chosen as the average
278 location of stations in the subarray. F-vespagrams showing time versus
279 (c) slowness and (d) back-azimuth. PKPdf shows a strong back-azimuth
280 anomaly, while PKPbc does not, as is predicted by 3D ray-tracing
281 (Supplementary Figure 2). PKPab appears weak owing to the Hilbert
282 transform, reducing the amplitude and impulsiveness of the phase. The
283 picked PKPdf slowness and back-azimuth is shown by the blue
284 diamond, the maximum F-amplitude, which corresponds to PKPbc, is
285 shown by the red diamond, and predicted arrivals are shown for the
286 direct PKP phases (purple circles) and depth phases (open circles).

287

288 The subarray method averages the effects of the structure sampled on
289 all rays used to form the beam to a single location, the beam point. To
290 estimate the minimum spatial resolution of our method we calculate
291 the first Fresnel zone radius for a 1Hz PKP wave at 200 km depth
292 beneath the surface and add this to the aperture of an example
293 subarray. We find that the minimum resolution is thus approximately
294 220 km, or 2°, and thus we cannot interpret structures smaller than
295 this size, which is about 2 grid points in the regular grids shown in
296 Figures 3.

297

298 We use synthetic signals to test the resolution of our method. We
299 simulate signals, combined with real noise at a noise level equivalent
300 to our data, arriving at an example array from a range of incoming
301 directions. We apply the same vespagram and cross-correlation 302 approaches as used with the data and determine our time, slowness, 303 and back-azimuth resolution to be ±0.1 s, ±1°, and ±0.1 s/deg, 304 respectively. We test the effect of the number of stations in a subarray 305 on beam amplitude and find only a 3% difference between the smallest 306 and largest subarrays. We are thus well able to resolve signals of the 307 magnitude that we observe. 308

308
309 We seek to determine the influence of the Alaskan upper mantle on 310 incoming wave direction and slowness. We forward model PKPdf ray 311 paths through our regional tomographic model of Alaska using a 3D 312 ray-tracer derived from the joint inversion approach described in 313 (Roecker et al., 2010; Comte et al., 2016) and used in the construction 314 of the 3D model (Roecker et al., 2018). In this approach, we compute 315 travel times in the 1D model ak135 from the source up to the edges of 316 the regional tomographic model, and then within the box we apply an 317 eikonal equation solver in a spherical frame (Zhiwei et al., 2009) to find 318 the fastest path through the box to the receiver. We calculate PKPdf 319 travel times through this model and through a simple model, which is 320 1D throughout. Using the predicted travel times we calculate the 321 incoming direction of the PKPdf wave at the subarrays used in the 322 vespagram process. Unlike the vespagram process where we use 323 waveforms recorded at each station in the subarray, in the ray-tracing
process we only have predicted travel times for each station. We select the same stations used in each subarray and fit a plane to the variation of travel time as a function of station location in latitude and longitude, which represents the moveout of the signal. The slope of this surface can be decomposed into a slowness and a back-azimuth. We calculate a single travel time for each subarray as the average of the predicted times for each station. By comparing predictions of the 3D versus the 1D models we compute the travel time (dT), slowness (du), and back-azimuth (dθ) anomalies resulting from the 3D upper mantle structure.

In order to account for the influence of inner core anisotropy on PKPdf data, we construct a model of inner core western hemisphere anisotropy (167° W and 40° E) using the PKPab-df and PKPbc-df measurements used in Frost and Romanowicz, (2019) and Frost et al. (in prep). To construct a model of inner core anisotropy that can be used to correct PKPdf travel times on the SSI-Alaska path, but is not dependent on the SSI-Alaska data, we select only PKPdf data observed at stations outside of Alaska and with PKPdf paths turning less than 450 km below the ICB (which corresponds to the range of depths sampled by SSI-Alaska paths). We attribute the entire PKPdf travel time anomaly to structure in the IC, and convert travel times to velocity anomalies relative to ak135 as: $\frac{dt}{t} = \frac{-dv}{v}$, where t and v are reference
346 travel times and velocities in the IC, respectively, calculated in model
347 ak135. This accounts for the difference in path length between the
348 shallow and more deeply travelling waves. We construct cylindrically
349 symmetric models of anisotropy, in which the perturbation to an
350 spherically symmetric model, after Song (1997), is expressed as:

$$
\frac{\delta v}{v_0} = \alpha + \varepsilon \cos^2 \xi + \gamma \sin^2 2\xi \quad (2)
$$

353
354 where $v$ and $\delta v$ represent the reference velocity and velocity
355 perturbations, respectively, and $\xi$ the IC paths make with the rotation
356 axis. By fitting our data with an L1-norm, we determine the coefficients
357 $\alpha$, $\varepsilon$, and $\gamma$ to be: -0.028, 2.626, and -0.996, respectively
358 (Supplementary Figure 1).

359
360 Modelling travel time, slowness and back-azimuth anomalies

361 After correction for inner core anisotropy as described above, the
362 observed PKPdf travel time, slowness, and back-azimuth anomalies
363 show systematic patterns as a function of location across the USAarray
364 (Figure 3). We measure travel time residuals of ±1.5 s, slowness
365 residuals of ±0.6 s/deg, and back-azimuth anomalies reaching ±15 deg
366 but more commonly around ±5 deg. The patterns are consistent
367 between events. The most obvious features are:
368 (1) a trend from late to early arrival from the southeast of Alaska,
369 overlying the Yakutat terrain, towards the northwest

370 (2) low slownesses in the southeast of Alaska, sharply contrasted by a
371 band of high slownesses trending northeast-southwest across the
372 middle of Alaska

373 (3) a patch of low back-azimuth residuals in the centre of Alaska,
374 surrounded by high residuals

375 When viewed in the context of our 3D tomographic model, we find that
376 these sharp contrasts surround the slab (where the slab is defined by
377 >+0.8 % dVp).

378

379
<figure><img src="image_8.png" /><figcaption>**Figure 3:** Observed (left), predicted (middle) and comparison (right) of absolute PKPdf ray anomalies from 3D ray-tracing through our preliminary tomography model of Alaska, for all 6 events. (a, b and c): travel time residuals. (d, e, f): slowness residuals; (g, h, i) back-azimuth residuals. The outline of the Alaskan slab at 200 km depth (+0.8% dVp) from the preliminary tomography model is shown in black. The median observed absolute PKPdf travel time is subtracted from each event to account for origin time and location errors.</figcaption></figure>

380

389
390 The corresponding anomalies predicted by 3D ray-tracing through the
391 upper mantle tomography model of Alaska for all events show a
392 striking similarity to the observed travel time, slowness, and back-
393 azimuth anomalies, respectively (Figure 3b, e, and h). The predictions
394 replicate each of the three main features listed above, most strikingly
395 the slowness and back-azimuth anomalies. In addition, the model
396 replicates the trend of increasing and then falling travel time anomaly
397 with distance for rays on azimuths which intersect the slab
398 (Supplementary Figure 3), as observed by Romanowicz et al. (2003)
399 and Long et al. (2018). We see strong agreement of the trends of the
400 observed and predicted anomalies, but a mismatch in the travel time
401 anomaly amplitude, with the predicted anomalies being roughly half of
402 the strength of those observed (Figure 3c, f, and i).
403

404 We also predict travel time, slowness, and back-azimuth anomalies for
405 PKPab and PKPbc phases. Predicted differential PKPab-df anomalies
406 range between ±0.4 s, ±0.8 s/deg, and ±30 deg for time, slowness,
407 and back-azimuths respectively, while differential PKPbc-df anomalies
408 range between ±0.1 s, ±0.2 s/deg, and ±15 deg for time, slowness,
409 and back-azimuths respectively. The large variability in back-azimuth
410 anomalies matches our observations (Figure 2), and likely results from
411 the greater sensitivity of back-azimuth on a steeply incident phase
412 (e.g. PKPdf) to small directional changes.
413

414 The degree of qualitative agreement between the observations and predictions attests to the important influence of upper mantle heterogeneity on the raypaths and travel times of body waves used to investigate the inner core. Nonetheless, there are discrepancies, which point towards limitations: details and strength of the slab model, unmodelled structure outside of the upper mantle, and potentially the imprecision of the infinite frequency approximation of ray theory. We attempt to improve the fit to the observations by perturbing the slab model and investigate the effect that finite frequency effects may have by waveform modelling.

424

425 The clearest shortcomings of the model are the magnitude of the predicted travel time anomalies, which are less than half of those observed. Tomographic inversions often recover reduced amplitudes of velocity heterogeneity relative to those resolved by forward waveform modelling. The velocity anomaly of the slab as recovered in our model reaches a maximum of around ~3% dVp. We test the effect that stronger heterogeneity may have on the fit by saturating positive velocity anomalies in the slab regions (which we define as all grid points with dVp≥0.8 %) to 4%. We also test the effect of scaling the velocity anomalies in the entire model by factors of 2, 2.5, and 3. We find that the fit between the observed and predicted anomalies
436 improves as we increase the scaling of the tomography model
437 (Supplementary Figure 4 and Supplementary Table 2). This supports
438 our hypothesis that some of the misfit between the observed and
439 predicted times could come from the damping effects of tomographic
440 models. However, the scatter in the predicted measurements also
441 increases, which indicates that the details of the slab model should be
442 improved. Furthermore, the slope of the linear fit between the
443 observed and predicted slownesses and back-azimuths reaches 1 (thus
444 is directly proportional) at scaling factors lower than for the travel
445 times (red text in Suppl. Table 2), thus placing an upper limit on the
446 travel time anomaly that can come from the upper mantle, since
447 attempting to match the observed travel time anomalies by scaling
448 results in over-predicting slowness and back-azimuth anomalies. This
449 suggests either inaccuracy in modelling the incoming ray direction, or
450 that matching the observed travel time anomaly requires
451 heterogeneity outside of the upper mantle. Meanwhile, taking all these
452 factors into consideration, scaling the tomography model by a factor of
453 2.5 works best.

454

455 Predicted azimuth anomalies from our tomography model disagree
456 with the observed back-azimuth in the southeast portion of Alaska. Our
457 model predicts strong negative back-azimuth anomalies while we
458 observe strong positive anomalies (Figure 3g,h). However, the model
459 of Martin-Short et al., (2016) better matches the trend of our
460 observations (Supplementary Figure 5). This discrepancy may arise
461 from lack of resolution of the Yakutat anomaly in our tomography
462 model.

463

464 While our model is only resolved down to 400 km depth, previous
465 tomographic inversions of the Alaskan mantle resolve the slab down to
466 at least 600 km and potentially beyond, although the high velocity
467 anomaly of the slab becomes diffuse towards the bottom of the
468 modelled volume (Martin-Short et al., 2016). Although the model of
469 Martin-Short et al. (2016) covers a smaller region of Alaska than our
470 model and shows weaker heterogeneity by a factor of 1.5, this model
471 images the mantle down to 800 km depth. We use this model to test
472 the influence of the deeper section of the slab on predicted travel time,
473 slowness, and back-azimuth anomalies. We compute predicted
474 anomalies using the whole 800 km of the model, and using the model
475 cut at 400 km depth to determine the influence of the deeper part of
476 the slab. We find that fit between the predictions and observations is
477 marginally improved when calculated using the 800 km thickness of
478 the model (Supplementary Table 2).

479

480 We compare observations and predictions for different scaling factors
481 of the tomographic model along cross sections that are representative
482 of the effects of the Alaskan slab (Supplementary Figure 6). We choose
483 two slices where we observe both negative travel time residuals over
484 the slab, and positive travel time residuals either side of the slab.
485 These azimuth sections (Supplementary Figure 6) allow us to identify
486 the regional variation of misfit between the observations and
487 predictions across Alaska, which either point towards local inaccuracies
488 in the tomography model, or else some other unmodelled structure.
489 Across all of our events, it appears that the current model of Roecker
490 et al., (2018) underrepresents the magnitude of the velocity reduction
491 at shorter distances over the Yakutat (region A in Supplementary
492 Figure 6); this region is better fit when the model is scaled up by a
493 factor of 2. In contrast, the predictions of the current model for the
494 early arrivals caused by the high velocity slab fit the observations
495 (region B in Supplementary Figure 6) at all azimuths except in the far
496 southwest towards the Aleutians. The increasingly negative travel time
497 anomalies at distances >157° are not fully matched in magnitude by
498 any of our models, but are best matched by the standard model
499 (region C in Supplementary Figure 6). Increasing the scaling of the
500 model appears not to improve the fit to travel time anomalies at
501 distance >157°. We produce a hybrid model scaled by a factor of 2.5
502 before the slab the slab, and 1 over and after the slab. This model
503 generally fits the data better than any other model (Figure 4), although
504 it still fails to fully explain the data at distances beyond 157°. This
505 information will inform future iterations of the Alaskan upper mantle

506 tomography model.

507

508

<figure><img src="image_9.png" /></figure>

509

510 **Figure 4:** Left: Absolute PKPdf travel time anomalies as a function of

511 distance and for different sections through the slab for event 6 on
512 2018-12-11. Observations are shown in blue and predictions from 3D
513 ray-tracing through the standard and scaled tomography model
514 (shown on the right) are shown in red and purple, respectively. The
515 rough location of the slab in each cross section is marked by grey
516 shading. The tomography model (right) is scaled by a factor of 2.5
517 before the slab (south-east of the thick black line) and is kept as
518 standard over and after the slab (north-west of the thick black line).
519 The model is shown at 200 km depth, with stations shown as black
520 circles. Azimuths sections shown on the left are labelled on the right.
521
522 In order to estimate the effect of the slab and surrounding
523 heterogeneity on the travel times and amplitudes of PKPdf, we use
524 axiSEM (Nissen-Meyer et al., 2014) to simulate the effect of the upper
525 mantle on the wavefield. We take a 2D slice through the tomography
526 model (the same as that shown in Figure 1) and calculate waveforms
527 for a regular station spacing of 0.5° at a maximum frequency of 0.5 Hz.
528 We find that this results in both positive and negative PKPdf residual
529 times relative to the 1D prediction of ~1s (Figure 5), which is less than
530 that observed and predicted by the 3D ray-tracing.
531
<figure><img src="image_10.png" /><figcaption>**Figure 5:** 2.5D synthetic PKP waveforms generated for a 1D model (black) and for the cross-section shown in Figure 1 through a saturated version of our 3D model (green), aligned on the predicted arrival time for PKPdf showing (a) the whole PKP wavetrain, and (b) focussing on the PKPdf arrival. The slab model leads to both positive and negative travel time delays of the PKP waves and changes in amplitude, relative to 1D. Synthetics are calculated at 2s maximum period. Predicted arrival times in the 1D model are marked in red.</figcaption></figure>

To further test the robustness of the observed raypath anomalies, we calculate synthetic waveforms through our upper mantle model using a 0.04° station spacing to allow us to simulate high-resolution arrays. For the synthetics, both the subarray spacing and station spacing in each subarray are much higher than in our data, but subarray aperture is

532
approximately the same as in the data. We do this to resolve the effects of the heterogeneity on the waves as accurately as possible but with a similar spatial sensitivity to the data. This is not designed to serve as a test of the slowness resolution of our observations. We use the same vespagram approach as is applied to the data to measure the slowness anomaly that would result from this upper mantle heterogeneity. We find similar patterns of both travel time and slowness anomalies between the synthetics and our observations (Figure 6). We cannot assess back-azimuth anomalies due to the rotationally symmetric nature of the synthetic model. As we see in the 3D raytracing results, the observations of slowness are well fit by the standard model, but the travel times are better fit by a model scaled by a factor of 2. Some discrepancies may result from the simulations being run at a maximum period of 2 s for sake of computational cost, while we make observations on seismograms with a dominant period of around 1 s.
a

<figure><img src="image_11.png" /></figure>

b

<figure><img src="image_12.png" /></figure>

c

<figure><img src="image_13.png" /></figure>

563

**Figure 6:** (a) Travel time and (b) slowness anomalies of PKPdf resulting from propagation through the 3D upper mantle model relative to a 1D model. The wavefield is simulated using axiSEM through a 2.5D slice shown in Figure 1. Displayed are synthetics for the standard model (light green), the model scaled by a factor of 2 (dark green) and observations (blue inverted triangles) within 1° of the same profile for all events. (c) Map of the standard upper mantle tomography model at 200 km depth, showing the profile used in the waveform simulation in black, with the locations of the selected stations shown as
573 blue triangles. The rough location of the slab in the cross-sections is
574 shown by grey shading, and by the black contour on the map.

575

576 Modelling PKPdf amplitude variations

577 Amplitude variations of the PKPdf wave across Alaska measured
578 relative to PKPbc were recently reported by Long et al., (2018) and
579 were attributed to the effects of a high velocity layer in the lowermost
580 mantle. We measure the PKPdf amplitudes at stations across the
581 USArray in Alaska relative to the empirical PKPdf wavelet constructed
582 for each event. We find that PKPdf amplitude decreases over the slab
583 and that this pattern is consistent between events (Figure 7). The
584 range of amplitude ratios observed across Alaska is smaller than seen
585 in amplitude ratios measured on a global scale, which are ascribed to
586 inner core attenuation (Souriau and Romanowicz, 1997), thus we
587 suspect a different cause.

588

589 We measure the PKP amplitudes and amplitude ratios predicted by our
590 waveform models. We find that the trend in the predicted PKPdf
591 amplitude matches that in the data, except around ~152°, which
592 corresponds to the edge of the slab (Figure 7). The synthetics predict
593 larger changes in amplitude over a short distance than is observed.
594 This likely results from a combination of: (1) the limitations of the
595 synthetic models, the fact that the calculation is 2.5D and not fully 3D
and calculated at only 2 s period and (2) calculating the observed
amplitude on beams from sub-arrays. The aperture of our sub-arrays is
~1°, which would smooth out features as sharp as that seen in the
synthetics. We use moving averages of both the data and the
synthetics to smooth out the small-scale structure resulting in more
similar amplitude patterns (diamonds in Figure 7b).

<figure><img src="image_14.png" /><figcaption>**Figure 7:** (a) Observed amplitude of PKPdf relative to an empirical wavelet, averaged across all 6 events. Amplitudes are normalised to the maximum in each event before being combined in the average across all events. (b) Observed and synthetic PKPdf amplitudes within ±1° of section marked by black line, which is the section shown in Figure 1. Both observed and synthetic amplitudes are renormalised to the same scale. Moving averages and 1 standard deviation error bars are calculated every 1.5°. The outline of the Alaskan slab at 200 km</figcaption></figure>

603
612 depth (+0.8% dVp) from the preliminary tomography model is shown
613 in black in (a) and by grey shading in (b).

614

615 **Discussion**

616 In summary, we find that all of our observations of PKPdf travel time,
617 slowness, back-azimuth, and amplitude variations across Alaska are
618 consistent with the effects of the slab in the Alaskan upper mantle. In
619 particular, the subducted slab causes sharp deviations in wave
620 direction and wave amplitude. Meanwhile, the south-eastern portion of
621 Alaska shows consistently slow travel times, potentially caused by the
622 underlying Yakutat lithosphere. These complexities point to the upper
623 mantle contributing at least 2 s to PKPdf travel time anomalies, which
624 thus should not be attributed to inner core anisotropy.

625

626 To confirm this slab effect, we measured the travel time, slowness, and
627 back-azimuth anomalies from three events from the Caribbean and
628 South America that travel to the USAArray in Alaska along similar back-
629 azimuths as PKP paths from SSI, but at distances corresponding to P
630 waves (that do not sample the core). Event details are given in
631 Supplementary Table 3. We applied the same sub-array processing
632 described here for PKP. While direct P waves arrive at higher
633 slownesses than PKP, we find very similar patterns to those observed
634 for PKPdf, and a similarly strong fit between observations and
predictions from 3D ray-tracing through an Alaskan tomographic model (Supplementary Figure 7). Notably, the observed patterns as a function of azimuth and distance are better matched by predicted travel times for our unmodified tomographic models than for PKPdf (Figure 8). Because P waves sample the slab at shallower depths than PKPdf, this indicates that improvement in the deeper part of the slab model may be needed, which we will address in a forthcoming study.

<figure><img src="image_15.png" /><figcaption>**Figure 8:** Left: Absolute P wave travel time anomalies as a function of distance and for different sections through the slab for all three P wave</figcaption></figure>
645 events (Supplementary Table 3), averaged together. Observations 646 (blue) and predictions (red) from 3D ray-tracing through the standard 647 tomography model (Roecker et al., 2018). The rough location of the 648 slab in each cross section is marked by grey shading. To correct for the 649 different source-receiver distances of these events, we averaged the 650 observed and predicted P wave times as a function of receiver location, 651 and then projected the averaged receiver locations relative to the 652 average P source location. This allows for comparison with the PKPdf 653 profiles shown in Figure 4 and Supplementary Figure 6. Right: The 654 tomography model is shown at 200 km depth, with averaged stations 655 shown as black circles. Azimuths sections shown on the left are 656 labelled on the right. 657

658 Upper mantle structure in other regions, such as the Scotia slab under 659 the South Sandwich Islands source region (Fukao et al., 2001), may 660 also influence the observed anomalies, yet is not modelled here. 661 Measurements of PcP-P differential travel times in the region around 662 the Scotia slab show a large range of travel time anomalies (Tkalčić, 663 2010). The range of these anomalies is of a similar magnitude to PKPdf 664 travel time anomalies observed in Alaska from the same source region, 665 but unlike for PKPdf, they are scattered and show no systematic 666 variation. Furthermore, Romanowicz et al. (2003) demonstrated that 667 the patterns of PKP residual travel time with ξ, distance, and azimuth 668 recorded in Alaska were observed for all SSI events, regardless of 669 location. Long et al. (2018) observe that the location of the SSI event 670 does change the distance (relative to the event) at which the trend of
671 increasing dT is observed, but we find that the geographic location of
672 the trend is the same for all events: over the Alaskan slab. Thus, while
673 mantle structure near the Scotia slab may contribute to the
674 observations in terms of additional scatter, it is unlikely to be the
675 cause of the systematic pattern of PKPdf anomalies observed in Alaska.

676 Moreover, the range of source locations and depths used in this study
677 would likely reduce any systematic bias in our observations that would
678 result from the Scotia slab.

679

680 The travel time of PKPdf is known to be affected by anisotropy in the
681 inner core (Supplementary Figure 1), thus we add a correction to the
682 observed travel times. The model of inner core anisotropy used is
683 derived from data sampling the same depth range and in the same
684 hemisphere of the inner core as the South Sandwich Islands to Alaska
685 data. The strength of this correction affects the travel time anomaly
686 that we ultimately attribute to the upper mantle. Since the travel time
687 anomaly from the inner core does depend on station location this does
688 affect the moveout of the PKPdf wave across each sub array, but the
689 effect is negligible given the small size of the sub arrays. However, the
690 correction significantly improves the match between the observed and
691 predicted travel time anomalies (Supplementary Figure 8).

692
693 As recently suggested by Long et al. (2018) and mentioned earlier,
694 lower mantle heterogeneity could influence PKP travel time anomalies.
695 However, we calculate that the magnitude of lower mantle
696 heterogeneity that would also be compatible with other observations of
697 D'' structure, in particular PcP-P travel times (Ventosa and
698 Romanowicz, 2015), would contribute travel time anomalies on the
699 order of no more than ~1s. Core-Mantle Boundary structure instead
700 might contribute to measurement scatter or the event-specific shift
701 from the predicted times (listed in last column of Supplementary Table
702 1). Alternatively, the event-specific shift may result from source
703 location and origin time errors. Moreover, our upper mantle model
704 reproduces the pattern of travel time anomalies with distance from the
705 events in the South Sandwich Islands (Supplementary Figure 4). The fit
706 is more satisfactory than that achieved by Long et al. (2018) using
707 lower mantle heterogeneity, and is also capable of explaining the
708 change in pattern with back-azimuth (Supplementary Figure 3).
709 Furthermore, the upper mantle model is capable of reproducing the
710 patterns of slowness and back-azimuth anomalies. Contamination of
711 PKP waves by upper mantle heterogeneity thus provides a single, self-
712 contained explanation for patterns previously attributed to the lower
713 mantle, outer core, and or inner core.

714

715 **Conclusion**
716 We find that the pattern of slowness, back-azimuth, and travel time anomalies measured for PKPdf at sub-arrays of the USArray in Alaska match the patterns predicted by a high-resolution model of the Alaskan upper mantle. The strong similarity of the observed slowness and back-azimuths to those predicted using only upper mantle heterogeneity suggests that it is the main source of the anomalies. This is also confirmed by analysis of direct P waves along azimuths similar to the SSI to Alaska PKP paths considered here. While other structure in the lower mantle and upper mantle on the source side may also contribute to the observed scatter in travel time residuals, we conclude that the dominant cause of the SSI-Alaskan anomaly is the Alaskan subduction zone. As such, this motivates further improvements in characterizing the structure of the Alaska slab and its surroundings. More generally, care must be taken when interpreting travel time anomalies from regions with strong upper mantle structure in terms of inner core structure.

732

733 Acknowledgements

734 We thank the International Seismological Centre (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
739 used in this study. IRIS Data Services are funded through the
740 Seismological Facilities for the Advancement of Geoscience and
741 EarthScope (SAGE) Proposal of the National Science Foundation under
742 Cooperative Agreement EAR-1261681. Waveform simulations were
743 performed using The Extreme Science and Engineering Discovery
744 Environment (XSEDE) supported by grants TG-EAR180020 and TG-
745 EAR170001. This work was supported by EAR-1135452 and NSF grant
746 EAR-1829283.

747

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