## Introduction

The Earth’s lowermost mantle is dominated by two Large Low-Velocity Provinces (LLVPs) beneath Africa and the mid-Pacific. While tomographic models show coherent images of LLVPs at large scale1,2,3,4,5,6, discrepancies exist among different models regarding the fine-scale structures and detailed boundaries. There is no consensus about the origin of LLVPs but they are probably both thermally and chemically distinct structures7,8,9,10. Along the LLVP margins, thin patches (10–100 km in height) of ultra-low velocity zones (ULVZs), characterized by a reduction of 5–25% in compressional and 10–45% in shear velocity, are widely distributed at the core-mantle boundary (CMB)11,12. Different mechanisms have been proposed to explain the drastic velocity drops of ULVZs, including iron-enriched assemblages13, partial melting14, hydrogen-bearing iron peroxide15, and silicate sediments from the core16. Temporal and spatial correlations between hotspots and reconstructed large igneous provinces (LIPs) with LLVPs17 are suggested. Also, many ULVZs are likely to distribute over LLVP margins11. Thus, LLVPs and ULVZs may be reservoirs of recycled oceanic crust18 and/or primordial materials19,20, which can be viscously entrained by mantle plumes to generate a wide range of geochemical signatures in oceanic island basalts21.

Assessing the geometries and physical properties of LLVPs and ULVZs requires constraints from seismic waves sampling these structures. The LLVP beneath southern Africa is well studied with ideal seismic phases, such as SKS and Sdiff, which sample the edge of the LLVP and determine its boundary sharpness8,22. However, because of limited data coverage, most studies of the Pacific LLVP focus on characterizing its edge structure23,24 and in particular ULVZs25,26,27,28,29,30. Cottaar and Romanowicz25 propose a large-sized ULVZ near Hawaii (referred to as the Hawaiian mega-sized (HM) ULVZ hereafter) at the northern edge of the Pacific LLVP (Fig. 1), which is ~910 km in diameter, 20 km in height, and −20% in shear velocity perturbation (δVS), by mainly modeling strong Sdiff postcursors along a west-east (W-E) profile. Now with USArray moved to Alaska in recent years, we have an unprecedented opportunity to study the northern edge of the Pacific LLVP in a north-south (N-S) direction (Fig. 1) to resolve strong trade-offs among location, velocity perturbation, and size of the north Pacific mega-sized ULVZ. Other identified mega-sized ULVZs correlate with hot spots directly beneath Iceland31 and Samoa32,33. In contrast, the mega-sized ULVZ at the northern edge of the Pacific LLVP does not overlap with the Hawaiian hotspot geographically. Thus, resolving the boundaries of ULVZs and LLVPs is essential to uncover if mega-sized ULVZs are the root of deep mantle plumes.

In this study, we discover a mega-sized ULVZ at the northern edge of the Pacific LLVP and determine that its shear velocity perturbation is −10% and the size is ~1500 × 900 km. Combined with the imaged subvertical north-tilting edge of the Pacific LLVP, we demonstrate that a stable mantle flow converging at the LLVP edge can significantly affect the dynamic evolution of the ULVZ and LLVP.

## Results

### Height of the Pacific LLVP

For 13 events with simple source time function between 2016 and 2020 (Fig. 1, Supplementary Table 1) in the Tonga-Fiji-Kermadec region recorded by stations in Alaska, we measure the ScS-S differential travel time residuals (δtScS-S) relative to IASP9134 with epicentral distances smaller than 85°, at which S and ScS are well separated. For event B, we measure the δtScS-S with epicentral distance extending to 90° due to the high-quality data (Fig. 2c). Interestingly, δtScS-S correlates positively with ScS travel time residuals (δtScS) and negatively with S travel time residuals (δtS) (Fig. 2a, b, Supplementary Fig. 1), which suggests that both ScS and S contribute to δtScS-S. At azimuths of 0°−10°, δtScS-S of event B advances by ~5 s from distance 75° to 90° (Fig. 2c), which is typically attributed to the change of δtScS. However, δtScS appears constant along the distance profile. In contrast, δtS has a remarkable change up to 8 s with increasing distance, suggesting a strong anomaly in the lower mantle sampled by S (Fig. 3a).

Four events (events A–D in Fig. 1) in a N-S corridor with azimuth range of 0°–10° are selected to further examine δtS (Fig. 3c). For the southern event A, the change of δtS is up to 5 s from 80° to 90°. Event B displays a sharp 8 s change of δtS from 80° to 87°. Event C is similar to event B but with a smaller δtS jump of 6 s from 75° to 82°. For the northernmost event D, the change of δtS drops to 5 s. To evaluate the effects of shallow structure on travel time anomalies, we use the travel time anomaly of SKS (δtSKS) of event E (Fig. 3a, Supplementary Fig. 2) with ray sampling away from the northern edge of the LLVP to correct for upper mantle structure. After correction, the δtS variation is smaller but still has a ~6 s and ~5 s delay for event B and C (Fig. 3c), respectively. We also test using SS as the reference to correct for possible shallow effects, which displays a similar trend as using SKS correction (see Methods in detail, Supplementary Fig. 2). The consistency between corrections using different reference phases is true for all four events (Supplementary Fig. 2c), which further confirms that shallow mantle structure beneath stations or events has little effect on the corrected δtS. Instead, the delay of δtS is mainly controlled by S with its ray paths sampling a strong lower mantle structure, i.e. the Pacific LLVP.

When the S wave begins to encounter the top of the LLVP, δtS starts to increase. Thus, the distance of the initial increase of δtS provides a robust and tight constraint on the height of the Pacific LLVP (Supplementary Fig. 3). With events moving to the north, the distance at which δtS starts to increase becomes smaller (Fig. 3c), indicating the Pacific LLVP has a higher relief towards its northern edge. Based on these constraints, we outline a LLVP model that has the height varying from 720 km in the south to 920 km in the north (Fig. 3a), which is double the height in a previous model24. Then, we explore a series of models with different δVS in the LLVP and examine how δtS of different events are affected. We find that a LLVP with δVS varying gradually from -2% at the top to -4% at 300 km above the CMB and tilting to the north can best match the corrected δtS for events A–D on the N-S profile (Fig. 3b). For event A, the S wave consistently samples inside the LLVP so there is no obvious δtS jump. In contrast, the S ray paths of events B–D sample above the LLVP at smaller distance and δtS increases quickly when S samples more LLVP with increasing distance. A velocity drop of 2% across the top of the LLVP is needed to match the rapid change of δtS, and the gradual change of velocity perturbation at deeper depth reproduces the travel time anomalies for all events. To match the travel time of S for event A at larger distance, a uniform δVS of −4% is necessary in the lowermost 300 km of the mantle.

### Northern wall of the Pacific LLVP

The δtS from the W-E section for events in the Solomon Islands (Supplementary Table 1) recorded by stations at North America provides extra constraints on the basal structure of the LLVP24,35 in an orthogonal direction. From north to south, δtS slows up to 5 s (Fig. 4a, Supplementary Fig. 4). The largest gradient of δtS separating the S-wave turning points in the lowermost mantle is defined as the boundary of the Pacific LLVP. When δtS measured for the W-E profile in Fig. 4a are projected on a N-S profile (Fig. 4b) at their turning depth, it suggests a subvertical edge tilting to the north, which is different from a north-west dipping edge inferred from P-wave study35. With limited measurements, we expect to see differences among the obtained dip directions of the LLVP edge. Nevertheless, a north tilting edge better explains the gradual decrease of δtS at larger distance for events A–D along the N-S profile (Fig. 3c). In contrast, an LLVP with a south tilting edge and a wider base produces stronger delays at large distance than observed in the data, in particular for event A at distance larger than 90° (Supplementary Fig. 5).

### North Pacific (NP) ULVZ

A model that only includes the new LLVP structure as in Fig. 3a cannot reproduce δtScS-S of event B along the N-S profile (Fig. 5a, Supplementary Fig. 6a) and waveforms with late and strong ScS arrivals at a distance range of 90°–100° (Supplementary Fig. 6b), which suggests the existence of a ULVZ at the northern edge. We use the normalized cross-correlation coefficient (CC) between data and synthetics in a time window of 20 s before S and 20 s after ScS (Supplementary Fig. 7) to quantify the goodness of waveform fit (see Methods and Supplementary Note 1). Through the three-dimensional (3D) ULVZ structure, a two-dimensional (2D) slice spanning 12° in the N-S direction with 50±20 km height and −10±2% δVS predicts S and ScS data for all events A–D along this 2D corridor (Supplementary Figs. 8, 9). For this slice, we made series of sensitivity tests on the height, δVS, and extent of the ULVZ. In Supplementary Fig. 10, we show that the location and extent of the ULVZ are tightly constrained by matching the waveforms of S and ScS across all distances for the 2D waveform modelling. However, the strong azimuthal variation of δtScS-S (Supplementary Fig. 6) of event B suggests the existence of a 3D ULVZ structure.

The 3D HM ULVZ model25 near Hawaii is mainly derived from matching the azimuthal variation of strong delayed (>30 s) Sdiff postcursors at the period of 10–20 s along the W-E profile for event F (Fig. 5b), which are refracted from the circular boundary of the ULVZ due to its large velocity reduction. However, for event B along the N-S profile, the HM ULVZ model produces late ScS arrivals only at an azimuth of 10°–18° (Supplementary Fig. 6b). In contrast, distinct ScS arrivals emerge at an azimuth of ~4° and fade away at ~25° in the data (Supplementary Fig. 6b), which indicates a broader ULVZ extending further to the west (Fig. 1b). The HM ULVZ model also produces strong postcursors after both ScS and sScS (red dashed line in Supplementary Fig. 6a and yellow patches in Supplementary Fig. 6b), which are generated from multiple reflections in the ULVZ due to its strong velocity perturbation. Furthermore, the HM ULVZ model predicts more delayed ScS than data (Supplementary Fig. 6a). Thus, a broader ULVZ in the W-E direction with a weaker velocity perturbation than the HM ULVZ model is required as demonstrated in our 2D modelling.

Our new ULVZ model (referred to as the North Pacific (NP) ULVZ hereafter) fits the Sdiff postcursors along the W-E profile at different frequencies. At the period of 10–20 and 10–50 s, strong Sdiff postcursors extend to the azimuth of 48°, which is predicted by the NP ULVZ (Fig. 5b, Supplementary Fig. 11). The Sdiff at the period of 10–50 s exhibits two arrivals at the azimuth of 48° to 55° and broadening waveforms at larger azimuth (Supplementary Fig. 11). Both the HM ULVZ model and the NP ULVZ predict Sdiff waveforms broadening at azimuth larger than 55°, but neither produces Sdiff with double arrivals at smaller azimuth, which may originate from multi-pathing at the edge of the LLVP.

### Sensitivity tests on the ULVZ model parameters

The NP ULVZ in Fig. 1b inherits the shape of the HM ULVZ model in the east but extends further to the west. The shear velocity drop of the ULVZ should not exceed 10% to avoid strong arrivals after ScS for event B (Supplementary Fig. 6). The eastern boundary of the ULVZ can be defined at which S and ScS merge along the azimuth profile at an azimuth of ~25° (Fig. 1b, Supplementary Fig. 6b), which is also supported by ULVZ mapping using ScS pre/post cursors30. To further investigate how different 3D ULVZ model parameters, i.e. δVS, height (H), lateral size, shape, density, and possible existence of heterogeneities, affect the waveform complexities for both N-S and W-E profiles, we perform sensitivity tests (See Supplementary Note 1, Supplementary Figs. 1215). Based on grid searching, a model with δVS of –10% and H of 50 km provides the highest CC. In Supplementary Table 3, we describe how these model parameters affect waveform complexities in detail. In addition to using CC as the misfit function, we also test L1-norm and L2-norm (see Methods), which are typically applied in full waveform inversion, to examine the trade-offs between δVS and H of the ULVZ. We find that these two misfit functions give similar results as CC (Supplementary Figs. 1214), implying the CC values used in this study are robust. In general, only modelling Sdiff postcursors from the W-E profile cannot constrain δVS and the shape of the NP ULVZ well. A ULVZ extending along the W-E direction with different δVS can produce Sdiff postcursors similar to those predicted by the circular HM ULVZ model. However, combined with constraints from the N-S profile, we can better define the shape and δVS of the NP ULVZ.

In most cases, we assume a ULVZ model with uniform δVS and height. However, the NP ULVZ could be inhomogeneous considering its large scale. Thus, we test models with heterogeneities as well as multiple separated smaller ULVZs (Supplementary Fig. 15N–Z). Models with isolated ULVZs fail to explain the azimuthal variation on the N-S profile and the Sdiff postcursors on the W-E profile. ULVZ models with a gradual radial or randomly distributed δVS (Supplementary Fig. 15S, T) predict almost identical waveforms as the NP ULVZ model with uniform δVS. We also generate pseudo-tomographic models by enhancing global tomographic models or fitting the measured δtScS-S along the N-S profile (see Supplementary Note 1 and Supplementary Fig. 15U–Y). Results for these models suggest that a heterogeneous ULVZ cannot be constrained by fitting the waveform data at the frequency bands in this study. However, the δVS in the NP ULVZ is not likely to vary drastically at long wavelength. The δVS variation should not exceed 20% radially for layered ULVZ models, and not exceed 4% at the wavelength of ~200 km laterally, compatible with the Fresnel Zone of Sdiff at the period of 10 s (Supplementary Fig. 15A). Also, the NP ULVZ must be a continuous block at large scale, rather than many small disconnected patches (Supplementary Fig. 15Z). Despite the possible existence of small-scale heterogeneities, our uniform NP ULVZ model represents the bulk properties of the ULVZ located at the northern boundary of the Pacific LLVP. In addition, CMB topography of 20 km extending over 15°, which is comparable to the size of the NP ULVZ, has negligible influence on the waveform complexities at the frequency bands we focus on (Supplementary Fig. 16). In summary, our preferred 3D ULVZ model has a height of 50 km, lateral extent of ~1500 × 900 km at the CMB, and δVS of −10%, which best reproduces the waveform complexities from the two orthogonal profiles.

### P-velocity reduction of the NP ULVZ

Luo et al.28 define a ULVZ (Fig. 1b) overlapping with the NP ULVZ with a P-velocity reduction of ~10% by modeling the late PKPab arrivals and associated waveform complexity. We add more measurements of differential travel time residuals between PKPab and PKPdf (δtPKP(ab-df)) for events along the Tonga-Fiji-Kermadec region (Supplementary Table 2) recorded by stations in Europe and find that PKPab only displays ~1 s travel time variation and has no obvious amplitude reduction or waveform complexity (Supplementary Fig. 17b). We suspect that the observed waveform complexities and delayed PKPab in Luo et al.’s study may partly originate from strong upper mantle structure. With a δVP of −10%, the NP ULVZ model predicts the δtPKP(ab-df) of up to 3 s (Supplementary Fig. 17c). To match the observed ~1 s variation of δtPKP(ab-df) and simple waveforms of PKPab (Supplementary Fig. 17d), a P-velocity drop less than 5% is sufficient to keep PKPab normal compared to data, consistent with a ULVZ with a weak δVP.

## Discussion

The NP ULVZ (Fig. 6a) is about twice the size in both height and lateral extent of the mega-sized ULVZs beneath Iceland31 and Marquesas36. Heterogeneity probability maps of highly anomalous SPdKS waveforms suggest widely distributed mega-scale ULVZs32,33 along the Pacific Rim beneath Samoa, east of the Philippines and north of Papua New Guinea, and beneath North America and South America, which are comparable in size to the NP ULVZ. Despite the large size of the NP ULVZ, its aspect ratio (relief/width) is similar to the mega-sized ULVZs beneath Iceland and Marquesas.

ULVZs may represent patches of partial melt14 or iron-rich oxide13,32, which are denser than the ambient mantle. Compared with the large shear velocity drop of 20–45% for other mega-sized ULVZs31,36,37, the NP ULVZ has a weaker δVS of −10%, suggesting a less dense ULVZ13 and possibly different chemistry from other ULVZs. A smaller density tends to form a ULVZ structure with high aspect ratio (relief/width)38. Furthermore, a lighter ULVZ tends to be stirred more into the LLVP39, so replenishment of the NP ULVZ may be necessary to sustain its large size. For the “mild” NP ULVZ with a small velocity drop, its viscosity might be larger than ULVZs with extreme velocity drops40, which also favors a higher aspect ratio. Thus, the similar aspect ratio of the NP ULVZ and other mega-sized ULVZs may indicate the chemistry or dynamics of the ULVZs are different. The location of the NP ULVZ at the northern edge of the Pacific LLVP, the large size of the ULVZ, and δVSVP of ~2 suggests the ULVZ has distinct chemistry rather than solely partial melt, the latter of which favors a δVSVP of ~314,41. However, without precise constraints on the elastic and thermal properties of the ULVZ, it is difficult to distinguish the origin of the ULVZ. Iron-rich assemblages13,42, subducted related materials15,43,44,45, and partial melting may contribute to the chemical heterogeneity of the ULVZ. Due to a strong overlying hot upwelling, which has been imaged as “broad plumes”46, the mega-sized ULVZs beneath Iceland31 and Samoa32,33 may be more elevated and therefore have a higher aspect ratio than expected. Such a strong hot upwelling could also entrain and drain the ULVZ materials more efficiently than the NP ULVZ38,47, which further supports a more massive NP ULVZ compared to Iceland and Samoa.

Here we hypothesize that a long-term, stable, horizontally convergent mantle flow plays an important role in driving the migration of “mild” ULVZs in the north Pacific towards the northern wall of the Pacific LLVP and producing the NP ULVZ (Fig. 6c). Numerical models show flow in the deep lower mantle under the North Pacific from 100–50 Ma due to long-lasting subduction history48,49,50,51. Moreover, the Pacific LLVP could have been stable prior to Pangea at 330 Ma17. Thus, the long-lived Pacific LLVP and stable convergent mantle flow towards the northern edge of the Pacific LLVP may both promote and sustain the accumulation of ULVZ material at the LLVP edge39,52 (Fig. 6b).

The stable convergent mantle flow in the North Pacific is also evidenced by the northward tilting wall of the Pacific LLVP. The LLVP has a subvertical northern wall (Fig. 4b) which distinguishes it from a dynamic ridge-like structure with gradual sloping boundaries10. Such tilting away from the center of the LLVP is also observed along the eastern boundary of the African LLVP due to the mantle flow associated with the motion of the African plate9,53. A Dʺ discontinuity, characterized by 2% VS jump at 220 km above the CMB24, most likely linked to subducted slab, is also identified at the northern edge of the Pacific LLVP. Thus, the base of the Pacific LLVP may be impinged by slabs and associated stable convergent flow to develop a subvertical tilting wall (Fig. 6c). Walls that tilt away from the center of an LLVP indicate that LLVP materials cannot be too dense, otherwise ridges form with inward tilting walls. Also, LLVP materials cannot be too light, otherwise they produce unstable structures that do not persist through geological time9,48.

Interestingly, at the northeastern edge of the Pacific LLVP only patchy ULVZs are observed27,29,54,55. Hence based on our hypothesis of forming large-scale ULVZs, one may expect stable convergent mantle flow is absent in this region56 or these patchy ULVZs are fragments from a large-scale ULVZ. The later hypothesis is supported by dynamic calculations that show part of a large ULVZ advected into a linear shape along the LLVP boundary and fragmented into small patches by shearing flow39. Subsequently, these fragmented ULVZs may stir into the LLVP39 and entrain into the Hawaiian plume due to slab push29, supplying enriched geochemical heterogeneities in the plume. In any case, in a region with a large volume of pre-existing small ULVZs, a strong and stable convergent mantle flow may promote the formation of a mega-sized ULVZ such as the NP ULVZ. Thus, in future work, resolving detailed deep mantle flow patterns will be critical to deciphering both the geographic and geometric evolution of ULVZs. In turn, a detailed global map of ULVZs will provide extra constraints on the direction of deep mantle flow.

Flow in the deep mantle could produce a southward motion of the north tilting Hawaiian plume57, such that the current root of the Hawaiian plume is likely located south of the Hawaiian Islands49. Despite challenges in resolving the Hawaiian plume58, tomography models (depth cross-sections in Supplementary Fig. 18) and thinning transition zone identified beneath the south-southeast of Hawaii59,60 suggest the Hawaiian plume is rooted at the northeastern edge of the Pacific LLVP rather than the NP ULVZ. Thus, patchy ULVZs at the northeastern edge of the Pacific LLVP are likely be a plume generation zone57. In contrast, a recent study focusing on ScS pre/post-cursors further confirms the existence of a large-scale ULVZ beneath the west of Hawaii and prefers a closer relationship between the NP ULVZ and the Hawaii plume30. Nevertheless, to further understand how deep reservoirs fuel near-surface melting and volcanism, constraints on the physical properties of ULVZs and their spatial relation with the LLVPs and slabs are required. Thus, a detailed global mapping of the multi-dimensional structure of ULVZs using sampling from different directions will be crucial.

## Methods

### Data processing procedures and travel time measurements

We select 13 events with simple source time functions between 2016 and 2020 along the Tonga-Fiji-Kermadec region recorded by USArray stations in Alaska (Fig. 1, Supplementary Table 1) to examine the S-wave velocity structure at the northern edge of the Pacific LLVP. Raw data have been deconvolved with their instrument responses and bandpass filtered from 5–50 s before rotation into tangential (SH) and radial (SV) components. We also include 6 events (Supplementary Table 1) in the Solomon Islands recorded in North America to provide orthogonal direction sampling for an extra constraint on LLVP structure.

For the 13 events (Fig. 1) in the Tonga-Fiji-Kermadec region recorded by stations in Alaska, we measure the ScS-S differential travel time residuals (δtScS-S) with epicentral distances smaller than 85°, at which S and ScS are well separated. For event B, we extend the epicentral distance to 90° with the high-quality data of ScS. Then we correct the travel time residuals to one common station (AK.UNV) to remove possible errors of event origin time and location. For the W-E profile with events in the Solomon Islands recorded by stations at North America, we shift δtS to a common station MLAC to remove possible errors of the event origin time and location (Fig. 4a, Supplementary Fig. 4).

The ray paths of PKPab and PKPdf separate at deeper depth with PKPab piercing points covering a wider range at the CMB on the source side than on the receiver side and vice versa for PKPdf (Supplementary Fig. 17). Since small seismic velocity changes on the CMB can perturb the PKPab path effectively, ULVZs can be detected by δtPKP(ab-df). Here, 9 events in the Tonga-Fiji-Kermadec region (Supplementary Table 2) are selected for PKP study. All PKP data are selected with epicentral distance at which the PKPab and PKPdf are well separated. Travel time differences of each trace between PKPab and PKPdf are measured by cross-correlating the waveforms of PKPab and Hilbert transform of PKPdf when the amplitudes are normalized to PKPdf. The cross-correlation coefficients of all traces of each event are then normalized to the highest coefficient of that event.

### S-wave travel time correction of events A–D

The stations at Alaska are located above the Aleutian subduction system, which could include lateral varying structures. Thus, a correction of the travel time anomaly caused by shallow structures beneath the stations is necessary to determine the structure of the LLVP accurately. Here, we test both SKS and SS as reference phases to correct S-wave travel time. Note that the incident angles of SKS and SS are steeper and shallower than that of S, respectively (Supplementary Fig. 2a).

We use SKS travel time residuals from event E located further to the south to correct S-wave travel time residuals for events A–D. SKS ray paths are away from the Pacific LLVP (Supplementary Fig. 2a), so the SKS travel time residuals avoid being contaminated by the Pacific LLVP anomaly. Furthermore, SKS signals are simple in the distance range for event E to provide stable measurements. Supplementary Fig. 2b displays travel time residuals of SKS (red circles) up to ~3 s with increasing distance, which correlates with a slow mantle wedge beneath Alaska. For comparison, we also measure SS travel time residuals of events A–D whose ray paths are almost identical in the uppermost mantle beneath the source and station. Supplementary Fig. 2b displays travel time delays of SS (green circles) of event B as an example. Despite larger uncertainties in measuring the travel time of SS, the travel time residuals of SS are similar to those of SKS.

Supplementary Fig. 2c shows the corrected S travel time residuals by using both SKS from event E and SS from individual events A–D, which have similar trends. Such consistency implies that the observed travel time anomalies of SKS and SS mainly come from the crust and upper mantle anomaly beneath Alaska and the source side structures of events A–D have little effect. Thus, the lower mantle LLVP, which is only sampled by the S, contributes most of the travel time change of S after correcting SKS or SS travel time anomalies.

The height of the Pacific LLVP determines the initial epicentral distance of the δtS jump, at which the corresponding S wave starts to sample the top of the LLVP. Supplementary Fig. 2c shows that the initial epicentral distance where δtS increases is identical for different corrections. Therefore, whether the SKS or SS correction is applied, the height of the Pacific LLVP is a robust result. We do notice that δtSKS are slightly larger than δtSS by ~0.5–1 s. Thus, depending on which reference phase is chosen, the absolute value of the δVS of the LLVP can vary. For example, compared to SKS as the reference phase, if we use SS as the reference, the velocity perturbation is smaller (~1% less reduction of δVS) assuming the same geometry of LLVP.

### Synthetic seismograms

For most cases, we perform 3D wave propagation calculations using the SPECFEM3D GLOBAL package61 with the shortest period at ~8 s. Thus, we focus on modeling the data at the period of 10–50 s. For the N-S profile, we also apply a 2D finite-difference code, which has been widely used to generate 2D global synthetics at high frequency with high efficiency29. The grid spacing in the 2D run is 2 km, which allows accurate simulation up to 3 Hz. Hence for 2D simulations we generally bandpass filtered data from 5–50 s. We apply the same processing procedures as for the data. The focal mechanisms used in the simulations are selected from the USGS earthquake catalogue (http://earthquake.usgs.gov) and the Global Centroid-Moment-Tensor (CMT) solutions (https://www.globalcmt.org).

### Misfit between data and synthetics

The definition of the misfit function, the misfit between data (D) and synthetics (S), quantifies how well we model the data. Here, we first calculate the average normalized cross-correlation coefficient (CC) to evaluate the goodness of waveform fit between data and synthetics as:

$${CC}=\frac{1}{M}\mathop{\sum }\limits_{j}^{M}\left(\frac{1}{N}\mathop{\sum }\limits_{i}^{N}{{CC}}_{i}(D,S)\right)$$
(1)

where N is the number of traces for each event and M is the number of events.

For the N-S profile, the CCs are calculated within a time window of 20 s before S and 20 s after the ScS predicted by IASP91 (Supplementary Fig. 7). For the W-E profile, the time window is fixed as 20 s before and 80 s after Sdiff to include the postcursors as shown in the shaded region in Fig. 5.

In full-waveform inversions, a typical approach is to use the L2 norm of waveform difference between data and synthetics as the misfit function. Thus, we also use L1-norm and L2-norm as misfit function to examine trade-offs between δVS and H in the 3D simulations (Supplementary Figs. 13, 14). For an individual event, the L1-norm misfit is defined as

$${\sigma }_{L1}=\frac{1}{{{{{{\rm{N}}}}}}}\mathop{\sum }\limits_{i}^{N}{\int _{t0}^{t1}}\left|{D}_{i}(t)-{S}_{i}(t)\right|{dt}$$
(2)

and the L2-norm misfit is defined as

$${\sigma }_{L2}=\frac{1}{{{{{{\rm{N}}}}}}}\sqrt{\mathop{\sum }\limits_{i}^{N}{\int _{t0}^{t1}}{({D}_{i}(t)-{S}_{i}(t))}^{2}{dt}}$$
(3)

where N is the number of traces. Here, both Di and Si are aligned and normalized to the S and Sdiff for the N-S and W-E profile, respectively. The time window selections of [t0, t1] in the L1-norm and L2-norm calculations are the same as that in the calculation of CC.