Evaluation of 1-D and 3-D seismic models of the Pacific lower mantle with S, SKS, and SKKS traveltimes and amplitudes

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1 JOURNAL OF GEOPHYICAL REEARCH: OLID EARTH, VOL. 8,, doi:./jgrb.4, 3 Evaluation of -D and 3-D seismic models of the Pacific lower mantle with, K, and KK traveltimes and amplitudes Michael. Thorne, Yang Zhang, and Jeroen Ritsema Received eptember ; revised December ; accepted December. [] In this study, we analyzed the seismic phases, K, and KK from 3 deep-focus earthquakes in the Tonga-Fiji region recorded in North America between epicentral distances of 8 and. The differential traveltimes and amplitude ratios for these phases reveal clear epicentral distance trends not predicted by standard one-dimensional (-D) reference Earth models. The increase of the /K amplitude ratio up to a factor of is accompanied by an increase of the -K differential traveltime of up to s. KK-K differential traveltimes of 3 s and KK/K amplitude ratios of a factor of 4 across the epicentral range have maxima near 7. We examined these observations using full (-D and 3-D) waveforms for three -D seismic velocity profiles for the central Pacific region and for the tomographic model 4RT including modifications: different regularization parameters, great-circle path azimuthal variation, strength of wave velocity perturbations, wave velocity gradients in the lower mantle, and ultra low velocity zones. To explain these data, we constructed a hybrid model that combines both features of 4RT and short-wavelength features from the -D profiles. The large-scale seismic structure is represented by 4RT. Embedded within 4RT are a km thick ultra low velocity zone at the core-mantle boundary near the source side and a km thick negative velocity gradient zone near the receiver side of the paths. Our analysis demonstrates that the wave velocity structure of the Pacific large low shear-velocity province cannot be interpreted solely by global tomographic or regional modeling approaches in exclusion of each other. Citation: Thorne, M.., Y. Zhang, and J. Ritsema (3), Evaluation of -D and 3-D seismic models of the Pacific lower mantle with, K, and KK traveltimes and amplitudes, J. Geophys. Res. olid Earth, 8, doi:./jgrb.4.. Introduction [] eismic modeling of the lower mantle can be characterized by two approaches. The first approach involves imaging the large-scale (> km) three-dimensional (3-D) structure of the Earth s interior by tomographic and forward modeling of high-amplitude phase traveltimes and normalmode frequencies. These 3-D images provide a global perspective revealing two broad, low seismic velocity anomalies in the lower mantle [e.g., Garnero and McNamara, 8; Dziewonski et al., ]. These regions have been termed large low shear-velocity provinces (LLVPs) and exist above the core-mantle boundary (CMB) beneath the central Pacific Ocean and Africa [e.g., He and Wen, 9]. Recent studies show they have relatively sharp margins extending from the CMB to at least km into the mantle [e.g., To et al., ; Takeuchi et al., 8; un et al., ]. These LLVPs may be piles of compositionally distinct material [e.g., Ni Department of Geology and Geophysics, University of Utah, alt Lake City, Utah, UA. Department of Earth and Environmental ciences, University of Michigan, Ann Arbor, Michigan, UA. Corresponding author: M.. Thorne, Department of Geology and Geophysics, University of Utah, alt Lake City, Utah, UA. (michael.thorne@utah.edu) 3. American Geophysical Union. All Rights Reserved /3/./jgrb.4 and Helmberger, 3; Trampert et al., 4; Bull et al., 9] or signatures of thermal upwelling [e.g., chuberth et al., 9; immons et al., 9; Davies et al., ]. [3] The second seismic approach involves waveform modeling and array processing of low-amplitude signals. This approach typically renders one-dimensional (-D) profiles of seismic velocity for well-sampled mantle regions. The profiles reveal mantle layering [e.g., Russell et al., ] due to the mineral phase changes [e.g., Hernlund et al., ; Lay et al., 6], the presence of melt layers [e.g., Williams and Garnero, 996; Hernlund and Tackley, 7; Hutko et al., 9], and the shear-wave anisotropy [e.g., Pulliam and en, 998; Ford et al., 6]. ee Rost and Thomas [9] and Lay and Garnero [] for reviews. [4] Frequently, seismologists assume that the tomographic images and the wave speed profiles provide complementary views in which fine-scale (< km) layering of D is embedded within the large-scale (> km) convecting lower mantle. As an example, Figure shows -D and 3-D images of the lower mantle beneath the Pacific Ocean. In Figure a, an W NE-oriented cross section through tomography model 4RT [Ritsema et al., ] shows the Pacific LLVP extending from the CMB halfway into the mid-mantle between Tonga-Fiji and North America. Figure b shows the Preliminary Reference Earth Model (PREM) [Dziewonski and Anderson, 98] and three other -D wave velocity profiles for the lower mantle beneath the central Pacific Ocean.

2 a) Cross-section 4RT (T) o o 3 o 6 KK K 3 -wave velocity variation from -D (%) Depth (km) 4 6 PREM M L KG -6 -wave velocity perturbation (%) Figure. Event-receiver geometry, with the average great circle path indicated by the light blue line. The events (white stars) and receivers (yellow triangles) are from the Fiji- Tonga and North America regions, respectively wave velocity (km/s) CMB Figure. (a) hear velocity perturbation from PREM in a vertical cross section (T) through the mantle according to model 4RT [Ritsema et al., ]. The cross section T includes the Fiji-Tonga source region (indicated by the star) and North America. The solid, dashed, and dotted lines are, K, and KK raypaths for epicentral distances of 9,, and 3 calculated using the M [Ritsema et al., 997] velocity profile. (b) hear-velocity profiles for (black) PREM [Dziewonski and Anderson, 98], (blue) M [Ritsema et al., 997], (red) L [Lay et al., 6], and (green) KG (Kawai and Geller, ) for the Central Pacific. The discontinuities, velocity gradients, and absolute wave velocities in M [Ritsema et al., 997], L [Lay et al., 6], and KG [Kawai and Geller, ] have been attributed to phase transitions in perovskite and anomalous thermal gradients at the base of the Pacific LLVP [e.g., Tsuchiya et al., 4; Hernlund et al., ; Tsuchiya and Tsuchiya, 6]. [] In this paper, we illustrate how traveltimes and amplitudes can be influenced by both large- and fine-scale seismic heterogeneity. We focus on the trans-pacific cross section of the lower mantle shown in Figure, which has been studied thoroughly thanks to the large number of high-quality recordings of deep-focus earthquakes in the Fiji-Tonga region at seismic networks across Canada and the United tates. The cross section shown in Figure cuts through the center of the Pacific LLVP as shown in Figure. We hypothesize that the LLVP in Figure a and the -D velocity profiles of Figure b are models of the same low velocity structure and that the profound differences in the dimensions are accentuated by the different modeling procedures. [6] We test our hypothesis by analyzing waveform predictions for the -D profiles, 4RT, and a series of modifications to 4RT. We evaluate how the traveltimes and amplitudes of, K, and KK depend on () the applied regularization to 4RT, () the great circle path azimuthal variation, (3) the radial wave velocity gradients in D, (4) the magnitude of wave velocity anomalies tomographically recovered, and () the influence of ultra low velocity zone (ULVZ) layering.. Traveltimes and Amplitudes [7] We analyzed traveltimes and amplitudes of the seismic phases, K, and KK recorded in North America. The raypaths of, K, and KK are shown in Figure a for the entire epicentral distance range considered in this study. In the lower mantle, the direct wave passes through the center of the LLVP and propagates nearly parallel to the CMB in D with a path length greater than roughly km for epicentral distances larger than. KK also passes through the LLVP but intersects D at a relatively steep angle. K is steeper than KK and skirts the southwestern margin of the LLVP. [8] We analyzed traveltime differences and amplitude ratios of KK and relative to K. Relative traveltime and amplitude ratios are not strongly influenced by uppermantle heterogeneity, earthquake mislocation, or uncertainties in the seismic moment tensor. Using K as a reference phase, we denote the traveltime differences as

3 and and d ¼ T K obs ref T K ; () dkk ¼ TKK K obs ref TKK K : () [9] The amplitude ratios are defined as d ¼ log A obs A ref log ; (3) K K A obs KK A ref KK dkk ¼ log log : (4) K K [] The reference (i.e., second) terms in the right-hand side of equations (), (), (3), and (4) are computed using PREM [Dziewonski and Anderson, 98] and Global CMT source parameters. Thus, traveltime differences and amplitude ratios are defined as anomalies with respect to PREM. Values of dt and da equal to mean that the measurements are identical to PREM predicted values... Fiji-Tonga Recordings in North America [] We analyzed data from 3 events (99 7) in the Tonga-Fiji region with moment magnitudes larger than 6 (Table ) and focal depths greater than 3 km. The event epicenters have latitudes between 3 and 3 and longitudes between 7 E and 76 W (Figure ). We analyzed the broadband seismograms of these events recorded at the Transportable Array, ANA Backbone, IRI/GN, CNN, TriNET, BDN, and PACAL networks in North America at epicentral distances between 8 and 3 and source azimuths between 3 and 6. However, most stations in the United tates are within the azimuth range of 4 6. [] Data processing steps include low-pass filtering (T > s), instrument deconvolution, and rotation to radial (R) and transverse (T) components. We inspected all traces visually to select waveforms without obvious source complexity. [3] Recorded and synthetic waveforms for the Tonga-Fiji earthquake of 6 October 7, M W = 6.6, at stations CMB (84.7 ), CCM (4.6 ), and HRV (. ) are shown in Figure 3. These records show the prominent waveform characteristics of our data set. Namely,, K, and KK arrivals are delayed with respect to PREM predictions. In addition, the wave is recorded with an anomalously large amplitude on the radial component. These waveform a) Columbia College, CA (CMB) K = 84.7 o Radial Transverse Table. Fiji-Tonga Earthquakes Date Latitude ( ) Longitude ( E) Depth (km) M W 3 December July April August March October January April August October May eptember January March May June January May June August April June August January October October January April July July February b) Cathedral Cave, MO (CCM) = 4.6 o K K KK c) Harvard, MA (HRV) =. o KK diff Figure 3. An example of (solid lines) recorded and (dashed lines) synthetic waveforms (velocity) of K, KK, and waves at stations (a) CMB, (b) CCM, and (c) HRV for the 6 October 7 (H = km, M W = 6.6) Fiji Islands earthquake. The radial components are plotted above the transverse component waveforms. 3

4 attributes are indicative of, K, and KK having propagated through a low-velocity structure... KK-K and KK/K [4] The measurements of dkk traveltimes and dkk amplitudes are obtained by cross-correlating 3 s long waveforms centered on K and KK. The KK waveform is Hilbert transformed to account for its p/ phase shift with respect to K. Errors in the measurement have been evaluated following Tanaka []. We obtained 477 measurements of dkk and dkk for epicentral distances larger than 9 when KK is well developed and separated from K. [] Figures 4a and 4b show the variation of dkk and dkk as a function of epicentral distance. dkk is positive over the entire distance range increasing to a peak value of approximately. at an epicentral distance of 7. The dkk values are also primarily positive, indicating that KK is delayed more than K. These measurements also peak near an epicentral distance of K and /K [6] At diffraction distances (> for our study region), -arrivals on the T component (denoted as H) broaden and -arrivals on the R component (denoted as V) have complex wave shapes, thus complicating traveltime and amplitude measurements by waveform correlation. Therefore, we measured d traveltimes (Figure 4c) using H and K onsets and d (Figure 4d) from V and K peak amplitudes [see also Ritsema et al., 997]. Corrections for upper mantle anisotropy have been made using the K splitting tables of chutt and Humphreys []. d and d have been measured beginning at 8 and 9, respectively. We obtained 74 measurements of d and 83 measurements of d. Both d and d increase monotonously with increasing epicentral distance. d increases from at 8 to ~. at a distance of. 3. Modeling [7] To understand the observed trends in traveltimes and amplitudes, we analyzed a selection of recently published -D profiles and 3-D models derived for the central Pacific region from waveform modeling and tomographic inversion approaches. The models are primarily constrained by broadband recordings in North American from Fiji-Tonga earthquakes and thus sample the same mantle cross section as shown in Figures and a. 3.. One-Dimensional Models [8] We considered the three -D profiles of wave velocity for the central Pacific region, depicted in Figure b and discussed in ection. Profile M [Ritsema et al., 997] was derived from a similar but smaller collection of d and d measurements than used in this study. M is identical to PREM to a depth of km. Below km, M is composed of two linear segments. In the upper segment, the wave velocity decreases linearly to a value.% smaller than PREM at 7 km depth. Below 7 km depth, the wave velocity decreases to a value that is 3% lower than PREM at the CMB. [9] Model KG [Kawai and Geller, ] is based on waveform inversion of and c waveforms. The wave velocity is identical to PREM to a depth of km. Below km depth, the wave velocity profile has alternating negative and positive gradients. The wave velocity decreases from 7.8 km/s (the PREM value) at approximately 47 km depth to 6.99 km/s at approximately 47 km depth. Between 47 km and 89 km, the velocity increases from 6.99 to 7.4 km/s. In the lowermost 7 km of the mantle, the wave velocity decreases to 7. km/s at the CMB, a value that is 3.6% lower than the PREM value. [] Profile L is from Lay et al. [6], who analyzed the wave velocity beneath the central Pacific region from stacks of c precursors. In this study, three velocity profiles were determined based on c bounce point locations on the CMB. Model L is the second of these three velocity profiles a) KK c) KK b) KK d) KK o 9 o o o o 3 o 8 o 9 o o o o 3 o Epicentral distance (deg) Figure 4. Measurements (gray circles) and average values (including s uncertainties), determined in wide overlapping bins, of (a) dkk, (b) dkk, (c) dkk, and (d) d. 4

5 for a 4 km wide sampling region of the lowermost mantle. The wave velocity structure of L is similar to M but includes several discontinuous wave velocity increases (.6% at 6 km depth) and decreases (.% at km,.6% at 8 km, and.% at 86 km depth). 3.. Three-Dimensional Models [] We analyzed a cross section (which we call T) through 4RT [Ritsema et al., ], shown in Figure a. The midpoint of T is at 4 N and W and the great-circle arc crosses the meridian at this midpoint at an angle (i.e., azimuth) of 6 clockwise from North. [] We also analyzed several modifications to T, summarized in Table and shown in Figure. In models T H and T H, the wave velocity anomalies are set to be zero within the source side (from to 9 ) and receiver side (from 9 to 8 ) of the cross section, respectively. T H and T H enable us to separate the influence of the LLVP and the wave velocity structure beneath the northeast Pacific and North America on the observed traveltime and amplitude anomalies. [3] The cross sections T D and T D are based on 4RT inversions with different applied damping factors. These models let us determine whether the amplitude and traveltime anomalies depend on the strength of wave velocity anomalies in tomographic inversions. T D is damped more and T D is damped less than T. Therefore, the wave velocity variations in T D and T D are about a factor of two weaker and stronger than that in T, respectively. In addition, the wave velocity variations are smoothest in T D. However, T D, T D, and T yield comparable fit within error to the same data set used in the tomographic inversion. For additional discussion, see Ritsema et al. [7]. [4] Data used in this study are associated with sourcereceiver paths for a range of azimuths. However, model prediction of traveltimes and amplitudes are based on axisymmetric velocity structures as discussed in the next section. To examine the variability of the amplitude and the traveltime anomalies due to the 3-D nature of wave velocity variations in the lower mantle, we computed waveforms for slightly different cross section through 4RT. Models T A and T A are cross sections drawn with more northerly azimuths of, respectively, 4 and. Table. Models 3-D Models Remarks 4RT (see Figure b) T H T but dv = from to 9 T H T but dv = from 9 to 8 T A 4RT with azimuth 4 T A 4RT with azimuth T D 4RT inversion damped weakly T D 4RT inversion damped strongly T.7 Negative velocities scaled by.7 T. Negative velocities scaled by. T 3. Negative velocities scaled by 3. -D Models M Ritsema et al. (997) L Lay et al. (6) KG Kawai and Geller () Hybrid Models T HYB T plus ULVZ plus M (from 4 to 6 ) [] Previous efforts have suggested that the magnitude of velocity anomalies resolved in tomographic studies is underestimated. For example, Ni et al. [] scaled tomography model TXBW [Grand, 994], by a factor of 3. to model c precursors. We also tested the strength of wave velocity anomalies resolved in 4RT by multiplying the negative velocities in cross section T by a constant value. Models T.7, T., and T 3. are scaled by.7,., and 3. times, respectively PVaxi and Haxi ynthetics [6] The advent of relatively cheap computer clusters has spurred the development of techniques that are capable of solving the seismic wave equation for complex -D and 3-D structures on the global scale. For example, the -D hybrid approach of computing synthetic seismograms [e.g., He and Wen, 9], the -D pseudo-spectral approach [e.g., Rondenay et al., ; Cormier, ; Furumura et al., 998] and the 3-D pectral-element Method (EM) approach [To et al., ; Ni et al., ] have been used to investigate LLVP geometry. [7] Here we used the Haxi method [Jahnke et al., 8] and its P-V companion PVaxi [based on the method of Igel and Weber, 996] to compute the full seismic wavefield of P-V and H motions with the correct 3-D geometric spreading. In Haxi and PVaxi, the computation is performed on a -D grid in the plane of the great-circle arc. The -D grid of heterogeneity is expanded to a 3-D spherical geometry by rotating the grid around the radial axis passing through the seismic source. [8] This technique is, from a computational point of view, significantly cheaper than a full 3-D approach such as the EM [e.g., Komatitsch and Tromp, ]. The computation of synthetic seismograms at frequencies relevant to body waves (<. Hz) can be computed rapidly on modest computing resources. In this study, we computed synthetic seismograms with 7 s dominant periods, which is similar to the dominant period of broadband seismograms investigated. PVaxi and Haxi has been used in studies of the D discontinuity [e.g., Thorne et al., 7], global seismic scattering [Jahnke et al., 8], crustal structure [Yang et al., 7], and ULVZ structure modeling [Zhang et al., 9]. 4. Results 4.. One-Dimensional Models [9] Figure 6 shows the fit tod and d by models M, KG, and L. As demonstrated previously by Ritsema et al. [997], the negative wave velocity gradient in the lowermost km of the mantle (in M) explains the increase of d and d with increasing distance. The high V amplitudes are the result of the late onset of wave diffraction. In PREM, waves begin to diffract at a distance of (for a km deep earthquake). Diffraction begins at a larger epicentral distance of for model M. The onset of diffraction at a relatively large distance is also evident from the relatively sharp H waveforms seen at distances larger than [Ritsema et al., 997] (see also Figure 3). The increase of d with distance is due to relatively slow wave propagation through D.

6 THORNE ET AL.: EIMIC TRUCTURE OF THE PACIFIC MANTLE a) TH b) TH c) TD d) TD e) TA f) TA g) T.7 h) T3. -wave velocity variation from -D -% +% Figure. Cross sections (a) TH, (b) TH, (c) TD, (d) TD, (e) TA, and (f)ta. ee also Table. a) b) AKK.. M L A AKK A. -. KG -. c) - 8o T T TKK d) TKK 9o o o o 3o - 8o 9o o o o 3o Epicentral distance (deg) Figure 6. Observed values (Figure 4) and model predictions of dakk, da, dtkk, and dt for -D profiles M [Ritsema et al., 997], L [Lay et al., 6], and KG [Kawai and Geller, ]. 6

7 [3] M underestimates d between 8 and. This indicates that the arrival is influenced by a low wave velocity zone above the turning depth of waves at 8 (i.e., km). This is well above M s low-velocity layer in the lowermost (7 89 km) mantle. [3] Model L also predicts the increase of d and d with distance since it includes a low-velocity zone in the lowermost mantle with an overall vertical structure akin to M. The negative wave velocity gradient in L is weaker than in M. Hence, the increase in d and d at distances larger than is underestimated by L. ince the low velocity layers in L are, like M, confined to depths larger than 7 km, L also fails to explain the positive d values for the shortest distances. The discontinuous jumps in L do not affect the traveltimes and amplitudes. [3] Model KG does not predict the increase with distance of either d or d. Although wave velocities in KG are lower than that in L and M, model KG misses a negative gradient in the lowermost mantle that is necessary to postpone the onset of wave diffraction and hence to boost amplitudes. The drop in d between and is related to the strong positive wave velocity gradient between 6 and 8 km depths in KG. This is a model prediction that is inconsistent with the observations. However, in contrast to M and L, model KG explains the positive d values for the shortest distances since KG incorporates a strong wave velocity reduction near the wave turning point between 8 and. This observation points to the presence of wave velocity reductions above D. 4.. Three-Dimensional Models 4... The effects of the LLVP [33] Figures 7a 7d compares the observed amplitude and traveltime anomalies to the predictions for models T, T H, and T H. The predicted values for dkk are indistinguishable among the models, which demonstrates that large-scale variations of wave velocity in the mantle have little effect on KK and K amplitudes. [34] Model T H fails to predict the large wave delay, predicting a slight wave advance instead. The prediction of both T and T H match the traveltime observations, indicating that the traveltime delays are mostly due to the LLVP in the southwest Pacific. The LLVP in T (and T H ) predicts positive values of d, although the value of approximately 3 s near 8 is underestimated by both models. dkk and d are negative for T H. Thus, the predominantly high wave velocity structures beneath the northeastern Pacific and North America reduce the difference traveltimes by up to s. [3] The predicted values for d for T H are up to.3 larger than for T H (Figure 7c). This indicates that the LLVP enhances amplitudes of diffracted waves by perturbing wave paths through the lower mantle. Nevertheless, models T and T H underestimate d considerably. It is therefore clear that the LLVP as imaged by 4RT does not significantly distort wave paths in a manner that would enhance the amplitudes of diffracted waves The Effects of Damping [36] The effects of variable tomographic damping is illustrated in Figure 7e h. The traveltime and amplitude anomalies are slightly larger for model T D with the weakest damping and thus largest wave velocity anomalies. The traveltime anomaly dkk differs most among the models. For model T D, dkk is up to 3 s higher than model T D. This demonstrates that the KK and K traveltime difference is influenced by the contrast in wave velocities at the southwestern margin of the Pacific LLVP. [37] d and d are, respectively, s and. times smaller for T D. However, the overall trends in the amplitude and traveltime predictions are similar. Therefore, an uncertainty in the strength of the wave velocity anomalies in tomographic models does not significantly influence the interpretation of trends observed in our collection of differential traveltimes and amplitude ratios The Effects of Azimuth [38] imilar to the effect of tomographic damping, the predicted traveltime and amplitude anomalies change little if they are computed for cross sections with slightly different azimuths. The most significant effect is seen for d. The wave velocity reduction within the LLVP is lowest in T A. Therefore, shear waves propagating through the LLVP as imaged by T A are not as strongly delayed as for T A and T, and thus d are up to s smaller. Despite the different shape of the LLVP in cross section T A,the traveltimes and amplitude ratios are virtually identical for T A and T The Effects of Velocity caling [39] The effects of scaling the low wave velocities in T by a constant are shown in Figures 7i 7l. The stronger wave velocity reductions produce large KK and traveltime delays with respect to K. For each of the models tested, d is larger than the observed anomalies, yet the monotonic increase in d is not reproduced.. A Hybrid Model [4] The model comparisons from sections 4. and 4. demonstrate that both large-scale structure (Figure a) and finescale layered structure (Figure b) contribute to the traveltime and amplitude anomalies. Thus, we propose a hybrid model (T HYB, shown in Figure 8) for the Pacific lower mantle that incorporates the key attributes of the models. T HYB explains the linear increase of d and d, the positive value of d at relatively short distances, and the positive values of dkk and dkk. Results are summarized in Figures 8b 8e. [4] The increase of d to s at and of d to. require the presence of a negative wave velocity gradient in the lowermost mantle. In T HYB, we included an M wave velocity profile for the lowermost km of the mantle, which is confined to the northeastern edge of the LLVP (in the epicentral distance range from 4 to 6 ). We applied the M velocity structure in this limited angular distance range such that diff raypaths interact with this negative velocity gradient, yet we do not allow the extent of the M structure to extend beyond the northeast boundary of the LLVP. Because this M structure has a limited lateral extent, d and d are underestimated beyond. Extending the M structure to an angular distance of 7 increases both d and d. Nevertheless, at the largest epicentral distances, these data are still underestimated. Further investigation is required to reproduce these data at the largest distances, and here we just show results where M extends to the LLVP boundary. 7

8 KK KK KK KK KK KK o 9 o o o o 3 o - 8 o 9 o o o o 3 o Damping Effect (models T D and T D ) o 9 o o o o 3 o THORNE ET AL.: EIMIC TRUCTURE OF THE PACIFIC MANTLE tructural Effect (models T H and T H ) a) KK b) c) KK d) e) KK f) g) KK h) - 8 o 9 o o o o 3 o T T H T H T T D T D - 8 o 9 o o o o 3 o Velocity caling Effect (models T.7, T.,and T 3. ) i) KK j) k) KK l) Epicentral distance (deg) T T.7 T. T o 9 o o o o 3 o Figure 7. Measurements and model predictions of (a, e, i) dkk, (b, f, j) d, (c, g, k) dkk, and (d, g, l) d. Blue lines are the traveltime and amplitude predictions for T. The red lines are the prediction for T H (in a, b, c, d), T D (in e, f, g, h), and T. (in i, j, k, l). The green lines are the prediction for T H (in a, b, c, d), T D (in e, f, g, h), and T 3. (in i, j, k, l). The black lines are the prediction for T.7 (in i, j, k, l). [4] The anomaly of d of +3 s near 8 indicates a reduction of the wave velocity well above D. Model KG explains this anomaly and, as a -D model, places the wave velocity reduction at the wave turning depth of km. However, we argue that the delay is due to the LLVP. For 8, the wave propagates along a roughly km long path through the center of LLVP whereas the K wave (the reference phase in the d measurement) skirts the southwestern margin of the LLVP and is not delayed as strongly as. At 8, the d measurements are slightly improved by T HYB but are still underestimated. A slight decrease of the wave velocity in the LLVP may account for this difference as indicated by the constant velocity scaled models (Figure 7). [43] The effect of the LLVP on traveltimes is also clear from the dkk data. None of the -D models explain the positive values of dkk. imilar to our interpretation of d at 8, we interpret the positive values of dkk to 8

9 a) Cross-section T HYB 9 o o 3 o M K b) KK d) KK T T HYB ulvz -wave velocity variation from -D -% +% KK c) KK e) - 8 o 9 o o o o 3 o Epicentral distance (deg) - 8 o 9 o o o o 3 o Figure 8. Measurements and model predictions of (a) dkk, (b) d, (c) dkk, and (d) d. The predictions are determined for cross sections (blue) T and (red) T HYB. the relatively long propagation paths of KK through the center of the LLVP. [44] None of the -D or 3-D models previously considered have an appreciable effect on dkk. To explain dkk anomalies, we refer to the modeling of Zhang et al. [9]. They explained the increase in dkk by the early onset of PdK diffraction at the critical K refraction angle, consistent with the difference time between PdK and K [Garnero and Helmberger, 998]. They showed that high dkk values can be explained by a source-side ULVZ at the base of the mantle with a thickness of km and an wave velocity reduction of 3%. In T HYB,we include a ULVZ, as modeled by Zhang et al. [9], embedded at the base of the LLVP at the core-entry point of K. This ULVZ is km thick and has 3% wave velocity reductions. It does not strongly delay the K arrivals as K traverses the ULVZ at a steep angle. 6. Discussion and Conclusions [4] eismic studies of the lower mantle can be classified by tomographic and waveform modeling approaches. Lowresolution or long-wavelength (> km) tomographic models are designed to explain global sets of traveltimes and only provide a large-scale perspective of velocity variations in the mantle. These models suffer in explaining amplitude variations of seismic phases due to the presence of strong velocity gradients or discontinuities. High-resolution or short-wavelength models based on regional waveform data are capable of recovering amplitude and rapid traveltime variations. While the waveform modeling approach may provide seismic velocity models at a much finer scale than tomographic models, the models are generally limited to a single sampling region and are -D in nature. Asymmetric velocity structure in the mantle, as present in the central Pacific region, can bias these models. [46] In this paper, we have illustrated how a basic seismic data set can be affected by both large- and fine-scale structure. We have analyzed differential traveltimes for - K (d ), KK-K (dkk ), and the amplitude ratios /K (d ) and KK/K (dkk ) referenced to the PREM model (Figure 4). A large amount of scatter exists in these data, but they also reveal clear epicentral distance trends. The scatter is likely caused by small-scale structure in the lower mantle because earthquake mislocation and velocity heterogeneity in the uppermost mantle do not contribute strongly to the measured differential traveltimes. For example, variations in d and dkk exceed 3 s for a given distance, which far exceeds expected signal from upper mantle sources for these differential seismic phase pairs. As simulated traveltimes and amplitudes for the range of tomographic models and -D velocity profiles tested in this study (Figure 7) reproduce only a fraction of the observed variability, it is also unlikely that the observed scatter is due to large-scale structural features. [47] The epicentral distance variation of the differential traveltimes and amplitude ratios is due to both the largescale structure of the lower mantle and fine-scale layering 9

10 in D. Nonzero values of dkk and d (at 8 ) cannot be explained by -D seismic profiles. Using 4RT as a guide (Figure ), we associate the delays of and KK with respect to K to the presence of the Pacific LLVP. and KK propagate through the center of the Pacific LLVP while K skirts its southwestern margin. As a consequence, the LLVP slows down and KK but it has no, or a much smaller, effect on K. [48] The LLVP does not explain the anomalous d and dkk amplitude ratios. A minor increase in d can be accomplished by strengthening the shear-velocity reductions within the LLVP. Models T. and T 3., with and 3 stronger LLVP velocity reductions than 4RT, respectively, match d up to (Figure 7j). However, these models do not reproduce the monotonic increase of d, and they overpredict d for all distances. It is much more likely that an wave gradient in D is responsible for the high wave amplitudes. Model M, which includes a negative wave velocity gradient in D, explains both the high wave amplitudes and the delayed d traveltimes. waves propagating through an M structure begin to diffract around the core at an epicentral distance of approximately (instead of for PREM). As a consequence, the amplitudes of V do not decay as quickly as for PREM (hence d is anomalously high). [49] We interpret the anomalous values of dkk to a km thick ULVZ at the base of the mantle, which separates PdK from K [e.g., Garnero et al., 998; Thorne and Garnero, 4] at an earlier distance than that in PREM and causes the K amplitude to drop [Zhang et al., 9]. This region is also noted for strong scattering of short-period arrivals (e.g., PKP, PKKP) [Cormier,;Hedlin and hearer, ], which may also be linked to ULVZs. It must be emphasized, however, that a significant portion of the lower mantle is as yet unexplored for potential scatterers and their relation to ULVZs. [] Our work implies that the interpretation of -D and 3-D images of the mantle is difficult. Many interesting observations have been made regarding the nature of and/or consequences of LLVPs. For example, Garnero and McNamara [8] suggested that ULVZs may be concentrated at the edges of LLVPs. This suggests a relationship between LLVPs and dynamic processes such as the formation of plumes. Yet, it is questionable whether boundaries between high and low wave velocities in tomographic images such as 4RT represent sharp edges of LLVPs. In T HYB,we place the M structure in a limited angular range based on the lateral extent of the LLVP in 4RT. However, T HYB does not match d and d for distances larger than, possibly because the edge of the LLVP is located further to the northeast than imaged in 4RT. [] imilarly, seismic modeling using -D profiles can be biased by the presence of 3-D seismic velocity heterogeneity. Model KG [Kawai and Geller, ] has a velocity reduction of approximately.8% at the depth of km. This feature explains the delay of c with respect to as analyzed by Kawai and Geller [] and the delay of d at 8 as discussed in this paper. Kawai and Geller [] interpreted this strong low velocity zone as due to phase transitions in the mineral structure of pervoskite. Alternatively, the c- and -K delays may be related to the LLVP that has a stronger effect on than c and K. [] Large-scale mantle structure, as resolved through tomographic efforts, causes regional-scale traveltime variability; thus, studies analyzing fine-scale structure within D cannot exclude these large-scale mantle features. Conversely, the fine-scale structures imaged through forward modeling approaches are capable of explaining relative amplitude measurements that are not currently captured in the tomographic models. Full 3-D waveform tomographic approaches are being developed [Hara, 4; Tape et al., 9; Fichtner et al., 9]. However, on the global scale, these are still limited to relatively low-frequencies given the computational demands. To capture both the large-scale and small-scale seismic structure of the mantle, as discussed here for the Pacific, it is likely that the modeling of high-frequency body wave signals must involve iterative forward modeling. Overall, we recommend a combined approach of analyzing both traveltime and amplitude ratios to capture the real velocity of structure of the CMB region. Although extensive forward modeling is required to arrive at hybrid models as presented in this paper, we emphasize that the wave velocity structure of the Pacific lower mantle cannot be fully described by either global tomographic or regional modeling approaches in exclusion. [3] Acknowledgments. 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