Seismic velocity and attenuation structures in the top 400 km

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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111, B07308, doi:10.1029/2005JB003995, 2006

Seismic velocity and attenuation structures in the top 400 km
of the Earth’s inner core along equatorial paths
Wen-che Yu1 and Lianxing Wen1
Received 11 August 2005; revised 25 April 2006; accepted 1 May 2006; published 27 July 2006.
[1] We study seismic velocity and attenuation structures in the top 400 km of the Earth’s inner core based on modeling of differential traveltimes, amplitude ratios, and waveforms of the PKiKP-PKIKP phases observed at the epicentral distance range of 120°–141° and the PKPbc-PKIKP phases observed at the distance range of 146°–160° along equatorial paths. Our data are selected from the seismograms recorded in the Global Seismographic Network from 1990 to 2001 and many regional seismic networks. The observed PKiKP-PKIKP and PKPbc-PKIKP phases exhibit distinctive ‘‘east-west’’ hemispheric patterns: (1) At the distance ranges of 131°–141° and 146°–151°, PKIKP phases arrive about 0.3 s earlier than the theoretical arrivals based on the Preliminary Reference Earth Model (PREM) for the PKIKP phases sampling the ‘‘eastern hemisphere’’ (40°E–180°E) of the inner core and about 0.4 s later for those sampling the ‘‘western hemisphere’’ (180°W–40°E). At the distance range of 151°–160°, PKIKP phases arrive about 0.7 s earlier than the predicted arrivals based on PREM for those sampling the eastern hemisphere and about 0.1 s later for those sampling the western hemisphere. (2) Amplitude ratios of the PKIKP/PKiKP phases at the distance range of 131°–141° and of the PKIKP/PKPbc phases at the distance range of 146°–151° are, in general, smaller for the PKIKP phases sampling the eastern hemisphere than for those sampling the western hemisphere. At distances greater than 151°, the PKIKP/PKPbc amplitude ratios become indistinguishable for the two hemispheres. These observations can be best explained by two different types of seismic velocity and attenuation models along equatorial paths, one for each hemisphere, in the top 400 km of the inner core. For the eastern hemisphere, the velocity structure has a velocity increase of 0.748 km/s across the inner core boundary (ICB), a small velocity gradient of 0.0042 (km/s)/100 km in the top 235 km, followed by a steeper velocity gradient of 0.1 (km/s)/100 km extending from 235 km to 375 km, and a velocity gradient of 0.01 (km/s)/100 km in the deeper portion of the inner core; the attenuation structure has an average Q value of 300 in the top 300 km and an average Q value of 600 in the deeper portion of the inner core. For the western hemisphere, the velocity structure has a velocity increase of 0.645 km/s across the ICB and a velocity gradient of 0.049 (km/s)/100 km in the top 375 km; the attenuation structure has an average Q value of 600 in the top 375 km of the inner core. Our results suggest that the inner core hemispheric variations in velocity extend deeper than 375 km below the ICB and the top 235 km of the inner core in the eastern hemisphere is anomalous compared to the rest of the inner core in having a small velocity gradient, high velocity, and high attenuation.
Citation: Yu, W., and L. Wen (2006), Seismic velocity and attenuation structures in the top 400 km of the Earth’s inner core along equatorial paths, J. Geophys. Res., 111, B07308, doi:10.1029/2005JB003995.

1. Introduction [2] The seismic properties of the Earth’s inner core
exhibit complex patterns. They are constrained by two types of seismic observations: body wave and normal mode data.
1Department of Geosciences, State University of New York at Stony Brook, Stony Brook, New York, USA.
Copyright 2006 by the American Geophysical Union. 0148-0227/06/2005JB003995$09.00

Body waves, mostly the PKIKP (PKPdf) phases, are sensitive to the P wave velocity and attenuation structures of the inner core. Since Poupinet et al. [1983] first observed the polar PKIKP traveltime anomaly, the body wave studies have revealed various remarkable features of the Earth’s inner core: a magnitude of about 1 – 3% of velocity anisotropy with the fast direction parallel to the Earth’s rotation axis [Morelli et al., 1986; Creager, 1992; Song and Helmberger, 1993; Vinnik et al., 1994; Song, 1996; McSweeney et al., 1997; Sun and Song, 2002], the presence of a top

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isotropic layer overlying deep anisotropy [Shearer, 1994; Song and Helmberger, 1995a, 1998; Garcia and Souriau, 2000; Niu and Wen, 2001; Ouzounis and Creager, 2001; Niu and Wen, 2002] and a change of velocity anisotropy near the center of the inner core [Ishii and Dziewonski, 2002]. Inner core anisotropy also exhibits lateral variations from a hemispheric scale [Tanaka and Hamaguchi, 1997; Creager, 1999; Garcia and Souriau, 2000; Ouzounis and Creager, 2001; Niu and Wen, 2002] to a regional scale [Creager, 1997; Song, 2000]. Temporal variations of PKIKP traveltimes are also observed and are interpreted as caused by a differential motion of the inner core [Song and Richards, 1996; Creager, 1997; Song, 2000; Song and Li, 2000; Li and Richards, 2003; Zhang et al., 2005]. In addition to the anisotropic structure, seismic velocity structure along equatorial paths exhibits regional variations varying in different scales [Cormier and Choy, 1986; Kaneshima, 1996; Vidale and Earle, 2000; Niu and Wen, 2001; Wen and Niu, 2002; Stroujkova and Cormier, 2004; Koper et al., 2004]. The studies of the amplitudes and waveforms of the PKIKP phases also suggested complex features of the attenuation structure in the inner core, including its frequency dependence [Doornbos, 1983; Cormier et al., 1998; Li and Cormier, 2002], depth dependence [Doornbos, 1974; Cormier, 1981; Souriau and Roudil, 1995; Song and Helmberger, 1995b; Tseng et al., 2001; Li and Cormier, 2002; Cormier and Li, 2002], direction dependence [Souriau and Romanowicz, 1996, 1997; Cormier et al., 1998; Oreshin and Vinnik, 2004] and lateral variations [Tseng et al., 2001; Wen and Niu, 2002; Li and Cormier, 2002; Oreshin and Vinnik, 2004; Cao and Romanowicz, 2004a]. A recent study observed a ubiquitous correlation of high velocity with high attenuation, and suggested that the velocity attenuation correlation can be explained by attenuation anisotropy in the inner core [Yu and Wen, 2006]. In addition, precritical PKiKP amplitudes have been used to investigate the density contrast and the sharpness of the inner core boundary [Cummins and Johnson, 1988; Souriau and Souriau, 1989; Cao and Romanowicz, 2004b; Krasnoshchekov et al., 2005].
[3] The split of the normal modes of the Earth’s free oscillation provides another powerful probe to study the elastic properties and density of the inner core. Anisotropy, large-scale density and velocity anomalies, or structures departed from the spherical symmetry such as the Earth’s rotation or ellipticity of the Earth’s boundaries, would cause the singlet eigenfrequency to split. Anomalous splitting of the modes that are sensitive to the inner core structures was first identified by Masters and Gilbert [1981]. Subsequent studies of the normal modes indicated that the inner core anisotropy is a preferred explanation for the anomalous

splitting of those modes [Woodhouse et al., 1986; Tromp, 1993, 1995; Durek and Romanowicz, 1999; Ishii et al., 2002]. Anomalous splitting of the core sensitive modes has also been used to investigate the differential motion of the inner core [Laske and Masters, 1999] and the depth dependence of the anisotropy [Durek and Romanowicz, 1999; Beghein and Trampert, 2003].
[4] Recent seismic studies revealed ‘‘east-west’’ hemispheric variations in seismic isotropic velocity and attenuation in the uppermost 80 km of the Earth’s inner core [Niu and Wen, 2001; Wen and Niu, 2002; Garcia, 2002; Stroujkova and Cormier, 2004; Cao and Romanowicz, 2004a]. These studies indicated that the top portion of the inner core beneath the eastern hemisphere (40°E– 180°E) has higher velocities (about 0.8 –1.3% faster), a smaller velocity gradient, and higher attenuation than the western hemisphere (180°W – 40°E) [Niu and Wen, 2001; Wen and Niu, 2002; Garcia, 2002; Stroujkova and Cormier, 2004; Cao and Romanowicz, 2004a]. It is interesting to note that the velocity anisotropy observed in the deeper part of the inner core also exhibits a similar hemispheric pattern, with a large magnitude of anisotropy in the western hemisphere and a weak anisotropy in the eastern hemisphere [Tanaka and Hamaguchi, 1997; Song and Helmberger, 1998; Creager, 1999; Garcia and Souriau, 2000; Ouzounis and Creager, 2001; Niu and Wen, 2002]. It becomes important to establish one-dimensional seismic velocity and attenuation structures along equatorial paths (defined as the PKIKP ray angles are greater than 35° from the Earth’s rotation axis) in the top 400 km of the inner core for the two hemispheres for several reasons: (1) it remains unclear how deep the hemispheric variations in velocity and attenuation in the top portion of the inner core extend in the inner core; (2) seismic structures along equatorial paths serve as the baseline for understanding the magnitude of seismic anisotropy and the level of seismic heterogeneity; (3) seismic structures in the deeper portion of the inner core strongly depend on the inferred seismic structures in the top portion of the inner core, as the seismic waves sampling the deeper portion unavoidably propagate through the top portion of the inner core [Wen and Niu, 2002]; and (4) these inferred seismic structures would place fundamental constraints on the composition, geodynamics, and mineral physics of the inner core.
[5] In this paper, we establish seismic velocity and attenuation structures along equatorial paths in the top 400 km of the inner core for the eastern and western hemispheres, by studying the differential traveltimes, amplitude ratios, and waveforms of two core phase pairs sampling along equatorial paths. We discuss seismic data and coverage in section 2, detailed observations and seismic

Figure 1. (a) Ray paths of three PKP branches based on the Preliminary Reference Earth Model (PREM) [Dziewonski and Anderson, 1981]. PKIKP, PKiKP at an epicentral distance of 141°, and PKIKP, PKPbc at 147°. (b, c) Map view of great circle paths (gray lines) and ray segments of the PKIKP phases sampling the inner core (black lines) recorded by the Global Seismographic Network (GSN) (Figure 1b) and several regional seismic networks: Grafenberg (GRF), the German Regional Seismic Network (GRSN), GEOSCOPE, GEOFON, the Broadband Andean Joint Experiment (BANJO), the Brazilian Lithosphere Seismic Project (BLSP), the Seismic Exploration Deep Andes (SEDA), FREESIA, along with the GSN stations in Europe (Figure 1c). Stars and triangles represent locations of earthquakes and seismic stations, respectively. The geographic region of the two hemispheres is marked, with the eastern hemisphere defined between 40°E– 180°E and the western hemisphere defined between 180°W – 40°E.
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Figure 1
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Table 1. Event Lista

Event
19900220 19900322 19900508 19900517 19900728 19901104 19920416 19920528 19930110 19930209 19930224 19930502 19930530 19930608 19930826 19930929 19931008 19931011 19931019 19931110 19940506 19940813 19940822 19940830 19940831 19940930 19941018 19941109 19941124 19941218 19941230 19950115 19950120 19950121 19950218 19950318 19950325 19950331 19950408 19950502 19950518 19950525 19950623 19950707 19950817 19950818 19950823 19950824 19950824 19950912 19950918 19951014 19951210 19960507 19960526 19960530 19961025 19961114 19970311 19970401 19970401 19970411 19970412 19970420 19970503 19970826 19970928 19971005 19971008 19971022 19980127 19980325

Origin Date
1990/02/20 1990/03/22 1990/05/08 1990/05/17 1990/07/28 1990/11/04 1992/04/16 1992/05/28 1993/01/10 1993/02/09 1993/02/24 1993/05/02 1993/05/30 1993/06/08 1993/08/26 1993/09/29 1993/10/08 1993/10/11 1993/10/19 1993/11/10 1994/05/06 1994/08/13 1994/08/22 1994/08/30 1994/08/31 1994/09/30 1994/10/18 1994/11/09 1994/11/24 1994/12/18 1994/12/30 1995/01/15 1995/01/20 1995/01/21 1995/02/18 1995/03/18 1995/03/25 1995/03/31 1995/04/08 1995/05/02 1995/05/18 1995/05/25 1995/06/23 1995/07/07 1995/08/17 1995/08/18 1995/08/23 1995/08/24 1995/08/24 1995/09/12 1995/09/18 1995/10/14 1995/12/10 1996/05/07 1996/05/26 1996/05/30 1996/10/25 1996/11/14 1997/03/11 1997/04/01 1997/04/01 1997/04/11 1997/04/12 1997/04/20 1997/05/03 1997/08/26 1997/09/28 1997/10/05 1997/10/08 1997/10/22 1998/01/27 1998/03/25

Origin Time, UT
1817:00 0211:50 0140:00 1103:00 0842:00 1813:42 1833:00 0927:12 1439:03 1425:38 2221:37 1526:03 1632:28 2317:41 0332:42 1903:07 1823:46 1554:00 0402:22 0003:25 2239:29 2207:09 1726:38 0613:36 0907:26 1930:17 1712:51 1821:03 1321:15 2038:33 1512:26 2359:26 0335:46 0847:29 1329:06 0927:19 2244:28 1401:40 1745:18 0354:08 1431:14 0459:51 1610:56 2115:18 2314:00 0157:18 1314:42 0155:34 0628:54 1423:33 2022:14 0800:42 2347:00 2320:00 0143:44 0304:37 1959:41 1347:38 0313:59 1833:32 1842:00 0534:42 0921:56 1953:00 1646:02 1522:09 2313:13 1804:30 1047:49 0955:00 1955:00 2102:55

Latitude, °N
À21.54 À8.42 À17.01 À18.17 À15.32 À15.70 À20.11 À30.42 À59.37 45.69 À24.90 À21.11 À5.48 À31.59 À5.49 À6.07 46.49 32.00 À22.39 À4.68 À4.74 15.13 À11.50 44.71 43.70 À21.06 43.55 43.52 À5.33 À17.86 18.59 À5.26 43.26 43.34 46.67 29.28 À11.05 38.15
21.80 43.26 44.32 43.91 À24.58 33.95
36.47 13.21 À56.75 18.92 18.88 À21.60 À20.55 À25.57 À21.25 43.71 À22.19 À56.72 À17.38 À21.24 À21.13 À18.30 À18.35 39.53 À28.17 À34.04 À31.79 À25.51 À22.41 À59.74 À29.25 44.72 À22.54 À24.34

Longitude, °E
170.47 158.88 168.45 À69.82 167.35 À72.70 À68.53 À178.14 À26.29 141.93 À68.38 À175.88 150.49 À69.22 154.21 149.49 150.02 137.85 À66.00 151.91 153.10 145.87 166.42 150.14 145.99 À179.25 147.12 147.19 150.49 À178.69 145.27 152.03 146.82 146.72 145.89 140.69 166.11 135.06 142.63 147.35 147.58 147.37 À177.28 137.12 71.16 145.15 À141.68 144.95 145.01 À179.43 À178.68 À177.51 À178.11 147.61 171.48 À26.31 À69.99 À176.62 À178.86 À69.53 À69.35 76.94 À178.37 À69.98 À179.38 178.33 À68.45 À29.20 178.35 146.21 179.05 À66.99

Depth, km
159 115 226 109 111 114 122 60 84 306 117 123 110 113 135 63 163 365 278 113 78 87 148 54 80 613 65 60 142 551 234 66 60 62 354 103 77 364 318 50 103 76 108 323 239 71 10 588 600 599 617 70 403 54 108 84 116 192 553 114 116 15 184 105 108 610 107 274 617 154 611 197

Table 1. (continued)

Event

Origin Latitude, Longitude, Depth,

Origin Date Time, UT

°N

°E

km

19980414 1998/04/14 0341:22 À23.82 À179.87

499

19980901 1998/09/01 1029:49 À58.21 À26.53

152

19980912 1998/09/12 0903:48 À24.51 À67.12

187

19981008 1998/10/08 0451:42 À16.12 À71.40

136

19990205 1999/02/05 1139:00 À12.62 166.97

213

19990305 1999/03/05 0033:00 À20.42 À68.90

111

19990306 1999/03/06 2028:54 À21.73 À179.46

603

19990323 1999/03/23 1123:44 À20.91 À178.73

575

19990508 1999/05/08 1944:00 45.45

151.63

63

19990802 1999/08/02 0947:00 À12.55 167.18

251

19990918 1999/09/18 2351:30 À19.71 169.21

103

19991025 1999/10/25 2031:00 À38.70 175.80

159

19991121 1999/11/21 0351:00 À21.75 À68.78

101

19991206 1999/12/06 2312:00 57.41

À154.49

66

20000119 2000/01/19 0709:00 36.37

70.38

207

20000411 2000/04/11 0641:26 À27.94 À178.39

201

20000508 2000/05/08 2135:00 À31.32 179.84

383

20000512 2000/05/12 2310:00 35.97

70.66

108

20000614 2000/06/14 0215:26 À25.52 178.05

605

20000614 2000/06/14 0319:18 À24.03 À66.75

197

20000616 2000/06/16 0755:35 À33.88 À70.09

120

20000616 2000/06/16 2023:00 À28.88 À178.46

222

20001022 2000/10/22 2026:00 À15.23 167.70

143

20001218 2000/12/18 0119:21 À21.18 À179.12

628

20010704 2001/07/04 0706:32 À21.73 À176.71

184

aEvents in bold are the data recorded in regional seismic networks. Origin dates are year, month, day.

models in section 3, mantle effect on the differential traveltimes and amplitude ratios in section 4, and possible interpretations in section 5. In the following, the terms ‘‘eastern hemisphere’’ and ‘‘western hemisphere’’ refer to the ‘‘eastern hemisphere of the inner core’’ and ‘‘western hemisphere of the inner core,’’ respectively.

2. Seismic Data and Coverage
[6] Seismic velocity and attenuation structures along equatorial paths in the top 400 km of the Earth’s inner core are constrained by modeling the differential traveltimes, amplitude ratios, and waveforms of the PKiKP-PKIKP phases at the epicentral distance range of 120°– 141° and the PKPbc-PKIKP phases at the distance range of 146°– 160°. PKIKP is the P wave transmitted through the inner core; PKiKP is the P wave reflected off the inner core boundary (ICB); and PKPbc is the P wave propagating through the bottom portion of the outer core (Figure 1a). Since the ray paths of these phase pairs are close in the mantle, the seismic heterogeneities in the mantle would affect the PKIKP and PKiKP (PKPbc) phases in a similar way (Figure 1a). The differential traveltimes and amplitude ratios of the PKiKP-PKIKP and PKPbc-PKIKP phases are thus most sensitive to the velocity and attenuation structures of the inner core. In this study, we only use the PKiKPPKIKP phases observed at the distance range of 120° –141° and the PKPbc-PKIKP phases recorded at the distance range of 146° – 160°. The seismic data at these two distance ranges are sensitive to the seismic structures in the top 80 km and 140 –400 km of the inner core, respectively. At the distance range of 141° – 146° (corresponding to the PKIKP turning depth of 80– 140 km in the inner core), PKIKP and PKiKP phases are interfered with the long-period PKPBdiff, a P wave transmitted in the middle portion of the outer core,

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Figure 2. Observed PKiKP-PKIKP and PKPbc-PKIKP differential traveltime residuals with respect to PREM as a function of (a, b) ray angle and (c, d) PKIKP turning longitude. The meaning of the symbols is shown in the inset. Solid circles (labeled as EAST) are the observations for the PKIKP ray segments in the inner core confined in the eastern hemisphere; open triangles (labeled as west) are the observations for the PKIKP ray segments in the inner core confined in the western hemisphere. Gray squares (labeled as EW) in Figures 2b and 2d are the observations that the PKIKP ray segments in the inner core sample across the eastern and western hemispheres. The differential traveltime residuals do not exhibit any direction dependence for the ray angles (PKIKP ray directions in the inner core relative to the Earth’s rotation axis) being greater than 35° (Figures 2a and 2b). Note that the PKPbc-PKIKP differential traveltime residuals for the EW group lie between those for the eastern (east group) and western (west group) hemispheres (Figures 2b and 2d).

making the measurement of the differential traveltimes of the PKiKP-PKIKP phases difficult. Joint analyses of the PKiKP-PKIKP phases and PKPbc-PKIKP phases, however, can constrain the seismic structures in the top 80 km of the inner core and at depths larger than 140 km below the ICB.
[7] Broadband PKP seismograms are collected from the recordings in the Global Seismographic Network (GSN) of the Incorporated Research Institutions for Seismology (IRIS) Consortium from 1990 – 2001 and in many regional seismic networks: Grafenberg (GRF), the German Regional Seismic Network (GRSN), GEOFON, GEOSCOPE, MEDNET, the Czech Regional Seismological Network (CRSN), the Broadband Andean Joint Experiment (BANJO), the Seismic Exploration of Deep Andes (SEDA), the Brazilian Lithosphere Seismic Project (BLSP), the Kazakhstan, and the FREESIA. Part of the observations are the collections from previous studies used for studying the seismic structures in the top 80 km of the inner core [Niu and

Wen, 2001; Wen and Niu, 2002; Niu and Wen, 2002] and in the bottom of the outer core [Yu et al., 2005]. Broadband seismograms are band-pass filtered with the World-Wide Standard Seismograph Network (WWSSN) short-period instrument response. We select the data based on the simplicity of the earthquake source and high signal-to-noise ratio (see Table 1 and Table 1 of Yu et al. [2005] for the earthquake parameters). A total of 260 PKiKP-PKIKP and 830 PKPbc-PKIKP highquality observations are selected based on the above criteria from a collection of more than 16,000 seismograms. Our selected data exhibit good global coverage (Figures 1b and 1c). The amplitude ratios and differential traveltimes are measured based on the ratios and the time separations between the maximum amplitudes of these phase pairs, respectively. The traveltime measurement is proved to be comparable to that determined from the waveform cross correlation and the difference in traveltime measurement between the two methods is less than 0.05 s. The differential

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traveltime residuals are obtained from subtracting the predicted differential traveltimes based on the reference model PREM [Dziewonski and Anderson, 1981] from the observations. The observed amplitude ratios are corrected for the radiation patterns of the earthquake sources, although the

effect is very small due to the similar takeoff angles of these phase pairs.
[8] Since our goal is to derive seismic velocity and attenuation structures along equatorial paths for both the eastern and western hemispheres, we only analyze the data

Figure 3
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with the PKIKP ray segments confined in each of the hemispheres of the inner core and sampling along the equatorial direction. The differential traveltimes of both the PKiKP-PKIKP and PKPbc-PKIKP phases do not exhibit any direction dependence within the equatorial group (Figures 2a and 2b), indicating that the influence of inner core anisotropy is little for the data sampling along the equatorial paths we defined. The east-west hemispheric boundary at 40°E and 180°E longitudes is primarily determined by the geographic distribution of the sampling of the PKiKP-PKIKP differential traveltimes [e.g., Niu and Wen, 2001, Figure 1]. We have not specifically searched for the PKiKP-PKIKP data sampling the region near 40°E and 180°E longitudes to address the exact east-west hemispheric geographic boundary (Figure 2c), but our PKPbc-PKIKP data provide additional sampling of the east-west lateral transition (Figure 2d). The differential PKPbc-PKIKP traveltimes are consistent with the division of the two hemispheres inferred from the PKiKP-PKIKP observations (Figure 2d).
3. Seismic Observations and Detailed Seismic Velocity and Attenuation Structures Along Equatorial Paths
3.1. Seismic Observations
[9] Differential traveltime residuals, amplitude ratios, and waveforms exhibit clear east-west hemispheric patterns for both the PKiKP-PKIKP and PKPbc-PKIKP data sets. The observed PKiKP-PKIKP phases show these characteristics (Figures 2c, 3a, and 3c): (1) at the distance range of 131° – 141°, PKIKP phases arrive about 0.3 s earlier than the theoretical arrivals based on PREM for the PKIKP phases sampling the eastern hemisphere and about 0.4 s later for those sampling the western hemisphere; (2) the bifurcation of the PKiKP-PKIKP phases occurs at a closer distance for those sampling the eastern hemisphere (bifurcation refers to the beginning of the visual separation of the PKIKP phase from the PKiKP phase in the short period seismograms); and (3) PKIKP phases have smaller amplitudes for those sampling the eastern hemisphere [see also Wen and Niu,

2002, Figure 7]. The observed PKPbc-PKIKP phases show these characteristics (Figures 4 and 5): (1) at the distance range of 146°– 151°, PKIKP phases arrive about 0.3 s earlier than the theoretical arrivals based on PREM for the PKIKP phases sampling the eastern hemisphere and about 0.4 s later for those sampling the western hemisphere; at the distance range of 151° – 160°, PKIKP phases arrive about 0.7 s earlier than the theoretical arrivals based on PREM for the PKIKP phases sampling the eastern hemisphere and about 0.1 s later for those sampling the western hemisphere (Figure 4); and (2) at the distance range of 146°– 151°, the observed PKIKP/PKPbc amplitude ratios are, in general, smaller for the PKIKP phases sampling the eastern hemisphere than for those sampling the western hemisphere; at the distance range of 151° – 160°, the observed PKIKP/ PKPbc amplitude ratios become indistinguishable for the two hemispheres (Figure 5). The PKPbc-PKIKP observations at the distance range of 146°– 151° exhibit same hemispheric patterns as the PKiKP-PKIKP observations at the distance range of 131° – 141°. The east-west hemispheric patterns are also consistently observed in the data recorded in both the global and regional networks.
3.2. Seismic Velocity Structures in the Top 400 km of the Inner Core Along Equatorial Paths for the Two Hemispheres
[10] The observed PKiKP-PKIKP waveforms and the PKPbc-PKIKP differential traveltime residuals are used to constrain the seismic velocity structures in the top 400 km of the inner core along equatorial paths. Large (small) differential traveltimes would indicate high (low) velocities in the inner core. The PKiKP-PKIKP and PKPbc-PKIKP waveforms are sensitive to the seismic structures in different parts of the inner core. Joint modeling of both data sets is required as trade-offs exist for explaining each data set. The PKiKP-PKIKP waveforms are sensitive to the P velocity increase across the ICB and the radial velocity structure in the top 80 km of the inner core. The P velocity increase across the ICB can be derived from fitting the bifurcation (the visual separation of the PKIKP phase from the PKiKP phase in the short-period seismograms) distance. A smaller

Figure 3. (a, c) Examples of the observed waveforms for the PKiKP and PKIKP phases sampling the eastern (Figure 3a) and western (Figure 3c) hemispheres of the inner core recorded in the GSN (a) and the GSN and the Kazakhstan Network (Figure 3c); (b, d) synthetic waveforms based on E1 (black solid traces), E2 (black dashed traces), ECR (gray dashed traces), E11 (gray solid traces) (Figure 3b), and W1 (black solid traces), W2 (black dashed traces), WCR (gray dashed traces) (Figure 3d) (see Figure 6 for the velocity and attenuation models of E1, E2, W1, W2, and Figure 7 of Cao and Romanowicz [2004a] for the attenuation models of ECR, WCR; E11 has increased Q values from 200 to 400 in the depth range of 32 km to 85 km of the inner core). The maximum PKiKP amplitudes are impossible to pick at distances less than 127° for the seismic waves sampling the eastern hemisphere (Figure 3a) and at distances less than 130° for those sampling the western hemisphere (Figure 3c), due to the interference of the PKiKP and PKIKP phases. For those distances, the synthetics are aligned along the predicted PKiKP amplitudes based on E1 (black solid line, Figure 3b) and W1 (black solid line, Figure 3d). Observed waveforms are aligned according to waveform fitting the synthetics (Figure 3a based on Figure 3b; Figure 3c based on Figure 3d). Because of the interference of the PKiKP and PKIKP phases, there appears an offset in aligning the later maximum amplitudes at closer distances. At larger distances, synthetic and observed waveforms are aligned along the maximum amplitudes of the PKiKP phases. Distance corrections are made to a source depth of 200 km. Accordingly, synthetics are calculated based on a source depth of 200 km. PKIKP theoretical arrivals based on PREM and E1, W1 are indicated by the dotted and solid lines, respectively. Note that the PKiKP-PKIKP phases sampling the western hemisphere exhibit same characteristics for the seismic data recorded in the GSN and those recorded in the regional seismic networks: the Kazakhstan Network in Asia and the BLSP, BANJO, SEDA in South America (Figure 3c, and see also Figures 3 and 5 of Wen and Niu [2002]).
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Figure 4. Observed PKPbc-PKIKP differential traveltime residuals with respect to PREM as a function of epicentral distance (D), along with predictions based on E1, E2, W1, and W2 (see Figure 6a for the velocity structures). The meaning of the symbols and lines is shown in the inset. Black solid circles and black solid squares represent the differential traveltime residuals for the PKIKP phases sampling the eastern hemisphere recorded in the GSN and the regional seismic networks (GRF, GRSN, GEOFON), respectively. Open triangles and open squares represent the differential traveltime residuals for the PKIKP phases sampling the western hemisphere recorded in the GSN and the regional seismic networks (BLSP, BANJO, SEDA, FREESIA), respectively. Distance corrections are made so that the differential traveltime residuals are plotted at the distances equivalent to a source depth of 200 km. Accordingly, the predicted differential traveltime residuals are made based on a source depth of 200 km.

(larger) bifurcation distance would indicate a larger (smaller) magnitude of the P velocity increase across the ICB. The radial velocity gradient of the inner core can be derived from fitting the subsequent move outs of the PKiKP-PKIKP phases [Wen and Niu, 2002]. The velocity models E1 and W1 that are appropriate for explaining the observed PKiKP-PKIKP waveforms are derived by [Wen and Niu, 2002] (E1 for the eastern hemisphere and W1 for the western hemisphere). However, there is a trade-off between the seismic velocity structure in the bottom of the outer core and the seismic velocity structure in the top of the inner core in explaining the PKiKP-PKIKP waveforms (Figures 3b and 3d) [Wen and Niu, 2002]. For example, the synthetic waveforms produced by models E1, E2 (black solid and black dashed traces in Figure 3b; velocity structures of E1, E2 in Figure 6a) and W1, W2 (black solid and black dashed traces in Figure 3d; velocity structures of W1, W2 in Figure 6a) are indistinguishable (E1 and W1 have PREM velocity structure in the bottom of the outer core; E2 and W2 have a low-velocity structure OW in the bottom of the outer core. We will discuss OW later in this paper). However, because the trade-off exists in such a way that a smaller velocity gradient in the bottom of the outer core requires a lower velocity structure in the top of the inner core, these velocity structures can be distinguished by the joint modeling of the PKiKP-PKIKP waveforms and the PKPbc-PKIKP differential traveltimes in the distance range of 146° – 148°. In the distance range of 146° –148°, the PKPbc wave turns 400– 240 km above the ICB, whereas the PKIKP wave propagates through the bottom of the outer

core and the top 140– 180 km of the inner core. A smaller velocity gradient in the bottom of the outer core and its coupled lower velocity structure in the top of the inner core would delay the PKIKP traveltimes more and produce smaller differential PKPbc-PKIKP traveltimes, and are thus distinguishable by the joint modeling of the differential PKPbc-PKIKP traveltimes. In our earlier study, we have resolved the coupled outer core – inner core velocity structures for the two hemispheres, which best explain the PKiKP-PKIKP waveforms and the PKPbc-PKIKP differential traveltime residuals for the seismic data sampling the two hemispheres [Yu et al., 2005]. The eastern hemisphere has PREM velocity structure (a velocity gradient of 0.057 (km/s)/100 km) in the bottom of the outer core, a P velocity increase of 0.748 km/s across the ICB, and a coupled small velocity gradient of 0.0042 (km/s)/100 km in the top of the inner core (E1); the western hemisphere has a low-velocity structure OW (a velocity gradient of 0.041 (km/s)/100 km) in the bottom of the outer core, a P velocity increase of 0.645 km/s across the ICB, and a coupled steep velocity gradient of 0.049 (km/s)/100 km in the top of the inner core (W2) (Figure 6a). OW has reduced velocities relative to PREM linearly decreasing from 0% at 200 km above the ICB to À0.35% at the ICB (Figure 6a and Figure 6 of Yu et al. [2005]).
[11] With the velocity structures in the bottom of the outer core and the top of the inner core constrained by the joint modeling of the PKiKP-PKIKP waveforms and the PKPbcPKIKP differential traveltime residuals at the distance range of 146° – 148°, seismic velocity structures in the deeper part

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Figure 5. Observed PKIKP/PKPbc amplitude ratios as a function of epicentral distance (D) on a semilog scale, along with predicted amplitude ratios by W2 and E1 (see Figure 6 for the velocity and attenuation structures) based on a source depth of 200 km. The meaning of the symbols and lines is shown in the inset. Black solid circles and black solid squares represent the amplitude ratios for the PKIKP phases sampling eastern hemisphere recorded in the GSN and the regional seismic networks (GRF, GRSN, GEOFON), respectively. Open triangles and open squares represent the amplitude ratios for the PKIKP phases sampling the western hemisphere recorded in the GSN and the regional seismic networks (BLSP, BANJO, SEDA, FREESIA), respectively. Distance corrections are made so that the amplitude ratios are plotted at the distances equivalent to a source depth of 200 km. Predicted amplitude ratios are obtained from handpicking the maximum amplitudes of the PKIKP and PKPbc phases of the synthetic waveforms, calculated using the generalized ray theory [Helmberger, 1983].

of the inner core are derived from fitting the observed PKPbc-PKIKP differential traveltime residuals at distances greater than 148°. In what follows, we discuss velocity models and model resolution for the two hemispheres of the inner core on the basis of modeling the PKPbc-PKIKP differential time residuals.
[12] For the eastern hemisphere, the anomalously small velocity gradient in the top of the inner core is well resolved by the observed PKiKP-PKIKP move outs and the PKPbcPKIKP differential time residuals. Wen and Niu [2002] have discussed in detail how the anomalous radial velocity gradient in the top 80 km of the inner core beneath the eastern hemisphere is resolved by the PKiKP-PKIKP waveform data. Readers are referred to Wen and Niu [2002] for the detailed discussions. The PKPbc-PKIKP data in this study confirm the existence of such an anomalous radial gradient in the top part of the eastern hemisphere. Models with a larger radial velocity gradient would also produce unacceptable misfits to the observed PKPbc-PKIKP time residuals at the distance range of 146° – 156° (see an example in Figure 7a).
[13] The PKPbc-PKIKP time residuals further suggest that the anomalously small velocity gradient in the eastern hemisphere extends deeper than 80 km of the inner core. The extending depth of the small velocity gradient is in the range of 220– 250 km, constrained by the observed change of trend in PKPbc-PKIKP time residuals at the distance of about 151°. Models with a shallower or a deeper extending depth would produce misfits to the differential time resid-

uals. For example, an extending depth of 200 km would predict a change of differential time residual at a distance around 149° (Figure 7b), while an extending depth of 260 km would predict a change of differential time residual at a distance around 152° (Figure 7c). The extending depth of the anomalously small velocity gradient is constrained to be between 220 and 250 km.
[14] The increase and change of trend in the PKPbcPKIKP time residuals at distances greater than 151° are used to constrain the nature of velocity transition (e.g., a first-order discontinuity or a steep transition in velocity) and the velocity structure in the deeper part of the inner core. A first-order velocity discontinuity at 235 km would predict a kink in differential PKPbc-PKIKP time residual at the distances around 151°– 152° (gray solid line in Figure 7d; gray solid line in Figure 8). Such a kink is not observed either in the global data set (gray solid line, Figure 7d) or in the data recorded in the regional seismic networks for two events (see two examples in Figure 8). If we lower the velocity increase of the discontinuity and place the discontinuity at a slightly larger depth to fit the PKPbc-PKIKP time residuals at the distances of 151°– 152°, the predicted differential time residuals would still produce a kink and misfit the PKPbc-PKIKP time residuals at larger distances for both the global data set (gray solid line, Figure 7e) and the data recorded in the regional seismic networks for two events (black solid line, Figure 8). A velocity model, which has a steeper transition (a velocity gradient of 0.1 (km/s)/

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Figure 6. (a) Velocity and (b) attenuation structures in the bottom of the outer core and in the top 500 km of the inner core. The meaning of the lines in Figure 6a is shown in the inset. E1, W1 have PREM velocity structure in the bottom of the outer core; E2, W2 have a low-velocity structure OW in the bottom of the outer core. OW has reduced velocities relative to PREM linearly decreasing from 0% at 200 km above the ICB to À0.35% at the ICB [Yu et al., 2005]. E1 and W2 are the best fitting models for the eastern and western hemispheres, respectively. The velocity models shown here are used to compute the synthetic PKiKPPKIKP waveforms in Figure 3 and the synthetic PKPbcPKIKP waveforms in Figure 11.
100 km) extending from 235 km to 375 km of the inner core (Figure 6a), can best explain the PKPbc-PKIKP differential time residuals at the distance range of 151° – 154° for both the global data set (gray solid line in Figure 4; gray dashed line in Figure 7) and the data recorded in the regional seismic networks (gray dashed line, Figure 8).
[15] The PKPbc-PKIKP time residuals observed at distances greater than 155° suggest that a change of velocity gradient is needed following the steeper transition at a depth about 375 km below the ICB. A velocity model with a steeper transition extending larger than 400 km would predict differential traveltime residuals larger than the observations at greater distances (gray solid line, Figure 7f). A velocity gradient of 0.01 (km/s)/100 km, similar to the PREM gradient, at depths larger than 375 km below the ICB (gray solid line, Figure 6a) best predicts the observed differential traveltime residuals (gray solid line in Figure 4; gray dashed line in Figure 7). A velocity gradient smaller than the PREM gradient following the steeper transition would

produce slight misfits to the observations at the distance range of 157° –159° (gray solid line, Figure 7g).
[16] Our modeling results suggest that the velocity structure for the eastern hemisphere has PREM velocity structure in the bottom of the outer core (a velocity gradient of 0.057 (km/s)/100 km), a velocity increase of 0.748 km/s across the ICB, an anomalously small velocity gradient of 0.0042 (km/s)/100 km extending to 235 km, followed by a steeper velocity gradient of 0.1 (km/s)/100 km extending from 235 km to 375 km, and a velocity gradient of 0.01 (km/s)/100 km extending from 375 km to the deeper portion of the inner core (E1, gray solid line in Figure 6a).
[17] For the western hemisphere, the observed PKPbcPKIKP time residuals can be well explained by a simple velocity model W2 at the distance range of 146° –155° (open symbols, Figure 4). Because of the sparse data available at distances beyond 156°, we cannot resolve the velocity structure at depths larger than 375 km of the inner core. The velocity structure for the western hemisphere has an OW velocity structure in the bottom of the outer core (a velocity gradient of 0.041 (km/s)/100 km), a velocity increase of 0.645 km/s across the ICB, a steep velocity gradient of 0.049 (km/s)/100 km in the top 375 km, and an assumed PREM velocity at depths larger than 375 km of the inner core (W2, black solid line in Figure 6a).
3.3. Seismic Attenuation Structures in the Top 400 km of the Inner Core Along Equatorial Paths for the Two Hemispheres
[18] Seismic attenuation structures of the inner core are derived from joint fitting the observed PKIKP/PKiKP and PKIKP/PKPbc amplitude ratios. Smaller amplitude ratios would indicate smaller PKIKP amplitudes, and thus higher attenuation in the part of the inner core they sample. Attenuation is usually represented by quality factor Q, which is defined as the fractional loss of energy per cycle of wave oscillation as seismic waves travel through the medium. Wen and Niu [2002] have studied the attenuation structures in the top 80 km of the inner core along equatorial paths with an average Q value of 250 in the eastern hemisphere and an average Q value of 600 in the western hemisphere. In this study, we adopt Q models that are as simple as possible. The observed PKIKP/PKiKP amplitude ratios at the distance range of 131°– 141° and the PKIKP/ PKPbc amplitude ratios at the distance range of 146° –151° are consistently smaller for the data sampling the eastern hemisphere than those for the data sampling the western hemisphere; and the PKIKP/PKPbc data become indistinguishable for the two hemispheres at distances greater than 151°. For the eastern hemisphere, it is apparent that a change of Q with depth is required based on the observed amplitude ratios for the PKIKP/PKiKP data in the distance range of 131°– 141° and the PKIKP/PKPbc data at distances less than 151° versus the observed amplitude ratios for the PKIKP/PKPbc data at larger distances. We thus adopt a simple attenuation model with an average Q in the top part and another average Q in the deeper part of the inner core, and we emphasize on best fitting both the PKIKP/ PKiKP and PKIKP/PKPbc data sets (other than the PKIKP/ PKiKP data alone as by Wen and Niu [2002]). For the western hemisphere, the seismic data show no evidence for a depth dependence of Q. We thus explore attenuation models with an

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CoreHemisphereVelocity GradientDistance RangeVelocity