Constraints on the core mantle boundary topography from P4KP PcP differential travel times

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1 Click Here for Full Article JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115,, doi: /2009jb006563, 2010 Constraints on the core mantle boundary topography from P4KP PcP differential travel times Satoru Tanaka 1 Received 23 April 2009; revised 31 August 2009; accepted 20 November 2009; published 13 April [1] P4KP PcP differential travel times are examined to infer the core mantle boundary (CMB) topography. A total of 362 P4KP PcP times are measured with a measurement error of 0.5 s. The travel times are corrected for the Earth s hydrostatic ellipticity and mantle heterogeneity using a P wave tomographic model. Spherical harmonic expansion up to degree 4 is adopted for model parameterization. The P wave velocity heterogeneity is then estimated in the lowermost 150 km of the mantle to overcome the problem of underestimation of the velocity perturbation at the base of the mantle in the global 3 D P wave mantle model. Subsequently, the CMB topography is inferred using the residues of the above processes. Since the odd degree components of the CMB topography are insensitive to the P4KP PcP times, only the components of degrees 2 and 4 are solved for. The resultant features indicate that the maximum amplitude of the CMB topography does not exceed ±2 km, with an uncertainty of less than 0.5 km. A numerical test confirms that the pattern of degree 4 is more reliable with less amplitude recovery. The obtained degree 4 pattern shows an amplitude of less than ±1 km and indicates the presence of depressions under the circum Pacific, the central Pacific, and South Africa. Citation: Tanaka, S. (2010), Constraints on the core mantle boundary topography from P4KP PcP differential travel times, J. Geophys. Res., 115,, doi: /2009jb Introduction [2] The core mantle boundary (CMB) is one of the most interesting boundaries within the Earth. At the CMB, the silicate solid mantle meets the metallic liquid core, and the seismic velocity, density, and viscosity exhibit the largest contrasts [Souriau, 2007]. Furthermore, the CMB is a dynamic region where the core and mantle can exchange matter, heat, and angular momentum [Loper and Lay, 1995; Le Moüel et al., 1997]. The topography of the CMB is one of the most important topics of research for addressing issues relating to angular momentum. The irregular shape of the CMB may influence the flow in the outer core; a representative example is the formation of Taylor columns [Anufriyev and Braginski, 1975, 1977a, 1977b]. In addition, the Earth s rotation may fluctuate in terms of the length of day and the polar position through topographic core mantle coupling [Hide, 1969; Jault and Le Mouël, 1990; Kuang and Chao, 2003; Asari et al., 2006]. On the other hand, as mantle convection may deform the CMB topography, it may constrain the mantle properties such as viscosity and density variations [Steinberger and Holme, 2008; Yoshida, 2008]. The CMB topography has been inferred using various methods. For example, a geoid anomaly of degree Institute for Research on Earth Evolution, Japan Agency for Marine Earth Science and Technology, Yokosuka, Japan. Copyright 2010 by the American Geophysical Union /10/2009JB corresponds to a topography relief of less than 3 km [Hager et al., 1985; Bowin, 1986], and nutation studies implied a small excess ellipticity of the outer core of 490 m [Gwinn et al., 1986], a value that was subsequently modified to 380 m[mathews et al., 2002]. More detailed features are expected to be obtained from seismology studies. [3] Short wavelength CMB topography with a scale of tens to several hundred kilometers has been investigated on the basis of scattered waves [Earle and Shearer, 1997] and waveform interactions of core reflected waves [Kampfmann and Müller, 1989; Neuberg and Wahr, 1991; Rekdal and Doornbos, 1992], elucidating its statistical nature or localized features. However, I focus on global features with a scale of several thousand kilometers. Seismic studies of long wavelength CMB topography have produced results with widely ranging amplitudes and patterns. Pioneering studies were conducted by Creager and Jordan [1986] and Morelli and Dziewonski [1987]. Both studies used arrival time data reported in the Bulletin of the International Seismological Center (BISC). Creager and Jordan [1986] obtained an aspherical CMB map derived from the travel times of PKP(DF) and PKP(AB); they preferred to interpret the obtained map as a chemical boundary layer at the base of the mantle rather than as the CMB topography, with the total amplitude being 20 km. Morelli and Dziewonski [1987] inverted the travel time data of PcP and PKP(BC). They demonstrated that CMB topography maps derived from PcP and PKP(BC) data resemble each other, and they obtained the CMB topography with a maximum amplitude of ±6 km and lateral homogeneity in the outer core. 1of14

2 Figure 1. Seismic raypaths of P4KP (solid line) and PcP (dashed line) phases. The star represents a hypocenter. [4] Global scale studies have suffered from poor geographical coverage and the difficulty of separating CMB topography and lateral heterogeneity at the base of the mantle. Doornbos and Hilton [1989] analyzed PcP and PKP data and added the travel times of PKKP, PKKKP, and so on. The generic name of the additional phases is PmKP, indicating P waves in the mantle beneath a source and receiver that are refracted into the outer core, with m legs denoted as mk, and are reflected (m 1) times under the CMB. These phases are rarely reported in the BISC and are found in previous independent literature [e.g., Adams, 1972]. Moreover, Doornbos and Hilton [1989] jointly inverted the travel time residuals for the lateral heterogeneity at the base of the mantle and the CMB topography to obtain a smaller amplitude than that reported by Morelli and Dziewonski [1987]. Several studies suggested that PcP and PKP data from the current BISC and a spherical harmonic parameterization truncated at low degrees are not sufficient to determine the CMB topography [Pulliam and Stark, 1993; Rodgers and Wahr, 1993; Stark and Hengartner, 1993]. Obayashi and Fukao [1997] analyzed P and PcP travel times in the BISC, suggesting that other physical assumptions regarding CMB dynamics, such as isostasy, should be introduced to separate the CMB topography and heterogeneity at the bottom of the mantle. Garcia and Souriau [2000] selected the travel times of the core phases PcP, PKP(BC), and PKKP(BC) that had been reprocessed by Engdahl et al. [1998] (called the EHB catalog) because these phases are relatively insensitive to heterogeneity at the base of the mantle. They showed that it is quite difficult to separate the D heterogeneity from the CMB topography, and only the statistical characteristics of the CMB topography are valid. They obtained root mean square CMB topography amplitudes of 1 km for wavelengths larger than 1200 km. Sze and van der Hilst [2003] jointly inverted the travel times of PcP, PKP(DF), PKP(BC), PKP(AB), PKKP(BC), and PKKP(AB) phases from the enhanced EHB catalog for the D heterogeneity and CMB topography. They demonstrated that the D heterogeneity and CMB topography in some areas are successfully separated by incorporating PKP(AB) and PKKP(AB), which are sensitive to the D structure. However, because travel time measurement is a crucial issue for catalog data such as the BISC and EHB, there is a compelling case to exclude travel time residuals exceeding ±6 s [Garcia and Souriau, 2000] or ±4 s [Sze and van der Hilst, 2003]. Recently, Koper et al. [2003] determined PKiKP PcP differential travel times from their measurements. Although the geographical coverage is still limited, they discussed the statistical constraints on the CMB topography with a peak to peak amplitude of 3.5 km under the assumption that the topography of the inner core boundary is sufficiently small and uncorrelated because of the softness of the inner core. [5] As discussed above, most global studies have used the absolute travel times of the PcP, PKP, and additional PKKP phases taken from travel time catalogs. Although only Doornbos and Hilton [1989] incorporated PmKP (m 3) phases, the contribution of PmKP is not clear; presumably, these phases have a negligible contribution. Unfortunately, it seems that the data sets used in previous studies are unable to address many unresolved issues. Thus, I collect a novel data set, directly measuring the differential travel times of P4KP PcP from seismograms. I mainly examine the validity and limitations of the data set and discuss the implications of preliminary results. 2. Data [6] Among the various PmKP phases, P4KP is particularly advantageous in that its use can reduce the uncertainty in the travel time attributable to the origin time and the structure of the crust and upper mantle; this is because by using the P4KP phase, we can simply consider the differential travel time with respect to the PcP phase. Figure 1 illustrates the seismic raypaths of the P4KP and PcP phases, indicating their very similar paths in the crust and upper half of the mantle. Although several reports included the onset times of P4KP phases [Engdahl, 1968; Adams, 1972; Buchbinder, 1972], I collected the differential travel times of P4KP PcP. I used four data sets: (1) observations by a Japanese short period seismic network, J array, reported by Tanaka and Hamaguchi [1996], (2) data from short period seismic arrays provided by the International Monitoring System (IMS), (3) broadband seismograms of global networks provided by the Incorporated Research Institutions for Seismology (IRIS), and (4) data provided by the Japanese broadband seismograph network, F net. Since the IRIS and F net provide broadband seismographs, I applied a band pass filter with cut off frequencies of 1 and 5 Hz. To date, I have examined moderate sized, intermediate depth earthquakes as well as deep earthquakes. I selected 34 events and 242 stations, the geographical distributions of which are shown in Figure 2. Hypocenters and associated data sets are listed in Table 1. The main selection criteria are as follows: (1) the PcP phase should not be contaminated by depth phases such as pp and sp, (2) the source time function should be relatively simple, and (3) both the PcP and P4KP phases should be clearly identifiable on a single seismogram. [7] A typical observation is shown in Figures 3 5. Figure 3 is a map indicating the epicenter of a deep earthquake (the 25 July 2004 Sumatran event) and the IRIS stations used for this event. When the band pass filtered seismograms are magnified, clear P4KP signals can be observed at a lapse 2of14

3 Figure 2. Geographic distribution of (a) 34 events (stars) and (b) 242 stations (triangles) used in this study. time of about 47 min from the origin time, as shown in Figure 4. Such a record section allows us to easily recognize the P4KP signals and reduces misidentification. In some events, however, it was difficult to accurately measure the onset times, which are greatly influenced by the complexity of the source time function and various signal to noise ratios at different stations. For this reason, I avoid using travel time data reported in catalogs. When I picked the travel time difference between PcP and P4KP, I considered their waveform correspondence since the PcP phase is usually noisy because of the masking with P coda, whereas the P4KP phase is clearer and isolated if detected. Thus, I tried to read the rise or drop in the largest pulse for each phase, as shown in Figure 5. The effects of waveform differences between PcP and P4KP phases would be minor in a short period seismogram if we failed to read exactly corresponding waveform portions. On the basis of the halflength of the predominant periods of the PcP and P4KP phases, I assigned a value of 0.5 s to the uncertainty in measurement of the differential travel times. Tanaka and Hamaguchi [1996] measured the differential travel times by picking the corresponding phases using the same criteria as those used in this study. Finally, I collected 362 differential travel times for P4KP PcP. The associated raypaths, reflection points, and transmission points at the CMB are mapped in Figure 6. [8] The differential travel times were corrected for the hydrostatic ellipticity inside the Earth. Since the ellipticity correction of the P4KP phase could not be provided from a standard travel time table [Kennett and Gudmundsson, 1996; Kennett, 2005], I calculated it by integrating the Table 1. Event List Event Date (YYYYMMDD) Time (UTC) Latitude (deg) Longitude (deg) Depth (km) mb Data Set a :51: a :09: a :42: a :58: b :04: b, c :42: b :13: b :56: b :10: b :33: b :45: b :58: c :33: c :30: c :21: b, c :23: b, c :55: b :08: c :19: b :09: b, c :12: b, c :46: c :53: c :15: c :08: b, c :19: b, c :25: b :35: c, d :23: c :13: c :48: c :13: c :17: c :38: c a Data sets: a, J array [Tanaka and Hamaguchi, 1996]; b, International Monitoring System (IMS), IMS array; c, Incorporated Research Institutions for Seismology (IRIS); d, F net. 3of14

4 greater than the mean residual and are located around the upper part of the data plots in Figure 8. On the other hand, those obtained using iasp91 [Kennett and Engdahl, 1991] and SP6 [Morelli and Dziewonski, 1993] show satisfactory correspondence with the data. In addition, small modifications of PREM, for example, a small velocity reduction of 0.1% throughout the outer core or an increase in the core radius by 3 km, can fit the offset very well. To explain this large offset, SP6 was preferred in previous studies [Tanaka and Hamaguchi, 1996; Helffrich and Kaneshima, 2004]. However, a detailed study of the outermost core using SmKS phases does not support the SP6 and iasp91 predictions Figure 3. Map showing the epicenter of a Sumatran deep earthquake occurring on 25 July 2004 (star), and the IRIS stations (triangles) used in this study. travel time fluctuation caused by seismic velocity anomalies due to internal ellipticity along the raypaths of P4KP as well as PcP [Doornbos, 1988]. The tabulated values of ellipticity at several radii given by Bullen and Haddon [1973] were interpolated using the spline method. In addition, I corrected the travel time anomaly for the hydrostatic deformation of the CMB but not those for other discontinuities in the mantle because the raypaths of P4KP and PcP were very close to each other there. Furthermore, mantle heterogeneity was considered using the model pmean [Becker and Boschi, 2002]. The pmean is not an actual model, but rather an average of many models. I adopt it because it satisfactorily represents the long wavelength feature of mantle heterogeneity. The map for the base layer is shown in Figure 7 as an example. [9] Figure 8 shows the P4KP PcP residuals with respect to the travel time difference predicted from the preliminary reference Earth model (PREM) [Dziewonski and Anderson, 1981] as a function of epicentral distance. Figure 8 illustrates the improvement in data quality from the original data (open circles) to the corrected data (solid circles). The correction of the CMB ellipticity considerably reduced the scattering of the residuals. Large, positive outliers arising from equatorial paths disappeared when this correction was used. Smaller residuals arising from polar paths were raised. The mantle correction process slightly raised the residuals because the P4KP and PcP rays mainly sampled high velocity regions at the base of the mantle. Nevertheless, the residuals still had an offset of approximately 2.6 s. Theoretical travel time differences calculated from several Earth models are plotted for comparison. The predictions obtained using ak135 [Kennett et al., 1995] are approximately 1 s Figure 4. Record section of the Sumatran deep earthquake. The seismograms are passed through a zero phase Butterworth filter with cutoff frequencies of 1 and 5 Hz and an order of 2. These are aligned in order of epicentral distance with equal intervals. Amplitudes are magnified to emphasize small later phases. P P and P4KP phases are indicated by arrows. 4 of 14

5 Figure 5. Record sections of the Sumatran deep earthquake closing up (a) PcP and (b) P4KP phases. Lapse times are determined from theoretical travel times. [Tanaka, 2007]. Of course, it will be difficult to obtain a definitive conclusion from only the data set of P4KP PcP since this offset can be explained by considering a low basal velocity in the mantle, uniformly reduced seismic velocity in the outer core, a large core radius, or a combination of all three. Tentatively, I applied a correction of 0.8 s on the basis of a new outer core model with a slightly lower P Figure 6. Geographic distribution of P4KP piercing points (gray circles), P4KP reflection points under the core mantle boundary (CMB) (solid circles), and PcP reflection points (open circles). Gray lines indicate 362 great circle paths between events and stations. 5of14

6 der Hilst, 2003]. Thus, I consider its effect on the determination of the CMB topography. The D thickness and velocity perturbation have significant trade offs. Therefore, only for the purpose of this study, I assume that the D thickness is fixed at 150 km on the basis of PREM s value. The velocity perturbation dv approximately represented at the reflection points of PcP and the piercing points of P4KP at the CMB is expressed in terms of spherical harmonics as vð; Þ ¼ XL X l l¼0 m¼0 Cl m cos m þ D m l sin m p m l ðcos Þ; ð6þ Figure 7. Map of P wave velocity perturbation at km depth determined using the model pmean of Becker and Boschi [2002]. wave velocity structure than that of PREM in the outermost core [Tanaka, 2007]; the large offset remained. 3. Formulation [10] The CMB topography dr at the transmitted or bounce point is expanded using spherical harmonics as rð; Þ ¼ XL X l A m l cos m þ B m l sin m p m l ðcos Þ; ð1þ l¼0 m¼0 where A l m and B l m are the coefficients of spherical harmonics of degree l and order m, is colatitude, is longitude, p m l 1=2 ðcos Þ ¼ 2 m;0 ð2l þ 1Þ 1=2 ðl mþ! l þ mþ! 1=2 P m l ðcos Þ; ð2þ where C l m and D l m are the coefficients of spherical harmonics for degree l and order m. The travel time perturbation dt due to the velocity perturbation dv in the basal layer is expressed as T ¼ v T D 00; v D 00 where T D is the travel time in the D layer and v D is the average P wave velocity in the D layer (13.70 km/s) taken from PREM. The observation equation can be obtained by summarizing the formulas with respect to the coefficients of spherical harmonics: y j ¼ A ij x i ; where y j is the residual of differential travel times, A ij is a kernel matrix, and x i is the unknown of A l m and B l m for the CMB topography or C l m and D l m for velocity perturbation in ð7þ ð8þ and P l m is the associated Legendre function. [11] The travel time perturbations dt due to the topography are approximately expressed as T ¼ 2 r 2 1=2 p2 for P4KP reflection; ð3þ r core T ¼ r r n core þ 2 1=2 p2 2 p 2 1=2 o for P4KP transmission; ð4þ and T ¼ 2 r 2 1=2 þ p2 for PcP reflection; ð5þ r core where h ± = r core /v ±, p is the slowness value, r core is the radius of the core, and subscripts + and denote values above and below the CMB, respectively [Dziewonski and Gilbert, 1976; Doornbos, 1988]. [12] Heterogeneity in the D layer presented by global tomographic models is probably underestimated [Doornbos and Hilton, 1989; Garcia and Souriau, 2000; Sze and van Figure 8. P4KP PcP residuals with respect to the preliminary reference Earth model (PREM) as a function of epicentral distances. Open circles are raw residuals. Solid circles are the residuals obtained after ellipticity and mantle corrections. Theoretical travel time differences are drawn by color lines for comparison. iasp91 [Kennett and Engdahl, 1991] (blue); SP6 [Morelli and Dziewonski, 1993] (gray); ak135 [Kennett et al., 1995] (red); same as PREM, except for an increase in the core radius of 3 km (green); same as PREM except for a uniform P wave velocity reduction of 0.1% throughout the outer core (black). 6of14

7 [13] In practice, the individual elements of the kernel for odd degree components of A l m and B l m are much smaller than those for even degree components, as shown in Figure 9a, possibly because of the symmetrical distribution of the P4KP raypaths beneath the CMB. Unfortunately, the data coverage is still sparse. Thus, I solve the observation equation for the CMB topography only for the degrees 0, 2, and 4 (using the least squares method), resulting in 15 unknowns. On the other hand, the elements of the kernel for C l m and D l m seems to be well resolved (Figure 9b). Thus, I solve for all components up to degree 4, resulting in 25 unknowns. Figure 9. All the elements of the kernel matrix A ij with respect to spherical harmonics coefficients of degree and order up to 4 for (a) the CMB topography and (b) velocity perturbations in the lowermost 150 km of the mantle. Crosses and circles represent positive and negative values, respectively. Symbol sizes are proportional to the magnitude. Typically, the kernels of degree 0 (solution 1) for the CMB topography are approximately 0.9 s/km over the entire data range. All kernels for velocity perturbations are reduced by multiplying with 0.2. the lowermost mantle. The variance s 2 is the diagonal component of the error matrix and is given by 2 ¼ A A ~ ii ; ð9þ where A is the kernel matrix, Ã is its transpose, and S is the model error covariance matrix. 4. Inversion Procedure [14] As discussed in previous studies, the separation of the CMB topography and D heterogeneity is quite difficult [Doornbos and Hilton, 1989; Garcia and Souriau, 2000; Sze and van der Hilst, 2003]. Garcia and Souriau [2000] used a singular value decomposition to control model instability on the basis of data noise. Sze and van der Hilst [2003] used damped least squares. They controlled the damping factor to obtain a relevant velocity perturbation in the D layer. Since the rays of the P4KP and PcP phases are far from each other at the base of the mantle, we cannot completely ignore the trade off. In this study, I perform two kinds of numerical experiments to consider the trade off and the inversion procedure. Because I cannot consider a priori constraints on the separation of the D heterogeneity and the CMB topography if I adopt the joint inversion, I examine the behavior of separate inversions. [15] First, I prepared 25 models of the CMB topography. 0 A single coefficient of spherical harmonics selected from A 0 to B 4 4 was assigned for each model, the value of which was set as unity for simplicity. The travel time residuals of P4KP PcP were calculated on the basis of the actual combinations of hypocenters and stations. As no artificial noise was added to the travel times, the inversion for the CMB topography resulted in exactly the same output as the input. However, the inversion for the velocity perturbation in the lowermost 150 km in the mantle resulted in the other coefficients having values other than unity. [16] Figure 10 shows the relationship between the topography input and the velocity output. The symbol size of the outputs is quintupled. The input models (row) 1 4 and correspond to components of degrees 1 and 3, respectively. For these inputs, we observe output coefficients of zero or small values. For the inputs of degrees 2 and 4, we clearly observe mismapping onto the coefficients of degrees 1 and 3. Since this inversion retained some travel time residues, I carried out the inversion process for the CMB topography using these residues. The resultant outputs are presented in Figure 10. As I did not solve for components of degrees 1 and 3, solutions (column) 2 4 and do not appear in Figure 10. Compared with the input pattern, the recovery of degree 2 components is quite insufficient. On the other hand, that of degree 4 components is relatively good, although smearing of some degree 2 components is apparent. [17] Figure 11 shows example maps of the two step inversion for the velocity perturbation and CMB topography. The map of input model 22 (A 3 4 =1) is shown in Figure 11a. 7of14

8 CMB topography is similar to that of the input, meaning that the degree 4 components are relatively well recovered. However, the recovery amplitude is insufficient when I examine only the degree 4 components. The amplitude in a well recovered area comprises components of degrees 2 and 4. [18] Second, I prepared 25 models in which there was a velocity perturbation in the lowermost 150 km of the mantle. As before, a single coefficient selected from C 0 0 to D 4 4 was assigned for each model. I then calculated synthetic travel time data for the CMB topography to examine the trade off relationship. Figure 12 shows the relationship between the input velocity and the output CMB topography. Figure 10. Trade offs and recovery for the given CMB topography inputs. Input models 1 25 correspond to a single coefficient picked from A 0 0 to B 4 4, the magnitude of which is unity, and are represented by open circles. (a) Trade offs between the input CMB topography and the output D heterogeneity. Gray circles show the magnitude of the obtained coefficients as P wave velocity perturbations in the lowermost 150 km of the mantle, the sizes of which are multiplied by 5. (b) A recovery diagram of the CMB topography. Solid circles show the magnitudes of the recovered coefficients as the topography determined from the residues of the inversion for the D heterogeneity. The scale of the symbol size is the same as that of the input. The resultant map of the velocity perturbation at the base of the mantle indicates an artifact of a high velocity maximum beneath the central Pacific and off the southern coast of Africa, where no PcP reflection points or P4KP piercing points are distributed at the CMB. The map of the obtained Figure 11. Maps of (a) the input pattern of the CMB topography (model 22, A 3 4 = 1) with a contour interval of 0.5 km, (b) the output pattern solved as a D heterogeneity with a contour interval of 0.5 km/s, and (c) the output pattern determined from the residues of the D heterogeneity as a CMB topography with a contour interval of 0.5 km. 8of14

9 Figure 12. Trade offs between the given D heterogeneity inputs and the output CMB topography. Input models 1 25 correspond to a single coefficient picked from C 0 0 to D 4 4, the magnitude of which is unity, and are represented by open circles. Solid circles show the magnitude of the obtained coefficient as the CMB topography (reduced by a factor of 10). The output is reduced by a factor of 10. The most significant result is that the velocity input coefficients of degree 2 are reproduced as the topography output of the degree 2 component; in addition, the degree 1 and 4 input components are mapped to the degree 2 output components. This means that the resultant degree 2 components of the CMB topography are unreliable if the velocity heterogeneity is not well removed. Figure 13 shows example maps of input model 22 (C 4 3 =1) and the obtained CMB topography. The input velocity perturbation is as large as 2 km/s, corresponding to a maximum of 15%, and the obtained topography exceeds ±20 km at this maximum value. However, the reproduced pattern of the CMB topography does not resemble the input velocity heterogeneity. [19] These two numerical experiments suggest that (1) the degree 4 component of the CMB topography can be obtained with insufficient recovery of the amplitude even though velocity inversion is conducted prior to the topography inversion and (2) the degree 2 component of the D heterogeneity might be mismapped if only CMB topography inversion is conducted. Thus, I decided to conduct the inversion for the velocity perturbation in the D layer before that for the CMB topography. 5. Results [20] The observation equations for the D heterogeneity and the CMB topography were separately solved in that order, and the standard deviation of the residuals slightly improved from s = 0.77 to s = 0.71 s at the first inversion, and finally to s = 0.69 s, although kurtosis was also improved after the sequence of inversions (Figure 14). This means that the CMB topography signal is very small and subtle in nature. The average of the initial residuals became almost zero after the inversion of the D heterogeneity. The average velocity perturbation in the D layer of 0.18 km/s (approximately 1%) was probably too large a value to be used as a global average for the lowermost 150 km in the mantle. On the other hand, the solutions of the CMB topography are listed in Table 2 for only even degree coefficients with their standard deviations. The average radius (the solution for degree 0) was slightly larger than that of PREM by 0.12±0.08 km. However, the average velocity perturbation in the D layer and the core radius are not fundamentally constrained by the average residual. Moreover, a slightly low P wave velocity in the outer core cannot be ruled out as shown in Figure 8. The trade offs are significant if only P4KP PcP residuals are used. [21] Figure 15a is a map of the CMB topography comprising degree 2 and 4 components. The magnitude of the error was calculated using equation (9) and does not exceed 0.5 km. The predominant pattern included depressions of 1.5 km beneath Australia, the central Pacific, South Africa, and the North Atlantic. The South Pacific and the Middle East were elevated by +1.8 km. Figure 15b shows the map of the D heterogeneity. The velocity perturbation has large variation, from 0.9 km/s ( 7%) to 0.7 km/s (5%). However, we should not regard the D heterogeneity as a reliable solution because this pattern certainly contains some components of the CMB topography, as observed in the previous section. Furthermore, the biased distribution of the PcP bounce points and P4KP piercing points at the CMB yields artificial peaks, for example, high velocity anomalies Figure 13. Maps of (a) the input pattern of the D heterogeneity (model 22, C 3 4 = 1) with a contour interval of 0.5 km/s and (b) the output pattern solved for the CMB topography with a contour interval of 5 km. 9of14

10 Figure 14. Histograms of P4KP PcP differential travel time residuals (a) before inversion, (b) after inversion for the D heterogeneity, and (c) after inversion for the CMB topography. beneath the southeastern and central Pacific Ocean and a low velocity anomaly beneath the South Atlantic Ocean, where we have no sampling points for the PcP reflection and P4KP transition. [22] As observed in the previous section, the degree 4 components are well recovered even if the degree 2 components are mismapped to the D heterogeneity or smeared with regard to the actual degree 4 components. Thus, I plot the CMB topography composed of only degree 4 components in Figure 16. The amplitude varied from 1 to +0.8 km, which is probably an underestimated value. Depressed areas were distributed beneath Asia, Oceania, North America and South America (nearly circum Pacific), and the central Pacific and South Africa. Note that the depression beneath the central Pacific is not strongly constrained because of the lack of data sampling (Figure 6). Elevated areas were observed in the Pacific Rim, Middle East, South Indian Ocean, and Brazil. the D heterogeneity. There is no consensus on the geographic pattern in previous seismological studies. Morelli and Dziewonski [1987] (MD) emphasized that the rim of the Pacific is depressed (Figure 17a). Doornbos and Hilton 6. Discussion [23] Figures 17a 17c show three representative models of the CMB topography that were previously constructed using a seismic method [Morelli and Dziewonski, 1987; Doornbos and Hilton, 1989; Sze and van der Hilst, 2003]. They are expressed using spherical harmonics having degrees and orders up to 4. As discussed in section 1, the amplitude of the seismically derived topography tends to become smoother as time progresses, mainly because we consider Table 2. Resultant Coefficients and Their Standard Deviations for the Core Mantle Boundary Topography l m m A l s m B l s Figure 15. (a) Map of the CMB topography derived from P4KP PcP travel times. Components of degrees 2 and 4 are used. The contour interval is 0.5 km. (b) Map of the P wave heterogeneity in the D layer up to degree 4. The contour interval is 0.2 km/s. 10 of 14

11 Figure 16. Same as Figure 15a, except that components of degree 4 are used. The contour interval is 0.5 km. [1989] (DH) did not discuss their pattern of the CMB topography, but there is a large depressed area centered at South East Asia on their map (Figure 17b). In the map of Sze and van der Hilst [2003] (SV), there are significant elevations under Australia and Indonesia and depressions under the Middle East and Antarctica (Figure 17c). Sze and van der Hilst discussed their unsmoothed result, and, using checkerboard tests, they reliably estimated the elevations under Australia, Indonesia, and southern Africa and small depressions under Central America, North America, and central Eurasia. Although the geographical patterns of the MD model and our model are relatively similar, the correlation coefficients between our model and these three models for the components of degrees 2 and 4 are not significantly high (0.41 for MD, 0.23 for DH, and 0.16 for SV). To further assess these models, I examined how they explain the new data. The initial data set comprises the P4KP PcP differential travel time residuals that were processed in section 2, including only the corrections of the mantle heterogeneity and ellipticity. Figures 18a 18c show the histograms of the P4KP PcP residuals corrected for the three seismic topography models. Comparing with the histogram of the initial data shown in Figure 14a, we find that the data for the MD and DH models are more scattered than the initial data, whereas the data for the SV model have a similar degree of scattering, indicating that the previously established seismological models do not explain the new data. [24] Studies on topographic core mantle coupling have used seismological inferences of the CMB topography. A kinematic approach combines a topography model with an existing core surface flow model to calculate the pressure torque acting at the CMB [Jault and Le Mouël, 1990; Asari et al., 2006]. Jault and Le Mouël [1990] adopted the topography model of Morelli and Dziewonski [1987] and obtained an unrealistically high topographic torque. Asari et al. [2006] mainly examined the validity of core flow models by adopting a topography model associated with relatively large amplitudes [Boschi and Dziewonski, 2000]. A dynamical approach has been proposed to solve the core flow using the morphology of the existing topography model of Morelli and Dziewonski [1987] with amplitude variation to discuss the dependence of the amplitude on the pressure torque [Kuang and Chao, 2001, 2003]. Kuang and Chao [2001, 2003] concluded that the topographic torque is significant if the CMB topography is larger than 3 km and negligible if it is less than 1 km. The amplitudes of the CMB topography obtained in this study are less than 4 km for the composite components of degrees 2 and 4 and less than 2 km for the degree 4 component, which suggests that CMB topographic coupling is not negligible. The locations of elevations and depressions have not been frequently discussed in studies on topographic coupling. Unusually, Yoshida and Hamano [1993] inferred the sectorial pattern of the CMB topography using a relationship between the westward drift of the geomagnetic field and the length of the day. They did not reveal the locations of elevation and depression but presented a black and white pattern indicating only the alternation of the topographic sign. The black areas for the degree 4 component presented in their study are located beneath the eastern side of North America, East Asia, the central Pacific, and Africa. Of interest, these areas correspond well to the depressions of the CMB topography found in the degree 4 pattern of this study (Figure 16). [25] After Morelli and Dziewonski [1987] reported their seismological inference, it was expected that the CMB topography would provide constraints on the mantle dynamics, as noted by Forte and Peltier [1991]. Recently, Steinberger and Holme [2008] inferred the CMB topography from an instantaneous mantle flow due to a density anomaly derived from seismic tomography (Figure 17d, model SH). They estimated the viscosity in the mantle by fitting to a geoid and heat flow and also to the CMB excess ellipticity of Mathews et al. [2002], the root mean square CMB topography of Garcia and Souriau [2000], and the local CMB topography determined from the PKKP phase by Garcia and Souriau [1998]. In their resultant CMB topography, we can observe depressions beneath central Asia and the Americas and elevation beneath South Africa and the Pacific, where the amplitude is less than ±3 km. Yoshida [2008] systematically examined the effects of some parameters of mantle dynamics on the CMB topography derived from instantaneous mantle flow. He adopted a conversion factor [Karato, 1993] to derive a density anomaly from an S wave velocity perturbation in the mantle tomography model smean [Becker and Boschi, 2002] and prepared two radial viscosity variations, one of which remained constant through the lower mantle while the other showed a profile with smaller viscosity in the D layer than in the rest of the lower mantle. Furthermore, he was the first to consider a lateral viscosity variation, a dense pile beneath Africa and the Pacific, and a weak slab at the base of the mantle. He demonstrated that the amplitude of the CMB topography is mainly controlled by viscosity in the D layer. Lateral viscosity variation enhances depression beneath the circum Pacific, where subducting slabs develop, although the approximate pattern of depression and elevation is similar to that of Steinberger and Holme [2008] (Figure 17e, model H4). On the other hand, dense piles beneath Africa and the Pacific can result in additional depression even in regions with the large low seismic velocity provinces in the lowermost mantle (Figure 17f, model H4P3). The pattern of our CMB topography model comprising degree 2 and 4 components indicates four depressions and two elevations (Figure 15). However, as observed in the previous section, the 11 of 14

12 Figure 17. Models of the CMB topography derived from seismological and modeling studies. (a) MD [Morelli and Dziewonski, 1987] with a contour interval of 1 km, (b) DH [Doornbos and Hilton, 1989] with a contour interval of 1 km, (c) SV [Sze and van der Hilst, 2003] with a contour interval of 0.5 km, (d) SH [Steinberger and Holme, 2008] with a contour interval of 1 km, (e) H4 [Yoshida, 2008] with a contour interval of 1 km, and (f) H4P3 [Yoshida, 2008] with a contour interval of 1 km. degree 2 pattern is possibly disturbed. Thus, the degree 4 pattern presented in Figure 16 should be compared with the CMB topography derived from numerical modeling. Significant features are qualitatively similar to those of H4P3, in which we observe depressions beneath the circum Pacific, Africa, and the central Pacific [Yoshida, 2008]. Quantitative comparison of the patterns would be premature because I only fit data to spherical harmonics truncated at low degrees with uneven data coverage. Furthermore, I do not obtain odd degree components. Tentatively, however, I ex- amined how these dynamic models explain the new seismic data as above. Figures 18d 18f show histograms of the P4KP PcP residuals corrected for the three dynamic topography models. We see that SH and H4 increase the scatter equally. Although no model improves the data scatter, the scatter by H4P3 is less than the scattering by SH and H4, probably owing to the existence of depressions beneath Africa and the Pacific. This suggests that H4P3 is the best model among the three developed so far. To confirm this, we should expand the resolution and geographical coverage. 12 of 14

13 Figure 18. Histograms of P4KP PcP differential travel time residuals corrected for the CMB topography models of (a) MD [Morelli and Dziewonski, 1987], (b) DH [Doornbos and Hilton, 1989], (c) SV [Sze and van der Hilst, 2003], (d) SH [Steinberger and Holme, 2008], (e) H4 [Yoshida, 2008], and (f) H4P3 [Yoshida, 2008]. The average (Ave.) and standard deviation (Std.) of the residuals are presented. A more comprehensive data set is required, and it is necessary to exclude the arrival times reported in bulletins such as the BISC, EHB, and IMS because data quality is crucial in solving the subtle problems associated with the CMB topography. 7. Conclusions [26] I examine a novel data set of P4KP PcP differential travel times for seismic inference of the CMB topography and find that this data set is useful. Preprocessing for D heterogeneity is important to avoid mismapping to the CMB topography, and the limitations of the data set are presented. P4KP PcP data are sensitive only to even degree components of the CMB topography. The preliminary result for degree 2 and 4 components indicates an amplitude of less than ±2 km, with depressions located beneath Australia, the North Atlantic, the central Pacific, and South Africa. The degree 4 pattern is more reliable only as a geographical pattern. Its amplitude is estimated to be less than ±1 km, the recovery of which is likely to be insufficient. Depressions are observed under the circum Pacific, South Africa, and the central Pacific; the depressions under the central Pacific should be confirmed by further observation. This pattern is qualitatively consistent with the inference of instantaneous mantle convection on the basis of the assumption that dense piles exist beneath Africa and the Pacific. [27] Acknowledgments. I thank Richard Holme, Jan Hagedoorn, Christine Thomas, Masaki Yoshida, Jon Aurnou, and Yozo Hamano for fruitful discussions and encouragement during this study. I am also grateful to Richard Arculus, Christine Houser, and an anonymous reviewer for their invaluable suggestions. IRIS (GSN, PASSCAL), IMS, and NIED (F net) provided high quality digital seismograms. This work was supported by a Grant in Aid for Scientific Research (B) from JSPS and a Grant in Aid for Scientific Research in Priority Areas from MEXT. Most figures were drawn by the GMT system [Wessel and Smith, 1998]. References Adams, R. D. (1972), Multiple inner core reflections from a Novaya Zemlya explosion, Bull. Seismol. Soc. Am., 62, Anufriyev, A. P., and S. I. Braginski (1975), Influence of irregularities of the boundary of the Earth s core on the velocity and on the magnetic field, Geomagn. Aeron., 16, Anufriyev, A. P., and S. I. Braginski (1977a), Influence of irregularities of the boundary of the Earth s core on the velocity of the liquid and on the magnetic field. II, Geomagn. Aeron., 17, Anufriyev, A. P., and S. I. Braginski (1977b), Effect of irregularities of the boundary of the Earth s core on the speed of the fluid and on the magnetic field. III, Geomagn. Aeron., 17, Asari, S., H. Shimizu, and H. Utada (2006), Variability of the topographic core mantle torque calculated from core surface flow models, Phys. Earth Planet. Inter., 154, , doi: /j.pepi of 14

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