Trans-Paci c temperature eld in the mantle transition region derived from seismic and electromagnetic tomography

R Available online at www.sciencedirect.com Earth and Planetary Science Letters 217 (2004) 425^434 www.elsevier.com/locate/epsl Trans-Paci c temperature eld in the mantle transition region derived from seismic and electromagnetic tomography Yoshio Fukao a;, Takao Koyama b, Masayuki Obayashi c, Hisashi Utada a b c a Earthquake Research Institute, University of Tokyo, Yayoi 1-1-1, Bunkyo-ku, Tokyo 113-0032, Japan Institute for Frontier Research on Earth Evolution (IFREE), Japan Marine Science and Technology Center (JAMSTEC), Showa-machi 3173-25, Kanazawa-ku, Yokohama 236-0001, Japan Institute for Frontier Research on Earth Evolution (IFREE), Japan Marine Science and Technology Center (JAMSTEC), Natsushima-cho 2-15, Yokosuka 237-0061, Japan Received 30 June 2003; received in revised form 9 October 2003; accepted 11 October 2003 Abstract The trans-pacific temperature field for the depth range 350^850 km was inferred from global seismic tomography and semi-global electromagnetic tomography. The seismic tomography incorporated millions of reported first arrival times and 7000 PP^P differential travel times measured on broadband seismograms. The electromagnetic tomography used voltage data from trans-pacific submarine cables and magnetic field data from circum-pacific geomagnetic observatories. The resultant P-wave velocity anomalies and electrical conductivity anomalies were converted to temperature anomalies using a proposed conversion formula and experimental results for mantle minerals, respectively. These conversions show consistently high-temperature anomalies of 200^300 K in the mantle transition region beneath the Hawaiian hotspot. At subduction zones, where slab-related cold anomalies and wedge mantlerelated hot anomalies are likely to coexist in close proximity, the seismic and electromagnetic tomography did not always give consistent features, in part because of the preferred sensitivity of electromagnetic tomography to hot anomalies. Low-temperature anomalies of 200^300 K associated with subducted slabs are clearly resolved in the seismic tomography, but are less apparent in the electromagnetic tomography. The high-temperature anomaly in the intervening zone between the Mariana and Philippine slabs is very pronounced in the electromagnetic tomography but is marginal in the seismic tomography. ß 2003 Elsevier B.V. All rights reserved. Keywords: seismic tomography; electromagnetic tomography; temperature anomaly; hotspot; subducted slab 1. Introduction * Corresponding author. Tel.: +81-3-5841-5723; Fax: +81-3-3816-1159. E-mail addresses: fukao@eri.u-tokyo.ac.jp (Y. Fukao), tkoyama@jamstec.go.jp (T. Koyama), obayashi@jamstec.go.jp (M. Obayashi), utada@eri.u-tokyo.ac.jp (H. Utada). Many recent geodynamic modeling studies have attempted to relate, either explicitly or implicitly, the distribution of seismic velocity anomalies derived from global tomography to temperature variations [1], which are then converted to the thermally induced density anomalies by which 0012-821X / 03 / $ ^ see front matter ß 2003 Elsevier B.V. All rights reserved. doi:10.1016/s0012-821x(03)00610-1

426 Y. Fukao et al. / Earth and Planetary Science Letters 217 (2004) 425^434 mantle convection is driven [2,3]. A di culty with such modeling is the non-uniqueness of converting seismic velocity anomalies to temperature anomalies, given the possible signi cance of lateral heterogeneities in the chemical composition of the mantle [4]. Because the sensitivity of electrical conductivity to temperature and other environmental parameters is very di erent from that of seismic velocity, simultaneous mapping of seismic velocity and electrical conductivity distributions should more narrowly constrain the temperature eld of the mantle than seismic mapping alone, or, alternatively, may isolate temperature e ects from other environmental e ects. This is the rst report of the synthesis of temperature anomaly images in the transition region from seismic and electromagnetic (EM) tomography. Electrical conductivity is a temperature-sensitive parameter, although it also depends strongly on the degree of partial melting and the dissolution of hydrogen or water [5]. As examples, for Mg-rich olivine (Mg,Fe) 2 SiO 4, the relative temperature dependences of P- and S-wave velocities, d(ln V p )/dt and d(ln V s )/dt, are 35.4U10 35 /K and 37.3U10 35 /K at room temperature [6], while the relative temperature dependence of electrical conductivity, d(ln c)/dt, is 6.4U10 33 /K at 1700 K [7]. EM tomography is, therefore, a promising tool for detecting lateral variations in the temperature eld. Alternatively, if the temperature eld is reasonably well mapped by seismic tomography, EM tomography may be used to assess the degree of partial melting or dissolution of hydrogen in the mantle. 2. Comparison of seismic and EM tomography As compared to seismic tomography, three-dimensional EM tomography is still at a premature stage because of the inherent nature of the inverse problem. Some attempts [8,9] have been made to backproject global magnetic eld data to a threedimensional conductivity distribution at depths down to the mid-mantle. However, these results do not have su cient resolution to make a joint interpretation with seismic tomography results. More recently, Koyama [10] inverted electric and magnetic eld data for the three-dimensional conductivity distribution in the mantle transition region at depths from 350 to 850 km, under the Paci c Ocean. We have updated his result to compare the resultant model with that of Fukao et al. [11], who did a whole mantle P-wave travel time tomography by combining two million reported rst arrival times with more than 7000 PP^P differential travel times from broadband seismic records, which greatly improved the resolution in the upper to middle mantle beneath the central Paci c. Table 1 summarizes our EM tomography updated from [10] in comparison with seismic tomography [11]. Observations in seismic tomography measure the propagation speed of a change in the Earth s elastic eld, while observations in EM tomography measure the di usion characteristics of a change in the Earth s EM eld. With this di erence the underdetermined nature of the inverse problem is more serious in EM tomography. However, the lateral variation in electrical con- Table 1 Summary of seismic and EM tomography Seismic tomography [11] EM tomography, updated from [10] Data Reported rst arrivals+broadband PP^P times Submarine cable voltage data+magnetic eld data Target Whole mantle with higher resolution in western Paci c Depth range 350^850 km beneath northern hemisphere Paci c Method Iteratively linearized inversion by CG method [16] Iteratively linearized inversion by BFGS update [24] Parameters P-velocity perturbations of mantle blocks, dv 3D in Eq. 1 Electrical conductivity perturbations of mantle blocks, ln[c 3D /c 1D ]ineq. 2 Number of blocks 32U64U16 basic blocks with smaller blocks in 6U12U5 regular blocks (0^90 N, 90^270 E) western Paci c Radial variation Increase by a factor of 1.4 from Moho to 800 km depth Increase by a factor of 2000 from Moho to 800 km depth Lateral variation A fraction of 31.5 to 1.5% of the average A factor of 1/6 to 6 of the mean

Y. Fukao et al. / Earth and Planetary Science Letters 217 (2004) 425^434 427 ductivity is almost three orders of magnitude greater than that of seismic velocity, as demonstrated in Table 1, so that three-dimensional EM tomography should be still feasible. We used voltage data from eight submarine cables and magnetic eld data in observational periods ranging from 1 to 10 years from 17 geomagnetic observatories (see Fig. 3 for their locations), from which the MT (magneto-telluric) and GDS (geomagnetic deep sounding) responses were calculated. The spectral components of signal range from 1.3 to 28.4 days in period. Because of the long-period, long-wavelength nature of the signal, the conventional treatment of an EM plane source on a at Earth is not feasible. We assume a dipole EM source on a spherical Earth. The starting model was a radially symmetric conductivity model with an ocean^land contrast at the top [12] that can explain all the relevant data in a consistent way so that residuals may be attributed to the e ect of lateral heterogeneity. Fig. 1 shows this starting model in comparison with a standard radially Fig. 2. Sensitivity map of one-dimensional electrical conductivity [12]. Sensitivity is mapped in the (T,d) domain where d is source depth with 50-km increment and T is period of EM variation with 1-day increment. The gray scale indicates the logarithmic change in MT or GDS response R at period T against a unit logarithmic change in electrical conductivity at depth d. Fig. 1. Comparison of the radially symmetric distribution of P-wave velocity (IASP91 [13]) in a linear scale with that of electrical conductivity [12] in a logarithmic scale, over a depth range of 0^1000 km. The latter is used as the starting model for our electromagnetic tomography. symmetric P-wave velocity model (IASP91 [13]). Electrical conductivity increases by three orders of magnitude from the Moho to 1000 km depth, while P-velocity increases by only 40%. For the conductivity distribution a very large increase occurs at depths around 400 km depth. The depth range imaged by the EM tomography in this study is restricted between 350 and 850 km. Of course, it is well known that the conductivity distribution above 350 km depth is strongly heterogeneous (e.g. [14]). Such heterogeneity, however, does not a ect the EM responses at periods of our interest, as described below. Fig. 2 plots the sensitivity of radially symmetric conductivity distribution as functions of source depth d with an increment of 50 km and period T of EM variation with an increment of 1 day [12]. The intensity at point (T,d) de nes the logarithmic change in MT or GDS response at period T against a unit logarithmic change in electrical con-

428 Y. Fukao et al. / Earth and Planetary Science Letters 217 (2004) 425^434 Fig. 3. Tomographic maps at four di erent depths in the transition region. (Left) P-wave velocity perturbations [11]. High- and low-velocity anomalies are colored blue and red, respectively, in linear scale. Tomographic cross-sections were taken along pro le P. (Right) Electrical conductivity perturbations. High- and low-conductivity anomalies are colored red and blue, respectively, in logarithmic scale. Solid lines indicate submarine geopotential cables, and triangles represent magnetometer stations.

Y. Fukao et al. / Earth and Planetary Science Letters 217 (2004) 425^434 429 ductivity at depth d. Because of the conductivity contrast across 400 km depth, the signal we used has little sensitivity in the upper mantle above 400 km depth. This would be also the case for the aspherical part of conductivity distribution. Electric eld perturbation NE at the receiver due to lateral anomaly Nc of electrical conductivity in the electric eld E at the source can be described as a weighted volume integral of NcE [15]. We divide this volume integral into the contributions from the upper mantle (above 400 km) and from the transition region. For EM variations with periods longer than 1 day or induction length scales greater than 600 km, the shallower contribution should be much smaller than the deeper contribution because of large di erences in radially symmetric reference value c and its aspherical perturbation Nc between the shallower and deeper parts across 400 km depth. This expectation has been con rmed by extensive synthetic tests (Koyama et al., in preparation, 2003). Fig. 3 compares anomaly maps of P-wave ve- Fig. 4. Results of a checkerboard resolution test at two di erent depths in the transition region. At each depth the input pattern and the output from the test are shown. (Left) P-wave velocity perturbations in linear scale. (Right) Electrical conductivity perturbations in logarithmic scale.

430 Y. Fukao et al. / Earth and Planetary Science Letters 217 (2004) 425^434 locity with those of electrical conductivity at four di erent depths in the transition region. The corresponding checkerboard resolution maps are shown in Fig. 4 for two depths. A checkerboard resolution test examines to what extent an input alternate pattern of positive and negative anomalies can be recovered from a given synthetic dataset [16]. The test pattern for the seismic tomography is reasonably well recovered except for the eastern Paci c region. Taking this resolvability Fig. 5. Cross-sections along pro le P across Hawaii and Philippines. See Fig. 3 for the location of the pro le. (A) P-wave velocity anomalies at depths 200^1000 km. (B) Electrical conductivity anomalies at depths 350^850 km. (C) Temperature anomalies converted from P-wave velocity anomalies. (D) Temperature anomalies converted from electrical conductivity anomalies. (E) S-wave velocity anomalies at depths 200^1000 km in model SAW24B16 [21]. (F) S-wave Q 31 anomalies at depths 200^660 km in model QRLW8 [22].

Y. Fukao et al. / Earth and Planetary Science Letters 217 (2004) 425^434 431 into account, the transition region is extensively slow under Hawaii and remarkably fast behind the Japanese islands. The periphery of the Philippine Sea is marked by fast anomalies, presumably due to subducted slabs. By contrast, the area resolvable in the EM tomography is narrowly con- ned to the vicinity of the observational cables and stations. Taking this limitation into account, the transition region is highly conductive under Hawaii and almost featureless behind the Japanese islands. The transition region under the Philippine Sea is conductive at depths above 550 km but resistive below it. Fig. 5A,B shows cross-sections of the tomographic images along a pro le subparallel to the Hawaii^Guam^Philippines cables (see Fig. 3 for the location). This is one of the best resolved pro- les in the EM tomography. The Hawaiian highconductivity anomaly extends over a depth range from 450 to 750 km, with poor resolution for its upper and lower extensions. The corresponding seismic low-velocity anomaly extends upward well beyond this depth range, but its downward extension is limited to less than 1000 km in depth [11]. The low-conductivity anomaly under the Philippine Sea extends between depths of 550 and 850 km. The seismic tomography indicates that this is attributable to cold slabs now stagnant beneath the region around the Philippine Sea [17,18]. This low-conductivity anomaly is overlain by a high-conductivity anomaly at depths above about 550 km. The corresponding seismic crosssection in the same depth range is complicated by fast anomalies due to the subducted slabs of the Paci c plate from the Mariana trench, the Philippine Sea plate from the Philippine trench and the Indo-Australia plate from the Java trench. The intervening zone is marginally slow and may be compared to the conductive zone at depths above 550 km in the same region. Fig. 6 shows the crosssections for the checkerboard resolution tests, demonstrating that the above are the resolvable features. 3. Temperature anomalies derived from seismic and EM tomography The comparison of the images from the seismic and EM tomography points to a correlation between high- (low-) velocity anomalies and low- (high-) conductivity anomalies, although the cor- Fig. 6. Cross-sections of the results of the checkerboard resolution test along the same pro le as in Fig. 5. (A) Input synthetic P-wave velocity anomalies at depths 200^1000 km. (B) Input synthetic electrical conductivity anomalies at depths 350^850 km. (C) Result of inversion for synthetic anomaly pattern A. (D) Result of inversion for synthetic anomaly pattern B.

432 Y. Fukao et al. / Earth and Planetary Science Letters 217 (2004) 425^434 relation is not always perfect. Where such a correlation exists, we may invoke thermal origins for the velocity and conductivity anomalies. Assuming tentatively that all the anomalies are of thermal origin, we converted the velocity and conductivity anomalies to temperature anomalies to test for consistency (or inconsistency) between the two conversions. For the velocity-to-temperature conversion we used the depth-dependent conversion factor, c, proposed by Karato [19] on the grounds of mineral physics: dt 3D ¼ 3c½dV 3D =V 1D Š ð1þ where dt 3D is the lateral temperature perturbation from the radially symmetric temperature distribution T 1D, and dv 3D is the lateral velocity perturbation from the radially symmetric velocity distribution V 1D. For the conductivity-to-temperature conversion, we used the following formula: dt 3D =T 1D ¼ 3ln½c 3D =c 1D Š=ln½c 1D =c O Š ð2þ where c 1D is the radially symmetric conductivity model used as a starting model for inversion for the three-dimensional conductivity model c 3D. c O is the pre-exponential term of the Arrhenius formula for the representative mantle mineral in the relevant depth range: c ¼ c O expð3h=ktþ ð3þ where H is activation enthalpy and k is Boltzmann s constant. Eq. 2 may be derived from Eq. 3, assuming that dt 3D /T 1D I1. For T 1D at depth d, we adopted the simplest, smoothest model of Ito and Katsura [20]: T 1D = 0.5d+1500, where T and d are measured in K and km, respectively. For c O, we used a geometric mean of the laboratory values of c O for wadsleyite (L-spinel) and ringwoodite (Q-spinel) [7], two major mineral phases in the mantle transition zone. Fig. 5C,D shows cross-sections for the temperature perturbation dt 3D, calculated from the seismic and EM tomography, respectively. They indicate consistently that the Hawaiian hot anomaly is in excess of about 200^300 K over a horizontal length of 1000 km in the mantle transition region. The temperature eld under the Philippine Sea is more complex. In Fig. 5C, the most pronounced features are the cold anomalies of 200^300 K associated with the steeply subducted and then complexly distorted slabs from the Mariana trench and Philippine trench. Between these zones of cold anomalies is a region of marginally hot anomaly at depths above 600 km. By contrast, the most remarkable feature in Fig. 5D is a hot anomaly of 200^300 K in this intervening zone. The underlying cold anomaly of 200^300 K appears to correspond to the one due to the deeply subducted slabs as indicated in the seismic tomography. 4. Discussion The overall image of the temperature eld is consistent for the seismic and EM tomography. The anomalies in the transition region are on the order of 200^300 K at a scale of 1000 km. The mantle at 400^800 km depth beneath Hawaii is anomalously hot, a feature that is consistent in both seismic and EM tomography. The transition region under the Philippine Sea is characterized by cold anomalies due to subducted slabs, with a relatively hot anomaly in the intervening zone. It appears that the EM tomography emphasizes hot (conductive) anomalies and deemphasizes cold (resistive) anomalies, as compared to seismic tomography. This tendency is reasonable since EM signals mainly attenuate in conductive (hot) regions. The lack of quantitative agreement between Fig. 5C and D in the Philippine Sea region is likely to be due in part to this sensitivity di erence between seismic and EM tomography. Taking into account the limitations in the resolution and accuracy of the inversions, uncertainties in the conversion formulae, and possible factors other than temperature e ects, we consider that the temperature elds estimated from the seismic and EM tomography are in reasonable agreement. It would be intriguing to compare the crosssection of P-wave velocity anomaly with that of S-wave velocity anomaly, since their temperature dependences are expected to be qualitatively similar [19]. Fig. 5E shows the cross-section of the S- wave velocity model (SAW24B16) derived from surface wave and overtone data [21]. Because of the nature of the datasets, the structure in the

Y. Fukao et al. / Earth and Planetary Science Letters 217 (2004) 425^434 433 subduction zones is probably better resolved in the P-velocity model (Fig. 5A) but the structure in the mid Paci c region is probably better resolved in the S-velocity model (Fig. 5E). The Hawaiian slow anomaly extends down to the uppermost lower mantle in the P-velocity model but is limited to the upper mantle in the S-velocity model. The slab subducted from the Mariana trench is imaged as an anomalously fast zone in the P-velocity model. In the S-velocity model, on the other hand, the slab-related fast anomaly is less outstanding than a pair of slow and fast anomalies on the Paci c side of the Mariana trench which is not obvious in the P-velocity model. The S-wave slow anomaly in the intervening zone between the Mariana and Philippine trenches is quite strong but is con ned to the upper mantle (above 400 km depth), below which the slab-related fast anomalies are pronounced. Thus, although the overall patterns are similar to each other between the P- and S-velocity models, detailed comparison must await further studies. It would be even more intriguing to compare the cross-section of electrical conductivity anomaly with that of seismic attenuation anomaly, because both electrical conductivity and seismic wave attenuation Q 31 follow the Arrhenius formula as of Eq. 3. Fig. 5F shows the cross-section of the upper mantle S-wave Q 31 model (QRLW8) derived from surface wave and overtone data [22]. The Hawaiian hot plume is imaged as high-conductivity and high-attenuation anomalies. In both the EM tomography and Q 31 tomography the slab subducted from the Mariana trench has not been imaged. The mantle beneath the Philippine Sea has been imaged as high-conductivity anomaly at depths above 550 km with low-conductivity anomaly below it. This mantle part has also been imaged seismically as high-attenuation anomaly at depths above 300 km with low-attenuation anomaly below it. Thus, although there is a substantial discrepancy in vertical extent of anomaly, the upper mantle under the Philippine Sea has been imaged as high-conductivity and high-attenuation anomalies with little signature of the Mariana slab of the Paci c plate on the Paci c side. Together with seismic parameters including Q 31 [23], electrical conductivity should become an increasingly important parameter for exploring the mantle environment three-dimensionally. Acknowledgements We are grateful to two anonymous reviewers for useful comments. This study was supported by the Ocean Hemisphere Network Project sponsored by the Ministry of Education, Culture, Sports, Science and Technology, Japan.[VC] References [1] D.A. Yuen, O. Cadek, A. Chopelas, C. Matyska, Geophysical in uences of thermal-chemical structures in the lower mantle, Geophys. Res. Lett. 20 (1993) 899^902. [2] B.H. Hager, R.W. Clayton, M.A. Richards, R.P. Comer, A.M. Dziewonski, Lower mantle heterogeneity, dynamic topography and the geoid, Nature 313 (1985) 541^545. [3] A.M. Forte, R.L. Woodward, Seismic-geodynamic constraints on three-dimensional structure, vertical ow, and heat transfer in the mantle, J. Geophys. Res. 102 (1997) 17981^17994. [4] A.M. Forte, H.K. Claire Perry, Geodynamic evidence for a chemically depleted continental tectosphere, Science 290 (2000) 1940^1944. [5] S. Karato, The role of hydrogen in the electrical conductivity of the upper mantle, Nature 347 (1990) 272^273. [6] O.L. Anderson, E. Schreiber, R.C. Liebermann, N. Soga, Some elastic constant data on minerals relevant to geophysics, Rev. Geophys. 6 (1968) 491^524. [7] Y. Xu, B.T. Poe, T.J. Shankland, D.C. Rubie, Electrical conductivity of olivine, wadsleyite, and ringwoodite under upper-mantle conditions, Science 280 (1998) 1415^1418. [8] P. Tarits, M. Alexandrescu, 3D analysis of very long period geomagnetic data: The conductivity of the lower mantle, in: Mantle and Global Studies Including Laboratory and Satellite Results, Proceedings of the 14th workshop on electromagnetic induction in the Earth, 1998, pp. 90^91. [9] A. Schultz, G. Pritchard, Three-dimensional inversion for large-scale structure in a spherical domain, in: B. Spies, M. Oristigliano (Eds.), Three-Dimensional Electromagnetics, Geophysical Development Series, vol. 7, AGU, Washington, DC, 1999, pp. 429^452. [10] T. Koyama, A Study on the Electrical Conductivity of the Mantle by Voltage Measurements of Submarine Cables, Ph.D. Thesis, University of Tokyo, 2001, 129 pp. [11] Y. Fukao, A. To, M. Obayashi, Whole mantle P-wave tomography using P and PP-P data, J. Geophys. Res. 108 (2003) 10.1029/2001JB000989. [12] H. Utada, T. Koyama, H. Shimizu, A.D. Chave, A semi-

434 Y. Fukao et al. / Earth and Planetary Science Letters 217 (2004) 425^434 global reference model for electrical conductivity in the mid-mantle beneath the north Paci c region, Geophys. Res. Lett. 30 (2003) 16092^16095. [13] B.L.N. Kennett, E.R. Engdahl, Traveltimes for global earthquake location and phase identi cation, Geophys. J. Int. 105 (1991) 429^465. [14] R.L. Evans, P. Tarits, A.D. Chave, A. White, G. Heinson, J.H. Filloux, H. Toh, N. Seama, H. Utada, J.R. Booker, M.J. Unsworth, Asymmetric electrical structure in the mantle beneath the East Paci c Rise at 17 degrees S, Science 286 (1999) 752^756. [15] H. Utada, H. Munekane, On galvanic distortion of regional three-dimensional magnetotelluric impedances, Geophys. J. Int. 140 (2000) 385^398. [16] H. Inoue, Y. Fukao, K. Tanabe, Y. Ogata, Whole mantle P-wave travel time tomography, Phys. Earth Planet. Inter. 59 (1990) 294^328. [17] Y. Fukao, M. Obayashi, H. Inoue, M. Nenbai, Subducting slabs stagnant in the mantle transition zone, J. Geophys. Res. 97 (1992) 4809^4822. [18] Y. Fukao, S. Widiyantoro, M. Obayashi, Stagnant slabs in the upper and lower mantle transition region, Rev. Geophys. 39 (2001) 291^323. [19] S. Karato, Importance of anelasticity in the interpretation of seismic tomography, Geophys. Res. Lett. 20 (1993) 1623^1626. [20] E. Ito, T. Katsura, A temperature pro le of the mantle transition zone, Geophys. Res. Lett. 16 (1989) 425^428. [21] C. Me gnin, B. Romanowicz, The three-dimensional shear velocity structure of the mantle from the inversion of body, surface and higher-mode waveforms, Geophys. J. Int. 143 (2000) 709^728. [22] B. Romanowicz, Y. Gung, Superplumes from the coremantle boundary to the lithosphere, Science 296 (2002) 513^516. [23] B. Romanowicz, J. Durek, Attenuation in the earth: a review, AGU Geophys. Monogr. 117 (1999) 161^180. [24] C.G. Broyden, J.E. Dennis Jr., J.J. More, On the local and superlinear convergence of quasi-newton methods, J. Inst. Math. Appl. 12 (1973) 223^245.