ANISOTROPY OF THE EARTH'S INNER CORE

Transcription

1 ANISOTROPY OF THE EARTH'S INNER CORE Xiaodong Song Lamont-Doherty Earth Observatory Palisades, New York Department of Earth and Environmental Sciences Columbia University, New York Abstract. The inner core has the intriguing property that seismic waves traveling parallel to the Earth's spin axis arrive earlier than those traveling parallel to the equatorial plane. The travel time is some 6 s faster from pole to pole than across the equator. This difference is not the result of different polar and equatorial radii of the inner core, for it would require the inner core to be elongated at the poles by more than one third of its radius. Rather, this 6-s travel time difference is the result of the inner core's being anisotropic; wave speeds differ for different directions of wave propagation. This anisot- ropy, discovered only in the last decade, is characterized by cylindrical symmetry about an axis approximately aligned with the Earth's spin axis. The anisotropy is believed to be due to a preferred orientation of anisotropic iron crystals composing the inner core, but the mechanisms responsible for creating such a preferred orientation remain uncertain. With the anisotropy now well established as a basic property of the inner core, its quantification and that temporal variations of its orientation have become a vital tool for probing the structure, composition, and dynamics of the Earth's deep interior. INTRODUCTION The Earth's inner core, consisting of solid iron, is 30% smaller in radius but more than 30% heavier in mass than the Moon. It is separated from the rocky mantle by an outer core composed of liquid iron and some light elements. The late Inge Lehmann discovered the inner core 60 years ago [Lehmann, 1936], but this innermost part of the Earth has once again turned up earthquakes that occurred over about 3 decades. Subsequently, Suet al. [1996] used a vast collection of arrival times reported by the International Seismological Centre (ISC) in Edinburgh, Scotland, to solve the inverse problem of determining the time-dependent orientation of the inner core and found that the inner core appears to rotate at 3ø/year, also in the eastward direction. These results support Glatzmaier and Roberts's [1995b] numerical modeling of the dynamo, which predicted that the inner core is driven to rotate eastward at a few degrees a year by the magnetic coupling between the electrically conductive inner core and the magnetic field generated in the fluid core. surprises in the recent years. The inner core plays a role in the Earth's dynamo, which generates and has maintained the magnetic field over much of the Earth's history. It has been long recognized that the slow growth of the solid inner core, as Underlying the discovery of the inner core rotation is liquid iron freezes at the inner core boundary, drives the the establishment and characterization of the seismic convection in the outer core and therefore provides a source of energy for the geodynamo [Braginsky, 1963; Gubbins, 1977; Loper and Roberts, 1978; Loper, 1978]. It was only recently recognized, however, that a solid inner core can stabilize the dynamo and establish a constant polarity of the field such as we have on the Earth [Holierbach and Jones, 1993]. Geodynamo models containing a finite conducting inner core have also been shown to undergo a magnetic reversal [Glatzmaier and Roberts, 1995a, b]. The most recent surprise comes from the reported seismological evidence [Song and Richards, 1996a] that the inner core is rotating eastward at about lø/year faster than the crust and mantle. They observed a small but systematic variation in the travel times of seismic waves traversing the inner core along selected pathways from anisotropy of the inner core, the result of a series of studies in the last decade. Anisotropy is the general term used to describe a medium whose properties (i.e., elastic properties in the case of seismic anisotropy) depend on orientation. Seismic waves in an anisotropic medium travel with different speeds depending on both their polarization and propagation directions. Unless otherwise noted, in the discussion below I use the term "anisotropy" specifically to mean P wave velocity anisotropy. Seismic waves can be observed over a frequency range spanning more than 3 orders of magnitude (from periods of less than a second to almost an hour). At the high frequency end of the spectrum are body waves (with periods of 1-20 s). Of particular interest in this paper are compressional waves (sound waves) that penetrate the fluid outer core, generically called PKP (Figure 1). Sev- Copyright 1997 by the American Geophysical Union /97/97 RG ß 297 ß Reviews of Geophysics, 35, 3 / August 1997 pages Paper number 97RG01285

2 298 ß Song' ANISOTROPY OF EARTH'S INNER CORE 35, 3 / REVIEWS OF GEOPHYSICS 9ter seismometer ake inner core outer core mantle "-' ,.,,, 3,. ' pk KP F- Figure 1. (a) Ray paths and (b) travel times as functions of distance for seismic PKP waves. Distance (A by convention) is measured by the angle subtended at the Earth's center by the source and the station locations. These PKP waves were used in numerous body wave studies of the anisotropy of the inner core. 18 I 120, I I / distance (deg) b eral phases (or "branches") of PKP can be distinguished inside the Earth, and the angular order l and the aziby the paths they follow and by their travel times: waves muthal order m determine the patterns of surface dethat pass through both the outer core and inner core, formation in the form of spherical harmonics. The two PKP(DF) (also called PKIKP); waves reflected off the simplest normal modes of the Earth are 0S2, correinner core boundary, PKP(CD) (also called PKiKP); sponding to ellipsoidal deformation of alternating beand waves that turn in the middle and the bottom of the tween prolate and oblate (thus known as a football outer core, PKP(AB) and PKP(BC), respectively. Since mode), and 0T, corresponding to alternating twisting of the inner core is solid, both compressional waves (P the upper and lower hemispheres (Figure 2). For every waves) and shear waves (S waves) can propagate l, there are 2l + 1 azimuthal order numbers (m from -l through it. However, no shear waves that have traversed to l). On a spherically symmetric, nonrotating, isotropic the inner core have been unambiguously observed. Earth, all the 2l + 1 singlets associated with a multiplet Julian et al. [1972] reported seismic phases that they (n, l) would vibrate with the same frequency (i.e., 2l + associated with PKJKP (waves that travel through the 1 degenerate). Departures from isotropic sphericity recrust, mantle, and the fluid core as compressional waves move this degeneracy and causes the multiplet (n, l) to but travel through the inner core as shear waves), but split into 2l + 1 modes with slightly different natural their association has yet to be confirmed. frequencies, a phenomenon analogous to the Zeeman At the low-frequency end of the seismic wave spectrum are the free oscillations (normal modes) of the Earth. Like a musical instrument, the Earth resonates at discrete frequencies after a large earthquake. These resonances are normal modes of the Earth and are often classified as spheroidal modes ns n, for which elastic dilatation and radial motion occur, and toroidal (torsional) modes n T n, which involve only shear motion parallel to the Earth's surface. The overtone n defines the number of nodal surfaces (with zero displacement) splitting of lines of atomic spectra by a magnetic field. The largest departure from isotropic sphericity arises from the Coriolis forces and from ellipticity associated with the Earth's rotation [e.g., Dahlen and Sailer, 1979]. Additional splitting arises from lateral variations in ve- locity and density, from anisotropy, and from boundary undulation and thus can be used to' map the threedimensional structure of the Earth [e.g., Woodhouse and Dahlen, 1978]. As I discuss below, the splitting of fre-

3 35, 3 / REVIEWS OF GEOPHYSICS Song: ANISOTROPY OF EARTH'S INNER CORE ß 299 quencies of modes for which vibrations in the inner core are strong also implies anisotropy. The anisotropy of the inner core is, to first order, dominated by cylindrical anisotropy throughout the bulk of the inner core with the axis of symmetry aligned approximately with the Earth's north-south spin axis. This cylindrical anisotropy exhibits the same type of symmetry as hexagonal crystals, whose elastic properties are invariant when rotated around one fixed direction (the axis of symmetry). This type of anisotropy is also known as transverse isotropy, axisymmetric anisotropy, or azimuthal anisotropy if the axis of symmetry is horizontal. Transverse isotropy is of broad geophysical applicability (see the review by Thomsen [1986]) owing to its relative simplicity and its approximation of many actual situations in the Earth, such as stacked layers of isotropic media [e.g., Backus, 1962; Anderson, 1989] or cracked isotropic solids [e.g., Crampin, 1984] in shallow crust, both of which are of great interest in seismic exploration of oil fields [e.g., Thomsen, 1986; Crampin, 1987]. Transverse isotropy is sufficiently well established in the upper mantle that it was incorporated into the premlimary reference Earth model (PREM) [Dziewonski and Anderson, 1981], a standard Earth model. A 6-s difference in travel times between waves that go straight through the center of the inner core from pole to pole and those that go across the equatorial plane implies that the P wave velocity is about 3 % faster along the spin axis than in the equatorial plane. The cause of the inner core anisotropy is believed to be preferred orientation of hexagonal close-packed (hcp) iron, a high-pressure polymorph of iron [Takahashi and Bassett, 1964]. In this paper I review basic observations and possible mechanisms of the anisotropy of the inner core and point out the impact of this newly gained knowledge of the structure on the dynamics of the Earth's deep inte- rior. First, I will briefly summarize wave propagation in transversely isotropic media. This is followed by a review of basic seismological observations of the P wave anisotropy of the inner core and theories of its cause. One of the most remarkable features of the inner core anisot- ropy is its temporal variation, which I discuss below. Finally, I show that P wave anisotropy of the inner core reveals strong bounds on the shear wave structure of the inner core. It may hold the key to identifying PKJKP, which has become a "Holy Grail of body wave seismology," as was pointed out by P.M. Shearer [Tromp, 1995a]. WAVE PROPAGATION IN ANISOTROPIC MEDIA The current body wave studies on the anisotropy of the inner core rely on the recognition that wave speeds are direction-dependent in an anisotropic medium. I give the formula of such direction dependences for the case of transverse isotropy below. Equivalent expres- sions were used to derive models of inner core anisot- os minutes ot minutes Figure 2. Ground deformation associated with the two simplest modes of the Earth's free oscillations: (a) spheroidal, "football" mode 0S 2, which is the lowest-frequency normal mode with a period of 54 min, and (b) toroidal, "twisting" mode 0T2. The schematic illustration shows how the planet changeshape during these vibrations, but the actual movements are only a small,fraction of a millimeter for a large earthquake. ropy in various body wave studies discussed later. A derivation of normal-mode splitting due to transverse isotropy is given by Tromp [1995b], who demonstrated that transverse isotropy with a symmetry axis parallel to the rotation axis produces splitting of the simple form tom = to(a' + c'm 2 + dm4), where m denotes the azimuthal order of a specific singlet within a given multiplet with degenerate frequency to; the scalars a', c', and d represent the effects of transverse isotropy on the particular normal mode. Let us now consider plane wave propagation in transversely isotropic media. For a completely general elastic medium, the equations of motion in Cartesian coordinates are = Cijkl, (1) P 02t Oxj Ox l J where i, j, k, l = 1, 2, 3; u i is displacement vector; civet is elastic modulus tensor; and p is density. For a plane wave u (xt, t) = A e im(t-pzj/c), wherea is polarization vector, p is propagation direction, is angular frequency, t is time, and c is phase velociff, we have Bil l = C2 i, (2) where Bi = ci tp p /p is a 3 x 3 positive-definite symmetric matr (known as the Christoffel matra). The phase velocities, c, and corresponding polarizations can be found by solving for the eigenvalues of (2). In general, there are three real eigenvalues with three orthogonal eigenvectors. In an isotropic medium the eigenvectors correspond to one compressional P wave, whose polarization vector coincides with the propagation direction, and two shear S wave components, whose polarization vectors are normal and binormal to the P eigenvector. In an anisotropic medium the P eigenvector in general is not parallel to the propagation direction; hence such body waves are often called quasi-compressional wave, or quasi-shear waves. For simplicity, I drop the distinctions in this paper.

4 300 ß Song' ANISOTROPY OF EARTH'S INNER CORE 35, 3 / REVIEWS OF GEOPHYSICS For a transversely isotropic medium such as the inner core, five independent elastic constants, often denoted as A, C, F, N, and L [Love, 1927], are needed to describe C i kl. These elasti coefficients can be arranged in a matrix C, related to Cijkl by C = Cijkl with o = i =jifi =j ando = 9 - i -jifi 4=j, and by [3 = k = lifk- lando = 9 - k- lifk 4= l. Takingthe x3 axis to be parallel to the axis of symmetry, we have (C ) Cll Cll- 2C66 C13 C C66 Cll C13 C13 C13 C33 A A-2N F A - 2N A F F F C C44 C44 C66 (C o)- L. (4) L (3) axme -- O'(O 0/[ 0) 2 sin 2 cos 2, (9) Seq- sin 2, (10) where ot o - X/ p and [30 = X/ 7p are the P wave velocity in the equatorial plane and the degenerate S velocity for propagation along the symmetry axis, respectively; 8 - (C-.4)/(2.4); cr = (.4 + C - 4L - 2F)/(2.4); and / - (N - L)/(2L). Equations (8)-(10) are arranged in such a way that the variations of Vp, Sme, and Seq are controlled by 8, or, and % respectively. Note that four elastic constants,.4, C, L, and F, can be determined from the P velocity, the S velocity, and two anisotropic parameters of the P velocity. The fifth elastic constant, N, is completely decoupled from the P wave and can be determined only directly from the observation of the shear wave polarized along the equatorial plane. SEISMOLOGICAL OBSERVATIONS FOR THE ANISOTROPY OF THE INNER CORE N Evidence for Inner Core Anisotropy The evidence for the anisotropy of the inner core The exact solution of (2) for this case can be found comes from two different kinds of data sets, namely, (1) analytically [e.g., Daley and Hron, 1977]. For weak an- directional variations of travel times of seismic body isotropy the phase velocities can be approximately by waves that go through the inner core and (2) anomalous low-order harmonics [Backus, 1965; Crampin, 1977; splitting, or splitting not explainable simply by Coriolis Tromp, 1995b]: and ellipticity effects, of the Earth's normal modes. Two 1 1 kinds of travel time data have been used in studying the pvp 2- (3A + 3C + 4L + 2F) + (C -A) cos 2 inner core anisotropy: PKP(DF) arrival times reported by the ISC Bulletins and relative (differential) times + (A + C - 4L - 2F) cos 4, (5) between two PKP branches: one crossing the inner core and the other not (Figure 1). The ISC collects measured ps2me = (A+C+4L-2F) arrival times of seismic waves for all major earthquakes and locates the earthquakes using P wave arrival times - k 8 (A + C - 4L - 2F) cos 4, (6) and the travel time tables of JeJfreys and Bullen [1940]. The principal advantage of using ISC arrival times is the pxe2q _ 1 (L + N) + l(l - N) cos 2, (7) extremely large number of data and the global station where is the angle between the propagation direction coverage, which an individual seismologist cannot and the symmetry axis, Vp is the velocity of the quasi-p achieve. One disadvantage of using ISC data is that the wave, and Sme and Seq are the velocities of the quasiarrival times have been measured using a ruler to estishear waves, whose particle motions are meridional (in mate distances on paper seismograms. A second is that the plane defined by the symmetry axis and the propa- many different people, with different judgment as to gation direction) and equatorial (perpendicular to the where a signal begins, have made the measurements, plane defined by the symmetry axis and the propagation commonly using data from a single seismometer and direction), respectively. By weak anisotropy we mean therefore without comparing recordings by other stathat the anisotropic terms (cos 2 and cos 4 ) are much tions. Measurements of differential times rely on examsmaller than the corresponding constant (direction-inining PKP waveforms and can be obtained either didependent) terms. Note the anisotropic term of S2me is rectly from cross correlations of waveforms from the same as the cos 4 term of V (with the opposite different PKP branches or from fitting synthetic seismosign), thus the anisotropy of the meridional shear wave grams to the PKP waveforms. Greater accuracy in differential travel-time measurements is achieved with such can be derived from the anisotropy of the P wave. From (5)-(7) the velocity perturbations for weak anisotropy analysis than is possible with arrival times reported rouare tinely by the ISC. In addition, unlike absolute arrival times, differential times are relatively insensitive to eravp = e cos 2 - {r sin 2 cos 2, (8) rors in earthquake locations and to unknown three-

5 35, 3 / REVIEWS OF GEOPHYSICS Song: ANISOTROPY OF EARTH'S INNER CORE ß 301 Figure 3. PKP(DF) travel time residuals from the International Seismological Centre (ISC) plotted at station locations and expanded in spherical harmonics (up to degree 4) (reprinted with permission from Nature [Poupinet et al., 1983]; copyright Macmillan Magazines Ltd.). Values are in tenths of a second. A low number means a fast transit of the core. The difference between slow and fast regions is about 2 s. The PKP(DF) residuals were corrected by P residuals at the same stations to reduce the influence of upper mantle structure underneath the stations. dimensional heterogeneities of the crust and mantle along the ray paths. Unfortunately, measuring differential travel times require sufficient effort that such data are very sparse and their global coverage is much poorer than that of the ISC-based data. In analyzing travel time data, residuals of arrival times are formed by subtracting the times predicted for a standard Earth model from measured arrival times; similarly, residuals of differential travel times are formed by subtracting the time differences between two phases concerned predicted for a standard Earth model from measured differential travel times. Poupinet et al. [1983] were first to observe the anomalous travel times associated with PKP(DF). They examined station residuals of PKP(DF) times from the ISC, which were corrected by P residuals at same stations to reduce the biases due to lateral variation in the mantle underneath the stations. They found PKP(DF) through the inner core near the north and south poles to travel about 2 s faster than those near the equatorial plane (Figure 3). They attributed the difference to either heterogeneity near the inner core boundary, in which the polar regions are faster than the equatorial belt, or elongation of the inner core at the poles by 200 km. Masters and Gilbert [1981] first identified the anomalous splitting of the normal modes which have significant normal-mode data. Woodhous et al. [1986] examined seven anomalously split modes that are sensitive to the energy in the core (core-sensitive modes). Subsequently, inner core structure and found that anisotropy of the Ritzwoller et al. [1986] found that about one third of the inner core provides a plausible explanation for the 34 modes whose splitting was resolved are in fact split anomalous splitting. Assuming uniform transverse isotmore, by 30%, than could be predicted solely by the ropy, they estimated the amplitude of P wave anisotropy Earth's rotation. An example of a well-observed anom- to be about 3.4%. This model, or an alternative model alously split mode is shown in Figure 4. All of these with a quadratic depth dependence, predicts PKP(DF) anomalously split modes are sensitive primarily to structure in the core, providing compelling evidence for the existence of aspherical structure at or below the coremantle boundary. Since a number of these modes are sensitive primarily to outer core structure, Ritzwoller et al. [1986] inferred an aspherical structure in the outer core, although they also recognized that such a structure is difficulto sustain in a convecting fluid [Stevenson, 1987]. The hypothesis that the inner core is anisotropic was first proposed by Morelli et al. [1986] and by Woodhouse et al. [1986] in the same issue of Geophysical Research Letters. Morelli et al. [1986] examined PKP(DF) travel times from the ISC catalog at ranges between 120 ø and 180 ø. They found it difficult to fit PKP(DF) travel times at different ranges by introducing perturbations to P wave speeds near the poles or on the equator of the inner core; they recognized, however, that anisotropy within the inner core with cylindrical symmetry aligned with the Earth's spin axis could account for the observed 2-s difference in the travel times for the rays passing through the central part of the inner core. Although they estimated an average P velocity along the symmetry axis about 1% faster than in the equatorial plane, their preferred model included a 3.2% P velocity variation near the surface of the inner core, diminishing quadratically with depth, which is in closer agreement with the travel times 2-4 times as large as those observed in the ISC. Despite this discrepancy, the models of the inner

6 302 ß Song' ANISOTROPY OF EARTH'S INNER CORE 35, 3 /REVIEWS OF GEOPHYSICS '7..o Frequency (mhz) ' g e 1230 L i, Kernels - CMB -, ' i- - i... (' -.-.-' i I,/ ICB Subsequent studies using travel time data [Shearer et al., 1988; Shearer and Toy, 1991] continued to favor the existence of inner core anisotropy. Shearer et al. [1988] examined both PKP(BC) and PKP(DF) travel times reported by the ISC and compared the observed residual patterns with those predicted by models of heterogeneity at the core-mantle boundary and in the inner core and with those predicted by inner core anisotropy. They found no significant anomalies for the PKP(BC) rays, suggesting that the PKP(DF) anomalies are mainly from the inner core. The PKP(DF) residual patterns at various distances could be best explained by a model of uniform anisotropy within the inner core with about 1% velocity variation. The lack of significant travel time variations from the outer core or inner core boundary topography was supported by Roudil and Souriau [1993], who also used PKP(BC) travel times reported by the ISC, and Souriau and Souriau [1989], who examined reflections from the inner core boundary. The latitudinal variation in differential travel times between nearly vertical waves reflected from the inner core boundary (PKiKP) and those from the core-mantle boundary (PcP) suggests that the ellipticity of the inner core boundary is close to that of the hydrostatic equilibrium (1/413) [Souriau and Souriau, 1989]. Furthermore, Shearer and Toy [1991] examined BC-DF (i.e., differential travel times between PKP(BC) and PKP(DF)) at distances of 145 ø to 155 ø, derived from the ISC times and the short-period digital seismograms recorded by the Global Digital Seismograph Network (GDSN). BC-DF differential times are ideally suited for studying the inner core because these phases have very similar ray paths in the mantle and the outer core (Figure la). Unfortunately, because of poor ray path coverage and the lack of ray paths close to the spin axis from high-quality GDSN Figure 4. Example of an anomalously split normal mode. (a) Amplitude spectra of singlets composing the multiplet 8S4 seismograms, they found it difficult to discriminate un- [from Widmer et al., 1992]. The singlets are arranged in ascend- ambiguously between heterogeneity and anisotropy. ing azimuthal order with the one corresponding to the m = Nevertheless, a model of inner core anisotropy with -4 in the front. (b) Observed and predicted singlet frequenhexagonal symmetry and about 1% velocity variation cies (left) and sensitivity kernels (right) for the multiplet 8S4 (courtesy of J. Tromp). The kernels show the sensitivity of 8S4 provides the simplest explanation of the observed residto perturbations in compressional velocity o (solid), shear ual pattern. velocity [3 (short-dashed), and density p (long-dashed) as a Meanwhile, more observations of mode splitting were function of depth. The mode has 52% of its elastic energy in identified and were used to invert for both mantle modthe Earth's core, among which 6% is in the inner core. On the left, the triangles indicates singlet frequencies determined by Widmer et al. [1992]. The observed splitting between singlets els and core structures. Unfortunately, the interpretation that anomalous splitting of core-sensitive modes is caused primarily by the anisotropy of the inner core m = _+ 4 and m - 0 is 1.8 times that predicted for a rotating, remained controversial [Giardini et al., 1987; Ritzwoller et hydrostatic Earth model (dashed line). Anomalous splitting of al., 1988; Li et al., 1991; Widmer et al., 1992]. All of these normal modes with significant energy in the Earth's core (corestudies yielded consistent results that the modes with sensitive modes) such as this were used to infer aspherical significant energy in the Earth's mantle can be explained structure of the core, including the anisotropy of the inner core. The solid line indicates the predicted splitting for transby three-dimensional mantle structures, but the obverse isotropy of the inner core using the model of Tromp served anomalously split core-sensitive modes require [1993], and rotation and ellipticity. aspherical structure at or below the core mantle boundary, which must be dominantly axisymmetric. These authors disagreed, however, over where in the core the core anisotropy were presented as a viable explanation aspherical structure is located (outer core, inner core, for the observed anomalies of the travel times and nor- core-mantle boundary, or inner core boundary) and mal modes available at that time. about its nature (lateral heterogeneity or anisotropy). The underlying difficulties in addressing these questions

7 35, 3 /REVIEWS OF GEOPHYSICS Song' ANISOTROPY OF EARTH'S INNER CORE ß 303 are first, that even the core-sensitive modes have more than 50% of their energy in the mantle, with a number of them having very little energy in the inner core (less than 3%), and second, that both heterogeneity and anisotropy contribute to splitting. In particular, Li et al. [1991] derived a much more complicated anisotropic model, which provided an adequate fit to both the normal mode and the travel time data then available. Widmer et al. [1992], however, examined the model of Li et al. [1991] and found it difficult to fit the splitting of the modes with 3% energy in the inner core without overpredicting the splitting of modes with more than 7% energy in the inner core, which led them to conclude that the aspherical structure is in the outer core. Furthermore, Suda and Fukao [1990] failed to observe anomalous splitting of certain core-sensitive modes. The evidence for the inner core anisotropy remained inconclusive until the early 1990s, when new sets of information started to emerge. Like Shearer and Toy [1991], Creager [1992] picked BC-DF differential travel times between 146 ø and 160 ø from short-period digital recordings of the GDSN. He found that rays traveling through the inner core nearly parallel (within 40 ø ) to the rotation axis arrive 2 to 4 s faster than rays following other paths (Figure 5a). The mean of the residuals of these near-polar paths (2.9 s) exceeds the mean of nonpolar paths (0.2 s) by seven standard deviations (Figure 5b). He argued that because of their dependence on ray direction, and not on geographical sampling, the anomalies are most plausibly explained by inner core anisotropy, even though from the differential travel times alone he could not distinguish anisotropy in inner core (affecting DF) from anisotropy in a boundary layer at the base of the outer core (affecting BC). He found the P wave velocity at the outermost 300 km of the inner core is 3.5 % faster along the Earth's spin axis than along the equatorial plane (assuming uniform transverse isotropy). Most of the anomalies of Creager [1992], however, are from one path (earthquakes in South Sandwich Islands region to station COL at College, Alaska) and all the DF waveforms look complicated. In an effort to confirm the anisotropy of the inner core, Song and Helmberger [1993] conducted a systematic search for PKP ray paths with a variety of angles from the Earth's spin axis, using all seismogram archives available (analog and digital, earthquakes and nuclear explosions). The most nearly polar paths are within 9ø-18 ø from the spin axis. For all the polar paths, differential times of BC-DF consistently yield residuals of s larger than equatorial paths. These anomalies are correlated with faster DF times of the same magnitude (1-4 s) from the same records but are not correlated with the absolute B C times, suggesting the observed BC-DF anomalies are due to structure in the inner core. The DF anomalies do not correlate with geographicalocations in the inner core, suggesting that inner core heterogeneity is not likely the cause. The difference between equatorial paths and polar m GOS A(deg) Figure 5. Measured differential travel time residuals (circles) between PKP(BC) and PKP(DF) plotted with respecto (a) cos 2 ( and (b) source-station distance A (reprinted with per- mission from Nature [Creager, 1992]; copyright Macmillan Magazine, Ltd.). Here ( is the angle between the Earth's spin axis and the inner-core leg of the ray path. Bars show mean and two standard deviations of binned data at intervals of 0.1 in Figure 5a and 1.0 ø in Figure 5b. In Figure 5b the mean and standard deviations are calculated using only times with cos 2 (() < 0.6. In Figure 5a, predicted times are calculated for a surface focus using the anisotropy models of Morelli et al. [1986] (longdashed line), Shearer et al. [1988](short-dashed line), Shearer and Toy [1991] (dotted line), developed mostly from the ISC travel times, at A = 151 ø and using the model of Creager [1992] developed from his measured differential travel times, at A = 150 ø (lower solid line) and at A = 152 ø (upper solid line). paths is nicely demonstrated by PKP seismograms from several nuclear explosions (Figure 6). The DF waves in these short-period seismogramsample the inner core at various ray angles from the spin axis (from 10 ø to 60ø). Clearly, the polar paths (right pair of columns) show anomalously early DF arrivals relative to B C compared with the equatorial paths (left pair of columns). Furthermore, these anomalies can been seen in more stable long-period waveforms (Figure 7) and in broadband waveforms [Vinnik et al., 1994], which, in general, are less affected by scattering. The fitting of synthetic seis- mograms to such waveforms provides additional constraints on the nature of the anisotropy, such as its depth

8 ß ß 304 ß Song' ANISOTROPY OF EARTH'S INNER CORE 35, 3 / REVIEWS OF GEOPHYSICS 144 NTS(Handley) (D=30-37 ø Amchitka (D=37-43 ø Novaya Zemlya =65 o Novaya Zemlya =81 o. B' 146 PRE(Long, I SNA i ; ',', 148 P SN i, 150, ;,, i ' DF BC AB GRM(Milrow) [ 10 sec. I... I Figure 6. Short-period PKP seismograms with respecto ray orientations in the inner core [from Song and Helmberger, 1993]. The data are from nuclear explosions at Nevada (NTS), Amchitka, and Novaya Zemlya test sites recorded at World-Wide Standardized Seismograph Network (WWSSN) stations in South Africa (BUL, GRM, PRE, GRM), South America (SOM) and Antarctica (SNA). ß is the angle for the PKP(DF) ray leg in the inner core and the equatorial plane (complementary to the angle of the inner core leg with the Earth's spin axis). From left to right, the ray orientations in the inner core change from equatorial to polar. The dashed lines show predicted arrival times for a surface focus using the preliminary reference Earth model (PREM)[Dziewonski and Anderson, 1981]. It is clear that the polar path show large BC-DF residuals with respect to PREM ( s), compared with typical residuals (within 0.5 s) for the equatorial paths. These anomalies are more dramatic near the PKP caustic, where all branches of PKP come together and only one strong arrival is normally observed, as in the BUL record from NTS and the PRE record from Longshot. However, early DF arrivals are clearly observed in the SNA record from a bomb at Novaya Zemlya, on November 2, 1974 (SNAl10274). dependence (see discussion below). Moreover, wave- larger, newly observed BC-DF travel time anomalies. forms allow the study of shallow events, for which shortperiod signals on seismograms are often complex and arrival times are difficult to measure. With the exhaus- An example of the fit of Tromp's [1993] model to an anomalously split mode is shown in Figure 4b. In light of these results indicating large travel time tive da, ta selection and tremendous effort in isolating anomalies, Shearer [1994] reexamined PKP(DF) travel contributions from the mantle and outer COre, it was times reported by the ISC and concluded that the clear that the observed variations in differential travel previous ISC studies had underestimated the size of times and in waveforms arise from structure in the inner PKP(DF) travel time anomalies. He found the ISC data core an d that the apparent anisotropy in P velocity of the to be consistent with the stronger anisotropy of 3.5% inner: core is a real feature of the inner core. Song and [Creager, 1992] or 3% [Song and Helmberger, 1993] at key Helmberger [1993] estimated that the average amplitude distances of 149ø-166 ø, where data coverage is the best. of the anisotropy about 3% (assuming uniform trans- The underestimated travel time variations might have verse iso.tropy with a symmetry axis parallel to the spin led Widmer et al. [1992] to reject inner core structure as axis). a plausible explanation for the anomalou splitting of At the same time, a surprising support for inner core core-sensitive modes [Masters, 1993]. anisotropy came from free oscillation. Tromp [1993] inferred a transversely isotropic inner core in which Models of Inner Core Anisotropy anisotr, opy varies with depth. He showed that all of the The presence of significant anisotropy in the inner 18 anomalously split core-sensitive modes that had been core is now well established, with additional support identified could in fact be explained by transverse isot- from both travel time and normal mode data [l/innik et ropy of the Earth's inner core that is compatible with the al., 1994; Su and Dziewonski, 1995; Tromp, 1995a; Song,

9 35, 3 / REVIEWS OF GEOPHYSICS Song: ANISOTROPY OF EARTH'S INNER CORE ß 305 ' I ' DF BC AB pdf pbc pab 06/17/67 COL km 12/05/74 KOD o 162km 1 '[ 1 I % * - -/'"... I,,,,, I... I, Time (s) Figure 7. A comparison of PKP seismograms at a same distance recorded by long-period instruments between a polar path (from an earthquake in the South Sandwich Islands region to WWSSN station COL, at College, Alaska) and an equatorial path (from an earthquake in Peru to KOD, at Kodaikanal, India) [from Song and Helmberger, 1993]. The dashed line (middle) is a synthetic seismogram for a focal depth of 150 km using PREM. The synthetic seismogramatches the PKP waveform at KOD ahd the BC and AB waveforms at COL. The DF pulse at COL, however, arrives about 3 s earlier than those of the PREM synthetic and at KOD. The DF anomaly is also apparent in the reflected PKP waveforms, which were not modeled. 1996; McSweeney et al., 1997]. Table 1 summarizes the most recent models of inner core anisotropy. Creager [1992] gave a summary of earlier models. All models assume that inner core anisotropy is transversely isotropic, which appears to be adequate for the observations currently available. An important issue is the spatial distribution of the inner core anisotropy. How does it vary with depth? Does it Vary laterally? Is the symmetry (fast) axis tilted from the spin axis? Some resolution of the depth dependence of the inner core anisotropy has been obtained. Significant anisotropy seems to extend to the center of the Earth. Vinnik et al. [1994] and Song [1996] examined AB-DF differential times at distances of about 170 ø and beyond. TABLE 1. Models of Inner Core Anisotropy Model* œ? tr? /? ( Sme)ptp? Data Type, A Distribution Cr BC-DF, 146ø-160 ø uniform SH BC-DF, 145ø-158 ø uniform Tr to normal modes depth-varying (1.18) (1.05) (-4.81) (2.5) Sh94 similar to Cr92 similar to Cr92 similar to Cr92 similar to Cr92 ISC, 132ø-140 ø, 149ø-180 ø depth-varying or SH93, or SH93, or SH93, or SH93, except top except top except top except top km -50 km -50 km -50 km VRB94 similar to Cr92 similar to Cr92 similar to Cr92 similar to Cr92 AB-DF, 172ø-177 ø uniform SC theoretical calculation uniform SD (2.04) (3.61) (8.5) isc, 120ø-140 ø, 150ø-180 ø 3-D Tr to to to 18.8 normal modes + ISC depth-varying (1.58) (2.28) (0.43) (5.4) So AB-DF, 168ø-180 ø uniform SR BC-DF, 145ø-158 ø uniform MMC97 similar to Cr92 similar to Cr92 similar to Cr92 similar to Cr92 BC-DF, AB-DF, 145ø-175 ø depth-varying or SH93 or SH93 or SH93 or SH93 *References for the coded models are, from top to bottom, Creager [1992], Song and Helmberger [1993], Tromp [1993], Shearer [1994], Vinnik et al. [1994], Stixrud and Cohen [1995], Su and Dziewonski [1995], Tromp [1995a], Song [1996], Song and Richards [1996a], and McSweeney et al. [1997].?All numbers are in percent; values in parentheses radial averages. Note from (8)-(10), œ determines the difference between Vp along the symmetry axis of anisotropy ahd that along the plane perpendicular to the axis, and the anisotropic variations (peak-to-pbak) of Sme and Seq are ( Sme)ptp -- ly(o 0/ 0)2/4 and % respectively. The reference P and S velocities ot 0 and [30 used in calculating ( Sme)ptp are krn/s and 3.66 km/s, respectively, and are taken from the preliminary reference Earth model [Dziewonski and Anderson, 1981] at the Earth's center.

10 306 ß Song: ANISOTROPY OF EARTH'S INNER CORE 35, 3 / REVIEWS OF GEOPHYSICS The observed time anomalies (3-8 s) are consistent with an overall anisotropy of %, although this level of anisotropy appears too large to be accounted for by mode splitting [Song, 1996]. However, the anisotropy in inner core does not seem to be uniform. PKP(DF) arrival times reported by the ISC are suggestive of a weaker anisotropy within the outermost 50 km of the inner core [Shearer, 1994]. The top km of the inner core is best resolved from PKP waveforms at distances of 130ø-146 ø [e.g., Choy and Cormier, 1983; Cummins and Johnson, 1988; Song and Helmberger, 1992]. At these distances the DF branch is partially obscured by stronger BC and CD arrivals (Figure lb). Moreover, PKP(DF) is often contaminated by precursory arrivals, which are generally thought to be associated with scattering at the core-mantle boundary [Cleary and Haddon, 1972] and make measuring arrival times very difficult and unreliable. Song and Helmberger [1995a] explored the depth dependence of the inner core anisotropy using PKP waveforms of near-polar paths at distances 120ø-173 ø, which were associated with a common set of seismic sources, so that source uncertainties were reduced. They compared the observed waveforms with those synthesized for models of the inner core anisotropy with and without depth dependence. The results suggesthat the top 150 km is only weakly anisotropic (less than 1%) and the top 60 km appears to be isotropic. Lateral resolution of the inner core anisotropy is poor, but the possibility that it is laterally varying has been suggested [Shearer, 1994; Song and Helmberger, 1995a; Su and Dziewonski, 1995; Song, 1996; Tanaka and Hamaguchi, 1997]. In particular, Su and Dziewonski [1995] undertook an effort to investigate three-dimen- sional structure of inner core anisotropy using PKP(DF) travel times from the ISC. They averaged the ISC travel time residuals by summing all rays within similar directions and depth ranges at which the rays bottom. Although the residual pattern thus obtained confirmed the dominance of transverse isotropy, it suggested a significant tilt of the symmetry axis from the spin axis and significant (_+1.5 s) longitudinal variations. Furthermore, in the inversion for a four-layer tilted axisymmetric model of anisotropy with each layer approximately 300 km thick, they found that the anisotropy is strongest in the innermost inner core. Tanaka and Hamaguchi [1997] reported a surprising result suggesting that in the top 500 km of the inner core sampled by B C-DF times, only the western hemisphere is anisotropic, which is also slow along equatorial paths. The eastern hemisphere is nearly isotropic with high speeds along equatorial paths. No evidence, however, suggests that this hemispherical pattern of the anisotropy extends to the deeper part of the inner core [Song, 1996]. The large-scale heterogeneity of fast eastern hemisphere and slow western hemisphere in the P velocity was first noted by Shearer and Toy [1991] and Creager [1992] from equatorial paths and appears to be robust with improved coverage of BD-DF differential time data [Creager, 1996]. The longitudinal variation in residuals, however, is small (_+0.5 s); thus lateral variations in the lowermost mantle, and at the core-mantle and inner core-outer core boundaries, are also likely to be important even though the ray paths of PKP(BC) and PKP(DF) are very close to each other throughout the mantle and most of the outer core (Figure la). The hemispherical pattern in the anisotropy of Tanaka and Hamaguchi [1997] has implications for the origin of the anisotropy and the formation of the inner core, and needs to be confirmed with improved longitudinal coverage of polar paths. The possibility that the symmetry axis might be tilted from the spin axis had first been suggested by Shearer and Toy [1991] and Creager [1992]. They found the symmetry axis that best fits the data deviates by 50-6 ø from the spin axis, but the difference in variance for tilted and nontilted axes was insignificant. However, Su and Dziewonski's [1995] inference of a 10.5 ø tilt of the symmetry axis, 10 times their estimated error of 0.95 ø, suggests that the tilt is statistically robust. Further studies from high-quality but sparse differential time measurements [Song and Richards, 1996a; McSweeney et al., 1997] found the optimum axis to be tilted by 10 ø and 8 ø, respectively, but the variance for such tilts differs insignificantly from that achieved without allowing for a tilt of the symmetry axis. SOURCES OF INNER CORE ANISOTROPY Apparent seismic velocity anisotropy can, in general, arise from preferred orientation of anisotropic crystals or from lamination of a solid [e.g.,anderson, 1989]. The Earth's core is composed primarily of iron diluted with light elements [Birch, 1952], and the properties of the inner core are widely believed to be consistent with those of iron in the hexagonal close-packed phase [e.g., Brown and McQueen, 1986; Anderson, 1986; Jephcoat and Olson, 1987; Sayers, 1989; Stixrude and Cohen, 1995]. The recent theoretical calculation of Stixrude and Cohen [1995] showed that a perfectly aligned aggregate of hcp crystals at the density of the inner core agrees with fhe seismic travel time anomalies, suggesting the possibility that the inner core is a very large single crystal. Thus it is natural that current attention is focusing on possible mechanisms for producing such a preferred alignment of iron crystals. The proposed models of preferred alignment fall into three categories: (1) alignment established during the solidification of iron crystals at the surface of the inner core [Karato, 1993], (2) alignment arising from large-scale convective flow in the inner core [Jeanloz and Wenk, 1988; Yoshida et al., 1996], and (3) alignment arising from preferential survival and growth of crystals with lowest energy [Stevenson, 1996]. Jeanloz and Wenk [1988] proposed that the preferred alignment might be caused by solid-state thermal convection driven by internal heating, which is thought to

11 35, 3 / REVIEWS OF GEOPHYSICS Song: ANISOTROPY OF EARTH'S INNER CORE ß 307 cause seismic anisotropy in the upper mantle through preferred orientation of olivine crystals in response to the large-scale shearing associated with plate tectonics [e.g., Francis, 1969]. Recently, Romanowicz et al. [1996] explored models of inner core anisotropy that are axisymmetric but not radially symmetric using core-sensitive mode-splitting data and differential PKP travel time data. They found that the anisotropy strength patterns of the best fitting models are suggestive of simple large scale convection regimes in the inner core. The difficulties of convection hypothesis, however, include (1) controversy over whether the inner core can convect at all [Weber and Machetel, 1992; Karato, 1993; Stevenson, 1996] and (2) the apparent failure to predict the observed symmetry of seismic anisotropy. Karato [1993] argued that hcp iron crystals in the of the inner core anisotropy, the predominant axisymmetric anisotropy with faster P wave velocity in the polar direction throughout the bulk of the inner core, and probable reduced magnitude at the very top of the inner core. No attempts have been made so far to explain more complex seismic observations discussed previously, such as lateral variation of the anisotropy and the tilt of the symmetry axis. This is sensible given the need to develop a first-order theory for the physical process and in view of still limited seismic observations. Neverthe- less, resolving three-dimensional seismic structure of the inner core anisotropy is extremely important in understanding the origin of the anisotropy. For example, significant lateral variation in anisotropy would suggest a different degree of alignment in different parts of the inner core and would favor the thermal convection inner core are magnetically anisotropic in susceptibility. mechanism. In addition, any quantitative model critically He proposed the magnetic field in the outer core aligns relies on an estimate of the phase properties of iron iron crystals as they solidify at the inner core boundary. under the pressure and temperature conditions of the Such a mechanism, however, would predict strong preferred alignment near the top of the inner core, incompatible with more recent seismic observations that the inner core. Recently, Mao et al. [1996] measured directly the elastic moduli of iron at the pressure of mid to outer core using three-dimensional X ray diffraction in a diatop -100 km of inner core is either weakly anisotropic mond cell. Although the results do not agree with the or isotropic [Shearer, 1994; Song and Helmberger, 1995a]. Yoshida et al. [1996] noted that geodynamo theory predicts that the inner core should grow faster in the equatorial belt than in its polar regions because heat transport near the polar regions is expected to be less efficient. They proposed that viscous flow toward hydrostatic equilibrium from the preferential growth creates a differential stress field in the inner core, which induces preferred orientation of anisotropic iron crystals. Applying Kamb's [1959] theory for stress-induced preferred theoretical calculations of Stixrude and Cohen [1995], it is encouraging to see that the inner core is now within experimental reach. As to why the symmetry axis is tilted a few degrees from the rotation axis, one imaginable mechanism is true polar wander of the inner core (D. J. Stevenson, personal communication, 1996), the slow migration of the whole inner core relative to its rotation axis due to redistribution of mass or angular momentum on or within the inner core [e.g., Gordon, 1987]. Depth variations of other physical properties of the orientation through recrystallization and assuming inner core, such as seismic attenuation, have also been Stixrude and Cohen's [1995] elastic coetticients of hcp iron, examined. Although there is no consensus on whether they obtained quantitative models of inner core anisotropy the attenuation varies with depth in the inner core [e.g., in general agreement with observed seismic anisotropy. Doornbos, 1974; Cormier, 1981; Choy and Cormier, 1983; Stevenson [1996] proposed an evolutionary model of inner core anisotropy. The inner core grains are randomly oriented when they first settle on the surface of Bhattacharyya et al., 1993; Song and Helmberger, 1992, 1995b; Souriau and Roudil, 1995], studies based on limited observations of relative amplitudes of short-period the inner core. As time passes, grains grow preferentially PKP waves with common sources and receivers for toward an alignment of lowest strain energy (analogous PKP(CD) and PKP(DF) and for PKP(BC) and to Darwin's selection rule "the survival of the fittest") under the influence of a small stress field, arising from sources such as tides or topography on the inner core boundary produced by deviations of hydrostatic equipo- PKP(DF) suggesthat the inner core P wave attenuation is very high in the top -100 km but decreases with depth [e.g., Doornbos, 1974; Song and Helmberger, 1992, 1995b; Souriau and Roudil, 1995]. An obvious question is tential surfaces due to mantle density anomalies [Buffett, whether the high attenuation and apparent lack of an- 1996]. Typical estimates of the mass anomalies in the mantle from seismic tomographic models yield perturbation of the equipotential surface at the inner core boundary of about 100 m (peak to peak). Since the innermost region of the inner core has been subjected to a stress field for the longest time, such a model would produce strongest alignment in the center of the inner core and a reduced degree of alignment toward the top. It could also produce easily the right symmetry, depending on the type of forcing. All these models concern only the principal features isotropy near the surface of the inner core are physically related. A mushy top region [Fearn et al., 1981] will result in high P wave attenuation, arising from a sharp increase in S wave attenuation with the onset of melting [e.g., Walsh, 1969; Anderson, 1989], and may be also unfavorable for preferred alignment of iron crystals. However, observations of high-frequency seismic waves reflected from the inner core, PKP(CD), at steep angles of incidence [Engdahl et al., 1970] pose a challenge to the existence of such a mushy zone. Another enigmatic observation is the anomalous

12 308 ß Song: ANISOTROPY OF EARTH'S INNER CORE 35, 3 / REVIEWS OF GEOPHYSICS 0.1 Figure 8. Derivative of travel time through the inner core with respect to the angle between ray path and the anisotropy symmetry axis. The curve is calculated for a surface focus at the distance of 151 ø using the P wave anisotropy model of Song and Helmberger [1993]. Note the variation is greatest at 10 ø -< _<45 ø (deg) waveforms associated with PKP(DF) arrivals for fast polar paths. As shown in Figures 6 and 7, amplitudes are small and waveforms are complex at short periods [Creaget, 1992; Song and Helmberger, 1993], suggesting interference between multipathed rays and broadening in long-period signals [Song and Helmberger, 1993]. The Sandwich Islands region to Alaska, and in the Kermadec Islands region to Norway) and one equatorial pathway (earthquakes in the Tonga Islands region to Germany) were examined. Systematic variations were observed for the two polar pathways but not for the equatorial pathway. This difference in temporal variations in travel time correlation between attenuation and velocity is convinc- residuals between a polar path and an equatorial path is ingly demonstrated by Souriau and Romanowicz [1996] from rays sampling the same region of the inner core with various directions. From this, they suggesthat the inner core is also anisotropic in attenuation. Attenuation alone, however, cannot explain the complicated wavewhat is expected from a change of the ray angle as the anisotropy orientation changes with an inner core rotation (Figure 8). The seismogramshown in Figure 9 recorded at the College, Alaska, station from earthquakes that occurred in the South Sandwich Islands forms. It remains to be seen whether the anomalous region from 1967 to 1995 provide the primary evidence waveforms are found at other distances and localities. of Song and Richards's [1996a] work. This pathway figured prominently in previous studies of inner core anisotropy [Creager, 1992; Song and Helmberger, 1993]. DIFFERENTIAL ROTATION OF THE INNER CORE Relative to outer core arrivals PKP(BC) the inner core arrivals PKP(DF) are progressively earlier with an av- As the inner core is surrounded by a liquid outer core of very low viscosity [Gans, 1972; Poirier, 1988], it is easy eraged shift of about 0.3 s over the 28-year period, suggesting that the fast axis of the inner core anisotropy for the inner core to rotate with respect to the mantle. has moved closer and closer to the South Sandwich- The idea that the solid inner core may move differently Alaska direction. The shift exceeds the standard deviafrom the once-a-day rotation of the mantle and crust was proposed more than a decade ago [Steenbeck and Helmis, 1975; Gubbins, 1981; Szeto and Smylie, 1984] and the possibility was greatly strengthened by the recent tions of the travel time measurements over 5-year bins by 2-5 times and reprents a phase shift of more than 90 ø for these short-period waves with dominant periods of less than 1 s (see Figure 9). Assuming that the inner core computer simulation of the Earth's dynamo [Glatzmaier rotates about the Earth's rotation axis, Song and Richand Roberts, 1995b], which predicts inner core rotation of a few degrees per year faster than the crust and the ards [1996a] obtained an eastward rotation of-- lø/yr. The most important source of errors in Song and mantle. Such fast rotation should affect PKP(DF) waves Richards's [1996a] study is event mislocation. A change as long as the rotation axis differs from the axis of the anisotropy. Moreover, the inner core anisotropy makes it straightforward to search for systematic variations as the orientation of the anisotropy moves with the inner core rotation. Song and Richards [1996a] first reported evidence for differential rotation of the inner core. They studied seismic waves that travel through the inner core reof only 50 km in source-station distance could change the B C-DF time by 0.3 s. Thus the observed temporal variation could potentially be an artifact of the use of different global networks used to locate the earthquakes in different years. However, rigorous relocation of the earthquakes shows that the observed systematic variation for the pathway from the South Sandwich Islands region to Alaska is robust [Song and Richards, 1996b]. corded at fixed monitoring stations from earthquakes The differential rotation of the inner core is to be with almost the same locations but a few years apart. Two polar pathways (from earthquakes in the South understood as a result of electromagneticoupling at the inner core boundary [Gubbins, 1981; Glatzmaier and

13 ,, 35, 3 / REVIEWS OF GEOPHYSICS Song: ANISOTROPY OF EARTH'S INNER CORE ß _ 1980 o... _-_-_- - '-'7- ---_,.._ >., ' i_-, _'. _-:_ :-' : : - '" -" - ' _-- ".- ' time, s Figure 9. All 38 seismograms of South Sandwich Islands events recorded at station COL (College, Alaska) used by Song and Richards [1996a] to infer a differential rotation of the inner core. The records are plotted with respect to earthquake origin times and are aligned with PKP(BC). The PKP(DF) waveforms are windowed out and corrected to a standard distance of 151 ø using PREM and the time-invariant inner core anisotropy model of Song and Helmberger [1993]. The PKP(DF) amplitudes are enlarged by 5 times. The PKP(AB) arrivals are corrected by /2 phase shift and are referenced to the standar distance of 151 ø using PREM. It is clear that the PKP(DF) waves arrive progressively earlier from the late 1960s to the 1990s. The dashed line shows the predictions for the best fitting model of inner core rotation of Song and Richards [1996a]. Roberts, 1995b, 1996; Aurnou et al., 1996; Bloxham and Kuang, 1996]. The inner core is driven to rotate by the average zonal flow at the floor of the fluid core through the magnetic field lines that thread the inner core. The Glatzmaier-Roberts dynamo calculations produce strong eastward zonal flow (toroidal field) near the inner core boundary, causing the superrotation of the inner core at a rate 2ø-3ø/yr faster than the mantle. The Kuang-Bloxham dynamo calculations produced a field very similar to those of the Glatzmaier-Roberts dynamo outside the core but very different inside the core. The strong toroidal field is well away from the inner core boundary, and the inner core can rotate either eastward or westward at slower rates. While it is still too early to decide which model provides a better approximation to the real Earth, it is clear that observations of inner core rotation provide important and unique constraint on dynamo simulations. Attempts to confirm the rotation of the inner core have been reported using seismic body wave data [Suet al., 1996; Creager, 1996; Souriau and Roudil, 1996] and normal mode analyses [Sharrock and Woodhouse, 1996]. Shortly after Song and Richards [1996a], Suet al. [1996] reported that PKP(DF) travel times reported by the ISC could be used to invert for the locations of the axis of anisotropy and therefore the inner core motions by dividing the 30-year-long data set into six 5-year segments. The solutions of the optimal axis showed complicated temporal changes, with significant variation in the years around 1970, a time when the magnetic field seems to have undergone a "jerk," or sudden change in the strength [Courtillot et al., 1978; Menill et al., 1996]. The average inner core rotation rate over the period was 3ø/year, also in the eastward direction. While this rotation rate estimate is considerably faster than that of Song and Richards [1996a] and cannot fit their B C-DF differential times from the seismogram shown in Figure 9, it is noteworthy that these seismological studies using independent data and methods as well as the predictions from the dynamo calculations of Glatzmaier and Roberts [1995b, 1996] andaurnou et al. [1996] all suggest that the inner core rotation is eastward. Considering that Song and Richards's observed time shift of 0.3 s, however, is well below the typical scatter (standard deviations of 1-3 s) of travel times from the ISC Bulletins and also below the error estimates after the data are averaged [e.g., Shearer, 1994; Su and Dziewonski, 1995], we must be careful about uncertainties in the determination of the inner core rotation using the ISC absolute travel times. The large scatter is due in part to most of these earthquakes occurring at shallow depths, for which the arrival times can be difficult to measure [e.g., Shearer, 1994; Song and Helmberger, 1995a; Song, 1996]. Moreover, the uneven station distribution, due to growth of the global network, and uneven earthquake distribution, associated with variations in global seismicity, that are used to infer inner core anisotropy at different times could result in snapshots of different parts of the mantle and the inner core in different periods. Hence changes in axes of symmetry might be the results of different sampling and not inner core motion.

14 310 ß Song: ANISOTROPY OF EARTH'S INNER CORE 35, 3 / REVIEWS OF GEOPHYSICS symmetry axis / Sm e Figure 10. Meridional shear velocities Sme of the inner core (solid line) with respect to propagation directions, which can be derived from a P wave anisotropy model. The dashed line indicates the shear velocity for an isotropic inner core. The P wave anisotropy model used in this plot is from Song and Richards [1996a], which suggests a 12% variation in Sm½ with the maximum at the propagation directions 45 ø from the anisotropy symmetry axis (see equation (9)). SHEAR WAVES IN THE INNER CORE from the sin 2 cos 2 term of the P wave Vp. The results for the recent anisotropy models, shown in Table 1, the inner core anisotropy in a frame of a rotating inner suggest that Sine anisotropy, measured by ( Sme)ptp core using more robust measurements, such as differen- (peak-to-peak amplitude), ranges from a few percent to tial PKP travel times from historical records and rapidly as much as 13% (averaged radially). Although the esti- expanding high-quality digital records. The deployment mates of shear wave anisotropy from normal modes of temporary seismic stations, such as the Program for [Tromp, 1993, 1995a] vary markedly with depth, it is Array Seismic Studies of the Continental Lithosphere interesting to note that the estimates of Sine anisotropy (PASSCAL) [Smith, 1986], at key locations can be jusfrom body wave travel times and theoretical calculations tified for this purpose. An improved anisotropy model of [Stixrude and Cohen, 1995] do not differ much (from 8.5 to 12.9%). The typical estimates of Sine anisotropy from differential PKP times are around 12%. Since it should take about 11 min for shear waves to pass through the inner core (at appropriate distances), this level of shear wave anisotropy would indicate that meridional shear waves travel faster by as much as 80 s along a direction 45 ø from the symmetry axis than those either along the symmetry axis or in the equatorial plane (Figure 10). The anisotropy of the shear waves polarized along the equatorial plane (Scq) cannot be obtainedirectly with- out actual observations of such shear waves. The esti- mates of anisotropic variations of Scq (i.e., /) from normal modes are poorly constrained, as is evident by an even stronger depth-dependence than for Sm½. Scq depends only on shear moduli L and N (see(7)), and only a few modes are sensitive to the shear wave structure of the inner core [Tromp, 1993]. Nevertheless, noticing the different dependences of Sine and Scq on propagation direction as indicated by (9) and (10), Stixrude and Cohen [1995] pointed out that the inner core would be the source of largest shear wave splitting in the Earth (as much as 50 s for their model). Yet such a splitting might never be observed, considering that the already small P and S conversions at the inner core boundary must be partitioned to both Sine and Seq. Future searches for PKJKP (or SKJKP/PKJKS) should examine broad time windows. Broadband arrays appear to be the key to their detection in order to avoid the frequency bands of high inner core attenuation [Doornbos, 1983]. The deviations from isotropic paths and the distortions of wavefronts of shear waves due to At present, the strongest evidence for the solidity of the inner core comes from the measured frequencies of the free oscillations [Derr, 1969; Dziewonski and Gilbert, 1971]. The identification of PKJKP remains one of the outstanding problems of seismology. The reported identification by Julian et al. [1972] was later thought not to be PKJKP because its travel times do not agree with 10% anisotropy are also likely to be important. those predicted by normal mode models. The inner core S wave velocity deduced by Julian et al. [1972] is 2.95 _+ 0.1 km/s, more than 10% slower than km/s of Dziewonski and Gilbert [1972] from free oscillations. CONCLUDING REMARKS The difficulty of detecting PKJKP is caused by the Clearly, the development of the inner core anisotropy inefficiency of P-to-S conversion (and S-to-P conver- calls for interdisciplinary investigation of its cause and sion) at the inner core boundary. Detection of PKJKP is also hindered by high attenuation at short periods, causing Doornbos [1974] to conclude that the amplitude of PKJKP is too small to be observed. Nonetheless, the observations of Julian et al. [1972] have not been explained and B. R. Julian (personal communication to consequences. If the inner core anisotropy is magnetically induced, it also has direct relevance to the morphology of the magnetic fields and the dynamo theory. In any event, inner core rotation is the first, and may be the only, opportunity to observe motions at depth within the fluid core, since these deep motions may have little P. G. Richards, 1994) has suggested that the phase to do with the magnetic observations at the Earth's velocity discrepancy might be due to anisotropy. As surface [e.g., Holierbach and Jones, 1993; Glatzmaier and equations (8) and (9) indicate, the directional variation Roberts, 1995a, b; Bloxham and Kuang, 1996]. As for of meridional shear wave velocity Sme can be determined seismology, it is high time that a significant commitment be made to determine three-dimensional structure of the inner core, documentation of historical seismograms at key stations (such as College, Alaska, which recorded

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