Earth's Solid Inner Core: Seismic Implications of Freezing and Melting

INTRODUCTION

Since its discovery (Lehmann, 1936), the Earth's solid inner core has posed a multitude of problems to be solved by the geophysical community, exhibiting heterogeneity and anisotropy at all length scales. An early model of global axisymmetric cylindrical anisotropy (Tromp, 1993; Shearer and Toy, 1991; Morelli et al., 1986; Woodhouse et al., 1986) was later revised to include an isotropic uppermost layer of variable thickness (Niu and Wen, 2002; Ouzounis and Creager, 2001; Song and Helmberger, 1998, 1995; Shearer, 1994), depth dependent anisotropy (Reaman et al., 2011; Sun and Song, 2008; Tanaka and Hamaguchi, 1997), and hemispherical differences in the degree of anisotropy (Irving and Deuss, 2011; Creager, 1999). A more perplexing feature is the hemispherical heterogeneity observed in isotropic velocities and attenuation deduced from travel times and amplitudes of seismic waves that propagate along equatorial paths in the inner core (Waszek and Deuss, 2011; Yu and Wen, 2006; Niu and Wen, 2003, 2001; Garcia, 2002; Tanaka and Hamaguchi, 1997; Creager, 1992). In this model, velocity and attenuation show a positive correlation with the Eastern Hemisphere being faster and more attenuating than the Western Hemisphere.

The transition between the liquid outer core and the solid inner core known as the F region (Bullen, 1942) has remained a contentious issue. Recent models derived from accurate body wave travel times indicate that the P velocity gradient with depth is less pronounced in the F region than in some early models, including PREM, consistent with global density stratification (Ohtaki et al., 2012; Zou et al., 2008; Garcia et al., 2006; Kennett et al., 1995; Song and Helmberger, 1995, 1992; Kaneshima et al., 1994; Souriau and Poupinet, 1991). An exception to this view is the hypothesis of hemispherical differences in the F region (Yu et al., 2005), in which the Eastern Hemisphere (40°E–180°E) has a steeper gradient than the Western Hemisphere (180°W–40°E).

While many recent studies have focused on the hemispherical structure in the inner core, the presence of some regional features have also been inferred. These include a thin low velocity layer beneath the Indian Ocean (Stroujkova and Cormier, 2004) and the possibility of small-scale (100 to 1 000 km) variations in the jump in the elastic impedance contrast across the ICB (Krasnoshchekov et al., 2005). Further evidence of small-scale heterogeneity is given by excitation of PKiKP coda waves, pulse broadening of PKIKP, and the scatter observed in differential travel time residuals and amplitude ratios sensitive to the inner core (Mattesini et al., 2010; Tkalčić et al., 2009; Leyton and Koper, 2007; Koper et al., 2004; Vidale and Earle, 2000; Cormier et al., 1998).

In the current study, we invert differential travel times and amplitude ratios of pairs of seismic phases sensitive to the upper 550 km of the inner core to determine seismic structure at intermediate spatial scales in an Earth parameterized by 45° wide longitudinal bins. The structure of the F-layer is determined at the same scale. The effects of source and mantle attenuation are handled by applying a spectral deconvolution procedure. We start by describing data and methods in the following section. Next we present our results followed by a discussion, in which we interpret our results based on possible geodynamic scenarios of inner core growth.

METHODS

Differential Travel Times

Studies of the inner core from observations of seismic body waves often exploit the concentrated sensitivity to inner core structure given by the difference in travel time between P waves that are transmitted through the inner core PKIKP (PKP-DF) and those that either bottom near (PKP-BC), are reflected by PKiKP (PKP-CD), or diffracted around the inner core (PKP-Cdiff). Since the ray paths and associated volumes of sensitivity of these pairs of waves overlap throughout most of Earth's mantle, their differential travel times are primarily sensitive to structure within the upper 500 km of the inner core and the lower 200 km of the outer core (Fig. 1). Likewise ratio of peak to peak amplitude of these paris of waves can be used to measure the apparent attenuation of the inner core. We thus used these differential travel times and amplitude ratios to model the velocity and attenuation respectively, in the inner core and the F region.

Figure  1.  Core wave nomenclature, ray paths, travel times, and displacement synthetic seismograms. Boxed regions in the synthetic seismogram profile are optimal distance ranges to study differential travel times and amplitude ratios of waves sensitive to structure of the upper 500 km of the inner core.

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The PKP wave transmitted through the outer core is strongly focused by a caustic surface that intersects Earth's surface near 145°, interfering with the waves interacting with the inner core in the 142° to 148° range. Hence, we chose to omit this distance range and analyze two distance ranges on either side of the PKP caustic, 129°–141° and 149°–161°. To ensure a high signal to noise ratio and simple waveforms, the download criteria included event moment magnitudes (M_w) between 5.5 and 7.0 and source depths between 80 and 700 km. We downloaded seismograms from repositories of the IRIS Data Management Center (DMC) and applied basic pre-processing steps such as windowing and deconvolving the instrument response simultaneously (e.g., Owens et al., 2004). From an initial collection of 25 704 seismograms, we picked 328 seismograms from 26 events in the 129°–141° distance range and 349 seismograms from 56 events in the 149°–161° distance range (Fig. 2). These had mean signal-to-noise ratios of 5.66 and 9.75, respectively. Direct P waves in the 30°–90° distance range of each of these 82 events were inverted for an effective far-field source-time function (ESTF). Each ESTF represents a convolution of the far-field source-time function with an average mantle attenuation operator (Li and Cormier, 2002).

Figure  2.  Ray coverage of the inner core in this study from PKiKP and PKIKP waveforms in distance ranges: (a) 129°–141° (top) and (b) 149°–161° (bottom). Black thick line segments and green circles represent PKIKP ray path in the inner core and bottoming points respectively. Stars and triangles represent earthquake epicenters and seismic stations respectively.

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From each windowed waveform we deconvolved an ESTF using a Tikhonov regularization procedure in the frequency domain (e.g., Aster et al., 2004). To enhance high frequencies, we converted the deconvolved displacement to particle velocity, from which travel times and amplitudes were hand-picked (Fig. 3). We first marked theoretical travel times from the AK135 model for all pairs of phases and searched for a clear phase arrival within +1.0s of the theoretical arrival time visually. Once the seismograms having clear signals were separated, we searched for an absolute peak (or trough) within a time window +0.5s about a manually picked peak (or trough). The time/amplitude corresponding to this peak (or trough) was measured as travel time/amplitude of that particular phase. The dominant frequency is 0.5 Hz, and our signals are broadband up to 1 Hz. We compared model predicted travel times to those obtained by our semi-automated hand-picking procedure with seismograms synthesized by the reflectivity method (Kennett, 1983). The reflectivity seismograms were filtered to match approximately the frequency spectrum of the deconvolved data. The differences between model predicted and hand-picked differential travel times of the synthetic seismograms were less than 0.1 sec.

Figure  3.  An effective source time function (ESTF), representing the effects of the far-field source time history and average mantle attenuation, was determined from P waveforms in the 30° to 90° range for each earthquake. The ESTFs were deconvolved from displacement seismograms, which were then converted to particle velocity to increase the frequency content of waves interacting with the inner core, allowing for more accurate picking of differential travel times.

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Source locations were corrected using the NEIC catalog, and travel time and distance corrections were added to standardize the source depth to 500 km. Before hand-picking travel times and amplitudes of respective phases using our semi automated procedure, we also corrected travel times for ellipticity (Kennett and Gudmundsson, 1996). Observed differential travel times were divided into eight 45°-longitudinal bins based on the PKIKP ray bottoming points in the inner core. Measurements were made from waveforms having rays making low angles with respect to the equatorial plane to minimize possible effects of cylindrical anisotropy of the inner core. The tangent of the PKIKP ray bottoming points made angles > 35° with respect to the rotational axis. By restricting our analysis to more equatorially oriented ray paths, we also hoped to enhance the observable signature of laterally varying heat transport across the inner core boundary due to the effects of either tangent cylinder(s) of large-scale convection in the outer core or smaller scale vortices (e.g., Calkins et al., 2012) near the inner core boundary.

The differential travel time PKIKP-PKiKP in the 129° to 141° range is largely sensitive to the P velocity jump across the ICB and the velocity structure of the uppermost 140 km of the inner core, whereas the differential travel time PKIKP minus PKP-BC and PKIKP minus PKP-Cdiff in the 141° to 161° range is strongly sensitive to structure 140 to 550 km beneath the ICB and the lowermost 200 km region of the outer core. These different structural sensitivities are used to invert for the velocity structure in a two-step procedure. First the velocity jump at the ICB and structure of the upper 140 km of the inner core are determined from the differential travel times of PKIKP-PKiKP in the 129° to 141° range. Then with the structure of the uppermost inner core held constant, PKIKP minus PKP-BC and PKIKP minus PKP-Cdiff differential travel times are used to invert for structure in the lowermost 200 km of the outer core and the structure 140 to 550 km below the ICB.

Amplitude Ratios

Ray paths and sensitivity volumes of PKIKP and PKiKP overlap throughout the mantle and outer core in the 129° to 141° range. In the 141° to 161° range, PKIKP and PKP-BC or PKP-Cdiff ray paths overlap throughout most of the mantle, except in the lowermost 200 km of the mantle and the outer core. Except possibly in the F region near the ICB (Zou et al., 2008), the viscoelastic attenuation of the outer core is well-documented to be nearly zero (e.g., Cormier and Richards, 1976). These properties make it possible to make at least a crude estimate of path averaged attenuation of the inner core from simple amplitude ratios PKIKP/PKiKP and PKIKP/PKP-BC or PKIKP/ PKP-Cdiff over a narrow band of frequency centered near 0.5 Hz. Since it was a relatively simple measure to make in our analysis, we measured apparent attenuation in the inner core from these amplitude ratios. We minimized an L₁ norm of the difference between the observed and predicted amplitude ratio, in which the predicted amplitude ratio was measured from Green's functions synthesized by the reflectivity method, with varying attenuation only in the inner core (Recall that the ESTFs contain an estimate of an averaged mantle attenuation operator and have been deconvolved from observations). This procedure assumes that the effects of crustal reverberations and attenuation and scattering in the crust and mantle are approximately identical on the two phases in an amplitude ratio due to the near similarity of the ray paths of the two phases in these regions.

Estimates of inner core attenuation have been made over a broader band in the time domain, including analyses of pulse dispersion (Cormier and Li, 2002; Li and Cormier, 2002; Doornbos, 1983). Even when these more precise measures have been made, however, the scatter in results is typically high. The scatter is not high enough to obscure a strong depth dependence of attenuation in the inner core, with the highest attenuation occurring in the upper 500 km of the inner core (Cormier, 2011). In this simple reconnaisance of amplitude ratios, the strong variations in the apparent Q^-1 within each bin possibly signify either small-scale heterogeneity in attenuation properties of the inner core or the effects of focusing and defocusing of small-scale elastic structure near or topography on the ICB and CMB.

Starting Velocity Models and Inversion

We identified starting models (Fig. 4) for the uppermost inner core for each longitudinal bin by selecting a pre-exiting model that minimized an L₁-norm of differential travel times observed in that bin. In each bin we perturbed these starting models for the final best fitting models by first searching for a minimum L₁-norm of differential travel times after increasing (or decreasing) the velocity in increments of 0.01% and then minimizing L₁-norm of amplitude ratios with a search range of Q_α=[50, 1 000]. Once these models were found in the distance range 129°–141°, we fixed the ICB and uppermost inner core structures and searched for best fitting models for the F region of the outer core and 140 to 500 km depth range of the inner core using the 149o–161o data. In the final step of the inversion for the F region, we tested if a PREM-like gradient, consistent with chemical homegeneity throughout the outer core, can improve the L₁-norm. If it did not, we concluded that the best fitting F region velocity profile is given by AK135-F, which has a reduced gradient in P velocity in the lowermost outer core near the ICB. After completing the velocity inversion, we inverted for the attenuation structure by fitting amplitude ratios, taking Q_α=1 000 as the initial condition and changing Q_α by ±100. This initial condition represents a lower bound to inner core attenuation (upper bound to Q) suggested by the study of Wookey and Helffrich (2008).

Figure  4.  Starting models include PREM (Dziewonski and Anderson, 1981), AK135-F (Montagner and Kennett, 1995), W2 and E1 inner core models coupled to their respective outer core models (Yu and Wen, 2006; Yu et al., 2005), isotropic models (WZDU) for the Eastern and Western hemispheres proposed by Waszek and Deuss (2011), JV2x (Cormier et al., 2011), and SPR (Ohtaki et al., 2012).

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RESULTS

Depths 0 to 140 km beneath ICB

Differential travel times sensitive to the upper 140 km of the inner core clearly exhibit a hemispherical/degree-one structure in P velocity when referenced to model AK135-F (Fig. 5). The mean of differential travel time residuals (PKIKP-PKiKP) in the Eastern Hemisphere (+0.018±0.178s) is smaller but with similar standard deviation than that of the Western Hemisphere (-0.300±0.223s), suggesting that the AK135-F reference model is a more appropriate representation of the Eastern Hemisphere. The reversals in the sign of velocity perturbations are close to the classical divisions of Earth's Eastern and Western hemispheres, with higher velocity between 40°E to 180°E (Eastern Hemisphere), and lower velocity between 40°E to 180°W (Western Hemisphere). It should be noted, however, that the apparent boundaries between positive and negative perturbations to velocity depend on both our choices for the reference Earth model and the boundaries of our 45° wide bins. Given the level of scatter in differential travel times and differences between our parameterization, reference model, and data paths and those of other recent studies, it is easy to reconcile differences of up to 40° in longitude reported for the apparent boundaries of quasi-hemispherical variations.

Figure  5.  Differential travel time residuals with respect to AK135-F model plotted geographically, illustrating that a hemispherical pattern of a fast Eastern Hemisphere and slow Western Hemisphere persists to at least 550 km depth. The blue and red columns represent positive and negative residuals respectively. The black column at (60S, 0) degrees represent a resdiual 1 second tall for reference.

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Depth 140 to 550 km beneath ICB

Evidence for the persistence of hemispherical differences to a depth of up to 550 km exists in the differential travel times measured in the 149° to 161° range (Fig. 5). To represent the depth sensitivity in this range, we allowed the depth range 140 to 550 km to be parameterized as a separate layer. The mean and standard deviation of differential times with respect to AK135-F were measured to be +0.345±0.371s in the Eastern Hemisphere and -0.189±0.353s in the Western Hemisphere. We generally found the sign of the required velocity perturbations in the deeper 140 to 550 km depth range to be strongly correlated but reduced in magnitude with the required velocity perturbations in the uppermost 140 km of the inner core. The magnitude of the velocity contrast between hemispheres was bound by 1% in the 0 to 140 km depth region but by 0.4% in the deeper 140 to 550 km region (Fig. 6). With the exception of bin 8 beneath the Atlantic Ocean, the discontinuities at 140 km depth resulting from our parameterization were all less than 0.3%, incapable of producing detectable waveform triplications in our frequency band. It may be significant, however, that the single exception were data in bin 8, which required a 1% velocity jump at 140 km. Longitudinal bin 8 is close to the mid-Atlantic location where Song and Helmberger (1998) found evidence for a discontinuity at 250 km below the ICB, separating an isotropic uppermost inner core from a deeper anisotropic inner core.

Figure  6.  Final inverted models of inner core P velocity structure parameterized by 45° wide longitudinal bins. Top panel: the upper and lower values in a given bin represent the number of PKIKP-PKiKP and PKIKP-PKP data points respectively. Bottom panel: the upper and lower Q_α values are for 0–140 km and 140–550 km layers below the inner core boundary.

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Recently, Tanaka (2012) proposed a depth dependent hemispherical model for the inner core by constraining velocity from PKP differential travel times in the 150°–160° distance range. This prediction can be easily reconciled with our binned-models by considering ray coverage. His slow Western Hemisphere (roughly our BIN5, BIN6, BIN7 and BIN8) converges to AK135 velocity profile at a depth of 250 km from the inner core boundary, which is a consistent feature in our BIN5, BIN6 and BIN7 (Fig. 6). It is likely that the narrow high velocity region we observed in BIN8 is masked in Tanaka's Western Hemisphere model by travel times of slow waves sampling the above three bins. On the other hand, he found that the high velocity in the Eastern Hemisphere to be converging to AK135 model at a depth of 400 km depth below the inner core boundary. Tanaka used differential travel times sampling BIN3 and BIN4 to constrain velocity in the upper 400 km and those that dominantly sample BIN4 to constrain velocity below 400 km. Recall that BIN3 has higher velocities than AK135, whereas that in BIN4 is almost equal to AK135 (Fig. 6). Therefore, a model derived from travel times of waves bottoming in BIN3 and BIN4 (his upper 400 km) is expected to exhibit higher velocities than AK135, while velocity below 400 km, inferred from waves bottoming in BIN4, will converge to AK135 model. Thus, the transition Tanaka observed in the Eastern Hemisphere results from preferential space-depth ray sampling. On the contrary, our model in BIN3 suggests higher velocity to persist at least to a depth of 550 km.

Lowermost Outer Core (F Region)

Differential travel times PKIKP minus PKP-BC and PKIKP minus PKP-Cdiff in the 149° to 161° range are also sensitive to structure in the lowermost 200 km of the outer core. By fixing the velocity jump at the ICB and velocity structure in the upper 140 km of the inner core from inverting differential times PKIKPPKiKP in the 129°–141° range, we were then able to examine the effects of additional velocity perturbation in the F region in combined distance ranges. Since PKP-Cdiff is a diffracted wave, its apparent travel time can be frequency dependent. Hence, we compared its travel time measured from source deconvolved seismograms with that picked from reflectivity seismograms filtered to approximately the same frequency band.

We examined the effects of F region perturbations by performing two tests. After reaching an L₁ norm minimum from velocity perturbations between 140 to 550 km depth range, we test if a P velocity gradient change of +0.65%, representing the difference between the P velocity gradients of PREM and AK135-F structures in the lowermost outer core, improved the L₁ norm. The L₁ norm was not improved in any of our 8 bins by a PREM-like perturbation to the velocity gradient in the F region. This result together with the results of a more detailed study of PKP-Cdiff (Zou et al., 2008), strongly suggests that a reduced P velocity gradient in the lowermost outer core is a globally robust observation. Further studies of the F region will udoubtedly reduce its tradeoff with inner core structure as more seismic data becomes available at distances breater than 150°.

Apparent Attenuation and Amplitudes

Within our parameterization, the inferred transitions in attenuation structure do not generally coincide with those inferred from velocities. The region of high attenuation (low apparent Q's on the order of 250 to 300) is concentrated in a 225° wide zone from beneath the eastern Atlantic to mid-Indian oceans (longitudes 45°E to 90°W). The region of low attenuation (high apparent Q's on the order of 600 to 700) is concentrated in a narrower 135° zone beneath the Americas between longitudes 90°W to 45°E. High apparent attenuation (low Q) often correlates with fast velocity, opposite in sign to the correlation commonly observed in the upper mantle, which has been observed in a number of previous studies starting with Souriau and Romanowicz (1996). The highest attenuation (lowest Q) includes the equatorial Pacific Ocean and is consistent with previous observations (Oreshin and Vinnik, 2004; Tseng and Huang, 2001). This region may be associated with the predicted region of inner core melting and broad upwelling in the outer core that Gubbins et al. (2011) find from numerical dynamo simulations incorporating lateral variations in core-mantle boundary heat flow. This highest attenuation patch (low apparent Q on the order of 250) also coincides with the patch of the upper inner core that Leyton and Koper (2007) map as a patch of strong back-scattering from the coda of PKiKP.

Significant scatter exists in apparent Q measurements within any given longitudinal bin. Hence, caution is needed not to over-interpret the attenuation results. A simple, frequency independent, model of viscoelasticity is assumed over the frequency band of observations and a characteristic frequency of 0.5 Hz is assumed to match the amplitude ratio of PKiKP/PKIKP and PKiKP/PKP-BC or PKiKP/PKPCdiff assuming a model of path integrated attenuation in the inner core. Strong frequency dependence of attenuation, either viscoelastic or scattering, has been proposed by Doornbos (1983) and Li and Cormier (2002) to explain anomalously small pulse dispersion measured from attenuated PKIKP waveforms. Small lateral variation in either the corners of a relaxation spectrum or the characteristic scale lengths of scatterers can then easily introduce strong lateral variations in the apparent attenuation. The scatter in apparent attenuation may also be a consequence of irregular properties of the ICB. Numerical modeling demonstrates that any lateral variation in either the impedance contrast (Krasnoshchekov, 2005) or topography of the ICB (Cao et al., 2006) will strongly affect the amplitude of PKiKP but have little effect on the amplitude of PKIKP. A change in the PKiKP/PKIKP amplitude ratio by a factor of 3 was measured by Cao et al. (2006) from an earthquake doublet separated by 10 years, from which they postulated either a temporal change in ICB topography or differential rotation of a rough ICB with scale lengths on the order of 10 km and heights between 0.3 to 5 km. From complex PKiKP waveforms, including precursors, Dai et al. (2012) have proposed the existence of two scales of ICB topography: one having a height variation of 14 km and wavelength of 6 km, and the other having a height variation of 4 to 6 km and wavelength of 2 to 4 km. Heights above 0.5 km have yet to be fully understood or reconciled with heights estimated from either the translating/convecting model of inner core evolution or from bounds on inner core viscosity inferred from estimates of differential rotation (Alboussière et al., 2010; Monnerau et al., 2010; Van Orman, 2004).

DISCUSSION

Two Hypotheses of Freezing and Melting

Two hypotheses have been proposed to explain the apparent hemispherical variation in inner core structure. Both require lateral variation in freezing and melting of the inner core concentrated at low latitudes. In each hypothesis the volume rate of freezing exceeds the volume rate of melting when averaged over the surface of the inner core. The prediction each hypothesis makes for freezing and melting hemispheres, however, differs. A translating convecting model of the inner core (Alboussière et al., 2010; Monnereau et al., 2010) predicts freezing in the Western Hemisphere and melting in the Eastern Hemisphere. In contrast, Aubert et al. (2008) and Gubbins et al. (2011) estimate heat flux across the inner core boundary to predict dominant freezing in the equatorial Eastern Hemisphere and a broad zone of melting in the Western (primarily Pacific) Hemisphere. Interpretation of evidence in support either hypothesis largely depends on how freezing and melting affects seismic velocities, anisotropy, attenuation, and scattering.

1   Translating/convecting hypothesis

The hypothesis of Monnereau et al. (2010) starts from assuming the existence of a degree-one thermal heterogeneity in the inner core, which shifts its center of mass toward its colder and denser hemisphere. The equilibrium position of the center of mass is restored by translation, inducing a topography that is not in equilibrium with the pressure and temperature conditions of lowermost outer core. Crystallization occurs on the denser hemisphere and melting on the opposite side to remove the topography. A convective flow is induced, moving material from the crystallizing hemisphere toward the melting hemisphere. In this process, the melting hemisphere fertilizes a stablystratified, iron enriched, 250 km thick region, in the lowermost outer core with narrow plumes of low viscosity liquid iron (Alboussière et al., 2010), uniformly distributed around the ICB. Hemispherical variations in seismic properties are explained by long wavelength averages of the seismic wavefield forward scattered by the boundaries of individual grains or organized patches of grains of intrinsically anisotropic crystals (Calvet and Margerin, 2008). Long wavelength averaging can also explain the observed low shear velocity of the inner core (3.5 km/sec) compared to the predictions of mineral physics for hcp iron. In a purely scattering mechanism of seismic attenuation, low attenuation in the Western Hemisphere and high in the Eastern Hemisphere are explained by grain sizes smaller than the wavelengths of seismic body waves sampling the younger, crystallizing, Western Hemisphere, and by grain sizes on the order of wavelengths of seismic body waves sampling the older, melting Eastern Hemisphere. Observed elastic anisotropy and its sense of correlation with attenuation (high attenuation correlated with high velocity/low attenuation with low velocity) can also be explained by the way in which the forward scattered wavefield samples the heterogeneous texture of distributed patches of grains, quantifying the mechanism proposed by Bergman (1997).

The translating/convecting model of the inner core requires a narrow range of dynamic viscosity (10¹⁸–10²¹ Pa·sec) to maintain the hemispherical variation in physical properties (Deguen and Cardin, 2011). It also must be embellished with details to explain observations of an innermost inner core with different properties in elastic anisotropy and attenuation (Cao and Romanowicz, 2007; Ishii and Dziewonski, 2002; Li and Cormier, 2002) as well lateral variations in the depth and strength of anistoropy (Irving and Deuss, 2011; Duess et al., 2010; Creager, 1999; Tanaka and Hamaguchi, 1997). Since its interpretation of seismic properties hinges on the predictions of scattering theory, important hypothesis tests include a quantification of the relative contributions of scattering and viscoelastic attenuation and an examination of alternative mechanisms to explain the observed anisotropy and lateral variations in elastic velocities and attenuation.

2   Coupling of ICB and CMB heat fluxes hypothesis

Starting from an estimates of heat flow across the core-mantle boundary inferred from seismic tomographic images of shear velocity near the CMB and assuming a temperature derivative of seismic velocity, Aubert et al. (2008) and Gubbins et al. (2011) have used dynamo models to estimate heat transport across the inner core boundary. From this they have predicted possible sites of freezing and melting of the inner core. Both studies predict a region of concentrated freezing beneath either the center or eastern edges of the equatorial Indian Ocean. Averaging heat flow over several magnetic diffusion times and assuming weaker coupling between CMB and ICB heat transport, Gubbins et al. (2011) predict two narrow zones of freezing, one beneath the eastern edge of the Indian Ocean and one beneath the Eastern Atlantic/West Africa region, separated by broad zones of melting inner core and upwelling outer core. If the heat flow and ICB freezing across this additional narrow zone is weaker, as suggested by their study (Fig. 7), then an approximate hemispherical (degree-one) structure is obtained. Thus in this hypothesis, the equatorial Eastern Hemisphere is predicted to be dominantly freezing, and the equatorial Western Hemisphere to be dominantly melting. A test of this hypothesis then remains in determining whether the melting and freezing regions can be consistent with observed seismic properties.

Figure  7.  Bins 3 and 8 having the highest equatorial P velocity at depths between 140 to 550 km correlate with regions that are predicted by Gubbins et al. (2011) to have the highest heat flow out of the inner core. That study predicts freezing in these narrow regions, which are surrounded by much broader regions in which the inner core is melting at a slower rate, the area averaged freezing greater than melting. Inferred boundaries of apparent hemispherical differences in elastic anisotropy are also shown from the study of Irving and Deuss (2011).

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Hypotheses Testing

The boundaries of the anomalously high equatorial seismic velocities of bins 3 and bin 8 in the inner core between 140 and 550 km depth are nearly coincident with Gubbins et al.'s prediction for the location of the narrow zones of inner core freezing (Gubbins et al., 2011). In this depth range these two longitudinal bins stand apart in the size of a fast velocity anomaly compared to a weaker hemispherical variation in longitude in the remaining bins. At shallower depths, up to 140 km beneath ICB, the P velocity perturbation in 8 appears to be part of a more continuous slower trend across a hemispherical transition. At depths between 140 and 550 km, the perturbation in bin 3 beneath the eastern edge of the Indian Ocean is significantly stronger than that in bin 8 beneath the Eastern Atlantic/West Africa region. Taken together the difference in the strength of velocity perturbations in bins 3 and 8 and their depth dependence may be most simply interpreted as the effects of freezing material at lower homologous temperature (T/T_m) compared to adjacent longitudinal bins, increasing the intensity of positive velocity perturbation the homologous temperature increases with depth. The intensity of velocity perturbation is higher in bin 3 than in bin 8, consistent with the prediction that the region beneath the eastern Indian Ocean is more intensely solidifying than the region beneath the Eastern Atlantic/West Africa region. Most studies refer to 180°W (±10°) longitude as the western boundary between the Eastern and the Western hemispheres, close to but not precisely near the boundaries of the predicted broad melting region beneath the Pacific. The broad melting region beneath the Pacific together with the relative weakness of the freezing region beneath bin 8 compared to bin 3 results in an apparent hemispherical velocity structure.

Attenuation of PKIKP measured from the pulse broadening or frequency content in the first several cycles of its waveform can be explained equally well by viscoelasticity or by the effects of forward scattering (Cormier and Li, 2002; Li and Cormier, 2002). In a hypothesis of freezing in the Eastern Hemisphere and melting in the Western Hemisphere, the attenuation in the Western (melting) Hemisphere may be best explained by a combination of scattering attenuation and viscoelastic attenuation, and the higher attenuation in the Eastern (freezing) Hemisphere primarily by viscoelastic attenuation. The large (several 0.1's to 1 km and greater) heterogeneity required to explain the strong backscattered PKiKP coda observed by Leyton and Koper (2007) beneath the Central Pacific predicts that scattering will be a significant contribution to the apparent attenuation. Leyton and Koper suggested that the scattering might contribute up to half of the apparent attenuation in regions where PKiKP coda is strong. The older region of the inner core may either contain thin pockets of partial melt concentrated along larger facets of grains and/or be characterized by relatively older larger randomly oriented grains having anisotropy. Weaker intrinsic attenuation in the Western (melting) Hemisphere will also enhance the observation of high-frequency energy in PKiKP coda created by backscattering from volumetric heterogeneity in the upper inner core. This is because, once scattered by a volumetric heterogeneity in the upper inner core, the remaining path of the scattered wave in the inner core suffers less intrinsic attenuation. The stronger attenuation and weak back-scattered energy in the coda of PKiKP in the eastern (freezing) inner core may then be explained primarily by strong viscoleastic attenuation characteristic of grain sizes much smaller (< 0.01 km) than wavelengths of observed teleseismic PKIKP waves. Recall that Leyton and Koper's observed region of observed strongest PKiKP coda benearth the Pacific correlates well with Gubbins et al.'s (2011) broad region of melting in Fig. 7.

Another seismic observation consistent with either freezing or melting in eastern equatorial hemisphere is a thin layer of reduced velocity at the top of the inner core that transitions rapidly enough to higher velocity with depth to produce multipathing observed as complexity in PKIKP+PKiKP waveforms around 130° range (Stroujkova and Cormier, 2004). This feature (equatorially centered in bin 3 in Fig. 7) strongly correlates with Aubert et al.'s (2008) predicted region of strong inner core growth/freezing, measurably thinning in toward the poles. Our longitudinal bin 2, having the highest measured apparent attenuation (lowest Q) penetrating to the greatest depth, is also centered on this inner core anomaly.

By restricting our study to ray paths sampling the inner core at angles more nearly perpendicular to Earth's rotation axis we have not addressed measurement of the anisotropy of velocity and attenuation nor have we discussed an explanation for correlation of high attenuation with high velocity and low attenuation with low velocity. It is noteworthy, however, that at least one recent study (Reaman et al., 2011) has provided a grain growth model that provides an explanation for both elastic and viscoelastic anisotropy, including the observed sense of the correlation between velocity and attenuation. Reaman et al. (2011) describe a mechanism in which shape-preferred orientation of grains are elongated in the equatorial direction with the fast direction of seismic waves correlating with the greatest attenuation. Interestingly, Irving and Deuss (2011) found the Voigt averages of the anisotropic velocity structures of the inner core to be such that the P velocity of the upper inner core in the Eastern Hemisphere is actually slower rather than faster than that of the Western Hemisphere. This small difference in Voigt averaged velocities might point to the Eastern Hemisphere being younger and freezing and the Western Hemisphere older and melting.

CONCLUSIONS

From measuring differential travel times from source-deconvolved body waves sensitive to structure of the upper 550 km of the inner core, we have found quasi-hemispherical differences in inner core P velocity and attenuation structure persist to at least 550 km depth. Confining our study to body waves traveling largely parallel to the equatorial plane, we find, similar to a growing body of studies, the quasi-Eastern Hemisphere (45°E to 180°E/165°E–165°W) to be faster and more attenuating than the quasi-Western Hemisphere (180°W to 45°E/30°E–60°E). Analyzing our results by 45° wide longitudinal bins we find two regions having significantly faster P velocity averaged over the depth range of 140 to 500 km from the ICB. These regions, centered beneath the eastern equatorial Indian Ocean, and the Eastern Atlantic/West Africa region agree with Gubbins et al.'s prediction (Gubbins et al., 2011) for concentrated freezing of the inner core in these regions. The velocity anomaly concentrated at greater depth beneath the eastern Indian Ocean is the stronger, resulting in apparent hemispherical/ degree-one structure of the inner core. A thin (< 40 km) lower velocity layer beneath the equatorial Indian Ocean in the Eastern quasi-Hemisphere, more intense back-scattering in the coda of PKiKP sampling the inner core beneath the Pacific, and the faint hint of a degree 2 structure in P velocity seems to be more consistent with coupled ICB and CMB heat fluxes than the simple degree 1 structure predicted by a translating/convecting inner core.

For either the translating or non-translating hypothesis to explain hemispherical structural differences persisting up to 550 km depth, secular variations in inner core travel times observed with earthquake doublets (e.g., Zhang et al., 2008) must be explained by either oscillations of the inner core or by rapid growth and decay of ICB topography rather than by a constant differential rotation. There are still major gaps in inner core sampling, which in combination with assumed lateral and vertical parameterization, complicate the separation of large scale structure from smaller scale structure and their relative depth dependencies.