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Anomalous splitting of core sensitive modes: a reevaluation of possible interpretations

B. Romanowicz and L. Bréger


Introduction

Inner core anisotropy was proposed 13 years ago to explain two categories of intriguing observations: (1) faster propagation times for seismic body waves that travel through the inner core along paths quasi-parallel to the earth's rotation axis, than for those that travel on equatorial paths (Poupinet et al., 1983; Morelli et al., 1986), and (2) anomalous splitting of core-sensitive free oscillations (Masters and Gilbert, 1981; Woodhouse et al., 1986). These observations have been confirmed in many subsequent studies (e.g. Shearer, 1991; Creager, 1992; Vinnik et al., 1994; Su and Dziewonski, 1995) and models of inner core anisotropy have been progressively refined. These models were originally cast in terms of constant transverse isotropy with fast axis parallel to the earth's rotation axis, for which an interpretation in terms of alignment of hcp-Fe crystals was proposed. Over the years, inner core anisotropy models have become more complex. Depth dependence was introduced (Su and Dziewonski, 1995; Tromp, 1993) and more complex spatial dependence suggested (Li et al., 1991; Romanowicz et al., 1996; Durek and Romanowicz, 1999). Most recently, several studies have proposed even stronger departures from simple models of inner core anisotropy. An asymmetry in the anisotropy pattern was pointed out (Tanaka and Hamaguchi, 1997; Creager, 1999), with one "quasi-hemisphere" of the inner core anisotropic and the other not, and it has been argued that the top 100-200 km of the inner core may be isotropic and laterally varying (Song and Helmberger, 1998). Strong, small scale variation in the anisotropy along a highly anomalous path between the South Sandwich Islands and station COL in Alaska has also been documented (Creager, 1997).

The necessity to modify the simple original model of constant anisotropy, and introduce significant complexity, has become quite clear. Moreover, we have recently proposed that an important contribution to the trend of travel time residuals, as a function of angle of the path with respect to the rotation axis, for PKP(AB)-PKP(DF) data, could come from strong heterogeneity in D" (Bréger et al., 1999a) and we proposed a possible trade-off between D" structure and inner core anisotropy in the interpretation of differential PKP travel time data (also PKP(BC)-PKP(DF), Bréger et al., 1999b).


  
Figure: Splitting data for C20, relative to the center frequency, in 10-6 units (cf He and Tromp, 1996) from various sources, and predictions for a global tomographic model of the mantle (SAW12D). UCB: from Durek and Romanowicz (1999); $R\&R$: from Resovsky and Ritzwoller (1998); $H\&T$: from He and Tromp (1996).

(a) "mantle modes"; (b) "core modes". The core modes have been subdivided (vertical broken lines) into those that have no sensitivity to inner core structure (1S2-7S7), those that have small sensitivity to inner core structure (2S3-21S8) and those that have more than 4% of their energy in the inner core (8S1-3S2).

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Even if we accept an interpretation of PKP observations in terms of a complex inner core anisotropy model, some of the recent observations are in contradiction with the normal mode splitting observations. Indeed, since normal modes are primarily sensitive to even order structure, it is difficult to reconcile the hemispherical model (Tanaka and Hamaguchi, 1997; Creager, 1999) with the dominant zonal "C20" component of anomalous splitting observations. Likewise, since modes are primarily sensitive to the uppermost third of the inner core, their splitting becomes more difficult to explain in terms of anisotropy if there is an isotropic layer several hundred km thick at the top of the inner core (Durek and Romanowicz, 1999).

Alternative interpretations for anomalous mode splitting have been proposed in terms of outer core heterogeneity (Ritzwoller et al., 1988; Widmer et al., 1992).

In view of the recent controversies regarding the level and complexity of inner core anisotropy, we have decided to reexamine the issue of interpretation of anomalous mode splitting data. We are assisted in this process by the recent accumulation of high quality low frequency data, owing to the expansion of the global digital broadband network and the occurrence of several very large deep earthquakes, in particular the M8.2 Bolivia earthquake of June 9, 1994.

Data Analysis

We have assembled a spheroidal mode splitting dataset for 79 normal modes sensitive either primarily to structure in the mantle (42 modes) or both to structure in the mantle and in the core (37 modes). These data are tabulated in terms of measured splitting coefficients, as defined below, from three sources: measurements by Resovsky and Ritzwoller (1998) mostly for mantle modes, by He and Tromp (1996) for a combination of mantle and core modes, complemented by our own dataset, primarily for core modes (Durek and Romanowicz, 1999).

Figure 22.1 shows a comparison of C20 measurements from the 3 sources considered, giving a sense of uncertainty on the splitting measurements. In most cases, agreement between different groups are excellent (also with measurements from Laske and Masters, personal communication). We have distinguished mantle modes (top panel) and modes with significant sensitivity to core structure (bottom panel). We classify the latter into "outer core" modes ("oc"), that are not sensitive to inner core structure, and two categories of "inner core" modes: (1) those with less than 4% sensitivity to inner core structure (modes 2S3-21S8, category "ic1") and (2) those with stronger sensitivity to inner core structure (modes 8S1-3S2, category "ic2"). Mode 3S2 has been assigned to category "ic2", only because it has significant sensitivity to S-velocity in the inner core. We will single out this particular mode, which exhibits the strongest anomalous splitting, the largest uncertainties in the measurements, as well as the largest sensitivity to inner core anisotropy. We have also plotted the splitting predictions of mantle model SAW12D (Li and Romanowicz, 1996), an SH-model of the mantle, obtained using body and surface waveform data. In converting the S-velocity from this model to density ($\rho$) and P-velocity (Vp), we have assumed standard conversion factors: dlnVp/dlnVs=0.5 and $dln\rho/dlnVs=0.25$, as proposed by Li et al. (1991). Predictions for other mantle models are similar. Two observations are striking: for mantle modes, the predictions of SAW12D follow the data quite closely for all branches, although the amplitudes in the 0S and 1S branches are underpredicted. For core sensitive modes, we note, as previous authors, that the mantle model predicts practically no splitting for modes with any sensitivity to inner core structure, whereas the data consistently show a high level of splitting. This is referred to in the literature as "anomalous" splitting. We note that, except for mode 3S2, the level of splitting observed for modes in categories ic1 and ic2 is comparable, with a few modes exhibiting somewhat larger splitting in both datasets (2S3 and 6S3 in ic1 and 13S1, 13S2 in ic2).

Inversion results

We invert these data using the following parametrization. We consider simple layered models of Vs, Vp and $\rho$ in the mantle (Table 1), Vp and $\rho$ in the outer core, as well as models of inner core anisotropy with various levels of complexity, as allowed by the axisymmetric formalism developed by Li et al. (1991) and applied more recently to broadband data (Romanowicz et al., 1996; Durek and Romanowicz, 1999). We also include topography on three discontinuities (Moho, 670 km discontinuity and core mantle boundary (CMB)). In order to better assess where the inversions naturally tend to put the structure, we do not apply smoothness constraints, only overall damping, as needed, and have, after some experimentation, arrived at a layer parametrization which yields stable inversions of mantle modes without smoothing (5 layers in the crust/upper mantle, 12 layers in the lower mantle). In the upper mantle, we invert for Vs only, assuming Vp and $\rho$ to be proportional to Vs, consistent with findings of independent studies based on normal modes and travel times (Robertson and Woodhouse, 1995; Su and Dziewonski, 1997; Ishii and Tromp, 1998; Kuo et al., 1998). In the lower mantle, we solve separately for Vs,Vp and $\rho$. Previous studies have shown that the proportionality between Vp and Vs breaks down below a depth of 1800-2000km, which may result in different depth profiles for C20 in Vs, Vp and $\rho$ respectively (Robertson and Woodhouse, 1995; 1996; Bolton and Masters, 1996; Ishii and Tromp, 1998; Kuo et al., 1998).

In the outer core, we consider one or several layers, and solve for Vp and $\rho$ without any a-priori constraints on the $\rho$ structure, or the absence thereof. Several one layer models are considered, with increasing thickness, starting from the top (or the bottom) of the outer core.

Three parametrizations of inner core anisotropy are considered: (1) a simple constant transverse anisotropy model (3 independent variables, "i1 models"), (2) a model of transverse anisotropy with depth dependence, described by a polynomial in r2 up to degree 4 (15 independent variables, "i2 models") and (3) a more general axisymmetric model including lateral variations expressed in spherical harmonics up to degree 4 (44 independent parameters, "i3 models"). We note that for the latter model, the inverse problem, with a total of 88 parameters, is under- determined. We consider results of inversions for 12 different depth parametrizations: 1- mantle only, 2-9 - mantle and outer core, 10-12 - mantle and inner core anisotropy.

Figure 22.2 shows the residual variance in the C20 coefficient data as a function of model number, when different subsets of modes are considered. When mode 3S2 is excluded from the dataset, our results indicate that outer core models provide much better fit to the data than models with inner core anisotropy. When mode 3S2 is included, the overall fit according to residual variance is better for inner core anisotropy models, however, this reflects primarily a better fit to the very anomalous splitting of 3S2, whereas the fit to other core and mantle modes is not significantly improved.

The results of our study can be summarized as follows: (1) inner core anisotropy improves the overall fit to data compared to a model with aspherical structure restricted to the mantle; (2) when mode 3S2 is excluded from the dataset, simple models with heterogeneity in the outer core fit the data consistently better than simple inner core anisotropy models; (3) when mode 3S2 is included, overall residual variances are smallest or inner core anisotropy models. However, the splitting of 3S2 is fit at the expense of that of the 5S mantle mode branch, sensitive to P-velocity in the mantle. (4) outer core models are more stable and consistent with each other than inner core models, when different subsets of core modes are inverted (i.e. modes with small versus large sensitivity in the inner core).(5) Lateral heterogeneity in the mantle alone (in particular D") cannot consistently account for the splitting of all modes.

Simple anisotropic models of the inner core are therefore not sufficient to simultaneously explain the splitting of spheroidal mantle and core modes, and a combination of deep mantle and outer core structure contributes significantly to the pattern of splitting. The outer core structure retrieved is consistent with either heterogeneity associated with the Taylor cylinder tangent to the earth's inner core, or the possible existence of a stagnant layer at the top of the outer core, enriched in light material. In the latter case, we conjecture that a small amount of shear could help reconcile the large splitting of 3S2 with that of other core and mantle modes. Such models deserve further investigation.


  
Figure 22.2: Residual variances for C20 as a function of model parametrization for the different subsets of data considered: (a) mantle, outer core and ic1 modes; (b) mantle, outer core and ic2 modes, without 3S2; (c) all modes without 3S2; (d) same as (b) with 3S2; (e) all modes with 3S2.
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References

Bréger, L., H. Tkalcic, and B. Romanowicz, The effect of D" on PKP (AB-DF) travel time residuals and possible implications for inner core structure, in revision E.P.S.L., 1999.

Bréger, L., B. Romanowicz, and H. Tkalcic, PKP(BC-DF) travel times residuals and short scale heterogeneity in the deep earth, Geophys. Res. Lett., in press, 1999.

Creager, K.C., Anisotropy of the inner core from differential travel times of the phases PKP and PKIKP, Nature, 356, 309-314, 1992.

Creager, K.C., Inner core rotation rate from small-scale heterogeneity and time-varying travel times, Science, 278, 1284-1288, 1997.

Creager, K.C., Large-scale variations in inner core anisotropy, In press in J. Geophys. Res., 1999.

Durek, J. and B. Romanowicz, Inner core anisotropy inferred by direct inversion of normal mode spectra, In press Geophys. J. Int., 1999.

He, X. and J. Tromp, Normal-mode constraints on the structure of the Earth, J. Geophys. Res., 101, 20,053-20,082, 1996.

Li, X-D., and B. Romanowicz, Global mantle shear velocity model developed using nonlinear asymptotic coupling theory, J. Geophys. Res., 101, 22,245-22,272, 1996.

Li, X-D., D. Giardini, and J. H. Woodhouse, Large-scale three-dimensional even-degree structure of the Earth from splitting of long-period normal modes, J. Geophys. Res., 96, 551-557, 1991.

Morelli, A., A.M. Dziewonski, and J. H. Woodhouse, Anisotropy of the core inferred from PKIKP travel times, Geophys. Res. Lett., 13, 1545-1548, 1986.

Morelli, A., A.M. Dziewonski, and J. H. Woodhouse, Anisotropy of the core inferred from PKIKP travel times, Geophys. Res. Lett., 13, 1545-1548, 1986.

Poupinet, G., R. Pillet, and A. Souriau, Possible heterogeneity of the Earth's core deduced from PKIKP travel times, Nature, 305, 204-206, 1983.

Ritzwoller, M., G. Masters, and F. Gilbert, Observations of anomalous splitting and their interpretation in terms of aspherical structure, J. Geophys. Res., 91, 10203-10228, 1988.

Romanowicz, B., X.-D. Li, and J. Durek, Anisotropy in the inner core; could it be due to low-order convection? Science, 274, 963-966, 1996.

Shearer, P.M., PKP(BC) versus PKP(DF) differential travel times and aspherical structure in the Earth's inner core, J. Geophys. Res., 96, 2233-2247, 1991.

Song, X.-D. and D.V. Helmberger, Seismic evidence for an inner core transition zone, Science, 282, 924-927, 1998.

Su, W. and A.M. Dziewonski, Inner core anisotropy in three dimensions. J. Geophys. Res., 100, 9831-9852, 1995.

Tanaka, S. and H. Hamaguchi, Degree one heterogeneity and hemispherical variation of anisotropy in the inner core from PKP(BC)-PKP(DF) times, J. Geophys. Res., 102, 2925-2938, 1997.

Tromp, J., Support for anisotropy of the Earth's inner core from splitting in free oscillation data, Nature, 366, 678-681, 1993.

Vinnik, L., B. Romanowicz, and L. Bréger, Anisotropy in the central part of the inner core. Geophys. Res. Lett., 21, 1671, 1994.

Widmer, R., G. Masters, and F. Gilbert, Observably split multiplets-data analysis and interpretation in terms of large-scale aspherical structure, Geophys. J. Int., 111, 559-576, 1992.

Woodhouse, J.H., D. Giardini, and X.-D. Li, Evidence for inner core anisotropy from splitting in free oscillation data, Geophys. Res. Lett., 13, 1549-1552, 1986.


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