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On the origin of complexity in PKP travel time data

Barbara Romanowicz and Hrvoje Tkalcic

Introduction

Early inner core anisotropy models, proposed starting around 15 years ago to explain trends in PKP travel time data and anomalous splitting of core sensitive normal modes, were cast in terms of transverse isotropy with fast axis parallel to the earth's axis of rotation (e.g. Morelli et al., 1986; Creager, 1992), as would be expected if the anisotropy were due to the alignment of hcp-iron crystals with the axis of rotation (e.g. Stixrude and Cohen, 1995). Proposed physical mechanisms for anisotropy have involved convection in the inner core (Jeanloz and Wenk, 1988), magnetic effects (Karato, 1999), gravitational interaction with the mantle (e.g. Buffett and Creager, 1998) or texturing of iron during inner core solidification (Bergman, 1997). All of these mechanisms imply axisymmetry of the anisotropic structure.

As data have accumulated and revealed more details, inner core anisotropy models have become more complex. A most intriguing observation was made by Tanaka and Hamaguchi (1997), who observed that only one hemisphere, extending roughly from longitude $177^o W$ to $43^o E$ ("Quasi-western" hemisphere) was anisotropic. In order to account for the difference in the two hemispheres, as well as the possible existence of an isotropic region at the top of the inner core, Creager (2000) and Garcia and Souriau (2001) recently proposed very similar models which comprise a discontinuity within the inner core, separating an isotropic outer core from an anisotropic inner core. The ellipsoidal shape of this discontinuity is shifted with respect to the center of the inner core, so that the isotropic part is thicker in the eastern (400 km) than in the western ($<100km$) quasi-hemisphere.

Other complexities in the PKP(BC-DF) and PKP(AB-DF) travel time data have recently been documented by Bréger et al. (1999, 2000a,b) who pointed out how important it is to account accurately for the influence of strong heterogeneity at the base of the mantle, before making inferences on inner core anisotropy from the observation of core sensitive phases. It is difficult to find physical mechanisms to explain the increasingly complex structure of the inner core anisotropy required by recently accumulated high quality broadband data, and in particular, the hemispherical differences, given that the inner core is thought to be close to the melting point of its constituents. In view of the mounting evidence for strong heterogeneity in the deep mantle and the uneven distribution of PKP observations on polar paths around the globe (Bréger et al., 2000a), it is important to consider whether the complexity originates in the inner core or elsewhere, and whether it might all be accounted for by mantle structure.

We have continued to investigate this complexity, in particular by looking at data from the dense regional Alaska network, for which some of the most anomalous PKP travel time have been measured, on paths originating in the south Atlantic.

Assembled Datasets and observed trends

We have assembled a comprehensive dataset comprising PKP(AB-DF), PKP(BC-DF) differential travel times, and PKP(DF) absolute travel times, which we measured on vertical component records from broadband and short period stations worldwide for the time period 1990-1998 (Tkalcic et al., 2001), and complemented by datasets collected by several other authors.

We also measured absolute PKP(DF) travel times, whenever possible, and in particular for the southern hemisphere events for which Hrvoje Tkalcic collected waveforms from the short period Alaska network. For these measurements, we cannot take advantage of the accuracy of waveform comparison, and we must rely on direct picks of the onset of the DF phase, which is often emergent, especially for polar paths. Therefore, the measurement error is larger in general, than for differential travel times, and on the order of $1 sec$ for equatorial paths, and up to $2 sec$ in some cases, for polar paths. We thus expect a larger scatter in the data. However, absolute measurements are of great interest for the study of inner core anisotropy, and are the basis of most inferences made on the basis of data collected from ISC bulletins (e.g. Morelli et al., 1986; Su and Dziewonski, 1995). Moreover, global variations (i.e. differences between polar and equatorial paths) are largely in excess of the measurement error.

Origin of anomalous observations in Alaska

Creager and collaborators measured differential BC-DF travel times for several events in the south Sandwich islands observed on the Alaska network, and differential AB-DF travel times for the 90/04/30 Bouvet Islands earthquake. Creager (1997) proposed that the corresponding local trends in the data originate in a heterogeneous region in the inner core. We have collected waveforms from these and several other earthquakes recorded on the Alaska network (courtesy of Roger Hansen). Because of the density of recordings, it was possible to measure both absolute DF and absolute BC (or AB) with an accuracy of less than 0.5 sec for a range of epicentral distances and azimuths. The corresponding measurements are shown in Figure 30.1 for 4 of the events considered, as a function of the following three angles: epicentral distance, azimuth and angle $\xi $. We note the consistency of trends from one event to the other. In DF, the local variations across the network span between 2 and 3 sec.

Figure 30.1: Absolute DF (diamonds) ad absolute BC (triangles) measured across the Alaska network for four of the south Sandwich Islands events discussed in the text, plotted as a function of $\xi $ (left), azimuth (middle) and epicentral distance (right). Note that for the 91/12/27 event, all measurements are shifted by +3 sec, probably do to an error in the relocated epicentral parameters.
\begin{figure}\begin{center}
\epsfig{file=barbara01_3_fig1.eps, bbllx=19,bblly=92,bburx=562,bbury=656, width=8cm}\end{center}\end{figure}

The striking observation, however, is that the trends observed in DF are also present in BC, although with a smaller amplitude. For example, there is a relative maximum at azimuths close to $307^o$ in both BC and DF, and a decrease with epicentral distance from 147 to $153^o$, followed by a jump to more positive residuals at around $154^o$. We infer that the systematic 2 sec variation of BC-DF with epicentral distance across the Alaska network(not shown), and correlated with those of DF and BC (Figure 30.1) is not due to the inner core. The corresponding heterogeneous region, with whose quasi-vertical boundary both DF and BC are interacting, must be located in the deep mantle (actually, it could be on either side of the CMB), where the raypaths of DF and BC differ significantly in direction, but can still be affected by the same structure. It also must be located on the Alaska side of the paths. Indeed, on the source side, the entry points of DF (and BC) into the core overlap only partially for different events, in a way which is not compatible with the repeatability of trends with azimuth, from event to event, observed in Figure 30.1.

Figure 30.2: Absolute PKP(DF) (filled symbols) and absolute PKP(BC) (crosses) residuals observed at the Alaska network for events in the southern hemisphere and absolute PKP(DF) (stars) for events in Alaska observed at south pole station SPA, plotted at the entry point of DF (respectively BC) into the core. A strong southeast trending gradient is observed delineating the sharp border of an anomaly visible both by DF and BC. On the western side, "normal" data represented by inverted triangles and diamonds are less reliable as they correspond to noisy events in the southern Pacific.
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\epsfig{file=barbara01_3_fig2.eps,bbllx=87,bblly=70,bburx=462,bbury=547, width=8cm}\end{center}\end{figure}

On the other hand, if we consider absolute DF measurements (and when available absolute BC measurements) from a larger dataset that corresponds to events in a wider range of azimuths around Alaska, and includes absolute DF measurements for Alaska events observed at south pole station SPA, we find that the most anomalous observations (fastest DF), when plotted at the entry point of PKP(DF) into the core, on the Alaska side, form a well defined contiguous region with a strong gradient to the southeast, indicating a sharp termination of the anomaly (Figure 30.2. When plotted as a function of bottoming point of DF in the inner core, this coherency is lost, confirming that the origin of the largest anomalies in PKP(DF) is to be sought in the vicinity of the core-mantle boundary (CMB).

Another intriguing observation is that, when considering the global datasets of absolute PKP(DF) residuals and relative PKP(DF-AB) residuals, and plotting them as a function of entry point into the core in the northern hemisphere, the anomalous observations (which include those in Alaska), delineate a coherent polar region (figure 30.3, with a border that coincides under Alaska with the region of strong gradient observed in Figure 30.2, further pointing to an origin of the very anomalous paths (now on a global scale) in the vicinity of the CMB. Whether or not such an anomaly can be "hidden" on the mantle side or requires a component in the outer core remains to be clarified.

References

Bergman, M. I., Measurements of elastic anisotropy due to solidification texturing and the implications for the Earth's inner core, Nature, 389, 60-63 , 1997.

Bréger, L., B. Romanowicz, and H. Tkalcic, PKP(BC-DF) travel times: New constraints on short scale heterogeneity in the deep earth? Geophys. Res. Lett., 26, 3169-3172, 1999.

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, EPSL, 175, 133-143, 2000a.

Bréger, L., B. Romanowicz and S. Rousset, New constraints on the structure of the inner core from P'P', Geophys. Res. Lett., 27, 2781-2784, 2000b.

Buffett, B. A. and Creager, K. C., Rotation and deformation of the inner core, Eos 79, 218-219, 1998.

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 anisotropy and rotation, in Earth's deep interior: Mineral Physics and Seismic Tomography from the atomic to the global scale, Geophysical Monograph 117, AGU, 2000.

Garcia, R. and A. Souriau, Inner core anisotropy and heterogeneity level, Geophys. Res. Lett., 27, 3121-3124, 2001.

Jeanloz, R. and Wenk, H.R., Convection and anisotropy of the inner core, Geophys. Res. Lett., 15, 72-75, 1988.

Karato, S., Seismic anisotropy of the earth's inner core resulting from flow induced by Maxwell stresses, Nature, 402, 871-873, 1999.

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.

Stixrude, L. and R. Cohen, High-pressure elasticity of iron and anisotropy of Earth's inner core, Science, 275, 1972-1975, 1995.

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.

Tkalcic, H., B. Romanowicz and N. Houy, Constraints on D" structure using PKP(AB-DF), PKP(BC-DF) and PcP-P travel time data from broadband records, Geophys. J. Int., in revision, 2001.

Figure 30.3: Travel time residuals for all angles $\xi $ plotted at the entry point of DF in the northern (bottom) hemispheres. Top: absolute DF measurements. The color code is centered at $\delta t = -2.0 sec$; Bottom: DF-AB measurements. The color code is centered at $\delta t = -2.5 sec$.
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\epsfig{file=barbara01_3_fig3.eps,bbllx=136,bblly=107,bburx=503,bbury=681, width=8cm}\end{center}\end{figure}


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