Data and Results

We systematically downloaded broadband vertical component seismograms ($M_w >6.0$, depth$>$0 km) from the IRIS Data Management Center (DMC) corresponding to the epicentral distance range $150^o$ to $180^o$, and for the time period 1990 to 2003, for which the relocated EHB event catalog is available [Engdahl et al., 1998]. Thousands of seismograms recorded at global and regional networks were collected. Absolute PKIKP travel time residuals were measured with respect to the reference seismic model PREM, using relocated hypocenter and origin time as given in the EHB catalog, and correcting for ellipticity. We also conducted corrections for mantle heterogeneities using a P-wave global tomography model.

In order to test seismic models of ID02 and BT03, we calculate the predicted absolute PKIKP travel time residuals using the parameters of their respective anisotropic models [Cao and Romanowicz, 2007].

We divide our observations into four epicentral distance ranges (Fig. 2.65), corresponding to different depths of penetration of PKIKP in the inner core. In the epicentral distance range $173^o$ to $180^o$, which corresponds to rays that sample the very center of the inner core, we confirm the trend observed by ID02, namely that the travel time residuals are maximum at intermediate angles $\xi$, decreasing both for polar ($\xi \sim 0$) and for equatorial ($\xi \sim 90^o$) paths. This means that the slowest P-wave velocity direction is not along the equatorial plane. This is why ID02 proposed the existence of an IMIC with a radius of $\sim 300 km$ and a slowest direction oriented at $\sim 45^o$ with respect to the earth's rotation axis. However, our dataset indicates that the same trend is also present at shorter epicentral distances. More importantly, in the epicentral distance range $165^o$ to $180^o$, neither the ID02 model nor the BT03 model can fit our observations. This fact suggests two possibilities: (1) there is an IMIC, but its anisotropic character is different from that in ID02 and BT03; (2) there is no IMIC.

Figure 2.64: (a) Ray paths of PKIKP and PKP phases. The black solid line shows the ray path of PKIKP, which is used in this study. The event and stations are indicated by a star and squares, respectively. (b)-(d) Examples of PKIKP absolute travel time residual measurement.
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First, we assume the existence of an IMIC. While keeping the upper layer anisotropic structure fixed, as given in ID02 (bulk constant anisotropy) and in BT03 (depth-dependent), respectively, we correct the observed PKIKP travel time residuals ($\delta t'$) (Fig. 2.65) by subtracting $\eta _0$ and $\delta t_{upper}$ (contributed by the upper layer) and then invert for the anisotropic parameters A and B in the IMIC. It is clear that the constrained anisotropy in the IMIC strongly depends on the anisotropic structure in the upper layer of the inner core. If the upper layer has the bulk constant anisotropic structure as used in ID02, the optimal IMIC radius inverted from our dataset is $\sim 480 km$, and the corresponding variance reduction is 0.89. In contrast, the IMIC radius (300 km) suggested in ID02 is so small that the corresponding variance reduction is very low ($\sim 0.3$). If the upper layer has the depth-dependent anisotropic structure as suggested in BT03, the optimal IMIC radius inverted from our dataset is $\sim 530 km$, and the corresponding variance reduction is 0.94. Thus an IMIC with a depth-dependent anisotropic upper layer fits our dataset better. In both cases, the constrained IMIC radii are compatible with the radius suggested by Cormier and Stroujkova (2005) on the basis of PKIKP waveform modeling. In addition to the radius, the inverted IMIC anisotropic character is also strongly dependent on the upper layer anisotropy. The constrained slowest directions are $\sim 50^o$ and $\sim 55^o$, when considering a ID02 or BT03 upper layer, respectively. And the constrained P-wave velocities along the axis of the earth's rotation are $4.2\%$ and $1.1\%$ faster than that suggested in ID02, respectively.

Second, if there is no IMIC in the inner core, the variance reduction for a one-layer model is small (0.35). A constant anisotropy, one-layer, model can provide good fits to our observations in the epicentral distance range of $165^o$ to $170^o$, but in other ranges, particularly from $173^o$ to $180^o$, it does not (Fig.2.65). Both of the inverted ``two-layer" IMIC models fit our observations very well in the epicentral distance ranges of $173^o$ to $180^o$ and $170^o$ to $173^o$. In the other two epicentral distance ranges ($150^o$ to $165^o$ and $165^o$ to $170^o$), however, the model with an upper layer as in BT03-1 fits our dataset better (Fig. 2). This suggests that the anisotropic structure in the upper part of the inner core most likely changes with depth.

Figure 2.65: Theoretical PKIKP travel time residuals as a function of $\xi$, which include $\delta t_{IMIC}$ (contributed by our inverted IMIC), $\delta t_{upper}$ (contributed by the upper layer), and $\eta _0$. The solid and dashed black lines correspond to the best fitting IMIC models with a bulk constant (ID02-1) and a depth-dependent (BT03-1) anisotropic upper layer, respectively. The dashed grey line corresponds to a one-layer (i.e., no IMIC) anisotropic inner core model. The grey dots are data.
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