We systematically downloaded broadband vertical component seismograms (, depth0 km)
from the IRIS Data Management Center (DMC) corresponding to the
epicentral distance range to , 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 to , 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 , decreasing both for polar () and for equatorial () 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 and a slowest direction oriented at 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 to , 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.

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 () (Fig. 2.65)
by subtracting and
(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 ,
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 (). If the upper layer has the depth-dependent
anisotropic structure as suggested in BT03, the optimal IMIC radius inverted from our
dataset is , 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 and ,
when considering a ID02 or BT03 upper layer, respectively. And the constrained
P-wave velocities along the axis of the earth's rotation are and 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 to , but in other ranges, particularly from to , 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 to and to . In the other two epicentral distance ranges ( to and to ), 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.

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