Supplementary Figure 1
Supplementary Table 1: Statistical results for various inversions
Comparison of statistical results for a variety of models and radial
parameterizations, where VR is the variance reduction, N=2850 is the
number of data and M is the number of model parameters. In model S6,
we determine lateral variations in S velocity up to degree~6,
and assume that lateral variations in P velocity and density
are proportional to the S velocity variations by constant scaling
factors of 0.55 and 0.2, respectively. In model SP6, we invert for
independent lateral variations in S and P velocity, but
assume that the density model is proportional to the S model.
These two inversions use only the mode data. The third inversion, model
SPRD6, allows for independent lateral variations in S velocity,
P velocity and density, and additional variations in topography
on the free surface, the 660 and the CMB. This inversion
includes constraints imposed by the free-air gravity anomaly. K13
indicates that models are expanded radially in Chebyshev polynomials up
to order 13 (over-parameterized inversion), and K7 models use Chebyshev
polynomials up to order 7.
| Model |
VR (%) |
c2/N |
c2/(N-M) |
M |
| S6 (K13) |
89.4 |
2.7 |
3.1 |
378 |
| SP6 (K13) |
90.3 |
2.5 |
3.3 |
758 |
| SPRD6 (K13) |
91.5 |
2.1 |
3.7 |
1215 |
| S6 (K7) |
88.1 |
3.0 |
3.2 |
216 |
| SP6 (K7) |
90.1 |
2.5 |
2.9 |
432 |
| SPRD6 (K7) |
91.7 |
2.1 |
2.8 |
729 |
Changes in c2/(N-M) indicate whether the increase in the number
of model parameters is warranted by the data. However, this test is not
useful when the models are over-parameterized, as in K13 inversions.
We prefer to over-parameterize our models and damp higher-order
polynomials more strongly rather than parameterizing the models with
lesser degrees of freedom. When the models are expanded radially up to
order 7, which we believe gives a reasonable number of model parameters
with respect to the number of data, c2/(N-M) improves with the
addition of P, and again when density and boundary topography
are added.
Miaki Ishii, Department of Earth and Planetary Sciences, Harvard University, copyright ©1999, all rights reserved
Last modified: September 8, 1999