Other
Scientific paper
Apr 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994jgr....99.6931p&link_type=abstract
Journal of Geophysical Research (ISSN 0148-0227), vol. 99, no. B4, p. 6931-6943
Other
8
Earth Mantle, Least Squares Method, Mathematical Models, P Waves, S Waves, Seismology, Computer Aided Tomography, Distance, Propagation Velocity, Ray Tracing, Tectonics, Time Series Analysis
Scientific paper
Least squares tomography models of mantle P and S velocity structure from travel times have shown large-scale variations correlated with surface tectonic features, as well as coherent structures in the lowermost mantle. The reliability of these global features of velocity models depends on whether velocity throughout the features can be estimated well simultaneously: one needs to be able to say with confidence that a feature involving many voxels is likely to be real. We find a lower bound on how wide a 95% simultaneous confidence region for least squares estimates of mantle P or S velocity perturbations must be, as a function of position in the mantle. Suppose that summary ray travel time errors are independent with mean zero and standard deviation 0.25 s for direct P phases, and standard deviation 0.5 s for all other phases, regardless of distance. If summary travel time residuals are fitted by least squares to a mantle model parametrized by 4872 10 deg to 10 deg voxels, the half width of a 95% confidence region for P velocity (using 889,909 summary P rays, 84,046 summary PP rays, 67,228 summary pP rays, 23,024 summary PcP rays, 11,239 summary PKPab rays, 47,227 summary PKPbc rays, and 141,843 summary PKPdf rays) ranges from +/- 0.025 to +/- 99.8 km/s. It is wider than 0.193 km/s in half of the mantle and wider than 0.593 km/s in a quarter of the mantle by volume. Under the same assumptions and using the same parametrization, a 95% confidence region for S velocity based on 163,354 summary S rays, 13,781 summary SS rays, 7441 summary ScS rays, and 12,494 summary sS rays ranges from +/- 0.031 to +/- infinity km/s, is wider than 0.254 km/s in half of the mantle and is wider than 0.554 km/s in a quarter of the mantle. With this ray set, parametrization, and error model, the 95% confidence region around the least squares estimate of P velocity includes the radially symmetric iasp91 model for 86.6% of the mantle's volume. A 95% confidence region around the least squares S estimate includes iasp91 for 88.9% of the mantle's volume. On a global scale, the mantle's velocity structure is nearly consistent with the iasp91 radially symmetric model. Smaller voxels, more realistic assumptions about the errors, more accurate modeling of the physics, and three-dimensional structure outside the mantle would make the confidence regions still wider.
Pulliam Jay R.
Stark Philip B.
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