CONFIDENCE-REGIONS FOR MANTLE HETEROGENEITY

Least squares tomographic models of mantle P and S velocity structure from travel times have shown large-scale variations correlated with su rface tectonic features, as well as coherent structures in the lowermo st 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 squar es estimates of mantle P or S velocity perturbations must be, as a fun ction of position in the mantle. Suppose (perhaps optimistically) that summary ray travel time errors are independent with mean zero and sta ndard deviation 0.25 s for direct P phases, and standard deviation 0.5 s for all other phases, regardless of distance. If summary travel tim e residuals are fitted by least squares to a mantle model parametrized by 4872 10-degrees by 10-degrees voxels, the half width of a 95% conf idence region for P velocity (using 889,909 summary P rays, 84,046 sum mary 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 PKP df rays) ranges from +/-0.025 to +/-99.8 km s-1. It is wider than 0.19 3 km s-1 in half of the mantle and wider than 0.593 km s-1 in a quarte r of the mantle, by volume. Under the same assumptions and using the s ame parametrization, a 95% confidence region for S velocity based on 1 63,354 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-1, is wider than 0.254 km s-1 in half of the mantle and is wider than 0. 554 km s-1 in a quarter of the mantle. With this ray set, parametrizat ion, and error model, the 95% confidence region around the least squar es 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 vol ume. On a global scale, the mantle's velocity structure is nearly cons istent 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.