Resolution, uncertainty and data predictability of tomographic Lg attenuation models—application to Southeastern China

• Published in: Geophysical journal international 2017-07, Vol.210 (1), p.166-183
• Main Authors: Chen, Youlin, Xie, Jiakang
• Format: Article
• Language: English
• ISSN: 0956-540X; 1365-246X
• DOI: 10.1093/gji/ggx147

Abstract We address two fundamental issues that pertain to Q tomography using high-frequency regional waves, particularly the Lg wave. The first issue is that Q tomography uses complex ‘reduced amplitude data’ as input. These data are generated by taking the logarithm of the product of (1) the observed amplitudes and (2) the simplified 1D geometrical spreading correction. They are thereby subject to ‘modeling errors’ that are dominated by uncompensated 3D structural effects; however, no knowledge of the statistical behaviour of these errors exists to justify the widely used least-squares methods for solving Q tomography. The second issue is that Q tomography has been solved using various iterative methods such as LSQR (Least-Squares QR, where QR refers to a QR factorization of a matrix into the product of an orthogonal matrix Q and an upper triangular matrix R) and SIRT (Simultaneous Iterative Reconstruction Technique) that do not allow for the quantitative estimation of model resolution and error. In this study, we conduct the first rigorous analysis of the statistics of the reduced amplitude data and find that the data error distribution is predominantly normal, but with long-tailed outliers. This distribution is similar to that of teleseismic traveltime residuals. We develop a screening procedure to remove outliers so that data closely follow a normal distribution. Next, we develop an efficient tomographic method based on the PROPACK software package to perform singular value decomposition on a data kernel matrix, which enables us to solve for the inverse, model resolution and covariance matrices along with the optimal Q model. These matrices permit for various quantitative model appraisals, including the evaluation of the formal resolution and error. Further, they allow formal uncertainty estimates of predicted data (Q) along future paths to be made at any specified confidence level. This new capability significantly benefits the practical missions of source identification and source size estimation, for which reliable uncertainty estimates are especially important. We apply the new methodologies to data from southeastern China to obtain a 1 Hz Lg Q model, which exhibits patterns consistent with what is known about the geology and tectonics of the region. We also solve for the site response model.