HR: 0800h
AN: S51B-0502    [Abstracts]
TI: General Importance of Covariance Components of Densely Sampled Observed Data in Inversion Analyses: Implications for Seismic Source Inversion
AU: * Fukahata, Y
EM: fukahata@eps.s.u-tokyo.ac.jp
AF: Department of Earth and Planetary Science, University of Tokyo, Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan
AU: Yagi, Y
EM: yagi-y@geol.tsukuba.ac.jp
AF: Graduate School of Life and Environmental Sciences, University of Tsukuba, 1-1-1 Tennoudai, Tsukuba, 305-8577, Japan
AB: In geophysical observations, unlike the case of laboratory experiments, data are always inaccurate and insufficient, and so, we need to introduce some prior constraints in order to compromise reciprocal requirements for model resolution and estimation errors in a natural way. For seismic source inversion, smoothness constraints in space and time is commonly applied. By incorporating the prior information into the information from observed data with Bayes' theorem, we can construct a highly flexible model with hyperparameters, which determine the relative weight between the prior and observed data (Yabuki and Matsu'ura, 1992). The optimal values of the hyperparameters can be objectively selected by using AkaikeOs Bayesian Information Criterion (ABIC). Before the introduction of ABIC, we have not had a definitive way to determine the relative weight between the information from observed data and prior constraints. The point of ABIC is that we can objectively determine it based on statistics. That is to say, when we have an enough amount of accurate data, a model that well explains observed data is selected. Conversely, when the data are inaccurate and/or insufficient, the model comes to follow prior constraints (Fukahata, Yagi and Matsu'ura, 2003). Due to an enhanced technology of computers, it has become possible to observe and invert seismic waveform data with a high sampling rate. Observed waveform data is not completely independent of each other due to the effect of un-elastic attenuation of the Earth. Then, if we neglect the data covariance, the situation is similar to the case that duplicated (or triplicated or more) data are inverted. In short, the information from observed data is overestimated, which results in an unstable solution with overfitting. A similar problem has already been reported for an analysis of InSAR data that have highly spatially correlated errors (Fukahata and Wright, 2007). In general, we must take data covariance into account in inverting densely sampled observed data.
DE: 1240 Satellite geodesy: results (6929, 7215, 7230, 7240)
DE: 3260 Inverse theory
DE: 7215 Earthquake source observations (1240)
SC: Seismology [S]
MN: 2007 Fall Meeting