Combining different types of data for geophysical inverse problems: Theory and applications

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400449
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Solid earth and planetary physics
• Research Institution: Kyoto University
• Principal Investigator: Xu Peiliang 京都大学, 防災研究所, 助教 (10293961)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: parameter estimation / inverse problems / errors-in-variables / multiplicative noise / integer estimation / variance components

Outline of Final Research Achievements

This project focuses on inverse problems to estimate the unknown parameters in errors-in-variables (EIV), multiplicative noise and discrete tomography models by combining different types of data. We achieve a number of new results and publish 9 papers in international journals. The applicant is invited to report the achieved results at several international conferences. We develop new LS-based estimators to reconstruct multiplicative error models and conduct quality evaluation of lattice basis reduction for discrete tomography, which can be directly affected by the probability distribution of the reduced Gram-Schmidt coefficients. We propose bias-corrected LS and N-calibrated estimators to estimate the EIV parameters, which are as good as total LS, but require much less computation. We prove that the variance components in an EIV model can be inestimable and unstable. We investigate how EIV can affect the parameter estimation and the weighting factors for different types of data.

Free Research Field

測地学