Stochastically established resolution analysis helps to determine empirical tuning parameters in general interpolation schemes
Abstract
Resolution analysis has been a crucial appraisal procedure in general estimation problems to help with the correct interpretation. However, complete resolution information is usually inaccessible due to the sizeable matrix inversion involved with the construction of the resolution matrix. Furthermore, there are not explicit forward kernels embedded within formulations for popular interpolation algorithms such as the kriging and the minimum curvature gridding schemes. Stochastic simulation has recently been proposed to make resolution evaluation for sizeable inverse problems tractable. We generalize the method of getting resolution information to the popular interpolation schemes. There are usually certain empirically determined tuning parameters involved in these interpolation schemes, for example, the ideal function and radius of influence for fitting the semi-variogram in the kriging method and the relative weighting of the membrane stress term in the minimum curvature gridding scheme. We show that our proposed resolution analysis not only provide the crucial spatial resolution pattern, more importantly, it helps to determine those critical tuning parameters that have been determined empirically and arbitrarily. Keywords: resolution analysis; stochastic simulation; kriging; minimum curvature gridding
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2013
- Bibcode:
- 2013AGUFM.H41G1319Y
- Keywords:
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- 3260 MATHEMATICAL GEOPHYSICS Inverse theory;
- 3225 MATHEMATICAL GEOPHYSICS Numerical approximations and analysis;
- 1800 HYDROLOGY;
- 3252 MATHEMATICAL GEOPHYSICS Spatial analysis