Multi-channel, multi-dimensional geophysical data models are explored in this thesis. The basic data model we develop, the one-pass, multi-channel, multi-dimensional autoregressive (OPMCTDAR) data model, describes data as the linear superposition of a causal, multi-channel, two-dimensional, deterministic AR filter with a stochastic innovation which is assumed to have minimum-variance, and to be uncorrelated and Gaussian. Two-pass and four-pass extension of this basic model (TP or FPMCTDAR) are also developed in this work as a generalization of the AR data models described by Gregotski (1989), Gregotski et al. (1991) and Jensen et al. (1990, 1993). Direct inversion for the parameters of the one-pass data model is employed in the inversion processes of two-pass and four-pass data models. Least-squares estimates of the causal AR filter coefficients are used to deconvolve original data sets to recover the assumed minimum-variance innovation process. Two-channel, two-dimensional synthetic data modelling examples are presented to prove the validity of this inversion scheme for these data models. I show that two-pass and four-pass inversion schemes extended from those of the corresponding single-channel case work for the only special cases of TP or FPMCTDAR data models. I employ two-dimensional z-transform for the mathematical derivation of the data models and the discussion on the stability of the multi-channel system functions.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.26144 |
| Date | January 1993 |
| Creators | Shen, Wei-Zhong |
| Contributors | Jensen, Olivia (advisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Master of Science (Department of Earth and Planetary Sciences.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001394259, proquestno: MM94524, Theses scanned by UMI/ProQuest. |
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