Date of Award

2003

Degree Type

Thesis

Degree Name

Doctor of Philosophy

Faculty

Faculty of Computing, Health and Science

First Advisor

Dr Ute Mueller

Second Advisor

Associate Professor Lyn Bloom

Abstract

This thesis introduces a number of conditional simulation algorithms using wavelet bases. These make use of two orthogonal wavelet bases, the Haar and the Db2 bases. Firstly, two single-level algorithms are introduced, HSIM: with the Haar basis and DB2SIM with the Db2 basis. HSIM reproduces the histogram and semivariogram model of isotropic samples but not the semivariogrnm model of anisotropic samples. DB2SIM reproduces the histogram and semivariogram model in both the isotropic and anisotropic cases but, because of the conditioning method employed, is not as computationally efficient as we would wish. Because of the limitations of HSIM and Db2SIM two multi-level wavelet-based conditional simulation algorithms PWSIM and DWSIM have then been developed. In PWSIM, the conditional realisations are obtained by post-processing non-conditional realisations generated via an available non-conditional simulation algorithm using kriging. In DWSJM the data are conditioned directly via properties of the discrete wavelet transform. Because of the conditioning method, DWSIM is faster than PWSIM. The performance of PWIM and DWSIM with respect to the Haar and the Db2 wavelet bases is assessed via the local and global accuracy of the results. Both quantitative and visual assessments indicate that, for both wavelet bases, the realisations obtained via PWSIM have more variability than those obtained via DWSIM. If the Haar basis is used, PWSIM and DWSIM perform equally well. If the Db2 basis is used then PWSIM performance is much better than DWSIM performance. For both PWSIM and DWSIM, the use of the Db2 basis rather than the Haar basis increases the computational effort without producing a comparable increase in algorithm performance. In PWSIM the use of the Db2 basis slightly improves algorithm performance but the use of the Db2 basis in DWSIM decreases algorithm performance. A performance comparison between DWSIM using the Haar basis and the commonly used conditional simulation algorithm SGSIM shows that DWSIM produces results that are at least as good as those obtained by SGSIM but with less computational effort. The computational advantage of DWSIM over SGSIM is especially pronounced when a large number of realisations are simulated. In addition, the result obtained via DWSIM does not depend on user defined parameters as is the case in both SGSIM and PWSIM. The final result here is a (Haar) wavelet-based conditional simulation algorithm DWSIM that performs well in both the isotropic and the anisotropic cases and, particularly when simulating a large number of realisations, is much faster than the standard algorithm in common use.

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