In turbulent and other nonlinear geophysical processes, extreme variability is built up multiplicatively from large to small scales via cascade mechanisms generally leading to (canonical) universal multifractal fields. This thesis clarifies the distinction between "bare" and "dressed" cascade processes, the classification of multifractal singularities and the related nontrivial problem of sampling and estimation of their scale properties. It then describes the first data analysis techniques applicable to these highly variable multifractals: previously existing techniques are limited to much calmer geometric or microcanonical multifractals. The two techniques developed here (Probability Distribution Multiple Scaling and Double Trace Moment) are analyzed theoretically and numerically and are tested on turbulent and topographic data, providing the first estimates of their universal multifractal parameters, the Levy index $ alpha$ which characterizes the degree of multifractality, and C$ sb1$ (the codimension of the mean singularity) which characterizes the mean inhomogeneity of the process.

The feasibility of using time-domain airborne electromagnetic and ground resistivity methods in geological mapping in tropical terrains is investigated. The investigation is based upon evaluation of the linear inverse theory in the determination of physical parameters of the weathered layer necessary for interpretation of underlying lithology. / Inversion of ground resistivity sounding data from the greenstone belt in western Kenya yields conductivities and thicknesses that are consistent with geology. A similar inversion of modelled time-domain airborne electromagnetic data shows that conductivity, thickness and depth to the top of the conductive weathered layer can be uniquely determined if its response does not suffer the thin sheet response problem. The results further show that this problem can be quite common in tropical regions since much of the weathered layer has low conductivity and thickness and, consequently, the response is weak. In this situation, conductivity and thickness are correlated and conductivity-thickness product is better determined than these two parameters independently. / By virtue of the weak time-domain AEM response of the weathered layer, much of the response remains buried in noise. This situation introduces further complications for an inverse problem that is highly non-linear. A method for reducing some of this noise before carrying out the inversion is presented.

Thesis (Ph. D.)--Massachusetts Institute of Technology and Woods Hole Oceanographic Institution. / Includes bibliographical references (p. [166]-169).

Thesis (Ph.D.)--University of Washington, 2006. / (UMI)AAI3230780. Adviser: Howard B. Conway. Source: Dissertation Abstracts International, Volume: 67-09, Section: B, page: 4942.

Thesis (Ph.D.)--Boston University, 2007. / (UMI)AAI3254458. Source: Dissertation Abstracts International, Volume: 68-03, Section: B, page: 1518. Adviser: Geoffrey A. Abers.

Thesis (Ph.D.)--University of Toronto (Canada), 2007. / (UMI)AAINR27727. Source: Dissertation Abstracts International, Volume: 68-05, Section: B, page: 2914.

Thesis (Ph.D.)--The University of Texas at Austin, 2007. / (UMI)AAI3290875. Source: Dissertation Abstracts International, Volume: 68-12, Section: B, page: 7888. Adviser: Donald D. Blankenship.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1984. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 158-166).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1972. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph.D.)--Indiana University, Dept. of Geological Sciences, 2005. / Source: Dissertation Abstracts International, Volume: 66-11, Section: B, page: 5867. Adviser: Gary L. Pavlis. Title from dissertation home page (viewed Oct. 11, 2006).