Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Earth and Planetary Science, 1979. / Microfiche copy available in Archives and Science. / Vita. / Bibliography: leaf 41. / by Robert Alvin Davis. / M.S.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Earth and Planetary Science, 1982. / Microfiche copy available in Archives and Science / Vita. / Bibliography: leaves 110-111. / by Gerald Alan LaTorraca. / Ph.D.

Thesis. 1978. Ph.D.--Massachusetts Institute of Technology. Dept. of Earth and Planetary Science. / Microfiche copy available in Archives and Science. / Vita. / Bibliography: leaves 200-203. / Ph.D.

A thesis submitted to the Faculty of Science, University of the Witwatersrand, in fulfilment of the requirements for the degree of Doctor of Philosophy University of the Witwatersrand School of Geosciences and Dublin Institute for Advanced Studies School of Cosmic Physics Geophysics Section February 2016 / Archean cratons, and the Proterozoic orogenic belts on their flanks, form an integral part of the Southern Africa tectonic landscape. Of these, virtually nothing is known of the position and thickness of the southern boundary of the composite Congo craton and the Neoproterozoic Pan African orogenic belt due to thick sedimentary cover. In this work I present the first lithospheric-scale geophysical study of that cryptic boundary and define its geometry at depth. The results are derived from two-dimensional (2D) and three-dimensional (3D) inversion of magnetotelluric data acquired along four semi-parallel profiles crossing the Kalahari craton across the Damara-Ghanzi-Chobe belts (DGC) and extending into the Congo craton. Two dimensional and three-dimensional electrical resistivity models show significant lateral variation in the crust and upper mantle across strike from the younger DGC orogen to the older adjacent cratons. The Damara belt lithosphere is found to be more conductive and significantly thinner than that of the adjacent Congo craton. The Congo craton is characterized by very thick (to depths of 250 km) and resistive (i.e. cold) lithosphere. Resistive upper crustal features are interpreted as caused by igneous intrusions emplaced during Pan-African magmatism. Graphite-bearing calcite marbles and sulfides are widespread in the Damara belt and account for the high crustal conductivity in the Central Zone. The resistivity models provide new constraints on the southern extent of the greater Congo craton, and suggest that the current boundary drawn on geological maps needs revision and that the craton should be extended further south. The storage possibilities for the Karoo Basins were found to be poor because of the very low porosity and permeability of the sandstones, the presence of extensive dolerite sills and dykes. The obvious limitation of the above study is the large spacings between the MT stations (> 10km). This is particularly more limiting in resolving the horizontal layers in the Karoo basin. However the 1D models provide layered Earth models that are consistent with the known geology. The resistivity values from the 1D models allowed porosity of the Ecca and Beaufort group lithologies to be calculated. It is inferred that the porosities values are in the range 5-15 % in the region below the profile. This value is considered too low for CO2 storage as the average porosity of rock used for CO2 is generally more than 10 to 12 percent of the total rock unit volume.

The thesis presents the application of the magnetotelluric (MT) sounding method to image Earth’s crust in Oman and South Australia. The aim of these MT surveys is to provide constraints on the geological interpretation of emplacement scenarios and the tectonic evolution of the geological domain. The thesis concentrates on the methodological aspects of the MT technique, e.g. the data analysis and modelling of electromagnetic fields. The phase tensor approach by Caldwell et al. (2004) is applied to the data and provides insights into the dimensionality of the MT data in even complex and electrically distorted terranes. Modelling and inversion of the MT data is performed with various 2-D and 3-D codes to show how the interpretation of the data can benefit from multiple modelling approaches. Data collected in a 2-D survey across the Oman ophiolite mountains show complex behaviour and 2-D inversion and 3-D forward modelling resolve ambiguities in the emplacement scenario of the Oman ophiolite. It is believed that initial underthrusting of the Jurassic-Cretaceous oceanic lithosphere was followed by exhumation. Further oceanic thrusting subsequently led to rising of lower-plate eclogites and eventually gravitational collapse of the ophiolite onto the margin (Gray et al., 2000). The 3-D inversion code by (Siripunvaraporn et al., 2005a) was expanded to incorporate static shift corrections and inversion model misfits have therefore improved significantly compared to inversion models without static shift correction. 2-D and 3-D surveys across the South Australian Gawler Craton reveal deep crustal conductors which are connected to near surface mineralisation systems of the IOCG Olympic Dam deposit in the north-eastern part of the craton and the Au-dominated central Gawler Craton provinces. / Thesis (Ph.D.) -- University of Adelaide, School of Earth and Environmental Sciences, 2008

Recent advances in computational power, as well as the hard work of a handful of brilliant scientists, have made Bayesian inversion of geophysical observations possible. This development is highly significant, as it permits the quantification of uncertainty, not only on the inverted model parameters, but also on related properties of interest. This dissertation focuses on the application of a particular kind of Bayesian inversion – trans-dimensional Markov chain Monte Carlo – to electromagnetic data, specifically airborne transient electromagnetic, magnetotelluric, and surface-towed controlled source electromagnetic data. In chapters 2-4, these data, both real and synthetic, are inverted for 1D models of subsurface electrical resistivity. In chapter 5, magnetotelluric data are inverted for 2D models of resistivity – the first time, to the best of my knowledge, that trans-dimensional Bayesian inversion of magnetotelluric data for 2D models has been achieved. In each instance, the uncertainty on bulk resistivity provided by the Bayesian inversion is used to estimate uncertainty on related subsurface properties, including pore fluid resistivity and salinity, porosity, melt fraction, melt volatile content, and bulk mantle volatile inventory. Chapter 1 introduces the topic of Bayesian inversion of electromagnetic data. Chapter 2 concerns trans-dimensional Bayesian inversion of airborne transient electromagnetic data. These data were collected above Taylor Glacier in the McMurdo Dry Valleys region of Antarctica in 2011, and were inverted using deterministic inverse methods to image a conductive channel beneath the glacier, interpreted as a package of brine-saturated sediments. The Bayesian inversion of these data confirms the existence of a conductive channel and provides quantitative uncertainties on the resistivity as a function of depth. These uncertainties are used in conjunction with Archie’s Law to estimate uncertainty on the resistivity of the pore fluids in the sediments. Additionally, the Kullback-Leibler divergence – a statistical measure of the dissimilarity of two distributions – is introduced as a measure of how much influence the observations have on the model parameters as a function of depth. The utility of Bayesian inversion in estimating the noise floor necessary to effectively resolve model structure is demonstrated. In chapter 3, a joint Bayesian framework for inverting electromagnetic data is introduced. A modified version of the algorithm utilized in chapter 2 is applied to jointly invert marine magnetotelluric and surface-towed controlled source electromagnetic data. These data were collected offshore New Jersey in 2015 to image a freshwater aquifer in the continental shelf. Deterministic inversions of this data clearly image a resistive body at depths consistent with low salinity from bore hole measurements collocated with the electromagnetic survey. The Bayesian inversion of this data set again confirms the existence of the resistive region while further providing uncertainty on the inverted resistivity with depth. In some instances, bimodality in the posterior distribution is found, demonstrating the importance of Bayesian inverse methods for fully exploring the model space. The uncertainty on bulk resistivity is used in conjunction with Archie’s Law and the porosity from bore hole measurements in a Monte Carlo framework to estimate uncertainty in the salinity of the pore water as a function of depth for three well locations. These estimates match well with measured salinities at these locations, validating the use of the Bayesian posterior in the context of a Monte Carlo framework to estimate uncertainty on related physical properties. In chapter 4, seafloor magnetotelluric data are again inverted for 1D models of subsurface resistivity, this time to image a conductive channel at the base of the lithosphere. The data are a subset of a deployment of 50 Broadband MT instruments on the seafloor above the Cocos plate offshore Nicaragua. Deterministic inversions of this data revealed a conductive structure at 45-70 km depth, beneath the Cocos plate. This earlier analysis concluded that melt was required at the lithosphere-asthenosphere boundary (LAB) to explain the inverted resistivity, but the deterministic inverse tools available at the time did not permit quantitative uncertainties – on the conductive anomaly itself, the requirement for partial melt, the degree of partial melt, or the degree of mantle hydration. Bayesian inversion of data from two magnetotelluric sites confirm that the conductor is indeed robust, and that melt is required by nearly 100% of the models that fit the data. Further, the resistivity uncertainty from the Bayesian inversion is used in conjunction with petrological modeling of partial melting in the mantle and an estimated probability distribution for temperature to place constraints on the degree of partial melt and mantle volatile (water and carbon) inventory over the depth range 45-63 km. This analysis concludes that large melt fractions and either high temperatures or a high degree of mantle hydration are likely needed to explain the resistivities produced by the Bayesian inversion, potentially explaining the mechanism for plate sliding that enables plate tectonics. Finally, chapter 5 introduces 2D trans-dimensional Bayesian inversion of magnetotelluric data, for the first time to my knowledge. A Gaussian Process-parametrized, trans-dimensional Markov chain Monte Carlo algorithm is used with MARE2DEM to invert synthetic data as well as field data from the Gemini data set from the Gulf of Mexico. For Bayesian inversion to be computationally feasible beyond inverting for 1D models, the cost of forward modeling must be reduced, as well as the number of model parameters that the algorithm must sample over. The first challenge is addressed through high performance computing. The forward modeling is performed on a cluster. In addition, we implement parallel tempering, where multiple Markov chains are run in parallel and swap models at each iteration, vastly increasing the rate at which the model space is explored and sampled. The curse of dimensionality is addressed by utilizing a Machine Learning technique known as a Gaussian Process to represent the model with far fewer parameters than required in a typical discrete finite difference or finite element representation of the subsurface. The Bayesian inversion of the Gemini data successfully recovers the model structure obtained by deterministic inversion of the same data, but additionally provides uncertainty on bulk resistivity. This thesis demonstrates the power and utility of Bayesian inversion to move beyond single estimates of subsurface resistivity. Not only does the work in this dissertation show that Bayesian inversion can provide uncertainty on inverted resistivity, it shows that these inverted uncertainties can be used to place quantitative constraints on parameters related to bulk resistivity. This is crucial to rendering the information obtained from inversion of electromagnetic data useful to disciplines far beyond electromagnetic geophysics.