Natural climate variability over the past hundreds of thousands of years provides a uniquewindow into the drivers and processes that connect different parts of our climate system. This thesis investigates interactions between Earth’s mantle, its oceans, and ice sheets over the Quaternary. The dominant process that connects these spheres is glacial isostatic adjustment (GIA), which is the deformation of Earth’s mantle (and consequently its surface, gravity field, and sea level) in response to changes in ice and ocean mass loading. This dissertation focuses on time periods during which surface temperatures were warming or warmer than today to understand how these warm intervals affected ice sheets, permafrost, and sea level. I put my results in the context of current and future warming to improve predictions of future change and compare natural to anthropogenic variability. The thesis opens with an investigation of relative (i.e., local) sea level around Norway overthe last 16 thousand years (ka). Postglacial Norwegian sea level, though dominated by postglacial rebound and associated sea-level fall, is punctuated by two periods of sea-level rise. The causes of these episodes, named the ‘Tapes’ and ‘Younger Dryas’ transgressions, remain debated despite more than a century of study. I produce the first standardized and quality-controlled compilation of Norwegian sea-level data, then employ an ensemble of empirical Bayesian hierarchical statis- tical models to estimate relative sea level along the Norwegian coastline. The resulting model enables an examination of the relative contributions of isostatic rebound and global mean sea-level (GMSL) rise to the Tapes transgression, and lays the foundation for future applications such as in- version of sea-level data for Fennoscandian ice-sheet volume and the comparison of modern rates of Norwegian sea-level rise to pre-industrial rates. Chapter Two aims to better understand sea-level and Antarctic ice-sheet variability during the Holocene, which is the last time global temperatures may have exceeded early industrial (1850 CE) values. Both the Greenland and Antarctic ice sheets likely retreated inland of their present- day extents during the Holocene, yet previous GMSL reconstructions suggest that Holocene GMSL never surpassed early industrial levels. I use relative sea-level observations, GIA predictions, and new estimates of postglacial thermosteric sea-level and mountain glacier evolution to show that the available evidence is consistent with GMSL that exceeded early industrial levels in the mid- Holocene (8-4 ka) and an Antarctic Ice Sheet that was smaller than present at some time in the last 6000 years. I also demonstrate that Antarctic ice retreat lags Antarctic temperature by 250 years, which highlights the vulnerability of the future Antarctic ice sheet to 20th and 21st century warming. Comparing our reconstruction to projections for the future indicates that GMSL rise in the next 125 years will very likely (?>0.9) be faster than at any time in the last 5000 years, and that by 2080 GMSL will more likely than not be the highest of any time in the past 115,000 years. In Chapter Three, I explore the effect of GIA on subsea permafrost. Subsea permafrost forms when sea-level rise submerges terrestrial permafrost. Subsea permafrost underlies ∼1.8 million km² of Arctic continental shelf, with thicknesses in places exceeding 700 m. Sea-level variations over glacial–interglacial cycles control subsea permafrost distribution and thickness, yet no permafrost model has accounted for GIA, which leads to deviations of local sea level from the global mean. I incorporate GIA into a pan-Arctic model of subsea permafrost over the last 400,000 years. Including GIA significantly reduces estimates of present-day subsea permafrost thickness, chiefly because of hydro-isostatic effects and deformation related to Northern Hemisphere ice sheets. Additionally, I extend the simulation 1000 years into the future for emissions scenarios outlined in the Intergovernmental Panel on Climate Change’s sixth assessment report. I find that subsea permafrost is preserved under a low-emissions scenario but mostly disappears under a high-emissions scenario. In the final chapter, I turn to the Last Interglacial (LIG, 129–116 ka), a time interval considered a partial analogue for future warming due to its elevated temperatures. Observations of oscillations in LIG local sea level, combined with an assumption that the Laurentide Ice Sheet collapsed prior to the LIG, have been used to infer Antarctic and Greenland ice-sheet melt histories as well as oscillations in LIG global mean sea level. However, evidence of a Laurentide Ice Sheet outburst flood at ∼125 ka suggests that Laurentide Ice Sheet remnants may have persisted longer into the LIG than typically thought. Here we explore the effect on LIG sea level of a Laurentide collapse that occurred during rather than prior to the LIG and a West Antarctic Ice Sheet that collapsed in the early LIG. We find that due to GIA, this asynchronous ice-sheet evolution produces a global pattern of sea-level oscillations that is similar to field observations. We demonstrate that the oscillation pattern can be produced by the combination of ongoing GIA from the penultimate deglaciation with the fingerprint of West Antarctic collapse. By showing that LIG Laurentide persistence would lead to an RSL oscillation that accords with field evidence, we highlight the need for LIG climate simulations to consider Laurentide ice-sheet dynamics and for more constraints on the LIG history of the Laurentide Ice Sheet.

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.

Investigating the solid-state properties of the Earth’s core and mantle presents a formidable challenge due to the extreme conditions that prevail in these areas. Although we can achieve high pressures using a variety of static and dynamic compression techniques, it is still unfeasible to comprehensively sample the entire pressure-temperature (𝑃-𝑇) domain for materials. Therefore, computational methodologies have evolved as a crucial instrument for examining material properties under increased pressures and temperatures. These techniques have demonstrated their efficacy in navigating the phase space, thereby contributing significantly to the understanding of the intrinsic behavior of materials within the Earth’s interior. In this work, we present 𝚎𝚡𝚙𝚛𝚎𝚜𝚜, a comprehensive suite of simulation tools designed for conducting 𝘢𝘣 𝘪𝘯𝘪𝘵𝘪𝘰 calculations within the realm of the physical sciences. These tools are specifically engineered to streamline the associated data processing tasks, and they leverage the capabilities of the Julia programming language. At the core of this toolset lies a versatile, high-throughput, and user-friendly workflow framework. This framework is capable of automating a wide range of 𝘢𝘣 𝘪𝘯𝘪𝘵𝘪𝘰 calculations. By addressing the limitations encountered with existing libraries, 𝚎𝚡𝚙𝚛𝚎𝚜𝚜 simplifies intricate workflows, offers a software-agnostic interface, and ensures modularity—all of which are pivotal features within this domain. In addition to the workflow, we have developed a diverse set of software packages tailored to tackle the challenges inherent in data manipulation for 𝘢𝘣 𝘪𝘯𝘪𝘵𝘪𝘰 calculations. These packages encompass a wide spectrum of functionalities, including crystal symmetry search, conversion of units and reference frames, data visualization, parsing and generation of files, estimation of computing resources, and database storage, among other capabilities. We proceed to showcase the effectiveness of express across a diverse spectrum of mineral materials. For each substance, we conducted calculations of their thermodynamic properties using the quasi-harmonic approximation (QHA). This method was executed with the assistance of a Python package called 𝚚𝚑𝚊, which we developed specifically for multi-configuration quasi-harmonic approximation computations. In pursuit of our objective, we employ three distinct sets of exchange-correlation functionals: the local-density approximation (LDA), the Perdew–Burke–Ernzerhof generalized gradient approximation (PBE-GGA), and the PBE functional revised for solids (PBEsol). Subsequently, we compared these results with other calculations and experimental data, thereby elucidating the varying suitability of these functionals. Notably, the LDA functional, when integrated with thermal effects, exhibited exceptional overall performance. This observation implies that numerous studies that favored GGA functionals but solely relied on static DFT outcomes may have inadvertently incorporated erroneous material characteristics into their research.