From Dark Matter to the Earth's Deep Interior: There and Back Again

This thesis is a two-way transfer of knowledge between cosmology and seismology, aiming to substantially advance imaging methods and uncertainty quantification in both fields. I develop a method using wavelets to simulate the uncertainty in a set of existing global seismic tomography images to assess the robustness of mantle plume-like structures. Several plumes are identified, including one that is rarely discussed in the seismological literature. I present a new classification of the most likely deep mantle plumes from my automated method, potentially resolving past discrepancies between deep mantle plumes inferred by visual analysis of tomography models and other geophysical data. Following on from this, I create new images of the upper-most mantle and their associated uncertainties using a sparsity-promoting wavelet prior and an advanced probabilistic inversion scheme. These new images exhibit the expected tectonic features such as plate boundaries and continental cratons. Importantly, the uncertainties obtained are physically reasonable and informative, in that they reflect the heterogenous data distribution and also highlight artefacts due to an incomplete forward model. These inversions are a first step towards building a fully probabilistic upper-mantle model in a sparse wavelet basis. I then apply the same advanced probabilistic method to the problem of full-sky cosmological mass-mapping. However, this is severely limited by the computational complexity of high-resolution spherical harmonic transforms. In response to this, I use, for the first time in cosmology, a trans-dimensional algorithm to build galaxy cluster-scale mass-maps. This new approach performs better than the standard mass-mapping method, with the added benefit that uncertainties are naturally recovered. With more accurate mass-maps and uncertainties, this method will be a valuable tool for cosmological inference with the new high-resolution data expected from upcoming galaxy surveys, potentially providing new insights into the interactions of dark matter particles in colliding galaxy cluster systems

Crustal Structure of the Western U.S. From Rayleigh and Love Wave Amplification Data

Surface wave amplification measurements have narrower depth sensitivity when compared to more traditional seismic observables such as surface wave dispersion measurements. In particular, Love wave amplification measurements have the advantage of strong sensitivity to the crust. For the first time, we explore the potential of Love wave amplification measurements to image crustal velocity in the western U.S. The effects of overtone interference, radial anisotropy and Moho depth are all explored. Consequently, we present SWUS‐crust, a three‐dimensional shear‐wave velocity model of crustal structure in the western U.S. We use Rayleigh wave amplification measurements in the period range of 38‐114 s, along with Love wave amplification measurements in the period range of 38‐62 s. We jointly invert over 6,400 multi‐frequency measurements using the Monte‐Carlo based Neighbourhood Algorithm, which allows for uncertainty quantification. SWUS‐crust confirms several features observed in previous models, such as high‐velocity anomalies beneath the Columbia basin and low‐velocity anomalies beneath the Basin and Range province. Certain features are sharpened in our model, such as the northern border of the High‐Lava Plains in southern Oregon in the middle crust

Posterior sampling for inverse imaging problems on the sphere in seismology and cosmology

In this work, we describe a framework for solving spherical inverse imaging problems using posterior sampling for full uncertainty quantification. Inverse imaging problems defined on the sphere arise in many fields, including seismology and cosmology where images are defined on the globe and the cosmic sphere, and are generally high-dimensional and computationally expensive. As a result, sampling the posterior distribution of spherical imaging problems is a challenging task. Our framework leverages a proximal Markov chain Monte Carlo (MCMC) algorithm to efficiently sample the high-dimensional space of spherical images with a sparsity-promoting wavelet prior. We detail the modifications needed for the algorithm to be applied to spherical problems, and give special consideration to the crucial forward modelling step which contains computationally expensive spherical harmonic transforms. By sampling the posterior, our framework allows for full and flexible uncertainty quantification, something which is not possible with other methods based on, for example, convex optimisation. We demonstrate our framework in practice on full-sky cosmological mass-mapping and to the construction of phase velocity maps in global seismic tomography. We find that our approach is potentially useful at moderate resolutions, such as those of interest in seismology. However at high resolutions, such as those required for astrophysical applications, the poor scaling of the complexity of spherical harmonic transforms severely limits our method, which may be resolved with future GPU implementations. A new Python package, pxmcmc, containing the proximal MCMC sampler, measurement operators, wavelet transforms and sparse priors is made publicly available

Sparse Bayesian mass-mapping using trans-dimensional MCMC

Uncertainty quantification is a crucial step of cosmological mass-mapping that is often ignored. Suggested methods are typically only approximate or make strong assumptions of Gaussianity of the shear field. Probabilistic sampling methods, such as Markov chain Monte Carlo (MCMC), draw samples form a probability distribution, allowing for full and flexible uncertainty quantification, however these methods are notoriously slow and struggle in the high-dimensional parameter spaces of imaging problems. In this work we use, for the first time, a trans-dimensional MCMC sampler for mass-mapping, promoting sparsity in a wavelet basis. This sampler gradually grows the parameter space as required by the data, exploiting the extremely sparse nature of mass maps in wavelet space. The wavelet coefficients are arranged in a tree-like structure, which adds finer scale detail as the parameter space grows. We demonstrate the trans-dimensional sampler on galaxy cluster-scale images where the planar modelling approximation is valid. In high-resolution experiments, this method produces naturally parsimonious solutions, requiring less than 1% of the potential maximum number of wavelet coefficients and still producing a good fit to the observed data. In the presence of noisy data, trans-dimensional MCMC produces a better reconstruction of mass-maps than the standard smoothed Kaiser-Squires method, with the addition that uncertainties are fully quantified. This opens up the possibility for new mass maps and inferences about the nature of dark matter using the new high-resolution data from upcoming weak lensing surveys such as Euclid

Fast emulation of anisotropies induced in the cosmic microwave background by cosmic strings

Cosmic strings are linear topological defects that may have been produced during symmetry-breaking phase transitions in the very early Universe. In an expanding Universe the existence of causally separate regions prevents such symmetries from being broken uniformly, with a network of cosmic string inevitably forming as a result. To faithfully generate observables of such processes requires computationally expensive numerical simulations, which prohibits many types of analyses. We propose a technique to instead rapidly emulate observables, thus circumventing simulation. Emulation is a form of generative modelling, often built upon a machine learning backbone. End-to-end emulation often fails due to high dimensionality and insufficient training data. Consequently, it is common to instead emulate a latent representation from which observables may readily be synthesised. Wavelet phase harmonics are an excellent latent representations for cosmological fields, both as a summary statistic and for emulation, since they do not require training and are highly sensitive to non-Gaussian information. Leveraging wavelet phase harmonics as a latent representation, we develop techniques to emulate string induced CMB anisotropies over a 7.2 degree field of view, with sub-arcminute resolution, in under a minute on a single GPU. Beyond generating high fidelity emulations, we provide a technique to ensure these observables are distributed correctly, providing a more representative ensemble of samples. The statistics of our emulations are commensurate with those calculated on comprehensive Nambu-Goto simulations. Our findings indicate these fast emulation approaches may be suitable for wide use in, e.g., simulation based inference pipelines. We make our code available to the community so that researchers may rapidly emulate cosmic string induced CMB anisotropies for their own analysis

Australian sedimentary thickness from seismic receiver functions

<p>This dataset contains data relating to the publication "Sedimentary thickness across Australia from passive seismic methods" (submitted).  The files are as follows:</p><ol><li>rfstream.h5<ul><li>Contains a <a href="https://rf.readthedocs.io/en/latest/#rf.rfstream.RFStream">rf.RFStream</a> object containing all the receiver functions used in the study</li></ul></li><li>summary_table.csv<ul><li>Summarises the key seismic measurements of the paper at each seismic station</li></ul></li><li>summary_table.geojson<ul><li>Same data as summary_table.csv for use in, for example, <a href="https://geopandas.org/en/stable/">GeoPandas</a></li></ul></li></ol><p> </p&gt

The Probability of Mantle Plumes in Global Tomographic Models

Abstract While the downward mass flux in the Earth's deep interior is well constrained by seismic tomography, the upward flux is still poorly understood and debated. Recent tomography studies suggest that we are now starting to resolve deep mantle plume structures. However, a lack of uncertainty quantification impedes a full assessment of their significance and whether they are statistically distinct from noise. This work uses a spherical wavelet transform and random noise realizations to quantify the probability of deep plume‐like features in six recent global tomographic models. We find that out of 50 possible mantle deep plumes, 12 are highly likely, with probabilities larger than 80%, and 12 are likely, with probability between 70% and 80%. Objective, quantitative approaches as proposed in this study should be used for model interpretation. The five most likely deep mantle plumes are Tahiti, Macdonald, East Africa, Pitcairn, and Marquesas, which have some of the largest buoyancy fluxes estimated in a previous study that used hotspot swell volumes. This could resolve past discrepancies between deep mantle plumes inferred by visual analysis of tomography models and flux estimations from hotspot swell data. In addition, a notable unlikely deep mantle plume is Yellowstone, with probability lower than 50%. We also identify a likely deep mantle plume associated with the Amsterdam‐St Paul hotspot, a region scarcely discussed in previous studies and that deserves future investigation. Hence, our automated, objective approach is a valuable alternative approach for the quantitative interpretation of tomographic models

Calcam

<p>Calcam is a Python package for geometric calibration of cameras and for performing related analysis, i.e. for finding the mapping between pixel coordinates in a camera image and physical positions in 3D space. It was created for use with camera diagnostics on fusion experiments, but may be useful in other applications too. As well as calibrating existing cameras, it can also be used to define synthetic camera diagnostics, e.g. to simulate or help define new viewing geometries when designing new camera diagnostics.</p> <p>The full calcam documentation can be found at: <a href="https://euratom-software.github.io/calcam/">https://euratom-software.github.io/calcam/</a></p&gt