| Summary: | This thesis aims to further our understanding of mantle dynamics by investigating two fundamental parameters that govern such motion: density and viscosity. The variation of mantle density and viscosity dictates the direction, length-scale and time-scale of flow and thus improving our knowledge of these fields represents an important preoccupation of global geophysics. My contributions to these efforts are partitioned between Chapters 2-4 where attention is turned to the development and application of a technique called “tidal tomography” with the goal of determining deep mantle density structure; and Chapter 5 which applies nonlinear Bayesian inversion techniques to observations related to glacial isostatic adjustment in order to infer the radial viscosity profile of the mantle. Normal mode treatments of the Earth’s body tide response were developed in the 1980s to account for the effects of Earth rotation, ellipticity, anelasticity and resonant excitation within the diurnal band. Recent space-geodetic measurements of the Earth’s crustal displacement in response to luni-solar tidal forcings have revealed geographical variations that are indicative of aspherical deep mantle structure, and they thus provide a novel data set for constraining deep mantle elastic and density structure. In light of this, in Chapter 2, we make use of advances in seismic free oscillation literature to develop a new, generalized normal mode theory for the body tidal response within the semi-diurnal and long-period tidal band. Our theory involves a perturbation method that permits an efficient calculation of the impact of aspherical structure on the tidal response. In addition, we introduce a normal mode treatment of anelasticity that is distinct from both earlier work in body tides and the approach adopted in free oscillation seismology. We present several simple numerical applications of the new theory and benchmark these applications against independent finite-volume numerical calculations to confirm the accuracy of the theory. In Chapter 3 we focus on the treatment of anelasticity in the new theory. To date, the widely adopted approach uses a pseudo-normal mode framework for predicting the impact of anelastic effects on the Earth’s body tides. There are two noteworthy differences between the traditional and new theories: (1) the traditional theory only considers perturbations to the eigenmodes of an elastic Earth, whereas the new theory augments this set of modes to include the relaxation modes that arise in anelastic behaviour; and (2) the traditional theory approximates the complex perturbation to the tidal Love number as a scaled version of the complex perturbation to the elastic moduli, whereas the new theory computes the full complex perturbation to each eigenmode. We highlight the above differences using a series of synthetic calculations, and demonstrate that the traditional theory can introduce significant error in predictions of the complex perturbation to the Love numbers, and the related predictions of tidal lag angles, due to anelasticity. For the simplified Earth models we test, the computed lag angles differ by ~20 percent. The assumptions adopted in the traditional theory have important implications for previous studies that use model predictions to correct observables for body tide signals or that analyze observations of body tide deformation to infer mantle anelastic structure. Finally, we also highlight the fundamental difference between apparent attenuation (i.e. attenuation inferred from observations or predicted using the above theories) and intrinsic attenuation (i.e. the material property investigated through experiments), where both are often expressed in terms of lag angles or Q-1. In particular, we demonstrate the potentially significant (factor of two or more) bias introduced in estimates of Q-1 and its frequency dependence in studies that have treated Q-1 determined from tidal phase lags or measured experimentally as being equal. The observed or theoretically predicted lag angle (or apparent Q-1) differs from the intrinsic, material property due to inertia, self-gravity and effects associated with the energy budget. By accounting for these differences we derive, for a special case, an expression that accurately maps apparent attenuation predicted using the extended normal mode formalism derived in Chapter 2 into intrinsic attenuation. The theory allows for more generalized mappings which may be used to robustly connect observations and predictions of tidal lag angles to results from laboratory experiments of mantle materials. In Chapter 4, we present a new bound on buoyancy structure within Earth’s deep mantle derived by applying a tidal tomographic procedure to a global data set of GPS-based body tide deformations in the semi-diurnal band. Earth’s body tide response is uniquely sensitive to the density within two massive regions—beneath Africa and the Pacific—extending ~1000 km upward from the base of the mantle, known as Large Low Shear Velocity Provinces (LLSVPs). Their integrated buoyancy remains a source of debate within the geophysical literature. Using a probabilistic approach, we bound excess density within the base and middle section of the LLSVPs to interquartile ranges of (0.61–0.74)% and (0.44–0.64)%, respectively. We conclude that the buoyancy of these structures is dominated by the enrichment of high-density chemical components, likely related to subducted oceanic plates and/or primordial material associated with Earth’s formation. Our result has important implications for the stability of these structures and, more broadly, the long-term evolution of the Earth system. Turning our attention to viscosity in the mantle, in Chapter 5 we perform joint nonlinear inversions of GIA data, including: postglacial decay times in Canada and Scandinavia, the Fennoscandian relaxation spectrum (FRS), late-Holocene differential sea level (DSL) highstands (based on recent compilations of Australian sea level histories), and the rate of change of the degree 2 zonal harmonic of the geopotential, J2. Our resolving power analyses demonstrate that: (1) the FRS constrains mean upper mantle viscosity to be ~3×1020 Pa s, (2) postglacial decay time data require the average viscosity in the top ~1500 km of the mantle to be 1021 Pa s, and (3) the J2 datum constrains mean lower mantle viscosity to be ∼ 5 × 1021 Pa s. To reconcile (2) and (3), viscosity must increase to values of 1022 − 1023 Pa s in the deep mantle. Our analysis highlights the importance of accurately correcting the J2 observation for modern glacier melting in order to robustly infer deep mantle viscosity. We also perform a large series of forward calculations to investigate the compatibility of the GIA data sets with a viscosity jump within the lower mantle, as suggested by geodynamic and seismic studies, and conclude that the GIA data may accommodate a sharp jump of 1–2 orders of magnitude in viscosity across a boundary placed in a depth range of 1000–1700 km, but these data do not require such a feature. Finally, we find that no 1-D viscosity profile appears capable of simultaneously reconciling the DSL highstand data and suggest that this discord is likely due to laterally heterogeneous mantle viscosity. Taken together, this thesis attempts to deepen our understanding of the nature of mantle dynamics. The major accomplishments include tightly bounding deep mantle density structure and confirming some previous arguments for the significant increase in viscosity from the shallow upper mantle to the base of the mantle. Chapter 6 discusses future research directions that will further the efforts described herein. Earth and Planetary Sciences Geophysics; Geodynamics; Earth Science
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