Post-seismic deformation and glacial isostatic adjustment are two processes by which the Earth deforms viscoelastically. In both cases, the details of the deformation depend on the rheological structure of the Earth as well as the forcing, which is the earthquake and further movement on the fault in the case of post-seismic deformation, and the change in load on the surface of the Earth due to the redistribution of water and ice mass in the case of glacial isostatic adjustment. It is therefore possible to learn about the Earth's rheological structure and the processes' respective forcings from measurements of the deformation. In order to use measurements in this way, it is first necessary to have a method of forward modelling the processes, that is, calculating the deformation due to a given forcing and in an earth model with a given structure. Given this, a way of calculating derivatives of measurements of the deformation with respect to the parameters of interest is then desirable. In this dissertation, the adjoint method is used. This, for the first time, enables efficient calculation of continuous derivatives, which have many potential applications. Firstly, they can be used within a gradient-based optimisation method to find a model which minimises some data misfit function. The derivatives can also be used to quantify the uncertainty in such a model and hence to provide understanding of which parts of the model are well constrained. Finally, they enable construction of measurements which provide sensitivity to a particular part of the model space. In this dissertation, new methods for forward modelling both post-seismic deformation and glacial isostatic adjustment are presented. The adjoint method is also applied to both problems. Numerical examples are presented in spherically symmetric earth models and, in the case of glacial isostatic adjustment, models with laterally varying rheological structure. Such examples are used to illustrate the potential applications of the developments made within this dissertation.

Aim of this work is a systematic investigation of the modes of thermal convection (onset of convection, stationary solutions, periodic solutions, chaotic states) in a material whose properties vary with depth like the material of Earth mantle; the problem was solved in Cartesian geometry. The Stokes equation set was consistently formulated in the spectral region not only horizontally but also vertically, and thus in the model consisting of layers with a constant viscosity but with general course of velocity and temperature in each layer. This equation set was solved with matrix method for each wave vector. Thermal equation was solved in the spatial domain and the transition of velocity and temperature between spectral and spatial domains was performed using the fast Fourier transform. This procedure allows a straightforward parallelization, thereby opening the possibility of not only two-dimensional but also three-dimensional modeling and modeling of chaotic regimes. On the basis of the numerical difficulties of method presented here an model investigated in finite elemens was used. The basic modes of thermal convection were then investigated using model assembled in the software Comsol. Powered by TCPDF (www.tcpdf.org)

Title: Influence of depth dependence of the Earth's mantle properties on thermal-convection characteristics Author: Hana Šustková Department: Department of Geophysics Supervisor: doc. RNDr. Ctirad Matyska, DrSc. Abstract: This thesis concerns the study of convection in Cartesian models in two and three dimensions. Specifically, it deals with the systematic monitoring of critical Rayleigh numbers based on the geometry model, on the functional dependence of the viscosity or of other parameters. Models has been created with layered viscosity and constant or temperature- and depth- dependent parameters (thermal expansion and conductivity). The system has been described by conventional dimensionless Boussinesq approximation. Part of the work is devoted to the application of matrix method for solving the appropriate Stokes flow and use of Euler's method for solving the thermal equation. The actual calculations were then performed in an environment of commercial software Comsol and thus by using the finite element method. It was shown that the dominant influence on the critical Rayleigh numbers has a viscosity model (with increasing viscosity the critical Rayleigh numbers increase), other important parameter is system's geometry (larger size and dimension of the geometry reduce the critical Rayleigh number). The...

Glacial isostatic adjustment (GIA) is the process by which the solid Earth responds to past and present-day changes in glaciers, ice caps, and ice sheets. This thesis focuses on vertical crustal motion of the Earth caused by GIA, which is influenced by several factors including lithosphere thickness, mantle viscosity profile, and changes to the thickness and extent of surface ice. The viscosity of the mantle beneath Antarctica is a poorly constrained quantity due to the rarity of relative sea-level and heat flow observations. Other methods for obtaining a better-constrained mantle viscosity model must be investigated to obtain more accurate GIA model predictions. The first section of this study uses seismic wave tomography to determine mantle viscosity. By calculating the deviation of the P- and S-wave velocities relative to a reference Earth model (PREM), the viscosity can be determined. For Antarctica mantle viscosities obtained from S20A (Ekstrom and Dziewonski, 1998) seismic tomography in the asthenosphere range from 1016 Pa∙s to 1023 Pa∙s, with smaller viscosities beneath West Antarctica and higher viscosities beneath East Antarctica. This agrees with viscosity expectations based on findings from the Basin and Range area of North America, which is an analogue to the West Antarctic Rift System. Section two compares bedrock elevations in Antarctica to crustal thicknesses, to infer mantle temperatures and draw conclusions about mantle viscosity. Data from CRUST 2.0 (Bassin et al., 2000), BEDMAP (Lythe and Vaughan, 2001) and specific studies of crustal thickness in Antarctica were examined. It was found that the regions of Antarctica that are expected to have low viscosities agree with the hot mantle trend found by Hyndman (2010) while the regions expected to have high viscosity are in better agreement with the trend for cold mantle. Bevis et al. (2009) described new GPS observations of crustal uplift in Antarctica and compared the results to GIA model predictions, including IJ05 (Ivins and James, 2005). Here, we have generated IJ05 predictions for a three layered mantle (viscosities ranging over more than four orders of magnitude) and compared them to the GPS observations using a χ2 measure of goodness-of-fit. The IJ05 predictions that agree best with the Bevis et al. observations have a χ2 of 16, less than the null hypothesis value of 42. These large values for the best-fit model indicate the need for model revisions and/or that uncertainties are too optimistic. Equally important, the mantle viscosities of the best-fit models are much higher than expected for West Antarctica. The smallest χ2 values are found for an asthenosphere viscosity of 1021 Pa•s, transition zone viscosity of 1023 Pa∙s and lower mantle viscosity of 2 x 1023 Pa∙s, whereas the expected viscosity of the asthenosphere beneath West Antarctica is probably less than 1020 Pa∙s. This suggests that revisions to the IJ05 ice sheet history are required. Simulated annealing was performed on the ice sheet history and it was found that changes to the recent ice load history have the strongest effect on GIA predictions. / Graduate

L’objectif principal de ce travail est d’améliorer notre compréhension de la rhéologie terrestre et du mouvement de Chandler qui en dépend. Nous calculons le facteur gravimétrique complexe à la période de Chandler par une analyse conjointe de séries temporelles gravimétriques et du mouvement du pôle. Nous montrons l’importance et les limites des corrections gravimétriques dans les analyses locales et l’intérêt d’une combinaison des données de différentes stations. Suivant une approche plus théorique, nous menons une étude analytique puis numérique afin de déterminer les solutions du problème des petites déformations d’une Terre homogène anélastique en rotation. L’influence de l’anélasticité sur la période et le facteur de qualité de Chandler est étudiée, et nous montrons que ce dernier est plus sensible que la période aux paramètres rhéologiques, notamment à la viscosité de Kelvin. Enfin, nous étudions, en domaine de Laplace, l’influence de la fréquence de forçage par une surcharge. / The main goal of this work is to improve our understanding of the Earth’s rheology and of the Chandler wobble which depends on it. We compute the complex gravimetric factor at the Chandler frequency by a joint analysis of gravimetric and polar motion time series. We show the importance and the limits of gravimetric corrections for local analyses and the effectiveness of the combination of data from different stations. Using a more theoretical approach, we carry out an analytical and numerical study to determine the solutions of the small deformations of an anelastic homogeneous rotating Earth model. The influence of anelasticity on the Chandler wobble period and quality factoris studied and we show that the latter is more sensitive than the period to the rheological parameters, especially to the Kelvin’s viscosity. Finally, we study in Laplace domain the influence of the forcing frequency for the loading problem.

In the late Pleistocene, most of British Columbia and northern Washington was covered by the Cordilleran ice sheet. The weight of the ice sheet caused up to several hundred metres of depression of the Earth’s crust. This caused relative sea level to be higher in southwestern British Columbia despite lower global eustatic sea level. After deglaciation, postglacial rebound of the crust caused sea level to quickly drop to below present levels. The rate of sea-level fall is used here to determine the rheology of the mantle in southwestern British Columbia. The first section of this study deals with determination of the postglacial sea-level history in the Victoria area. Constraints on sea-level position come from isolation basin cores collected in 2000 and 2001, as well as from previously published data from the past 45 years. The position of sea-level is well constrained at elevations greater than -4 m, and there are only loose constraints below that. The highstand position in the Victoria area is between 75-80 m. Sea level fell rapidly from the highstand position to below 0 m between 14.3 and 13.2 thousand calendar years before present (cal kyr BP). The magnitude of the lowstand position was between -11 and -40 m. Though there are few constraints on the lowstand position, analysis of the crustal response favours larger lowstand. Well constrained sea-level histories from Victoria, central Strait of Georgia and northern Strait of Georgia are used to model the rheology of the mantle in southwestern British Columbia. A new ice sheet model for the southwestern Cordillera was developed as older models systematically underpredicted the magnitude of sea level in late glacial times. Radiocarbon dates are compiled to provide constraints on ice sheet advance and retreat. The Cordillera ice sheet reached maximum extent between 17 and 15.4 cal kyr BP. After 15.4 cal kyr, the ice sheet retreated, and by 13.7 cal kyr BP Puget Sound, Juan de Fuca Strait and Strait of Georgia were ice free. By 10.7 cal kyr BP, ice was restricted to mountain glaciers at levels similar to present. With the new ice model, and using an Earth model with a 60 km lithosphere, asthenosphere with variable viscosity and thickness, and transitional and lower mantle viscosity based on the VM2 Earth model, predicted sea level matches the observed sea level constraints in southwestern British Columbia. Nearly identical predicted sea-level curves are found using asthenosphere thicknesses between 140-380 km with viscosity values between 3x10^18 and 4x10^19 Pa s. Predicted sea level is almost completely insensitive to the mantle below the asthenosphere. Modeled present day postglacial uplift rates are less than 0.5 mm yr^-1. Despite the tight fit of the predicted sea level to observed late-glacial sea level observations, the modelling was not able to fit the early Holocene rise of sea level to present levels in the central and northern Strait of Georgia.