The structure of seismic discontinuities at depths of about 410 km and 660 km provides important constraints on mantle convection as the associated mineral phase transformations in the transition zone are sensitive to thermal perturbations. Teleseismic P-to-S receiver functions have been widely used to map the depths of the two discontinuities. In this study, we investigate the resolution of receiver functions in imaging topographic variations of the 410-km and 660-km discontinuities based on wave propagation simulations using a Spectral Element Method (SEM). We investigate finite-frequency effects of direct P waves as well as P-to-S converted waves by varying the length scale of discontinuity topography in the transition zone. We show that wavefront healing effects are significant in broadband receiver functions. For example, at a period of 10 to 20 seconds, the arrivaltime anomaly in P-to-S converted waves is about 50% of what predicted by ray theory when the topography length scale is in the order of 400 km. The observed arrival anomaly further reduces to 10-20% when the topography length scale reduces to about 200 km. We calculate 2-D boundary sensitivity kernels for direct P waves as well as receiver functions based on surface wave mode summation and confirm that finite frequency-effects can be properly accounted for. Three-dimensional wavespeed structure beneath seismic stations can also introduce significant artifacts in transition zone discontinuity topography if time corrections are not applied, and, the effects are dependent on frequency. / Master of Science

Biot's theory when applied to homogeneous media (involving the macroscopic flow mechanism) cannot explain the high level of attenuation observed in natural porous media over the seismic frequency range. However, several successful mesocopic inhomogeneity models have been developed to account for P wave attenuation. In this thesis I further develop the approaches to tackle S wave velocity and attenuation, to simulate transient wave propagation in poroelastic media, and to construct new models for determining the effective parameters of porous media containing mesoscopic inhomogeneities. As an important application of the double-porosity dual-permeability (DPDP) model, I have reformulated the effective Biot model using the total-field variables. This gives rise to new and more general governing equations than the previous approach based on the host phase field variables (which become a special case of the more general treatment). The analytical transient solution and dispersion characteristics for the double-porosity model and also for a poro-viscoacoustic model are derived over the entire frequency range for a homogeneous medium. The comparison between the results of the two models shows that dissipation by local mesoscopic flow of the double porosity model is very hard to fit by a single Zener element over a broad band. I chose the relaxation function to approximate the dispersion behaviour of the double porosity model just around the source centre frequency. It is shown that for most water-filled sandstones having a double porosity structure, wave propagation can be well described by the poro-viscoaoustic model with a single Zener element in the seismic frequency range. The transient solution for heterogeneous double porosity media is obtained by a numerical pseudospectral time splitting technique. This method is extended to 2.5-D poro-viscoelastic media to capture both P and S wave behaviour. I also demonstrate that if the frequency is below several Hz, then a single Kelvin-Voigt element gives an even better result than a single Zener element. I propose a two-phase permeability spherical inclusion model and obtain the dispersion curves of phase velocity and dissipation factor for the composite. I then determine the effective dynamic permeability of porous media with mesoscopic heterogeneities over the whole frequency range. This result is used to check the validity of other measures of effective dynamic permeability, deduced from the effective hydraulic permeability by replacing the permeability of the components with their dynamic values as determined from the Johnson, Koplik and Dashen (JKD) model. I also investigate the scattering of plane transverse waves by a spherical porous inclusion embedded in an infinite poroelastic medium. The vector displacement wave equations of Biot’s theory are solved as an infinite series of vector spherical harmonics for the case of a plane S-wave incidence. Then, the non-self-consistent theory is used to derive the dispersion characteristics of shear wave velocity and attenuation for a porous rock having mesoscopic spherical inclusions which are designed to represent either the patchy saturation model or the double porosity model with dilute concentrations of identical inclusions. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1457632 / Thesis (Ph.D.) -- University of Adelaide, School of Chemistry and Physics, 2009

To investigate seismic resolution of deep mantle plumes as well as the robustness of the anti-correlation between bulk sound speed and S wave speed imaged in the lowermost mantle, we use a Spectral Element Method (SEM) to simulate global seismic wave propagation in 3-D wavespeed models and measure frequency-dependent P-, S-, Pdiff- and Sdiff-wave traveltime anomalies caused by plume structures in the lowermost mantle. We compare SEM time delay measurements with calculations based on ray theory and show that an anti-correlation between bulk sound speed and S-wave speed could be produced as an artifact. This is caused by different wavefront healing effects between P waves and S waves in thermal plume models. The bulk sound speed structure remains poorly resolved when P-wave and S-wave measurements are at different periods with similar wavelength. The differences in wave diffraction between the two types of waves depend on epicentral distance and wave frequency. The artifact in anti-correlation is also confirmed in tomographic inversions based on ray theory using Pdiff and Sdiff time delay measurements made on the SEM synthetics. This indicates a chemical origin of "superplumes" in the lowermost mantle may not be necessary to explain observed seismic traveltimes. The same set of Pdiff and Sdiff measurements are inverted using finite-frequency tomography based on Born sensitivity kernels. We show that wavefront healing effects can be accounted for in finite-frequency tomography to recover the true velocity model. / Master of Science