Bayesian inference for deep earth structure using body waves and free oscillations of the earth
Creators: name: Pachhai, Surya
Publisher: name: The Australian National University
Year: 2015

description: Seismological observations reveal the strongest heterogeneities in the Earth's lowermost mantle. Ultralow velocity zones (ULVZs) are small-scale structures that cannot be detected in the tomographic images of the lowermost mantle derived from a large collection of body-wave travel time residuals or waveform inversion. These zones are characterised by a sharp decrease in velocity and an increase in density with respect to the ambient mantle. The distribution of heterogeneities in the lowermost mantle are linked/coupled via convection of the liquid iron in the outer core with the inner core structure and dynamics. The convection in the outer core generates and maintains the geomagnetic field. Significant progress has been made in the understanding of the deep Earth structure and dynamics with increased computational power, new geophysical inference techniques, and increased data quality. However, the interpretation of inversion results remains challenging because of the inherent non-uniqueness (many models explain the data equally well) and non-linearity of the inverse problem. To address these challenges, this thesis develops a probabilistic (Bayesian) and parameter optimisation approaches using earthquake body waves and normal modes (vibrational patterns due to large earthquakes). The ULVZs have been extensively studied using waveform modelling of body waves, however, the details of extent and fine structure are poorly understood due to the limited ability of these techniques to quantify non-uniqueness and address non-linearity. Here, a Bayesian inversion is developed to rigorously estimate the parameter values and their uncertainties. A Bayesian inversion considers parameters as random variables represented by probability densities. Parameters are assigned prior information and is updated by data information to produce the solution to the inverse problem from which parameter values and uncertainties can be inferred. The inversion is extensively applied to the observed ScP waveforms sensitive to the lowermost mantle beneath the Philippine and Tasman Seas. The inversions for the Philippine data yield a strong shear-wave velocity perturbation with high density that can be interpreted as the presence of iron-rich material. The results for the Australia data show a gradual decrease in shear-wave velocity as a function of depth while the compressional-wave velocity and density anomalies are highly uncertain. These ULVZs likely represent partial melting of iron-rich material in the lowermost mantle. Inner core structure has also been extensively studied using both body waves and normal modes. However, notable disagreements exist between different studies due to limitations of the inversion methods (e.g., results highly depend on the initial solution, earthquake source model and the stability of the inversion). Here, non-linear optimisation and Bayesian inversion are developed to estimate the 3-D structure of the inner core from normal modes. Our inversion method does not require an earthquake source model and damping/stabilisation of the inverse problem. Additionally, we can control the type of structures (e.g., elastic vs. anelastic) and all results are supplemented by the uncertainty estimates. The results from the parameter optimisation of inner core sensitive normal mode data support the previous results that the inner core is dominated by a spherical harmonic degree-2 axisymmetric structure.