Bayesian modelling of seismic scattering and intrinsic attenuation in the lithosphere

Heterogeneities present within the structure of our planet cause seismic waves to attenuate, especially when they are on the order of the seismic wavelength. Cracks, fluids, and patches of different temperature or composition are only a few examples of such inhomogeneities, all of which can produce complex wavefield fluctuations in time and amplitude and affect the signals recorded at the surface. Seismic source and velocity inversions, the discrimination and yield of a chemical or nuclear explosion, or peak ground velocity and acceleration are only a few examples of calculations directly derived from seismic data which require accurate amplitude measurements. However, while seismic amplitudes are particularly affected by scattering and absorption, many of the models used for these and other estimations are laterally homogeneous or smoothly varying, potentially biasing the results obtained from them. \n \nIn this thesis, I combine both single- and multi-layer energy flux models (EFMs) with a Bayesian inference algorithm to rigorously and probabilistically characterise the small-scale heterogeneity and attenuation structure of the lithosphere beneath seismic stations and arrays. The single-layer energy flux model, or EFM, characterizes the energy losses to the ballistic arrivals by means of the intrinsic, scattering and diffusion quality factors. I then use these values to compare the strength of these different attenuation mechanisms and their effects on the recorded signals. I implemented two main versions of the multi-layer EFM. The first of these, called here the Depth Dependent Energy Flux Model (EFMD), uses the intrinsic quality factor obtained from the EFM and a new Bayesian inversion algorithm to compute synthetic coda envelopes. By comparing synthetic and data envelopes, I can then obtain the scattering parameters (correlation length (a) and RMS velocity fluctuations (ε)) in each layer of the model. The second, expanded, version of the EFMD, called the E-EFMD, does not rely on the EFM and can simultaneously invert for both the scattering and intrinsic attenuation (intrinsic quality factor at 1 Hz (Qi0) and its frequency dependence coefficient (α)) parameters in each layer of the model. Both the EFMD and E-EFMD use the Metropolis-Hastings algorithm to sample the likelihood space and obtain posterior probability distributions for each parameter and layer in the model. \n \nMy thorough testing of these methods reveals the specific effect each of these parameters has on the seismic codas, with initial coda amplitudes being more affected by the scattering parameters and decay rates controlled mostly by intrinsic attenuation. Independent calculation of these parameters in multi-layer models using the EFMD or E-EFMD remains challenging due to complex and strong trade-offs between them and to solutions being extremely non-unique in most cases. This issue is accentuated by an apparent bias of the E-EFMD towards extreme values of the intrinsic quality factor at 1 Hz. Overall, my results highlight the importance and usefulness of the Bayesian inference framework in this kind of study, since it provides detailed information about the uncertainty and uniqueness of the solutions. I applied these approaches to large, high quality, datasets of teleseismic events recorded by the Pilbara (PSA), Alice Springs (ASAR), Warramunga (WRA), Eielson (ILAR), Lajitas (TXAR), Pinedale (PDAR), Yellowknife (YKA) and Boshof (BOSA) seismic arrays or stations. For PSA, ASAR and WRA, my EFM and EFMD results suggest scattering is the main driver of attenuation, with the crust beneath them presenting different heterogeneity strengths and the lithospheric mantle being mostly homogeneous. Data inversions of ILAR, PDAR, TXAR, YKA and BOSA data using the EFMD and E-EFMD point to the algorithm being unable to fit the data in many cases, likely because of the assumed power law frequency dependence for Qi not being good enough to explain the complex coda behaviours shown in their datasets but also due to the aforementioned bias of the algorithm towards extreme values of some parameters, which is also observed in PSA, ASAR and WRA E-EFMD data inversions. Relating these inversion results to the physical structure beneath the stations is, therefore, not possible. In general, my results suggest that parameter trade-offs and solution non-uniqueness in the E-EFMD are too extreme to allow for successful simultaneous recovery of all the parameters, while the combination of the EFM and EFMD can yield stable and reliable results for 1- and 2-layer models and also allow us to compare between different attenuation mechanisms.

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