Small-scale lithospheric heterogeneity characterization using Bayesian inference and energy flux models

Observations from different disciplines have shown that our planet is highly heterogeneous at multiple scale lengths. Still, many seismological Earth models tend not to include any small-scale heterogeneity or lateral velocity variations, which can affect measurements and predictions based on these homogeneous models. In this study, we describe the lithospheric small-scale isotropic heterogeneity structure in terms of the intrinsic, diffusion and scattering quality factors, as well as an autocorrelation function, associated with a characteristic scale length (a) and RMS fractional velocity fluctuations (ε). To obtain this characterization, we combined a single-layer and a multilayer energy flux models with a new Bayesian inference algorithm. Our synthetic tests show that this technique can successfully retrieve the input parameter values for 1- or 2-layer models and that our Bayesian algorithm can resolve whether the data can be fitted by a single set of parameters or a range of models is required instead, even for very complex posterior probability distributions. We applied this technique to three seismic arrays in Australia: Alice Springs array (ASAR), Warramunga Array (WRA) and Pilbara Seismic Array (PSAR). Our single-layer model results suggest intrinsic and diffusion attenuation are strongest for ASAR, while scattering and total attenuation are similarly strong for ASAR and WRA. All quality factors take higher values for PSAR than for the other two arrays, implying that the structure beneath this array is less attenuating and heterogeneous than for ASAR or WRA. The multilayer model results show the crust is more heterogeneous than the lithospheric mantle for all arrays. Crustal correlation lengths and RMS velocity fluctuations for these arrays range from ∼0.2 to 1.5 km and ∼2.3 to 3.9 per cent, respectively. Parameter values for the upper mantle are not unique, with combinations of low values of the parameters (a < 2 km and ε < ∼2.5 per cent) being as likely as those with high correlation length and velocity variations (a > 5 km and ε > ∼2.5 per cent, respectively). We attribute the similarities in the attenuation and heterogeneity structure beneath ASAR and WRA to their location on the proterozoic North Australian Craton, as opposed to PSAR, which lies on the archaean West Australian Craton. Differences in the small-scale structure beneath ASAR and WRA can be ascribed to the different tectonic histories of these two regions of the same craton. Overall, our results highlight the suitability of the combination of an energy flux model and a Bayesian inference algorithm for future scattering and small-scale heterogeneity studies, since our approach allows us to obtain and compare the different quality factors, while also giving us detailed information about the trade-offs and uncertainties in the determination of the scattering parameters.