Lithospheric scattering and intrinsic attenuation characterization from a Bayesian energy flux model

P waves are often used to calculate the yield of chemical or nuclear explosions in forensic seismology. These estimations often rely on amplitude measurements affected by seismic scattering and attenuation caused by the presence of heterogeneities on the scale of the seismic wavelength and seismic energy conversion into heat, both on the source and receiver side. It is therefore important to accurately characterize the effect of these phenomena on the recorded wavefields so that any source size (and type) obtained from them are not under or overestimated.  
In our previous study (González Alvarez et al., 2021), we combined single layer and multi-layer energy flux modeling with a Bayesian inference algorithm to characterize lithospheric small-scale heterogeneities beneath seismic stations or arrays by calculating the characteristic scale length and fractional velocity fluctuations of the crust and lithospheric mantle beneath them. Here, we take this approach further and remove the dependence on the less realistic, single layer energy flux model by including the intrinsic quality factor and its frequency dependence as free parameters into our Bayesian inference algorithm. We use the multi-layer energy flux model to produce synthetic envelopes for 2-layer models of the lithosphere for different values of the scattering and intrinsic attenuation parameters. We then use our improved Bayesian inference algorithm to sample the likelihood space by means of the Metropolis-Hastings algorithm and obtain posterior probability distributions for all parameters and layers in the model. To our knowledge, such an approach has not been attempted before. We thoroughly tested this inversion algorithm and its sensitivity to four different levels of crustal and lithospheric mantle intrinsic attenuation settings using 18 synthetic datasets. Our results from these tests, while showing complex trade-offs between the parameters, show that scattering parameters can be recovered accurately in most cases. Intrinsic attenuation shows higher variability and non-uniqueness in our inversions, but can generally be recovered for over half of the synthetic models. To further test the accuracy of the results obtained from this Bayesian algorithm, we applied this technique to the large, high-quality dataset from PSAR and IMS arrays ASAR and WRA used in our previous study and found excellent agreement between both approaches in all cases. 
Finally, we applied this technique to datasets of teleseismic earthquakes from several arrays part of the IMS (YKA, ILAR, TXAR, PDAR, BOSA and KURK) to characterize the lithospheric scattering and attenuation structure beneath them and relate our findings to the tectonic setting and history of the regions they are installed on.  

González Álvarez, I.N., Rost, S., Nowacki, A. and Selby, N.D., 2021. Small-scale lithospheric heterogeneity characterization using Bayesian inference and energy flux models. Geophysical Journal International, 227(3), pp.1682-1699.