GNGTS 2023 - Atti del 41° Convegno Nazionale

Session 1.1 GNGTS 2023 Fig. 1. Map of the analyzed earthquakes. Inverse method We invert the S-wave displacement amplitude spectrum . The model predictions are given by the forward operator: ; ( ) = 0 , , γ; ( ) = ~ ( 0 , , γ; )∙ ~ ( ; ) where is the source spectrum expected from a generalized Brune (1970) spectral model and is ~  ~  the Fourier transform of the Green’s propagator. We use a theoretical Green’s function and a frequency-independent anelastic attenuation factor Q. We seek for the best-fit solution m* by minimizing the squared L 2 -norm (cost function) ( ) between observed data and model predictions . ( ) We obtain m* by applying the basin-hopping global optimization technique (Wales and Doye, 1997). The latter combines a local (deterministic) minimization with a random exploration of the model space, by building a Markov chain with a transition probability given by the Metropolis criterion. To assess the uncertainty associated with the best-fit solution m* , we estimate the a-posteriori joint probability density function (PDF) over the model space, . σ( ) Under the hypothesis of a uniform a-priori PDF over the model space, and of modelization and data uncertainties normally distributed, it writes as , with K’ σ( ) = '∙ − 1 2 ( )∙ −1 ( ) normalization constant and mean squared error between and (Tarantola, 2005;  ( * ) Supino et al., 2019). We evaluate around m* , in a model space sub-domain which spans on σ( ) average more than three standard deviations. Source parameters joint PDF We integrate the joint PDF to obtain the marginal PDF of each source parameter (Fig. 2a). σ( ) The single-station solution and uncertainty are the mean and standard deviation of the parameter marginal PDF. The final event solution and uncertainty are respectively the weighted average and weighted uncertainty of single-station estimates.