An EGF technique to infer the source parameters of a circular crack growing at a variable rupture velocity

Circular crack models with a constant rupture velocity struggle to effectively model both the amplitude and duration of first P-wave pulses generated by small magnitude seismic events. Assuming a constant rupture velocity is unphysical, necessitating a deceleration phase in the rupture velocity to uphold the causality of the healing process. Moreover, a comprehensive failure model might encompass an initial nucleation phase, typically characterized by an increase of the initial rupture velocity. Studies have demonstrated that quasi-dynamic circular crack models featuring variable rupture velocities can accurately model the shape of the observed first P-wave pulse. Based on these principles, an Empirical Green's function (EGF) approach was previously formulated to estimate the source parameters of small magnitude earthquakes, called MAIN. In addition to determine the source radius and stress drop, this method also enables the inference of the temporal evolution of rupture velocity. However, this method encounters difficulties when the noise-to-signal ratio in the recordings of smaller earthquakes used as EGF exceeds 5%, a common situation when employing regional-scale recordings of small-magnitude earthquakes as EGF. Through synthetic tests, we demonstrated that, in such instances, the problem of this technique is that the alignment between the onset of P waves of EGF and MAIN is not rightly recovered after the initial inversion step. Consequently, a novel inversion method has been developed to address this issue, enabling the identification of the optimal alignment of P-wave arrivals in EGF and MAIN across all stations. A Bayesian statistical approach is proposed to meticulously investigate the solutions of model parameters and their correlations. Using the new technique on a small magnitude earthquake (M L = 3.3) occurred in Central Italy enabled us to identify the most likely rupture models and examine the issue of correlation among model parameters. Application of Occam's Razor Principle suggests that, for the investigated event, a circular crack model should be favored over a heterogeneous rupture model.