A probabilistic method for the estimation of earthquake source parameters from spectral inversion: application to the 2016–2017 Central Italy seismic sequence

Abstract

We develop a probabilistic framework based on the conjunction of states of information between data and model, to jointly retrieve earthquake source parameters and anelastic attenuation factor from inversion of displacement amplitude spectra. The evaluation of the joint probability density functions (PDFs) enables us to take into account between-parameter correlations in the final estimates of the parameters and related uncertainties. Following this approach, we first search for the maximum of the a-posteriori PDF through the basin hopping technique that couples a global exploration built on a Markov chain with a local deterministic maximization. Then we compute statistical indicators (mean, variance and correlation coefficients) on source parameters and anelastic attenuation through integration of the PDF in the vicinity of the maximum likelihood solution. Definition of quality criteria based on the signal to noise ratio and similarity of the marginal PDFs with a Gaussian function enable us to define the frequency domain for the inversion and to get rid of unconstrained solutions.We perform synthetic tests to assess theoretical correlations as a function of the signal to noise ratio and to define the minimum bandwidth around the corner frequency for consistent parameter resolution.As an application, we finally estimate the source parameters for the 2016-2017 Central Italy seismic sequence. We found that the classical scaling between the seismic moment and the corner frequency holds, with an average stress drop of 2.1 0.3 MPa     . However, the main events in the sequence exhibit a stress drop larger than the average value. Finally, the small seismic efficiency indicates a stress overshoot, possibly due to dynamic effects or large frictional efficiency. Short title : Probabilistic source parameters estimation

Insights into Mechanical Properties of the 1980 Irpinia Fault System from the Analysis of a Seismic Sequence

“…We chose the Brune source model [63] to infer source parameters (seismic moment, earthquake size, stress drop, and radiated energy released during the seismic event), which corresponds to an instantaneous pulse applied to the fault. We applied the SPAR (Source PARameters estimator) technique [64], which inverts the observed displacement spectra relying on a probabilistic framework based on the conjunction of states of information between data and model spaces. The inversion strategy allows to jointly retrieve source parameters along with their uncertainties and to investigate the between-parameter correlations.…”

Self-similarity of low-frequency earthquakes

“…The parameters to be retrieved are: the flat spectrum level, which is proportional to the seismic moment and a proxy for the event magnitude; the corner frequency, which is related to the event size; and the power-law of the high-frequency fall-off, which constrains the energy radiated by the earthquake. The source parameters are estimated by inversion 6 of the spectra, using a probabilistic approach (26). This method evaluates the joint probability density functions (PDFs) of the source parameters, which allows robust estimations together with uncertainty quantification.…”

“…For each LFE and each station, the geometrical mean of the smoothed spectra of the two horizontal components was inverted (26).…”

“…Source parameters for an event are obtained as the weighted means of single-station estimations, and their uncertainties are given by the standard errors (26).…”

“…In the spectral inversion, we do not consider site effects (26). The average of the corner frequencies in each bin comes from a large number of stations and mitigates possible single-station site effects, if any.…”