POSTER

A probabilistic approach for the estimation of earthquake source parameters from spectral inversion

Supino M., Festa G. and Zollo A.

MOTIVATION

The characterization of a seismic source is a fundamental step in the description of the mechanisms of generation and propagation of an earthquake; understanding the relationship between the energy budget and the size of a seismic rupture, allows to tackle the upscaling problem from microseismicity to large events. Systematic comparison between existing methodologies for source parameters estimation highlighted the lack of robustness of the results, due to the high correlation among the parameters.

The proposed method consists in a fully probabilistic approach : we provide an estimation of the joint probability density function in the parameter space, associated with a global exploration; this can provide a robust information about the expected values for the parameters, with consistent estimation of uncertainties accounting for parameter correlation.

ABSTRACT

The amplitude spectrum of a seismic signal related to an earthquake source carries information about the size of the rupture, moment, stress and energy release. Furthermore, it can be used to characterize the Green’s function of the medium crossed by the seismic waves.

[A] We describe the earthquake amplitude spectrum assuming a generalized Brune’s (1970) source model, and direct P – and S – waves propagating in a layered velocity model, characterized by a frequency-independent Q attenuation factor. The observed displacement spectrum depends indeed on three source parameters, the seismic moment (through the low-frequency spectral level), the corner frequency (that is a proxy of the fault length) and the high-frequency decay parameter. These parameters are strongly correlated each other and with the quality factor Q; a rigorous estimation of the associated uncertainties and parameter resolution is thus needed to obtain reliable estimations.

[B] In this work, the uncertainties are characterized adopting a probabilistic approach for the parameter estimation.[C.1] Assuming an L2-norm based misfit function, we perform a global exploration of the parameter space to find the absolute minimum of the cost function and then [C.2] we explore the cost-function associated joint a-posteriori probability density function around such a minimum, to extract the correlation matrix of the parameters.

The global exploration relies on building a Markov chain in the parameter space and on combining a deterministic minimization with a random exploration of the space ( Basin-hopping technique ).

The joint pdf is built from the misfit function using the maximum likelihood principle and assuming a Gaussian-like distribution of the parameters. It is then computed on a grid centered at the global minimum of the cost-function. [C.3] The numerical integration of the pdf finally provides mean, variance and correlation matrix associated with the set of best-fit parameters describing the model.

[D] The main benefits of the method are :

• CAPABILITY TO FIND THE BEST MODEL TO DESCRIBE THE DATA | Thanks to the global optimization, we are able to avoid local minima during the search for the best model to describe the observed data.
• A ROBUST UNCERTAINTIES ESTIMATION | The uncertainties are computed from the joint pdf σ_M ; they properly account for the correlation among the parameters.
• QUALITY AND A-POSTERIORI REJECTION OF SOLUTIONS | The quality of the solution is evaluated in terms of similarity of σ_M with a normal distribution, and it is rejected when it significantly differs from it. Moreover, the a-posteriori rejection allows to automatically process very large data-sets.

The technique has been applied to characterize the source parameters of the earthquakes occurring during the 2016-2017 Central Italy sequence, with the goal of investigating the scaling of source parameters with magnitude. The average stress drop is ∆σ = 2.7 ± 0.4 MPa. The largest events show a stress drop around 10 Mpa (∆σ = 7 ± 3 MPa for the main event).