Bayesian imaging of the 2000 Western Tottori (Japan) earthquake through fitting of strong motion and GPS data

Abstract

S U M M A R YWe image the rupture process of the 2000 Western Tottori earthquake (M w = 6.6) through fitting of strong motion and GPS data. We consider an observational network consisting of 18 strong motion and 16 GPS stations, located within three fault lengths from the epicentre. We assume a planar fault and compute Green's functions for a 1-D velocity model. The earthquake rupture is described as a shear dislocation parameterized in terms of peak slip velocity, rake angle, rupture time and rise time, defined on a regular grid of nodes on the fault surface and derived at inner points through bilinear interpolation.Our inversion procedure is based on a Bayesian approach. The solution of the inverse problem is stated in terms of a posterior probability density function (pdf), representing the conjunction of prior information with information contained in the data and in the physical law relating model parameters with data. Inferences on model parameters are thus expressed in terms of posterior marginal pdfs. Due to the non-linearity of the problem, we use a Markov Chain Monte Carlo (MCMC) method, based on the Metropolis algorithm, to compute posterior marginals.Except for a few cases posterior marginals do not show a Gaussian-like distribution. This prevents us from providing a mean model and from characterizing uncertainties in terms of standard deviations only. Resolution on each single parameter is analysed by looking at the difference between prior and posterior marginal pdfs.Posterior marginals indicate that the best resolved feature is a major slip patch (peak value of 311 ± 140 cm), located between the hypocentre and the top edge of the fault, centered at a depth of 4.5 km. This shallow slip patch is triggered about 3 s after the earthquake nucleated and required about 4 s to reach its final slip value. The presence of this shallow slip patch is common to all previous studies. In contrast to some previous studies, we do not identify any significant slip (>1 m) at the bottom of the fault.We also compare inferences from both strong motion and GPS data with inferences derived from strong motion data only. In both cases the shallow slip patch is identified. At other locations, the main effect of the GPS data is in reducing the probability associated with high values of slip. GPS data reduce the presence of spurious fault slip and therefore strongly influence the resulting final seismic moment.

Uncertainty in Earthquake Source Imaging Due to Variations in Source Time Function and Earth Structure

“…Along the edges of the assumed rupture plane, the range for slip is chosen such that slip occurs with a maximum possible peak slip rate of 200 cm=s, which is about half of the value at the inner nodes. This choice is more realistic than in Monelli and Mai (2008) and Monelli et al (2009), who did not allow this area to slip at all. Monelli et al (2009) also showed that there is a trade-off for the peak slip rate at neighboring points, characterized by a strong anticorrelation.…”

“…In this study, we extend the approach of Monelli et al (2009) by incorporating the spatial correlation between neighboring nodes and using the regularized Yoffe function (Tinti, Fukuyama, et al, 2005) as STF, which is compatible with dynamic rupture simulations. Additionally, we account for epistemic uncertainty (e.g., Abrahamson and Bommer, 2005) associated with inadequate knowledge about physical assumptions regarding a specific model under investigation.…”

“…However, several models with very different source-parameter distributions may fit the data equally well (Mai et al, 2007). This limitation of the optimization can be overcome using a Bayesian technique (Monelli and Mai 2008;Monelli et al, 2009) that infers posterior PDFs to characterize the ensemble of all possible parameters (peak slip rate, rise time, and rupture time) describing the STFs that are consistent with the data and the available prior information. This technique comprises a stochastic process in which the major sources of uncertainty include data noise, improper knowledge about Earth structure, nonunique fault parameterization, and intrinsic randomness of physical processes.…”

Analysing earthquake slip models with the spatial prediction comparison test

“…However, there are several impeding issues regarding the reliability of the inverted models arising from the ill-posed nature of the inverse problem, limited and non-uniform data coverage, differences in selection and processing of the available data, incompletely known Earth structure, and variations in a priori assumptions on the faultgeometry (Beresnev 2003;Mai et al 2007;Shao & Ji 2012). Hence, earthquake source inversions come with considerable uncertainty, which however is only rarely investigated in as much detail as by Hartzell et al (1991Hartzell et al ( , 2007, Custodio et al (2005), Monelli & Mai (2008), Monelli et al 2009 andRazafindrakoto &Mai (2014).…”

Joint Determination of Slip and Stress Drop in a Bayesian Inversion Approach: A Case Study for the 2010 M8.8 Maule Earthquake

“…Nevertheless, the multiplicity of solutions in slip inversion can be conveniently expressed using a Bayesian approach, which has been applied in several studies (e.g., YABUKI and MATSU'URA, 1992;FUKUDA and JOHNSON, 2008;MONELLI and MAI, 2008;MONELLI et al, 2009;SIMONS et al, 2011), where the inversion problem is formulated only from the kinematic point of view. Recently, some mechanical constraints have been incorporated into fault slip inversion.…”