Modeling earthquake dynamics

Abstract

Abstract. In this paper, we investigate questions arising in [89]. Pseudo causal models connecting magnitudes and waiting times are consider, through generalized regression. We do use conditional model (magnitude given previous waiting time, and conversely) as an extension to joint distribution model described in [77]. On the one hand, we fit a Pareto distribution for earthquake magnitudes, where the tail index is a function of waiting time following previous earthquake; on the other hand, waiting times are modeled using a Gamma or a Weibull distribution, where parameters are function of the magnitude of the previous earthquake. We use those two models, alternatively, to generate the dynamics of earthquake occurrence, and to estimate the probability of occurrence of several earthquakes within a year, or a decade.

Connecting the grain-shearing mechanism of wave propagation in marine sediments to fractional order wave equations

“…Such hardening behavior has already been shown to result in the Lomnitz logarithmic creep law, 24 the seismological applications of which can be witnessed in rock physics, 5 marine sediments 56 and earthquake modeling. 57 By establishing the equivalence of wave equations and dispersion relations of the GS model to the respective equations obtained in the fractional framework we have also demonstrated the possibility of modeling time-dependent non-Newtonian fluid properties using fractional derivatives. Such fluid properties have remained an open problem from modeling perspectives so far.…”

“…On comparing Eqs. (57) and (58) with Eqs. (46) and (47) respectively, we observe that in contrast to the compressional wave dispersion relations which are characterized by two different power-laws, the shear wave dispersion relations are characterized by a single power-law in the entire frequency regime.…”

A Bayesian spatial–temporal model with latent multivariate log‐gamma random effects with application to earthquake magnitudes

“…The Gutenberg–Richter relation (Gutenberg and Richter, ) is a standard model in seismology, which states that the expected number of the earthquakes exceeding a prespecified magnitude satisfies the following form: where a is the logarithm of the number of occurrences, the magnitude m is greater than a baseline m 0 , b is a real‐valued coefficient and N ( m ) is the number of events having a magnitude ≥ m . The moment magnitude is often the scale in which a magnitude is recorded (Charpentier and Durand, ). The relationship between the moment magnitude and the seismic moment can be written as where S is the seismic moment, M is the moment magnitude and the seismic moment is measured in Newton meters (Kanamori, ; Rhoades and Evison, ).…”

“…The Pareto distribution has become a standard modelling assumption for earthquake magnitudes (e.g. see Mega et al, ; Charpentier & Durand, ). Alternative distributional assumptions are also highly related to the Pareto distribution.…”

“…These approaches all use a generalized linear model strategy (e.g. see Charpentier & Durand, for a review). That is, the log shape parameter is modelled with a fixed effects term.…”