Arnaud Mignan

Bayesian Estimation of the Spatially Varying Completeness Magnitude of Earthquake Catalogs

Assessing the completeness magnitude Mc of earthquake catalogs is an essential prerequisite for any seismicity analysis. We employ a simple model to com- puteMc inspacebasedontheproximitytoseismicstationsinanetwork.Weshowthata relationship of the form M predd �� ad bc, with d the distance to the kth nearest seismic station, fits the observations well, k depending on the minimum number of stations being required to trigger an event declaration in a catalog. We then propose anewMc mappingapproach,theBayesianmagnitude ofcompleteness (BMC)method, based on a two-step procedure: (1) a spatial resolution optimization to minimize spatial heterogeneities and uncertainties in Mc estimates and (2) a Bayesian approach that merges prior information about Mc based on the proximity to seismic stations with locally observed values weighted by their respective uncertainties. Contrary to the cur- rentMc mappingprocedures,theradiusthatdefineswhichearthquakestoincludeinthe local magnitude distribution is chosen according to an objective criterion, and there are no gaps in the spatial estimation of Mc. The method solely requires the coordinates of seismic stations. Here, we investigate the Taiwan Central Weather Bureau (CWB) seismic network and earthquake catalog over the period 1994-2010.

Systematic survey of high‐resolution b value imaging along Californian faults: Inference on asperities

Understanding and forecasting earthquake occurrences is presumably linked to understanding the stress distribution in the Earths crust. This cannot be measured instrumentally with useful coverage. However, the size distribution of earthquakes, quantified by the Gutenberg-Richter b value, is possibly a proxy to differential stress conditions and could therewith act as a crude stress-meter wherever seismicity is observed. In this study, we improve the methodology of b value imaging for application to a high-resolution 3-D analysis of a complex fault network. In particular, we develop a distance-dependent sampling algorithm and introduce a linearity measure to restrict our output to those regions where the magnitude distribution strictly follows a power law. We assess the catalog completeness along the fault traces using the Bayesian Magnitude of Completeness method and systematically image b values for 243 major fault segments in California. We identify and report b value structures, revisiting previously published features, e.g., the Parkfield asperity, and documenting additional anomalies, e.g., along the San Andreas and Northridge faults. Combining local b values with local earthquake productivity rates, we derive probability maps for the annual potential of one or more M6 events as indicated by the microseismicity of the last three decades. We present a physical concept of how different stressing conditions along a fault surface may lead to b value variation and explain nonlinear frequency-magnitude distributions. Detailed spatial b value information and its physical interpretation can advance our understanding of earthquake occurrence and ideally lead to improved forecasting ability.

The debate on the prognostic value of earthquake foreshocks: A meta-analysis

The hypothesis that earthquake foreshocks have a prognostic value is challenged by simulations of the normal behaviour of seismicity, where no distinction between foreshocks, mainshocks and aftershocks can be made. In the former view, foreshocks are passive tracers of a tectonic preparatory process that yields the mainshock (i.e., loading by aseismic slip) while in the latter, a foreshock is any earthquake that triggers a larger one. Although both processes can coexist, earthquake prediction is plausible in the first case while virtually impossible in the second. Here I present a meta-analysis of 37 foreshock studies published between 1982 and 2013 to show that the justification of one hypothesis or the other depends on the selected magnitude interval between minimum foreshock magnitude mmin and mainshock magnitude M. From this literature survey, anomalous foreshocks are found to emerge when mmin < M − 3.0. These results suggest that a deviation from the normal behaviour of seismicity may be observed only when microseismicity is considered. These results are to be taken with caution since the 37 studies do not all show the same level of reliability. These observations should nonetheless encourage new research in earthquake predictability with focus on the potential role of microseismicity.

A mathematical formulation of accelerating moment release based on the stress accumulation model

Large earthquakes can be preceded by a period of accelerating seismic activity of moderate-sized earthquakes. This phenomenon, usually termed accelerating moment release, has yet to be clearly understood. A new mathematical formulation of accelerating moment release is obtained from simple stress transfer considerations, following the recently proposed stress accumulation model. This model, based on the concept of elastic rebound, simulates accelerating seismicity from theoretical stress changes during an idealized seismic cycle. In this view, accelerating moment release is simply the consequence of the decrease, due to loading, of the size of a stress shadow due to a previous earthquake. We show that a power law time-to-failure equation can be expressed as a function of the loading rate on the fault that is going to rupture. We also show that the m value, which is the power law exponent, can be defined as m = D/3, with D a parameter that takes into account the geometrical shape of the stress lobes and the distribution of active faults. In the stress accumulation model, the power law is not due to critical processes.

An observational test of the origin of accelerating moment release before large earthquakes

[1] A progressive increase of seismic activity distributed over a wide region around a future earthquake epicenter is termed accelerating moment release (AMR). This phenomenon has been observed in several studies over the last 15 years, although there is no consensus about the physical origin of the effect. In a recent hypothesis known as the stress accumulation (SA) model, the AMR is thought to result from the last stage of loading in the earthquake cycle. In this view, the increasing seismicity is due to minor stress release as the whole region becomes sufficiently stressed for the major event to occur. The stress accumulation model makes specific predictions about the distribution of events in an AMR sequence. Because the AMR is predicted to be a result of loading on the main fault, the precursory activity should be concentrated in the positive lobes of the far-field stresses calculated by a backslip dislocation model of the main shock. To test this model, AMR is first found in optimal circular regions around the epicenters of each of the M w ! 6.5 earthquakes in central and southern California since 1950. A backslip dislocation model is then used to determine which of the precursory events occur in the regions predicted by stress accumulation. AMR is shown to occur preferentially in the lobes of the backslip stress field predicted by the stress accumulation model.

The quantification of low-probability–high-consequences events: part I. A generic multi-risk approach

Abstract Dynamic risk processes, which involve interactions at the hazard and risk levels, have yet to be clearly understood and properly integrated into probabilistic risk assessment. While much attention has been given to this aspect lately, most studies remain limited to a small number of site-specific multi-risk scenarios. We present a generic probabilistic framework based on the sequential Monte Carlo Method to implement coinciding events and triggered chains of events (using a variant of a Markov chain), as well as time-variant vulnerability and exposure. We consider generic perils based on analogies with real ones, natural and man-made. Each simulated time series corresponds to one risk scenario, and the analysis of multiple time series allows for the probabilistic assessment of losses and for the recognition of more or less probable risk paths, including extremes or low-probability–high-consequences chains of events. We find that extreme events can be captured by adding more knowledge on potential interaction processes using in a brick-by-brick approach. We introduce the concept of risk migration matrix to evaluate how multi-risk participates to the emergence of extremes, and we show that risk migration (i.e., clustering of losses) and risk amplification (i.e., loss amplification at higher losses) are the two main causes for their occurrence.

Modeling aftershocks as a stretched exponential relaxation

The decay rate of aftershocks has been modeled as a power law since the pioneering work of Omori in the late nineteenth century. Considered the second most fundamental empirical law after the Gutenberg-Richter relationship, the power law paradigm has rarely been challenged by the seismological community. By taking a view of aftershock research not biased by prior conceptions of Omori power law decay and by applying statistical methods recommended in applied mathematics, I show that all aftershock sequences tested in three regional earthquake catalogs (Southern and Northern California, Taiwan) and with three declustering techniques (nearest-neighbor, second-order moment, window methods) follow a stretched exponential instead of a power law. These results infer that aftershocks are due to a simpler relaxation process than originally thought, in accordance with most other relaxation processes observed in Nature.

A three-level framework for multi-risk assessment

The effective management of the risks posed by natural and man-made hazards requires all relevant threats and their interactions to be considered. This paper proposes a three-level framework for multi-risk assessment that accounts for possible hazard and risk interactions. The first level is a flow chart that guides the user in deciding whether a multi-hazard and risk approach is required. The second level is a semi-quantitative approach to explore if a more detailed, quantitative assessment is needed. The third level is a detailed quantitative multi-risk analysis based on Bayesian networks. Examples that demonstrate the application of the method are presented.

Revisiting the 1894 Omori Aftershock Dataset with the Stretched Exponential Function

In 1894, Fusakichi Omori published his landmark article on aftershocks in which he described the temporal decay rate of aftershocks as a power law. In this article, I show that the expression proposed by Omori does not hold when the proper visualization method is used (i.e., complementary cumulative density function in log–log plot) and that the choice of a stretched exponential function should have been preferred on physical grounds. I reproduce the emblematic aftershock sequence of the 1891 Great Nobi earthquake used by Omori and show that a stretched exponential expression describes the data better than a power law.

Static behaviour of induced seismicity

Abstract. The standard paradigm to describe seismicity induced by fluid injection is to apply non-linear diffusion dynamics in a poroelastic medium. I show that the spatio-temporal behaviour and rate evolution of induced seismicity can, instead, be expressed by geometric operations on a static stress field produced by volume change at depth. I obtain laws similar in form to the ones derived from poroelasticity while requiring a lower description length. Although fluid flow is known to occur in the ground, it is not pertinent to the geometrical description of the spatio-temporal patterns of induced seismicity. The proposed model is equivalent to the static stress model for tectonic foreshocks generated by the Non-Critical Precursory Accelerating Seismicity Theory. This study hence verifies the explanatory power of this theory outside of its original scope and provides an alternative physical approach to poroelasticity for the modelling of induced seismicity. The applicability of the proposed geometrical approach is illustrated for the case of the 2006, Basel enhanced geothermal system stimulation experiment. Applicability to more problematic cases where the stress field may be spatially heterogeneous is also discussed.