Fabrice Cotton

On the Use of Logic Trees for Ground-Motion Prediction Equations in Seismic-Hazard Analysis

Logic trees are widely used in probabilistic seismic hazard analysis as a tool to capture the epistemic uncertainty associated with the seismogenic sources and the ground-motion prediction models used in estimating the hazard. Combining two or more ground-motion relations within a logic tree will generally require several conversions to be made, because there are several definitions available for both the predicted ground-motion parameters and the explanatory parameters within the predictive ground-motion relations. Procedures for making conversions for each of these factors are presented, using a suite of predictive equations in current use for illustration. The sensitivity of the resulting ground-motion models to these conversions is shown to be pronounced for some of the parameters, especially the measure of source-to-site distance, highlighting the need to take into account any incompatibilities among the selected equations. Procedures are also presented for assigning weights to the branches in the ground-motion section of the logic tree in a transparent fashion, considering both intrinsic merits of the individual equations and their degree of applicability to the particular application.

On the Use of Response Spectral-Reference Data for the Selection and Ranking of Ground-Motion Models for Seismic-Hazard Analysis in Regions of Moderate Seismicity: The Case of Rock Motion

The use of ground-motion-prediction equations to estimate ground shak- ing has become a very popular approach for seismic-hazard assessment, especially in the framework of a logic-tree approach. Owing to the large number of existing published ground-motion models, however, the selection and ranking of appropriate models for a particular target area often pose serious practical problems. Here we show how observed ground-motion records can help to guide this process in a sys- tematic and comprehensible way. A key element in this context is a new, likelihood based, goodness-of-fit measure that has the property not only to quantify the model fit but also to measure in some degree how well the underlying statistical model assumptions are met. By design, this measure naturally scales between 0 and 1, with a value of 0.5 for a situation in which the model perfectly matches the sample dis- tribution both in terms of mean and standard deviation. We have used it in combi- nation with other goodness-of-fit measures to derive a simple classification scheme to quantify how well a candidate ground-motion-prediction equation models a par- ticular set of observed-response spectra. This scheme is demonstrated to perform well in recognizing a number of popular ground-motion models from their rock-site- recording subsets. This indicates its potential for aiding the assignment of logic-tree weights in a consistent and reproducible way. We have applied our scheme to the border region of France, Germany, and Switzerland where the M w 4.8 St. Dieearth- quake of 22 February 2003 in eastern France recently provided a small set of ob- served-response spectra. These records are best modeled by the ground-motion- prediction equation of Berge-Thierry et al. (2003), which is based on the analysis of predominantly European data. The fact that the Swiss model of Bay et al. (2003) is not able to model the observed records in an acceptable way may indicate general problems arising from the use of weak-motion data for strong-motion prediction.

Toward a Ground-Motion Logic Tree for Probabilistic Seismic Hazard Assessment in Europe

*We study the rupture process of the 1992 Landers earthquake. To limit the trade-off between slip amplitude and rupture time that affects solutions using only seismological data, we adopt a two-step approach. We first constrain the slip distribution and its uncertainty by independent geodetic data to recover in the second step the temporal details of the rupture propagation. The first step consists of an inversion of interferometric data and Global Positioning System measurements, both independently and together, to constrain slip distribution on a three-segment fault model along both strike and dip direction. We use a genetic algorithm to test the uniqueness of the solution and a least squares formulation to find the model which best fits the data. We conclude from the results of these geodetic inversions that interferometric data are rich enough to access the slip distribution in the case of the Landers earthquake. Since the surface deformations are more sensitive to shallow slip in our configuration, the slip amplitude is better resolved near the surface than at depth. The resulting slip distribution is in agreement with geological observations at the surface and confirms the heterogeneous nature of the Landers earthquake. Most of the slip occurs at shallow depths, on the Homestead Valley fault (second segment), with a maximum value of around 7 m. Another high slip zone is observed on the Johnson Valley fault (first segment) at 8 km depth. In the second step, we invert strong motion data with the a priori final slip amplitude and its uncertainty deduced from geodetic data to constrain the time history of the rupture process. This second step emphasizes a strong variation of the temporal development of the earthquake. Fast rupture front velocities appear within high slip zones, and the rupture slows when it encounters a resistance along the fault. On average, the rupture front propagates with velocities close to the S wave velocity and terminates about 20 s after initiation. The large variations in both slip amplitude and rupture velocity suggest that the rupture process is better described by successively breaking asperities than by a pulse propagating with constant velocity.

On the Conversion of Source-to-Site Distance Measures for Extended Earthquake Source Models

The Seismic Hazard Harmonization in Europe (SHARE) project, which began in June 2009, aims at establishing new standards for probabilistic seismic hazard assessment in the Euro-Mediterranean region. In this context, a logic tree for ground-motion prediction in Europe has been constructed. Ground-motion prediction equations (GMPEs) and weights have been determined so that the logic tree captures epistemic uncertainty in ground-motion prediction for six different tectonic regimes in Europe. Here we present the strategy that we adopted to build such a logic tree. This strategy has the particularity of combining two complementary and independent approaches: expert judgment and data testing. A set of six experts was asked to weight pre-selected GMPEs while the ability of these GMPEs to predict available data was evaluated with the method of Scherbaum et al. (Bull Seismol Soc Am 99:3234–3247, 2009). Results of both approaches were taken into account to commonly select the smallest set of GMPEs to capture the uncertainty in ground-motion prediction in Europe. For stable continental regions, two models, both from eastern North America, have been selected for shields, and three GMPEs from active shallow crustal regions have been added for continental crust. For subduction zones, four models, all non-European, have been chosen. Finally, for active shallow crustal regions, we selected four models, each of them from a different host region but only two of them were kept for long periods. In most cases, a common agreement has been also reached for the weights. In case of divergence, a sensitivity analysis of the weights on the seismic hazard has been conducted, showing that once the GMPEs have been selected, the associated set of weights has a smaller influence on the hazard.

Analysis of Rock-Fall and Rock-Fall Avalanche Seismograms in the French Alps

One of the major challenges in engineering seismology is the reliable prediction of site-specific ground motion for particular earthquakes, observed at specific distances. For larger events, a special problem arises, at short distances, with the source-to-site distance measure, because distance metrics based on a point-source model are no longer appropriate. As a consequence, different attenuation relations differ in the distance metric that they use. In addition to being a source of confusion, this causes problems to quantitatively compare or combine different ground-motion models; for example, in the context of Probabilistic Seismic Hazard Assessment, in cases where ground-motion models with different distance metrics occupy neighboring branches of a logic tree. In such a situation, very crude assumptions about source sizes and orientations often have to be used to be able to derive an estimate of the particular metric required. Even if this solves the problem of providing a number to put into the attenuation relation, a serious problem remains. When converting distance measures, the corresponding uncertainties map onto the estimated ground motions according to the laws of error propagation. To make matters worse, conversion of distance metrics can cause the uncertainties of the adapted ground-motion model to become magnitude and distance dependent, even if they are not in the original relation. To be able to treat this problem quantitatively, the variability increase caused by the distance metric conversion has to be quantified. For this purpose, we have used well established scaling laws to determine explicit distance conversion relations using regression analysis on simulated data. We demonstrate that, for all practical purposes, most popular distance metrics can be related to the Joyner-Boore distance using models based on gamma distributions to express the shape of some “residual function.” The functional forms are magnitude and distance dependent and are expressed as polynomials. We compare the performance of these relations with manually derived individual distance estimates for the Landers, the Imperial Valley, and the Chi-Chi earthquakes.

The 2013 European Seismic Hazard Model: key components and results

This study reviews seismograms from 10 rock-fall events recorded between 1992 and 2001 by the permanent seismological network Sismalp in the French Alps. A new seismic magnitude scale was defined, which allowed us to compare and classify g round-motion vibrations generated by these Alpine rock-falls. Each rock-fall has also been cha racterized by its ground-motion duration t30 at an epicentral distance of 30 km. No relation was found between rock-fall parameters (fall height, runout distance, volume, potential energy) and rock-fall s eismic magnitudes derived from seismogram amplitudes. On the other hand, the signal duration t30 shows a rough correlation with the potential energy and the runout distance, highlighting the co ntrol of the propagation phase on the signal length . The signal analysis suggests the existence of at le ast two distinct seismic sources: one corresponding to the initial rupture associated with an elastic r ebound during the detachment and the other one generated by the rock impact on the slope. Although the fall phenomenon includes other complex processes (fragmentation of the block, interaction with topography, plastic deformation during and after impact) 2D finite-element simulations of thes e two seismic sources are able to retrieve the main seismogram characteristics.

Redistribution of dynamic stress during coseismic ruptures: Evidence for fault interaction and earthquake triggering

The 2013 European Seismic Hazard Model (ESHM13) results from a community-based probabilistic seismic hazard assessment supported by the EU-FP7 project “Seismic Hazard Harmonization in Europe” (SHARE, 2009–2013). The ESHM13 is a consistent seismic hazard model for Europe and Turkey which overcomes the limitation of national borders and includes a through quantification of the uncertainties. It is the first completed regional effort contributing to the “Global Earthquake Model” initiative. It might serve as a reference model for various applications, from earthquake preparedness to earthquake risk mitigation strategies, including the update of the European seismic regulations for building design (Eurocode 8), and thus it is useful for future safety assessment and improvement of private and public buildings. Although its results constitute a reference for Europe, they do not replace the existing national design regulations that are in place for seismic design and construction of buildings. The ESHM13 represents a significant improvement compared to previous efforts as it is based on (1) the compilation of updated and harmonised versions of the databases required for probabilistic seismic hazard assessment, (2) the adoption of standard procedures and robust methods, especially for expert elicitation and consensus building among hundreds of European experts, (3) the multi-disciplinary input from all branches of earthquake science and engineering, (4) the direct involvement of the CEN/TC250/SC8 committee in defining output specifications relevant for Eurocode 8 and (5) the accounting for epistemic uncertainties of model components and hazard results. Furthermore, enormous effort was devoted to transparently document and ensure open availability of all data, results and methods through the European Facility for Earthquake Hazard and Risk (www.efehr.org).

Analysis of Single-Station Standard Deviation Using the KiK-net Data

We investigate the spatiotemporal evolution of dynamic stress outside a rupturing extended fault. The dynamic stress variations caused by a coseismic rupture in a half space are computed by using the discrete wavenumber and reflectivity methods. After a transient phase, the stress time history evolves to the final static stress value. We compare the static stress changes resulting from this model with those computed from a static dislocation model. We have applied this method to study the interactions between the first two normal faults which ruptured during the 1980 (MS 6.9) Irpinia earthquake. These two subevents are separated in time by nearly 20 s, while the third (and last) subevent occurred 40 s after the rupture onset. We compute the dynamic stress changes caused by the rupture of the first subevent. Our modeling results show that the dynamic stress peak on the second subevent fault plane is reached between 7 s and 8 s after the rupture initiation on the main fault. On the average the static stress level on the second subevent (20 s) fault plane is reached nearly after 14 s. The dynamic rupture did not jump from a rupturing segment to the adjacent one immediately, but the triggering of the 20 s subevent is delayed by roughly 10 s with respect to the instant of occurrence of the dynamic stress peak induced by the 0 s event. The dynamic stress pulse propagates along the strike direction of the second subevent fault plane at an average velocity of nearly 3.4 km/s. The delayed triggering of the second subevent can be interpreted in terms of the frictional properties of the faults. In particular, rate- and state-dependent frictional law can explain a delayed instability after a sudden change in stress. Using the estimated values of the subevent triggering delay and the shear stress change, we attempt to constrain the parameter Aσ on the 20 s fault. The values here inferred agree well with those resulting from previous studies.

Composite Ground-Motion Models and Logic Trees: Methodology, Sensitivities, and Uncertainties

Estimates of single-station standard deviation can be used as a lower bound to probabilistic seismic hazard analyses that remove the ergodic assumption on site response. This paper presents estimates of single-station standard deviation using data from the KiK-net network. The KiK-net network has a dense array of stations that recorded a large number of earthquakes over the period of study, both at the surface and at colocated borehole instruments. The large number of records implies that there are a large number of stations with recordings from multiple events; hence, site terms and single-station standard deviations can be properly estimated. Borehole instruments permit a breakdown of residuals, considering the effect of amplification in the shallow surface layers. Random-effects regression was first used to develop a ground-motion prediction equation (GMPE) using both the surface and borehole data. The GMPE was constrained such that event terms were the same at the surface and borehole. Residuals were then computed and the within-event (intraevent) residuals were separated into a repeatable site-term and a remaining residual, for both the ground motion itself and for the empirical amplification factor between surface and borehole. Results show that single-station standard deviations are considerably lower than standard deviations using the ergodic assumption, and these standard deviations are further reduced if only a small bracket of station-to-event azimuths is considered for each station such that path variability is minimized. Moreover, analyses of residuals indicate that most of the differences between ergodic standard deviations of surface and borehole data are the results of a poor parametrization of shallow site effects. However, the contribution of site-to-site variability in the empirical amplification factor is only limited. Finally, a comparison with results from other studies at different tectonic regions indicates that the values of single-station standard deviations are strikingly similar for all studies.