Frank Scherbaum

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.

Scaling relations of earthquake source parameter estimates with special focus on subduction environment

Abstract Earthquake rupture length and width estimates are in demand in many seismological applications. Earthquake magnitude estimates are often available, whereas the geometrical extensions of the rupture fault mostly are lacking. Therefore, scaling relations are needed to derive length and width from magnitude. Most frequently used are the relationships of Wells and Coppersmith (1994) derived on the basis of a large dataset including all slip types with the exception of thrust faulting events in subduction environments. However, there are many applications dealing with earthquakes in subduction zones because of their high seismic and tsunamigenic potential. There are no well-established scaling relations for moment magnitude and length/width for subduction events. Within this study, we compiled a large database of source parameter estimates of 283 earthquakes. All focal mechanisms are represented, but special focus is set on (large) subduction zone events, in particular. Scaling relations were fitted with linear least-square as well as orthogonal regression and analyzed regarding the difference between continental and subduction zone/oceanic relationships. Additionally, the effect of technical progress in earthquake parameter estimation on scaling relations was tested as well as the influence of different fault mechanisms. For a given moment magnitude we found shorter but wider rupture areas of thrust events compared to Wells and Coppersmith (1994). The thrust event relationships for pure continental and pure subduction zone rupture areas were found to be almost identical. The scaling relations differ significantly for slip types. The exclusion of events prior to 1964 when the worldwide standard seismic network was established resulted in a remarkable effect on strike-slip scaling relations: the data do not show any saturation of rupture width of strike-slip earthquakes. Generally, rupture area seems to scale with mean slip independent of magnitude. The aspect ratio L / W , however, depends on moment and differs for each slip type.

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

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.

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

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.

Seismic slip on a low angle normal fault in the Gulf of Corinth: Evidence from high‐resolution cluster analysis of microearthquakes

The Gulf of Corinth in Western Greece is one of the most active extensional zones in the Aegean region. It is still an open question whether extension can be actively accommodated on low angle faulting or if those faults as seen in geological records have been rotated. Whilst numerous fault plane solutions obtained from a dense temporary network deployed in the western part of the gulf in July-August of 1991 showed one of the nodal planes as a subhorizomal plane, slip on the high-angle conjugate plane is equally probable from the focal mechanism data (Rigo et al. 1996). Since part of the activity occurred in spatial clusters with similar focal mechanisms, we used a high resolution cluster analysis to determine the most likely active plane. Exploiting the waveform similarity of these events, relative onset times of P and S waves could be determined at subsample accuracy (less than 0.01 s). The cluster analyzed here contains 12 evems, among these 8 have a well con- strained normal faulting fault plane solution with a shal- low (12-20 o) north dipping plane and a steeply south dipping plane. A master evem relocation shows that the relocated 12 hypocenter cemroids are aligned along the low angle plane showing clear evidence for active low angle normal faulting.

The Use and Misuse of Logic Trees in Probabilistic Seismic Hazard Analysis

Logic trees have become a standard feature of probabilistic seismic hazard analyses (PSHA) for determining design ground motions. A logic trees purpose is to capture and quantify the epistemic uncertainty associated with the inputs to PSHA and thus enable estimation of the resulting uncertainty in the hazard. There are many potential pitfalls in setting up a logic tree for PSHA, mainly related to the fact that in practice, it is questionable that the requirements that the logic-tree branches be both mutually exclusive and collectively exhaustive can actually be met. Careful consideration is also required for making use of the output; in particular, in view of how PSHA is employed in current engineering design practice, it may be more rational to determine the mean ground motion at the selected design return period rather than to find the ground motion at the mean value of this return period.

Estimating Background Activity Based on Interevent-Time Distribution

The statistics of time delays between successive earthquakes has re- cently been claimed to be universal and to show the existence of clustering beyond the duration of aftershock bursts. We demonstrate that these claims are unjustified. Stochastic simulations with Poissonian background activity and triggered Omori- type aftershock sequences are shown to reproduce the interevent-time distributions observed on different spatial and magnitude scales in California. Thus the empirical distribution can be explained without any additional long-term clustering. Further- more, we find that the shape of the interevent-time distribution, which can be ap- proximated by the gamma distribution, is determined by the percentage of main- shocks in the catalog. This percentage can be calculated by the mean and variance of the interevent times and varies between 5% and 90% for different regions in California. Our investigation of stochastic simulations indicates that the interevent- time distribution provides a nonparametric reconstruction of the mainshock magnitude-frequency distribution that is superior to standard declustering algorithm.

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

Logic trees have become a popular tool in seismic hazard studies. Commonly, the models corresponding to the end branches of the complete logic tree in a probabalistic seismic hazard analysis (psha) are treated separately until the final calculation of the set of hazard curves. This comes at the price that information regarding sensitivities and uncertainties in the ground-motion sections of the logic tree are only obtainable after disaggregation. Furthermore, from this end-branch model perspective even the designers of the logic tree cannot directly tell what ground-motion scenarios most likely would result from their logic trees for a given earthquake at a particular distance, nor how uncertain these scenarios might be or how they would be affected by the choices of the hazard analyst. On the other hand, all this information is already implicitly present in the logic tree. Therefore, with the ground-motion perspective that we propose in the present article, we treat the ground-motion sections of a complete logic tree for seismic hazard as a single composite model representing the complete state-of-knowledge-and-belief of a particular analyst on ground motion in a particular target region. We implement this view by resampling the ground-motion models represented in the ground-motion sections of the logic tree by Monte Carlo simulation (separately for the median values and the sigma values) and then recombining the sets of simulated values in proportion to their logic-tree branch weights. The quantiles of this resampled composite model provide the hazard analyst and the decision maker with a simple, clear, and quantitative representation of the overall physical meaning of the ground-motion section of a logic tree and the accompanying epistemic uncertainty. Quantiles of the composite model also provide an easy way to analyze the sensitivities and uncertainties related to a given logic-tree model. We illustrate this for a composite ground-motion model for central Europe. Further potential fields of applications are seen wherever individual best estimates of ground motion have to be derived from a set of candidate models, for example, for hazard maps, sensitivity studies, or for modeling scenario earthquakes.

Double beam imaging: Mapping lower mantle heterogeneities using combinations of source and receiver arrays

We present a new technique for imaging spatially distributed heterogeneities using information from combinations of source and receiver arrays. The method is based on the single scattering assumption and is closely related to the double beam method of Kruger et al. [1993, 1995, 1996] in that it exploits amplitude, delay time, slowness, and azimuth information in two arrays simultaneously. A crucial step in the method is the application of static time corrections for a chosen reference phase (here PcP). One type of image is obtained as a spatial likelihood distribution for prescribed source and receiver array slowness and azimuth values and delay times with respect to a reference phase. This allows the determination of the spatial origin of coherent phases in the P coda. In a complementary approach, we perform a double beam stack migration according to the theoretical slowness and azimuth values for candidate scatterers distributed over a three-dimensional (3-D) grid. The scattering strength is expressed as the resulting beam power, beam amplitude, or semblance in a time window determined from the theoretical delay time with respect to the reference phase. While likelihood mapping provides an image reflecting the probability of a region to explain observed kinematic phase properties by single scattering, double beam migration provides information about the scattering strength. The method is applied to nuclear explosion sources in eastern Kazakhstan recorded at the Yellowknife array in northern Canada. We identify several scattering volumes within the lower mantle below the arctic producing individual anomalous lower mantle phases in the P coda. These anomalies range in depth from the core-mantle boundary (CMB) up to 500 km into the lowermost mantle and are mainly located under the Eurasian side of the arctic. The joint interpretation of these results with the results of previous studies suggests a connection of these anomalies to the Cenozoic and Mesozoic subduction of the Pacific plate and the Kula plate. The determination of the nature of such 3-D anomalies necessitates further array studies with better azimuthal coverage