2008

2006

Earthquake dynamics: models and observations

Raul Madariaga
Laboratoire de Géologie
Ecole Normale Supérieure
Paris, France

Understanding of the rupture process of individual earthquakes – rupture dynamics - has made substantial progress in recent year leading to a reappraisal of certain classical concepts of friction laws and the energy balance of seismic ruptures. One of the most important features, predicted by seismologists and phycisists in the eighties and now currently observed, is that earthquakes are complex at all scales and that complexity can not be simply filtered out because it determines scaling, the way moment, energy and other integral properties of seismic source scale with size or magnitude.  A key to understanding earthquake dynamics is the proper understanding of seismic wave radiation. Indeed, waves recorded in the vicinity of the fault are used to invert for the details of rupture using a mixture of kinematic and quasi-dynamic methods.  A significant number of earthquakes have been studied in detail by these techniques. Unfortunately, in order to stabilize the inverse problem, many authors are forced to make assumptions about rupture velocity and the propagation of rupture on the fault. The combination of GPS, seismic and geologic data contributes to improve inversions, but they are yet to produce stable solutions for rupture velocity. For certain earthquakes super-shear rupture has been inferred from near field data, notably Izmit and Alaska. In spite of this considerable progress in understanding earthquake dynamics, there are still a number of obscure points about elastic energy radiation and its role in controlling rupture. Several authors determined that apparent energy release rate was of the order of several MJ/m**2 for earthquakes of magnitude 7.3 or so, a huge number that probably reflects the fact that seismic rupture do not occur on a simple fault surface as modeled in laboratory experiments. Recently, Ide and Favreau and Archuleta showed that total energy release rate during the Imperial Valley and Kobe earthquakes was of the same order of magnitude as radiated energy and strain energy released by those earthquakes. This seems to confirm, the claim by Madariaga and Olsen that earthquakes propagate at an almost critical level so that the Griffith criterion for shear rupture is barely satisfied. This may explain why super-shear rupture is only observed in very special circumstances. So far, inversion has been used to study earthquakes at relatively long wavelengths, extending these results to higher frequencies requires improved understanding of the fundamentals of seismic energy balance which remain obscure, even if the fundamental theorems were established by Kostrov 30 years ago.

Introducing Stochasticity in the Computation of Fragility Curves

Dr. Guillermo Franco
Post-doctoral Research Fellow
The Earth Institute at Columbia University
New York, USA

In the spring of 2002, an interdisciplinary team from Bogazici University and from Columbia University among other institutions, assessed the vulnerability of a typical residential building in Kadikoy, in the southeastern part of Istanbul. The fragility curves, which describe the vulnerability of the building in an earthquake scenario, where used to carry out a subsequent cost-benefit analysis of three possible retrofits.
The fragility curves were elaborated on the basis that an accurate description of the structure was available, like precise geometric measurements and precise data on the quality of the materials employed. This information is often not at hand and a high degree of stochasticity is associated with these values.

During the last months, a method has been developed to account for stochasticity in all the parameters that describe the structure within the process of elaborating the fragility curves. With a set of easy-to-use computer programs, it is now possible to include a broad range of variation of the structure in the fragility analysis. This process results in widely applicable fragility results which can be implemented into GIS systems or in ulterior economic analyses.

In the presentation, this methodology will be explained along with some examples and the programs will be analyzed briefly. Also, some lines for the potential continuation of this work will be suggested and discussed.

Stochastic Green’s Function Technique with Characterized Source Model and Phase Dependent Site Response: Case of the Düzce Basin, Turkey 

Dr. Gülüm Birgören
Bogazici University, KOERI,
Department of Earthquake Engineering,
Istanbul, Turkey

This study discusses the improvement of strong ground motion simulation at basin sites with the Stochastic Green’s Function Simulation Method using an empirical site response estimation technique. Traditional approaches to calculating site responses in places underlain by sedimentary layers do not effectively take into account the phase properties of a seismic signal. However, the phase part of the signal keeping arrival times of seismic waves becomes essential when the basin induced waves are considered. The site response estimation technique proposed in the present study preserves both amplitude and phase parts of the site response in the analysis so that the extended duration of the earthquake motion can be simulated realistically for the regions whose velocity structure information is limited.

An application of the site response estimation technique has been performed using the aftershock data set of the 1999 Düzce, Turkey Earthquake recorded at observation stations inside and outside of the Düzce Basin. Generation of the Stochastic Green’s Functions and consequently, the mainshock simulation of the 1999 Düzce, Turkey Earthquake (Mw: 7.1) with a characterized source model and phase dependent site response have been carried out for the frequency range of 0.5-10 Hz at selected stations. The observed and synthesized ground motions are highly compatible, which reflects the efficiency of the method.

Earthquake Ground Motion in the San Francisco Bay Area Using Fully Three-Dimensional Finite Difference Simulations

Arthur Rodgers
Lawrence Livermore National Laboratory
Livermore, CA USA

Simulation of earthquake ground motions is important for understanding damaging motions from past earthquakes and predicting motions from possible future large scenario events.  We are modeling earthquake ground motions in the San Francisco Bay Area using a three-dimensional (3D) geologic/seismic model of the region and anelastic finite difference method.  The 3D model was created by the USGS-Menlo Park (Brocher et al., 2006).  For the simulations we use a new open-source anelastic finite difference code, called WPP.  WPP is a second-order node-centered code passed upon the summation by parts principle.  The code features depth-dependent mesh refinement for memory and computational efficiency.  We have used WPP to model moderate (M_W 4-5) earthquakes to test ground motion predictions from the USGS 3D model.  These events are well suited for the testing the model because they can be represented as simple point double-couple sources.  Results indicate that the model predicts features in the data related to complex 3D structure, suggesting that the model can be used for scenario earthquake simulations with reasonable confidence.  We have simulated large (M_W ~ 7) scenario earthquakes on the Hayward Fault as part of a multi-institutional effort lead by the USGS. 

This figure shows the vertical displacement for the August 8, 2003 Glen Ellen earthquake (circle) with focal mechanism shown and the USGS 3D model of the region (left).  Three-component observed (blue) and computed (red) ground displacements are compared in the band 33-4 seconds (0.03-0.25 Hz) (right).  Note that the long duration Love coda on the transverse component is well modeled by the synthetics.