Main navigation  Main content
Mathematics in Geosciences, September 2001  June 2002
Frederic Paik Schoenberg
Department of Statistics
University of CaliforniaLos Angeles
frederic@stat.ucla.edu
David
R. Brillinger
Department of Statistics
University of CaliforniaBerkeley
brill@stat.berkeley.edu
Bruce
A. Bolt
Department of Geology and Geophysics
University of CaliforniaBerkeley
boltuc@socrates.berkeley.edu
Statistical methods have proven to be useful in many seismology applications, such as estimation of seismic hazard, assessment of earthquake prediction schemes, and quantification of uncertainties in estimates of earthquake locations or magnitudes. However, there is still much room for further application of statistics in seismology. In particular, much dialog is needed in order for statistical models and methods to be better understood and made more accessible to seismologists. In addition, applied statisticians and point process theorists need to better understand which assumptions may be reasonable, and which statistical methods are useful under conditions appropriate to seismological problems.
This workshop will focus heavily on getting seismologists and other applied earth scientists to learn useful statistical methods and concepts, and on getting statisticians to focus on problems that are of real practical interest. We will experiment with creative ways to get the two groups talking about the overlap of theory and application.
The workshop will focus on several topics, which will be explored in sequence. The topics are listed below. The examination of each topic will be broken up into three parts. The first part will be a tutorial, in which concepts, methods and applications relevant to the topic are surveyed. A purpose of the tutorial is to attempt to bridge the gap between the seismological and statistical and/or mathematical communities and to ensure that all participants can agree on a common terminology. The tutorial will be followed by several lectures, which will have a more technical focus, emphasizing statistical issues of contemporary interest and recent developments with potential seismological applications. Finally, each topic will conclude with an interdisciplinary forum. The forum will provide an opportunity for a statistician or seismologist to present a cuttingedge research problem and provide an opportunity for another participant to respond and for the audience to participate in the discussion. As an illustration, a seismologist could present a new class of problem, discuss its statistical issues, and survey methods of addressing those issues, and a statistician might suggest refinements that may improve upon those methods. Alternatively, a statistician might discuss a new class of models or methods of potential use in seismology, and a seismologist might respond with insights on the nature of how assumptions or methods might be modified in order for statistical methods or results to be more broadly applicable to seismological problems.
The workshop will conclude with a panel discussion of what has been learned and a formulation of how in the future we can examine problems of interest both to seismologists and statisticians. In particular, the panel will report on the following three questions: a) What problems in seismology most deserve immediate attention and how can statisticians help in addressing them; b) What useful statistical methods can be built around assumptions germane to the real world; c) How can we bridge the communication gap between seismologists and statisticians and mathematicians and nurture an ongoing dialog.
The daily topics will include the following.
1) Introduction to earthquakes. This topic will motivate the workshop. Seismic hazard estimation will be examined as a paradigm of a problem in the Earth Sciences for which there already is a repertoire of statistical methodology and substantial room for improvement in the use of statistics.
2) The role of `randomness' in seismology. While seismologists traditionally describe earthquakes via deterministic, physical models, applied statisticians have increasingly explored the use of stochastic, or "random" models for earthquake behavior. It is important to explore questions such as: Which characteristics of earthquakes may usefully described as "random"? What roles can stochastic point process or time series models play in addressing useful seismological problems? In particular, questions of scale come into play, as deterministic models may be useful in describing phenomena which, on a relatively macroscopic scale, appear to behave randomly, and vice versa.
3) Time series versus point processes. The main stochastic models used for describing earthquakes come from the areas of time series and point processes. Time series models are generally used in describing random processes that appear to be sampled at discrete time points. Point processes are useful for modeling random processes that appear at irregularly spaced times, and which may conceivably occur anywhere in a continuum of possible times. Rather little attention has been given to how these two classes of models compare, and in which applications to use one type of model as opposed to the other. These questions will motivate an introduction and discussion of the two types of models in a context that will be both useful and accessible to seismologists and other earth scientists. In addition, special attention will focus on conditional rate (or conditional intensity) models for point process, which have proven useful in describing earthquake occurrences but whose descriptions are rather intricate.
4) Statistical models for seismological processes. Seismologists have predominantly explored physical models in describing earthquakes. Such models are generally deterministic descriptions of physical phenomena and how they interact within a closed and welldefined environment, and typically are expressed as differential equations, ordinary or partial (e.g. Newton's laws of motion). By contrast, statistical models are often used to describe observations of phenomena which are thought to have some inherent variability or which are observed with incomplete information, such as data recorded with error or events occurring at an irregular and uncertain pattern of locations and times. (Sometimes the statistical model incorporates the mathematical solution to a physical model, but in many situations this is not entirely possible.) Statistical models may be especially useful in quantifying uncertainties related to previously observed phenomena as well as to forecasts of future events. We will explore examples of these models in detail, and discuss how they may be used to address basic seismological problems of concern. Of particular interest are point process models including stressrelease processes and other statespace models, branching processes, renewal processes, and mixture models. Special attention will be paid to issues involving spatialtemporal marked point processes and their applications to seismological data.
5) Evaluation of statistical models. Many different statistical models can and indeed have frequently been used to describe the same seismological phenomena. Thus, given a statistical model, a very important and basic question is: how adequately does the model describe the data (observations or simulations) to which it applies, and how does the fit of the model in question compare to competing statistical models? We will survey methods, both graphical and numerical, for assessing goodnessoffit for stochastic models for seismological processes. Further, we will discuss practical implications, including which types of models appear to fit well to which seismic datasets, and what can be deduced in terms of construction of confidence intervals, standard errors, and statistical tests.
Keywords: Risk assessment, seismic hazard estimation, prediction, point process (theory and applications), marked point process, earthquakes, insurance
Monday  Tuesday 
MONDAY,
JUNE 10 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 


Chair: Bruce Bolt 

8:15 am  Coffee and Registration 
Reception Room EE/CS 3176 

9:15 am  Douglas N. Arnold, Robert Gulliver, and Frederic Paik Schoenberg  Welcome and Introduction  
9:30 am  Tutorial:
Bruce Bolt University of CaliforniaBerkeley 
Earthquake Morphology  
10:30 am  Coffee Break  Reception Room EE/CS 3176  
11:00 am 


12:00 pm 
Lunch
Break


1:30 pm  Norm
Abrahamson Pacific Gas & Electric Company, San Francisco, CA 
Methodology for Evaluation of Characteristic Earthquake Models Using Paleoseismic Measurements of Fault Slip from Sites with Multiple Earthquakes  
2:20 pm 


2:30 pm  Coffee Break  Reception Room EE/CS 3176  
3:00 pm  James
W. Dewey U.S. Geological Survey 
Mapping Earthquake Shaking and Earthquake Damage  
3:50 pm 


4:00 pm 


4:30 pm 


TUESDAY,
JUNE
11 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

Chair: David R. Brillinger 

9:00 am  Coffee  Reception Room EE/CS 3176  
9:30 am  David
R. Brillinger University of California, Berkeley 
Uses of point process and time series models in seismic risk analysis (Tutorial) 

10:30 am  Coffee Break  Reception Room EE/CS 3176  
11:00 am  David
Harte Statistics Research Associates, Wellington, New Zealand 
Interpretation and Uses of Fractal Dimensions in Modelling Earthquake Data Slides: pdf postscript 

11:50 am 


12:00 pm 
Lunch
Break


2:00 pm  Didier
Sornette Institute of Geophysics and Planetary Physics and Department of Earth and Space Science at UCLA and LPMC at University of Nice, France 
Renormalized Omori Law, Conditional Foreshocks, Spatial Diffusion and Earthquake Prediction with the Etas Model  
2:50 pm 


3:00 pm 


WEDNESDAY,
JUNE
12 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

Chair: David VereJones 

9:00 am  Coffee  Reception Room EE/CS 3176  
9:30 am  Tutorial:
David VereJones Victoria University, New Zealand 

10:30 am  Coffee Break  Reception Room EE/CS 3176  
11:00 am 


12:00 pm 
Lunch
Break


1:30 pm  Stephen
L. Rathbun Pennsylvania State University 
A Marked SpatioTemporal Point Process Model for California Earthquakes 

2:20 pm 


2:30 pm  Coffee Break  Reception Room EE/CS 3176  
3:00 pm  David
VereJones (on
behalf of Yan
Y. Kagan)
Transparencies (Email questions to kagan@equake.ess.ucla.edu) 
Earthquake Occurrence: Statistical Analysis, Stochastic Modeling, Mathematical Challenges Based to a large degree on the joint paper (Kagan and VereJones, Lecture Notes in Statistics 114, C.C. Heyde et al. eds., New York, Springer, pp. 398425, 1996) Presentation
Slides 

3:50 pm 


4:00 pm 


THURSDAY,
JUNE
13 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

Chair: Yosihiko Ogata 

9:00 am  Coffee  Reception Room EE/CS 3176  
9:30 am  Tutorial
by Yosihiko Ogata Institute of Statistical Mathematics, Tokyo 

10:30 am  Coffee Break  Reception Room EE/CS 3176  
11:00 am  Valerie
Isham University College, London 

11:50 am 


12:00 pm 
Lunch
Break


2:00 pm  Pierre
Brémaud INRIA/ENS 
A review of recent results on Hawkes processes  
2:50 pm 


3:00 pm 


6:00 pm  Workshop Dinner  Gardens
of Salonika 19 N.E. 5th Street, Minneapolis 

FRIDAY,
JUNE
14 All talks are in Lecture Hall EE/CS 3180 unless otherwise noted. 

Chair: Frederic Paik Schoenberg 

9:00 am  Coffee  Reception Room EE/CS 3176  
9:30 am 
Tutorial: Frederic Paik Schoenberg University of California, Los Angeles 

10:30 am  Coffee Break  Reception Room EE/CS 3176  
11:00 am 


12:00 pm 
Lunch
Break


1:30 pm  Lothar
Heinrich Universität Augsburg 

2:20 pm 


2:30 pm  Coffee Break  Reception Room EE/CS 3176  
3:00 pm  Mark
S. Bebbington Massey University, New Zealand 
More ways to burn CPU: A macedoine of tests, scores and validation 

3:50 pm 


4:00 pm 

Monday  Tuesday 
Name

Department  Affiliation 

Norm Abrahamson  &PG&E  
Greg Anderson  US Geological Survey  
Doug Arnold  Institute for Mathematics & its Applications  
Mark Bebbington  Institute of Information Sci & Tech.  Massey University 
Bruce A Bolt  Geology & Geophysics  University of CaliforniaBerkeley 
W. John Braun  Statistics & Actuarial Science  University of Western Ontario 
Pierre Bremaud  Institute of Communications Systems  Ecole Polytechnique Fédérale de Lausanne 
David R. Brillinger  Statistics  University of California, Berkeley 
Daryl Daley  Centre for Mathematics and its Applications  Australian National University 
James Dewey  Geologic Hazards Team  U.S. Geological Survey 
Licia Faenza  Geophysics  University of Bologna 
Robert Gulliver  Institute for Mathematics & its Applications  
David Harte  Statistics Research Associates Limited  Victoria University 
Lothar Heinrich  Institut fur Mathematik  Universitat Augsburg 
Valerie Isham  Statistical Science  University College London 
Steven C. Jaume  Geology  College of Charleston 
Sung Eun Kim  Mathematical Sciences  University of Cincinnati 
Anna Maria Lombardi  
Alexey Lyubushin  Institute of Physics of the Earth  Russian Academy of Sciences 
Maura Murru  Istituto Nazionale di Geofisica e Vulcanologia  
Roger Musson  Global Seismology and Geomagnetism  British Geological Survey 
Robert Nadeau  Earth Sciences  Lawrence Berkeley National Lab 
William I. Newman  Earth and Space Sciences, Physics and Astronomy, and Mathematics  University of California, Los Angeles 
Dan O'Connell  Seismotectonics Group  U.S. Bureau of Reclamation 
Yosihiko Ogata  The Institute of Statistical Mathematics  
Stephen L Rathbun  Statistics  Eberly College of Science  The Pennsylvania State University 
Enders Anthony Robinson  Earth and Environmental Engineering  Columbia University, Henry Krumb School of Mines 
Renata Rotondi  CNR IMATI  
Fadil Santosa  Institute for Mathematics & its Applications  
Michael W. Smiley  Mathematics  Iowa State University 
Didier Sornette  Earth and Space Sciences  University of California, Los Angeles 
Robert Uhrhammer  Seismological Laboratory  University of California  Berkeley 
David VereJones  Mathematics and Computing Sciences  Victoria University 
20012002 IMA Thematic Year on Mathematics in the Geosciences