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IMA Workshop
Pint Process Modeling and Seismological Applications of Statistics
June 10-14, 2002

Mathematics in Geosciences, September 2001 - June 2002


Frederic Paik Schoenberg
Department of Statistics
University of California-Los Angeles

David R. Brillinger
Department of Statistics
University of California-Berkeley

Bruce A. Bolt
Department of Geology and Geophysics
University of California-Berkeley


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 cutting-edge 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 well-defined 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 stress-release processes and other state-space models, branching processes, renewal processes, and mixture models. Special attention will be paid to issues involving spatial-temporal 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 goodness-of-fit 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
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
Theme: Introduction to earthquakes
Chair: Bruce Bolt
8:15 am Coffee and Registration

Reception Room EE/CS 3-176

9:15 am Douglas N. Arnold, Robert Gulliver, and Frederic Paik Schoenberg Welcome and Introduction
9:30 am Tutorial: Bruce Bolt
University of California-Berkeley
Earthquake Morphology
10:30 am Coffee Break Reception Room EE/CS 3-176
11:00 am
Forum: "Are earthquakes random?" (Abstract)
11:00 am

Frederic Paik Schoenberg, presents Yan Y. Kagan work

Transparencies   (Email questions to kagan@equake.ess.ucla.edu)

11:10 am David R. Brillinger, University of California, Berkeley rejoins
11:15 am Brillinger presents
11:25 am Schoenberg rejoins
11:30 am Discussion led by Discussants: Robert Nadeau, William Newman
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 3-176
3:00 pm James W. Dewey
U.S. Geological Survey
Mapping Earthquake Shaking and Earthquake Damage
3:50 pm
4:00 pm
Second Chances (Bruce Bolt, moderator)
4:30 pm
IMA Tea/Poster Session
A variety of appetizers and beverages will be served.
400 Lind Hall

K. Borovkov
University of Melbourne and

Mark S. Bebbington
Massey University

A stochastic two-node stress transfer model reproducing Omori's law

Steven C. Jaume
College of Charleston and

Mark S. Bebbington
Massey University

Accelerating Moment Release in Modified Stress Release Models of Regional Seismicity

Slides:   html   pdf  powerpoint

3. Alexey A. Lyubushin
Russian Academy of Sciences http://www.ima.umn.edu/~lyubushi/
Multidimensional Wavelet Analysis of Point Processes

Renata Rotondi
CNR - IMATI, Milano, Italy and

E. Varini
Universiat` "L. Bocconi", Milano, Italy

Bayesian Analysis of a Marked Point Process: Application in Seismic Hazard Assessment
5. Renata Rotondi
CNR - IMATI, Milano, Italy
Renewal processes for great events: Bayesian nonparametric interevent time density estimation
6. Daniel R.H. O'Connell
U.S. Bureau of Reclamation, Denver, Colorado
Do You Live in a Bad Neighborhood?: Maybe Site-Specific PSHA is an Oxymoron

Sung Eun Kim
University of Cincinnati

Robert H. Shumway
University of California, Davis

Multiple Infrasound Arrays Processing
8 Yosihiko Ogata
Institute of Statistical Mathematics, Tokyo
Demonstrations of space-time seismicity analysis (Poster)
9 Maura Murru
Istituto Nazionale di Geofisica e Vulcanologia

Bath's Law and the Gutenberg-Richter Relation

pdf    html    doc

All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
Theme: Uses of time series & point process models in seismology
Chair: David R. Brillinger
9:00 am Coffee Reception Room EE/CS 3-176
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 3-176
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
Second Chances (David Brillinger, moderator)
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
Theme: Stochastic models for earthquake occurrences
Chair: David Vere-Jones
9:00 am Coffee Reception Room EE/CS 3-176
9:30 am Tutorial: David Vere-Jones
Victoria University, New Zealand

Stochastic models for earthquake occurrences

Tutorial Slides

10:30 am Coffee Break Reception Room EE/CS 3-176
11:00 am
Forum: "Which models are acceptable?" (Abstract)
11:00 am Renata Rotondi, CNR/IAMI, Milan presents
11:10 am Daryl Daley, Australian National University rejoins
11:15 am Daley presents
11:25 am Rotondi rejoins
11:30 am Discussion led by Discussants: Alexey Lyubushin, Greg Anderson
12:00 pm
Lunch Break
1:30 pm Stephen L. Rathbun
Pennsylvania State University

A Marked Spatio-Temporal Point Process Model for California Earthquakes

Slides.pdf    Slides.html

2:20 pm
2:30 pm Coffee Break Reception Room EE/CS 3-176
3:00 pm David Vere-Jones (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 Vere-Jones, Lecture Notes in Statistics 114, C.C. Heyde et al. eds., New York, Springer, pp. 398-425, 1996)

Presentation Slides
Debate Contribution Slides Set 1
Debate Contribution Slides Set 2   

3:50 pm
4:00 pm
Second Chances (David Vere-Jones, moderator)
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
Theme: Point process models
Chair: Yosihiko Ogata
9:00 am Coffee Reception Room EE/CS 3-176
9:30 am Tutorial by Yosihiko Ogata
Institute of Statistical Mathematics, Tokyo

Analysis of Seismic Activity Through Point-Process Modeling

Tutorial Slides

10:30 am Coffee Break Reception Room EE/CS 3-176
11:00 am Valerie Isham
University College, London

Applications of point process models in hydrology


11:50 am
12:00 pm
Lunch Break
2:00 pm Pierre Brémaud
A review of recent results on Hawkes processes
2:50 pm
3:00 pm
Second Chances (Yosihiko Ogata, moderator)
6:00 pm Workshop Dinner Gardens of Salonika
19 N.E. 5th Street, Minneapolis
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
Theme: Evaluation of statistical models for earthquakes
Chair: Frederic Paik Schoenberg
9:00 am Coffee Reception Room EE/CS 3-176
9:30 am Tutorial: Frederic Paik Schoenberg
University of California, Los Angeles

Evaluation of statistical models for earthquakes


10:30 am Coffee Break Reception Room EE/CS 3-176
11:00 am
Forum: "Which models seem most promising?" (Abstract)
11:00 am Yosihiko Ogata, Institute of Statistical Mathematics, presents    Forum Slides
11:10 am David Vere-Jones, Victoria University, New Zealand rejoins
11:15 am Vere-Jones presents
11:25 am Ogata rejoins
11:30 am Discussion led by Discussants: Steven Jaume, Dan O'Connell
12:00 pm
Lunch Break
1:30 pm Lothar Heinrich
Universität Augsburg

Testing the Poisson Hypothesis and Higher-Order Normal Approximation for Statistics of Poisson-Based Point Process Models


2:20 pm
2:30 pm Coffee Break Reception Room EE/CS 3-176
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
Second Chances (Frederic Paik Schoenberg, moderator)
Monday Tuesday


As of 6/4/2002 ta
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 California-Berkeley
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 Vere-Jones Mathematics and Computing Sciences Victoria University

2001-2002 IMA Thematic Year on Mathematics in the Geosciences

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