Earthquake Simulations with Rate and State Friction and Fast Multipoles

2 August 2001


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Table of Contents

Earthquake Simulations with Rate and State Friction and Fast Multipoles

Outline of Talk

Background - What has been done pre multipole

Problems Studied

Perspective View, Parkfield Model

Closer View of Model

Color Scale Added to Fault Plane

Removal of Extra Elements

Slip Velocity Scale Added

Strain Rates on Surface and Scale

Final Display with Time Dial

Video of Model

Fastest Strain Rate on Surface

Increase of Slip Rate Before EQ

Possibility for Predicting Time

Overlay of Parkfield Microseismicity

Reasons More Elements and Hence Multipole Method is Needed

Summary of Previous Results

Problems Studied

Loma Prieta Model Geometry

Background - What has been done pre multipole

General Approach

Background - What has been done pre multipole

Features included

After a Step in Slip Velocity, Friction Evolves with Displacement

True vs. Approximate Rate and State Friction

Friction at High Slip Velocity

Empirical Equations

Differential Equations (state variable eliminated)

Radiation Damping - 1

Radiation Damping - 2

Differential Equations with Radiation Damping - 1, Slip Law

Differential Equations with Radiation Damping - 2, Slowness Law

Background - What has been done pre multipole

Graphical Display - 1

Graphical Display - 2

Illustration of Zooming

1 Min. Before - Hypocenter Cell 105X Ave.

Outline of Talk

Background - Multipole Approach and Fast Multipoles

Problem Common to Many Fault Mechanics Numerical Computations

Idea of Multipole Approximation

Hierarchical Structure of Multipoles

Spatially Adaptive Character of Multipole Approach

Additional Approaches to Make it Fast

Space Filling Curves

Additional Approaches to Make it Fast

A Library Exists That Implements The Fast Multipole Method

Outline of Talk

Code Description - General

Code Description - Restrictions on Grid Geometry

Code Description - Principal Subroutines, 1

Code Description - Principal Subroutines, 2

Code Description - RK4 4th Order Runge-Kutta Integration Scheme

Code Description - RKQC Runge-Kutta Quality Control

Code Description - Changes for multipole

Code Description - Changes for multipole

Code Description - tree.c listing

Code Description - tree.c listing

Code Description - tree.c listing

Code Description - tree.c listing

Code Description - Other changes required for Multipole Library to work with your code

Code Description - Changes to Run in Parallel

Conclusions

Author: Terry E. Tullis

Email: Terry_Tullis@brown.edu

Home Page: www.geo.brown.edu/faculty/ttulllis/index.html