Earthquake and Volcano Deformation

Transcription

1 Earthquake and Volcano Deformation Paul Segall Stanford University Draft Copy September, 2005 Last Updated Sept, 2008 COPYRIGHT NOTICE: To be published by Princeton University Press and copyrighted, c 2007 by Paul Segall. All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. Users are not permitted to mount this file on any network servers. For more information, send to permissions@press.princeton.edu.

2 Contents 1 Deformation, Stress, and Conservation Laws Strain Strains in Curvilinear Coordinates Rotation Stress Coordinate Transformations Principal Strains and Stresses Compatibility equations Conservation Laws Equilibrium equations in curvilinear coordinates Constitutive Laws Reciprocal Theorem Dislocation Models of Strike Slip Faults Full Space Solution Half Space Solution Coseismic Faulting Interseismic Deformation Postseismic Slip Distributed Slip Application to the San Andreas and Other Strike Slip Faults Displacement at Depth Summary Dip Slip Faults and Dislocations in Three Dimensions Volterra s Formula Body Force Equivalents and Moment Tensors Screw Dislocations Two Dimensional Edge Dislocations

3 4 CONTENTS Dipping Fault Coseismic Deformation Associated with Dipping Faults Displacements and Stresses due to Edge Dislocation at Depth Dislocations in three dimensions Full Space Green s Functions Half-Space Green s Functions Point Source Solutions Finite rectangular sources Examples Distributed Slip Strain Energy Change due to Faulting Problems References Crack Models of Faults Inversion of the Integral Equation Displacement on Earth s Surface A Brief Introduction to Fracture Mechanics Non Singular Stress Distributions Comparison of Slip Distributions and Surface Displacements Boundary Element Methods Fourier Transform Methods Some Three Dimensional Crack Results Problems References Elastic Heterogeneity Long Strike-Slip Fault Bounding Two Media Strike-Slip Fault Within a Compliant Fault Zone Strike-Slip Fault Beneath a Layer Strike-Slip Within a Layer over Half-space Propagator Matrix Methods The Propagator Matrix for Antiplane Deformation Vertical Fault in a Homogeneous Half-Space Vertical Fault Within Half-Space Beneath a Layer Vertical Fault in Layer over Half-Space General solution for an arbitrary number of layers Displacements and Stresses at Depth Propagator Methods for Plane Strain Propagator Solutions in Three Dimensions

4 CONTENTS Approximate Solutions for Arbitrary Variations in Properties Variations in Shear Modulus Screw dislocation Edge dislocation Effects of Elastic Heterogeneity on Inversions Problems References Postseismic Relaxation Elastic Layer over Viscous Channel Visco-Elasticity Correspondence Principle Strike-slip Fault in an Elastic Plate overlying a Viscoelastic Half-space Stress in Plate and Half-Space Strike Slip Fault in Elastic Layer Overlying a Viscoelastic Channel Dip Slip Faulting Examples Three Dimensional Calculations Concluding Remarks References Problems Volcano Deformation Spherical Magma Chamber Center of Dilatation Volume of the uplift, magma chamber, and magma Ellipsoidal Magma Chambers Magmatic Pipes and Conduits Dikes and Sills Crack models of dikes and sills Surface Fracturing and Dike Intrusion Other Magma Chamber Geometries Viscoelastic Relaxation Around Magma Chambers Problems References Topography and Earth Curvature Scaling Considerations Implementation Considerations Center of Dilatation beneath a volcano

5 6 CONTENTS 8.4 Earth s Sphericity Summary Problems References Gravitational Effects Non-dimensional Form of Equilibrium Equations Inclusion in propagator formulation Surface Gravity Approximation Gravitational effects in viscoelastic solutions Incompressible Half-Space No Buoyancy Approximation Wang approach Comparison of Different Viscoelastic Models Relaxed Viscoelastic Response Changes in Gravity Induced by Deformation Gravity Changes and Volcano Deformation An Example Problems Poroelastic Effects Constitutive Laws Macroscopic Descriptions Micromechanical Description Field Equations Analogy to Thermoelasticity One Dimensional Deformation Step Load on the Free Surface Time varying fluid load at the free surface Dislocations in Two Dimensions Inflating Magma Chamber in a Poroelastic Half-Plane Cummulative Poroelastic Deformation in Three Dimensions Solution when pore pressure distribution is known References Exercises Fault Friction Slip Weakening Friction Velocity Weakening Friction Rate and State Friction

6 CONTENTS Linearized Stability Analysis Implications for earthquake Nucleation Spring-Slider Stick Slip Cycles Non-linear stability analysis Afterslip Transient Slip Events Concluding Remarks Problems References Interseismic Deformation and Plate Boundary Cycle Models Elastic Dislocation Models Dip-slip faults Plate Motions Elastic Block Models Viscoelastic Cycle Models Viscoelastic Strike-Slip Earthquake Cycle Models Comparison to data from San Andreas Fault Viscoelastic Models with Stress Driven Deep Fault Creep Viscoelastic Cycle models For Dipping Faults Rate-State Friction Earthquake Cycle Models References Problems A Integral Transforms 495 A.1 Fourier Transforms A.2 Laplace Transforms B A Solution to the Diffusion Equation 501 C Solution of an Integral by Contour Methods 505