Nonlinear Dynamics and Predictability of Geophysical Phenomena

Geophysical Monograph Series......Page 1
GEOPHYSICAL MONOGRAPH SERIES......Page 2
Nonlinear DynaInics andPredictability ofGeophysical PhenoInena......Page 5
CONTENTS......Page 7
PREFACE......Page 8
FOREWORD......Page 10
1. SEVENTEENTH-CENTURY BACKGROUND......Page 11
a Developments in Perturbation Theory......Page 12
b Chaotic Behavior......Page 13
3. LIMITS TO PREDICTABILITY FOR CHAOTICSYSTEMS IN GENERAL......Page 14
REFERENCES......Page 15
INTRODUCTION......Page 16
EARTHQUAKE SEQUENCES......Page 17
SPATIAL HETEROGENEITY......Page 18
HIERARCHICAL AND FRACTAL STRUCTURES......Page 19
REFERENCES......Page 20
INTRODUCTION......Page 23
TRANSITION FROM STABLE SLIDING TO CYCLIC STICK-Slip: EXPERIMENTAL OBSERVATIONS......Page 24
Effect of cumulative slip on the frictional sliding behavior: destabilization vs stabilization......Page 25
Nonlinear dynamical behavior in response to velocity perturbation......Page 27
Dieterich-Ruina friction constitutive relation: multiple state variables and high-speed cutoff of velocity dependence......Page 29
Analytic results for the onset of Hop! bifurcation......Page 30
TRANSITION FROM STABLE SLIDING TO CYCLIC STICK-SLIP: NUMERICAL SIMULATIONS......Page 31
Effect of variations in stiffness and frictional constitutive parameters......Page 32
Effect of velocity perturbation......Page 33
Triggering of dynamic instability by very large velocity perturbations......Page 36
DISCUSSION......Page 37
APPENDIX......Page 39
REFERENCES......Page 42
RECONSTRUCTION OF LITHOSPHERE DYNAMICS FROM THE EARTHQUAKE CATALOG......Page 44
EARTHQUAKE ANALYSIS......Page 45
DISCUSSION AND CONCLUSION......Page 47
REFERENCES......Page 48
INTRODUCTION......Page 49
OBSERVATIONS......Page 50
Time Distribution of Seismic Activity......Page 51
Fractal Analysis of Earthquake Space Distribution......Page 53
Earthquake Size Distribution......Page 55
A POSSIBLE DRIVING MECHANISM FOR EARTHQUAKES......Page 56
EARTHQUAKE PREDICTABILITY: CHANCE OR CERTAINTY?......Page 57
REFERENCES......Page 58
INTRODUCTION......Page 60
PRAcricAL EXAMPLES......Page 61
REFERENCES......Page 64
INTRODUCTION......Page 66
CHAOTIC A'TTRACTORS......Page 67
ALGORITHM FOR NONLINEAR TIME SERIES ANALYSIS......Page 68
IDENTIFICATION OF ATTRACTOR DIMENSION IN LOD TIME SERIES......Page 69
DISCUSSION......Page 70
REFERENCES......Page 71
INTRODUCTION......Page 73
SOC SPRING-BLOCK MODELS OF EARTHQUAKES......Page 74
Temporal Correlations......Page 76
ARE EARTHQUAKES CHAOTIC?......Page 77
REFERENCES......Page 78
INTRODUCTION......Page 79
PERIOD-DOUBLING BIFURCATIONS LEADING TO CHAOS......Page 80
REFERENCES......Page 84
NONLINEAR MODEL......Page 85
RESULTS......Page 87
CONCLUSION......Page 91
REFERENCES......Page 93
INTRODUCTION......Page 94
VARIATIONAL ASSIMILATION METHOD......Page 95
REMOVAL OF SENSITIVITY TO THE INITIAL STATE IN A MODEL VALIDATION......Page 96
REFERENCES......Page 98
FORMULATION OF THE PROBLEM......Page 100
CONSERVATION LAWS IN THE ABSENCE OF FRICTION......Page 101
NONSTATIONARY JUMP CONDITIONS IN THE NEIGHBORHOOD OF THE TONGUE......Page 102
CALCULATION RESULTS......Page 103
THE FIRST CORRECIION TERM DUE TO A LARGE SURFACE TENSION COEFFICIENT......Page 104
REFERENCES......Page 105
INTRODUCTION......Page 106
NOTATION AND ALGORITHM......Page 107
RESULTS AND DISCUSSION......Page 108
REFERENCES......Page 110