The Omega-Theory

Summary of the Omega-Theory

1. Introduction

Synchronizations of Seismic Chaos and Predictability of Earthquakes
Acknowledgments
References
Further Reading

I COSSERAT CONTINUUM THEORY OF FAULTING

2. Cosserat Continuum

Notation
Kinematics of the Cosserat Continuum
The Method of Virtual Power
Hyperelasticity
J2 Plasticity Model
References
Further Reading

3. The Multiple-Slip Mechanism of Plastic Cosserat Deformation

Kinematics of Elastoplastic Cosserat Continuum
References

4. Stress Along the Faults

Mohr Representation of Stress
Fault Reactivation in the Cosserat Continuum: Amontons’s Law
References

5. Wedge Faulting: The L2 Kinematics

Equation of the Wedge Faulting
The effect of the stress asymmetry and the couple-stresses
References
Further Reading

6. Parallel Fault and Parallel Wedge Interactions: The Gamma-Scheme

Three Possible Types of Parallel Fault Interaction
Parallel Wedge Interaction
Stress Permutations and Parallel Wedge Interactions
References

7. Båth’s Law and the Cosserat Extension of the Reid Rebound Model

Introduction
Simple Models of Faults
Derivation of Båth’s Law
References

II INTRODUCTION TO THE OMEGA-THEORY

8. Omega-Sequences

Definition of the Omega-Sequences
General Structure of the Omega-Sequences
Constructing the Omega-Sequences
Generalized Equations of the Omega-Sequences (GEOS)
Numerical Tests
Fibonacci Omega-Sequences
Discussion and Conclusions
References

9. Omega-Cells: “Seismic Oscillators”

External Structure
Internal Structure: Omega-Configurations
Description of Numerical Tests
Results
Discussion
References

10. Omori’s Law

Omori’s Law and the Omega-Sequences
Derivation of Omori’s Law
Can Earthquakes be Predicted?
References

11. Felzer-Brodsky’s Law

Derivation of the Felzer-Brodsky Law
Discussion
References

12. Strain Waves and Conservation Laws

Two Bi-Magnitude Signals and the Omega-Cells
The Kobayashi Equation
Strain Waves: Velocities of the Seismic Migration
Conservation Laws
The Meaning of the Static Stress Drop
Discussion: Dynamic Versus Kinematic Approaches
References

13. Phase Transitions

Earth’s Crust as a Two-Phases Cosserat Material
Velocity Transference
Vikulin’s Scaling Equations: Type 1 Magnitude Shift
Vikulin’s Conservation Law
Scaling Laws for the Recurrence Time
Type 2 Magnitude Shift
Discussion and Conclusions
References

14. Gutenberg-Richter’s Law

Derivation of Gutenberg-Richter’s Law
Discussion
References

15. What Causes Earthquakes?

The General Mechanism of Earthquakes (GME)
Seismic Generalization of Amontons’s Law
Why Is the B2-Magnitude Signal Not Seismic?
A Link to the LEFM
References

III SYSTEMS, PLATE TECTONICS, AND ORDER

16. Omega-Interactions

Clustering of Seismic Events
Binding of Omega-Sequences
Entanglement of Omega-Sequences
Self-Similarity and the Multifractal Nature of Omega-Sequences
Disturbances
Transitions
Discussion
The Omega-Cycle
What Is Entangled?
References
Further Reading

17. Critical Behavior: Large Earthquakes Can Be Predicted

Subcritical, Critical, and Supercritical Behavior
Critical Behavior: The Kraljevo (2010) Case Study
Predictability of the Large Earthquakes
Predicting the Kraljevo (2010) Earthquake
Discussion
References
Further Reading

18. Supercritical Behavior: Aftershock Sequences

The First and the Second-Order Omega-Sequences
Discussion
References

19. The B-Spectral Theorem and the Synchronized Earth

The B-Spectral Theorem
The Synchronized Earth
The Full Form of the B-Spectral Theorem
Reference

20. Quantum Numbers of Earthquakes: Seismic Back Action and Reverse Causality

The B-Spectral Theorem
Ideal Omega-Sequences
Generalization of the B-Spectral Theorem
Extrapolation of the Omega-Sequences: The Echo Earthquakes
The Seismic Echo: What Do Two Large Earthquakes Define?
Seismic Back Action and Reverse Causality: The Nepal (2015) Case Study
Omega-Limitation Law: The Final Development of the Omega-Sequences
The Twinning Effect
2B-Spectrum and the Extended B-Spectrum
Discussion
References

21. Seismic Induction and the Theory of Plate Tectonics

The Problem: Introduction
The Theory of Plate Tectonics and the Cosserat Continuum
Why Should Tectonic Plates Interact Each With Other?
Forces of Interaction
Discussion and Conclusions
References
Further Reading

22. Earthquakes as Computation: Origin of Order

Test 1: Slovenia Region
Test 2: Northern Italy Region
Test 3: Brezˇice Earthquake 2015
Origin of Order
Origin of Synchronizations
Conclusions: Earthquakes as Computation

IV SEISMIC CHAOS SYNCHRONIZATIONS

23. T-Synchronizations: Predicting Future Seismic States of the Earth

The Synchronization Equation
The Omega-Interactions: Binding, Entanglement, and Synchronization Function
Predicting the Future Seismic States of the Earth
The Nepal (2015) Experiment
References

24. M-Synchronizations: The B-Megasignal and Large Earthquakes

The Magnitude-Synchronization Function
B-Megasignal: The Papua New Guinea Case Study
The Southern California Case Study
References

25. S-Synchronizations: The Reciprocity Theorem and the Failure Localization Law

Phenomenological Observations
The Reciprocity Theorem
The B-Spectral Theorem and the MARS Structure
Seismic Activity of the MARS
The Failure Localization Law
Verifying the Failure Localization Law
Confirmation of the Third Conservation Law
References

26. Maximum Effectiveness of Predictions: - 1 Rule

Case Study: Northern Italy Region
Conclusions

27. Open Systems

Mathematical Formalism
Test 1: Central Italy
Test 2: Slovenia-Northern Croatia
Conclusions
References

28. Further Observations on S-Synchronizations

Visualizing Spatial Interactions Between the Earthquakes
Test 1: Distribution of Nonsynchronized Earthquakes
Test 2: Distribution of Synchronized Earthquakes
Test 3: Region of Slovenia
Test 4: Analysis of the Žužemberk Region
Conclusions
References

V STRAIN WAVES, PLATE TECTONICS, AND THE LOOP THEOREM

29. Description of Seismic States

Superimposed and Product Seismic States
T-Synchronizations
M-Synchronizations
Seismic Computing
Testing the LE-Rule
Conclusions
References

30. Epicenter Prediction: Turbal’s Principle

Strain Waves for the Individual Omega-Sequences
The Mechanism of Epicenters: Turbal’s Principle
Global Predictions of Large Earthquakes
Analysis of the Global Strain Waves
Conclusions
References

31. Structure of the Aftershock Sequences

Introduction
Strain Waves as the Cause of the Round-the-World Seismic Echo
Sumatra-Andaman Earthquake, 26/12/2004
Tohoku Earthquake, 11/03/2011
Relationship Between the Foreshocks and Aftershocks
Conclusions
References

32. Synchronizations and Fault Reactivations

Introduction
Ravne Fault, Slovenia
North Anatolian Fault
Conclusions
References

33. Predictability of Volcanic Eruptions

1980 Mount St. Helens Eruption
2004 Mount St. Helens Eruption
2011 Mount St. Helens Increased Seismic Activity
Conclusions
References

34. Strain Waves at the Tectonic Plates Boundaries

The California Region
The Japan Region
Mid-Atlantic Ridge System
Arabian Sea and Gulf of Aden
Conclusions
References

35. Origin of Plate Tectonics: The Loop Theorem

Introduction to the Loop Theorem
Fault Patterns and Earthquake Interaction Patterns
The Loop Theorem
Tilings and Tiles
Properties of the Penrose Tiling
Earthquake Interaction Patterns
Penrose Clockwork: Toward the Plate Tectonic Theory
Origin of the Global Strain Waves
Discussion and Conclusions: Origin of the Plate Tectonics
References