The Omega-Theory

Summary of the Omega-Theory

1. Introduction

Synchronizations of Seismic Chaos and Predictability of EarthquakesAcknowledgmentsReferences 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-SequencesDiscussion 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 MaterialVelocity 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 EarthThe 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

IntroductionStrain Waves as the Cause of the Round-the-World Seismic Echo Sumatra-Andaman Earthquake, 26/12/2004 Tohoku Earthquake, 11/03/2011Relationship 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