# The Omega-Theory

### A New Physics of Earthquakes

## Description

## Key Features

- Brings together twenty years of research in the field of geophysics and attacks the problem within the framework of the Cosserat continuum theory
- Heavily tested on tens of natural examples and numerical tests
- Includes 350 color figures and graphs
- Spans across many fields of theoretical physics and geology, such as plate tectonics, synchronization of chaotic systems, solitons and fractals, mathematical set theory, and quantum mechanics

## Readership

Structural geologists, Seismologists, Researchers in the field of Plate tectonics, Chaotic synchronization, and Earthquake forecasting/prediction theory

## Table of Contents

Summary of the Omega-Theory

1. Introduction

Synchronizations of Seismic Chaos and Predictability of Earthquakes

Acknowledgments

References

Further ReadingI 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 Reading3. The Multiple-Slip Mechanism of Plastic Cosserat Deformation

Kinematics of Elastoplastic Cosserat Continuum

References4. Stress Along the Faults

Mohr Representation of Stress

Fault Reactivation in the Cosserat Continuum: Amontons’s Law

References5. Wedge Faulting: The L2 Kinematics

Equation of the Wedge Faulting

The effect of the stress asymmetry and the couple-stresses

References

Further Reading6. 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

References7. Båth’s Law and the Cosserat Extension of the Reid Rebound Model

Introduction

Simple Models of Faults

Derivation of Båth’s Law

ReferencesII 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

References9. Omega-Cells: “Seismic Oscillators”

External Structure

Internal Structure: Omega-Configurations

Description of Numerical Tests

Results

Discussion

References10. Omori’s Law

Omori’s Law and the Omega-Sequences

Derivation of Omori’s Law

Can Earthquakes be Predicted?

References11. Felzer-Brodsky’s Law

Derivation of the Felzer-Brodsky Law

Discussion

References12. 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

References13. 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

References14. Gutenberg-Richter’s Law

Derivation of Gutenberg-Richter’s Law

Discussion

References15. 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

ReferencesIII 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 Reading17. 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 Reading18. Supercritical Behavior: Aftershock Sequences

The First and the Second-Order Omega-Sequences

Discussion

References19. The B-Spectral Theorem and the Synchronized Earth

The B-Spectral Theorem

The Synchronized Earth

The Full Form of the B-Spectral Theorem

Reference20. 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

References21. 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 Reading22. 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 ComputationIV 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

References24. 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

References25. 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

References26. Maximum Effectiveness of Predictions: - 1 Rule

Case Study: Northern Italy Region

Conclusions27. Open Systems

Mathematical Formalism

Test 1: Central Italy

Test 2: Slovenia-Northern Croatia

Conclusions

References28. 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

ReferencesV 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

References30. 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

References31. 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

References32. Synchronizations and Fault Reactivations

Introduction

Ravne Fault, Slovenia

North Anatolian Fault

Conclusions

References33. Predictability of Volcanic Eruptions

1980 Mount St. Helens Eruption

2004 Mount St. Helens Eruption

2011 Mount St. Helens Increased Seismic Activity

Conclusions

References34. Strain Waves at the Tectonic Plates Boundaries

The California Region

The Japan Region

Mid-Atlantic Ridge System

Arabian Sea and Gulf of Aden

Conclusions

References35. 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

## Product details

- No. of pages: 570
- Language: English
- Copyright: © Elsevier 2018
- Published: May 10, 2018
- Imprint: Elsevier
- eBook ISBN: 9780128145814
- Paperback ISBN: 9780128145807