# The Omega-Theory, Volume 2

## 1st Edition

### A New Physics of Earthquakes

**Authors:**Jure Žalohar

**Paperback ISBN:**9780128145807

**eBook ISBN:**9780128145814

**Imprint:**Elsevier

**Published Date:**12th May 2018

**Page Count:**570

**View all volumes in this series:**Developments in Structural Geology and Tectonics

## Table of Contents

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

## Description

*The Omega-Theory: A New Physics of Earthquakes, Second Edition *offers a unifying, mathematical framework to describe and answer the most pressing and unexamined dilemmas of earthquake sequences. Those in the fields of seismology and geology are currently faced with a vast and complex mathematical structure, involving many new, natural laws and theorems. This book interprets this structure as a new physical theory and paradigm, helping users understand the tectonic and seismic processes within the Earth. As such, it is an essential resource for future researchers in the fields of structural geology, physics of the Earth, and seismology.

In the last decades, generations of seismologists, geophysicists, and geologists have accumulated enough knowledge and information to allow for the reformulation and solution of this essential problem. Hence, this book provides a great resource for researchers and professionals.

## 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

## Details

- No. of pages:
- 570

- Language:
- English

- Copyright:
- © Elsevier 2018

- Published:
- 12th May 2018

- Imprint:
- Elsevier

- Paperback ISBN:
- 9780128145807

- eBook ISBN:
- 9780128145814

## Ratings and Reviews

## About the Authors

### Jure Žalohar Author

Dr. Zalohar is a physicist and geologist working as an independent researcher, giving scientific and philosophical lectures at various institutions. He obtained his Ph.D. from the University of Ljubljana in 2008. Dr. Zalohar’s main research fields are physics of faults and earthquakes, stratigraphy, and palaeontology. Among his most important achievements are a series of articles on the Cosserat mechanics of faulting for the Journal of Structural Geology and the development of the T-TECTO software for fault-slip data and earthquakes analysis, which is now recognized and used by structural geologists around the world. During numerous field trips observing tectonic structures in the Alps he and his colleagues made important paleontological discoveries, including identifying the oldest and only-known fossils of seahorses, pipehorses and pygmy pipehorses, new fossil sites with complete skeletons of Triassic reptilians, and fish and other biota from the Tethys ocean. His most important contribution to science is a discovery of a new physical theory of earthquakes that brings a redefinition and solution of the earthquake prediction problem.

### Affiliations and Expertise

PhD Geology, BSc Physics, Structural Geology, Seimology, Software Developer, TH Quantectum AG