The Omega-Theory, Volume 2
1st Edition
A New Physics of Earthquakes
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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 Author
Jure Žalohar
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
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