Chapter
Chapter 2: Cosserat Continuum
Kinematics of the Cosserat Continuum
Deviatoric and Spherical Cosserat Strain and Torsion-Curvature
The Slip Direction Along the Faults
The Method of Virtual Power
Deviatoric and Spherical Stress
Linear Case: Isotropic Elasticity
Chapter 3: The Multiple-Slip Mechanism of Plastic Cosserat Deformation
Kinematics of Elastoplastic Cosserat Continuum
Interpretation of the Faulting-Related Cosserat Strain
Chapter 4: Stress Along the Faults
Mohr Representation of Stress
Fault Reactivation in the Cosserat Continuum: Amontons's Law
Chapter 5: Wedge Faulting: The L2 Kinematics
Equation of the Wedge Faulting
Geometry of the Interacting Wedge Systems
Plain Strain and Tectonic Wedges
The Necessity of the Residual Faults
The State of Stress Along Tectonic Wedges
The effect of the stress asymmetry and the couple-stresses
Chapter 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
Stress Permutations and the Homogeneous Cosserat Strain Approximation
Which Nodal Plane is the Fault Plane?
The Ghost Wedges and the Real Wedges
Chapter 7: Båth's Law and the Cosserat Extension of the Reid Rebound Model
Temporal Extension of Båth's Law
Part II: Introduction to the Omega-Theory
Chapter 8: Omega-Sequences
Definition of the Omega-Sequences
General Structure of the Omega-Sequences
Constructing the Omega-Sequences
Constant Strain Rate Model: The CSR Sequences
Constant Velocity Model: The DSR and ISR Omega-Sequences
Time Dependence of the Magnitudes
Transitional Part of the Omega-Sequences
Generalized Equations of the Omega-Sequences (GEOS)
Fibonacci Omega-Sequences
Discussion and Conclusions
Chapter 9: Omega-Cells: ``Seismic Oscillators´´
Internal Structure: Omega-Configurations
Geometric Omega-Configuration
Fibonacci Omega-Configuration
Central Omega-Configuration
Exact Notation for the Omega-Cells
Description of Numerical Tests
Sorting the Earthquakes and Nodal Planes
Identifying the Omega-Sequences
Analysis of the CSV Model for Båth's Law
Reconstructing the Internal Structure of the Omega-Cells: Wedge-Profiling Technique (WPT)
OmegaC257 and OmegaC234567 Sequences: The OmegaC234567-Cell
Omega1P4-Sequence: The Omega1P4-Cell
Proving the CSV Model for Båth's Law
Omega-Cells as Cellular Automata
Omega-Sequences and the B-Signals
Omega-Cells as Octahedral Bodies
Omori's Law and the Omega-Sequences
Results of the Numerical Test
Derivation of Omori's Law
Can Earthquakes be Predicted?
Chapter 11: Felzer-Brodskys Law
Derivation of the Felzer-Brodsky Law
What is Cascade Triggering?
The Full Form of Felzer-Brodskys Law
Chapter 12: Strain Waves and Conservation Laws
Two Bi-Magnitude Signals and the Omega-Cells
Strain Waves: Velocities of the Seismic Migration
The First Conservation Law
The Second Conservation Law
The Third Conservation Law: The Omega Planes
The Fourth Conservation Law
The Meaning of the Static Stress Drop
Discussion: Dynamic Versus Kinematic Approaches
Solutions of the Sine-Gordon Equation
Forward and Backward Migrations
Chapter 13: Phase Transitions
Earth's Crust as a Two-Phases Cosserat Material
Global Solution: The CSR Solution
Vikulin's Scaling Equations: Type 1 Magnitude Shift
Vikulin's Conservation Law
Scaling Laws for the Recurrence Time
Global Solution: The CSR Solution
Discussion and Conclusions
Chapter 14: Gutenberg-Richters Law
Derivation of Gutenberg-Richters Law
Gutenberg-Richters Law in the Omega-Theory
Chapter 15: What Causes Earthquakes?
B1=B2 Sequence Events/Earthquakes
The General Mechanism of Earthquakes (GME)
The Seismic Characteristic Length
The CSV Cosserat Velocity Splitting: The Time Delay in Earthquakes
Cosserat-Huygens Principle
Seismic Generalization of Amontons's Law
Stress and Couple-Stress Vectors on a Fault/Wedge
Four Cosserat Characteristic Lengths in the Omega-Cells
Why Is the B2-Magnitude Signal Not Seismic?
Part III: Systems, Plate Tectonics, and Order
Chapter 16: Omega-Interactions
Clustering of Seismic Events
Binding of Omega-Sequences
Entanglement of Omega-Sequences
Self-Similarity and the Multifractal Nature of Omega-Sequences
Chapter 17: Critical Behavior: Large Earthquakes Can Be Predicted
Subcritical, Critical, and Supercritical Behavior
Critical Behavior: The Kraljevo (2010) Case Study
Regional Geological Setting
Local Geologic Setting and Seismic Catalog
The Critical Behavior Before the Kraljevo (2010) Earthquake
Predictability of the Large Earthquakes
Predicting the Time of the Future Event
Predicting the Magnitude of the Future Event
Predicting the Time Window for the Future Event
Predicting the Kraljevo (2010) Earthquake
Accelerated Moment Release: Benioff Strain Release
Physical Background of the Critical State (Binding and Entanglement)
The Size of the Critical Regions in the Omega-Theory
Chapter 18: Supercritical Behavior: Aftershock Sequences
The Limon Earthquake (1991): Regional Geologic Setting
The First and the Second-Order Omega-Sequences
Analysis of the First-Order Omega-Sequences
Analysis of the Second-Order Omega-Sequences
Predictability of Large Aftershocks
Chapter 19: The B-Spectral Theorem and the Synchronized Earth
Omega-Sequences on the Planetary Scale
How Do We Know That the Planetary Omega-Sequences and Omega-Triplets Are Not Some Coincidental Groupings of Events?
The Full Form of the B-Spectral Theorem
Chapter 20: Quantum Numbers of Earthquakes: Seismic Back Action and Reverse Causality
Generalization of the B-Spectral Theorem
Extrapolation of the Omega-Sequences: The Echo Earthquakes
The Seismic Echo: What Do Two Large Earthquakes Define?
Do Seismic Echoes Really Exist? The Southern California Case Study
Seismic Back Action and Reverse Causality: The Nepal (2015) Case Study
Omega-Limitation Law: The Final Development of the Omega-Sequences
Why Should the Number of Sequence Events be Limited?
The Third Conservation Law for Fault Lengths
The Omega-Limitation Rule and the Omega-Limitation Law
Binding and the Surface Element SOmega(l)
2B-Spectrum and the Extended B-Spectrum
Chapter 21: Seismic Induction and the Theory of Plate Tectonics
The Problem: Introduction
The Theory of Plate Tectonics and the Cosserat Continuum
Basic Postulate of the Plate Tectonics Theory
Why Should Tectonic Plates Interact Each With Other?
Synchronizations and the Tidal Forces
Discussion and Conclusions
Chapter 22: Earthquakes as Computation: Origin of Order
Test 2: Northern Italy Region
Test 3: Brezice Earthquake 2015
Origin of Synchronizations
Conclusions: Earthquakes as Computation
Part IV: Seismic Chaos Synchronizations
Chapter 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
Step 1: Calculating the Generator Set
Step 2: Resolving the Hypocenter/Epicenter of the Future Earthquakes
Step 3: Predicting the Magnitude of Future Events
The Nepal (2015) Experiment
Test 1: Predicting the Nepal (2015) Main Shock
Test 2: Predicting the First Largest Aftershock of the Nepal (2015) Earthquake
Test 3: Calculating the Future Seismic Catalog
Chapter 24: M-Synchronizations: The B-Megasignal and Large Earthquakes
The Magnitude-Synchronization Function
B-Megasignal: The PAPUA New Guinea Case Study
Results and Interpretation: The B-Megasignal
The Southern California Case Study
Results and Interpretation: The Minimum Magnitude Rule
Chapter 25: S-Synchronizations: The Reciprocity Theorem and the Failure Localization Law
Phenomenological Observations
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
Chapter 26: Maximum Effectiveness of Predictions: -1 Rule
Case Study: Northern Italy Region
Demonstration of the -1 Rule
Analysis of the Product State
Test 2: Slovenia-Northern Croatia
Chapter 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 Zuzemberk Region
Part V: Strain Waves, Plate Tectonics, and the Loop Theorem
Chapter 29: Description of Seismic States
Superimposed and Product Seismic States
Superposition Principle: OR Operation
Product States: AND Operation
Product and Entangled States for the Omega-Cell
Stable and Metastable States
Product States and the S-Space Notation
Combined States and Seismic Entanglements
Pure M-synchronization functions
Product, Entangled, and Mixed States
Test 1: Kraljevo Earthquake 2010
Test 2: Emilia Earthquake 2012
Test 3: Seismic Computing
Test 4: Vertical Interactions Between Global and Local Seismic States
Chapter 30: Epicenter Prediction: Turbal's Principle
Strain Waves for the Individual Omega-Sequences
Test 1: Defining the vCSV for Natural Omega-Sequences
The Mechanism of Epicenters: Turbal's Principle
Test 2: The Bovec Earthquake 2015
Test 3: The Brezice Earthquake 2015
Test 4: The Emilia Earthquake 2012
Global Predictions of Large Earthquakes
Analysis of the Global Strain Waves
Test 6: Fast-Interacting Omega-Sequences (FIOS)
Cluster 1 (Day 1; 05/08/2016)
Cluster 2 (Day 2; 06/08/2016)
Test 7: All Strain Waves on 05/08/2016 and 06/08/2016
Chapter 31: Structure of the Aftershock Sequences
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
Kraljevo Earthquake, 03/11/2010
Nepal Earthquake, 25/04/2015
Chapter 32: Synchronizations and Fault Reactivations
Chapter 33: Predictability of Volcanic Eruptions
1980 Mount St. Helens Eruption
2004 Mount St. Helens Eruption
2011 Mount St. Helens Increased Seismic Activity
Chapter 34: Strain Waves at the Tectonic Plates Boundaries
Mid-Atlantic Ridge System
Arabian Sea and Gulf of Aden
Chapter 35: Origin of Plate Tectonics: The Loop Theorem
Introduction to the Loop Theorem
Fault Patterns and Earthquake Interaction Patterns
Periodic, Aperiodic, and Quasiperiodic Patterns
Penrose Tilings of the Plane
Properties of the Penrose Tiling
Ammann Quasilattices: Quasiperiodicity
Inflation and Deflation: Self-Similarity
Earthquake Interaction Patterns
Penrose Clockwork: Toward the Plate Tectonic Theory
Synchronized Stress Permutations as the Internal Motor of the Plate Tectonics
Numerical Test: The Kraljevo Earthquake 2010
Origin of the Global Strain Waves
Mode 1 Deformation of the Lithosphere
Mode 2 Deformation of the Lithosphere
Global Strain Waves and Rotation of the Earth
Discussion and Conclusions: Origin of the Plate Tectonics
The Omega-Theory
：A New Physics of Earthquakes
( Volume 2 )
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