The Omega-Theory

The Omega-Theory

A New Physics of Earthquakes

1st Edition - May 10, 2018
  • Author: Jure Žalohar
  • eBook ISBN: 9780128145814
  • Paperback ISBN: 9780128145807

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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

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

Product details

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

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