Eugeniusz Majewski

Earthquake source asymmetry, structural media and rotation effects

Macroseismic Rotation Effects and Micromotions.- Development of Earthquake Rotational Effect Study.- Sources of Rotation and Twist Motions.- Some Examples of Rotation Effects: the Tulbagh Earthquake, South Africa.- Theory of Continua and Fields of Defects.- Deviations from Symmetry and Elasticity: Asymmetric Continuum Mechanics.- Degenerated Asymmetric Continuum Theory.- Continuum with Rotation Nuclei and Defects: Dislocation and Disclination Densities.- Towards a Discrete Theory of Defects.- Fault Dynamics and Related Radiation.- A Review on Friction.- Soliton Physics.- Rotation Motions, Seismic Source Models, and Asymmetry of Fracture.- Rotational Motions Excited by Earthquakes.- Ground Rotational Motions Recorded in Near-Source Region of Earthquakes.- Fracture-Band Geometry and Rotation Energy Release.- Rotation Motions: Recording and Analysis.- Glacier Motion: Seismic Events and Rotation/Tilt Phenomena.- Rotational Energy and Angular Momentum of Earthquakes.- Bend-Rotation Wave as a Mechanism of Macroseismic Effects.- Solitary Waves in Crustal Faults and their Application to Earthquakes.- Seismic Rotation Waves: Spin and Twist Solitons.- Earth Rotation, Elasticity and Geodynamics: Earthquake Wave Rotary Model.- Effects Related to Medium Structures and Complexity of Wave Propagation.- Seismic Rotation Waves in the Continuum with Nonlinear Microstructure.- Tectonic Solitons Propagating Along the Fault.- Complexity of Rotation Soliton Propagation.- Micromorphic Continuum with Defects and Taylor-Bishop-Hill Theory for Polycrystals: Anisotropic Propagation of Seismic Waves and the Golebiewska Gauge.- Seismic Ray Theory for Structural Medium based on Kawaguchi and Finsler Geometry.- From Non-Local to Asymmetric Deformation Field.- Earthquake Hazard in the Valley of Mexico: Entropy, Structure, Complexity.- Seismic Rotational Motions: Recording Techniques and Data Analysis.- Note on the Historical Rotation Seismographs.- Ring Laser Gyroscopes as Rotation Sensors for Seismic Wave Studies.- Rotational Motions in Seismology: Theory, Observation, Simulation.- Absolute Rotation Measurement Based on the Sagnac Effect.- Design of Rotation Seismometer and Non-Linear Behaviour of Rotation Components of Earthquakes.- Rotation and Twist Motion Recording - Couple Pendulum and Rigid Seismometers System.- Equation of Pendulum Motion Including Rotations and its Implications to the Strong-Ground Motion.- Strong Motion Rotation Sensor.- High-Resolution Wide-Range Tiltmeter: Observations of Earth Free Oscillations Excited by the 26 December 2004 Sumatra -Andaman Earthquake.- Fiber Optic Sensors for Seismic Monitoring.- Rotations and Engineering Seismology.- Deriving Seismic Surface Rotations for Engineering Purposes.- Effects of Torsional and Rocking Excitations on the Response of Structures.

Physics of Asymmetric Continuum: Extreme and Fracture Processes

to Asymmetric Continuum and Experimental Evidence of Rotation Motions.- to Asymmetric Continuum: Fundamental Point Deformations.- Measurement of Short-Period Weak Rotation Signals.- Buildings as Sources of Rotational Waves.- Two-Pendulum Systems for Measuring Rotations.- Theory and Observations: Some Remarks on Rotational Motions.- Continuum with Defect Densities and Asymmetry of Fields.- Field Invariant Representation: Dirac Tensors.- Asymmetric Continuum: Standard Theory.- Fracture Processes: Spin and Twist-Shear Coincidence.- Inplane and Antiplane Fracturing in a Multimode Random Sequence.- 10 Charged Dislocations and Various Sources of Electric Field Excitation.- Friction and Fracture Induced Anisotropy: Asymmetric Stresses.- Asymmetric Fluid Dynamics: Extreme Phenomena.- Fracture Band Thermodynamics.- Interaction Asymmetric Continuum Theory.- Fracture Physics Based on a Soliton Approach.- Canonical Approach to Asymmetric Continua.- Deformations in Riemannian Geometry.- Continuum Theory of Defects: Advanced Approaches.- Spinors and Torsion in a Riemann-Cartan Approach to Elasticity with a Continuous Defect Distribution and Analogies to the Einstein-Cartan Theory of Gravitation.- Twistors as Spin and Twist Solitons.- Potentials in Asymmetric Continuum: Approach to Complex Relativity.

Spinors and Twistors in the Description of Rotational Seismic Waves and Spin and Twist Solitons

Abstract A noncommutative (anti-) self-dual Yang–Mills theory as a source of multisoliton solutions of nonlinear wave equations was applied to the description of rotational seismic waves that are excited in the earthquake source. Spinors and twistors are used to describe spin and twist solitons branching off dispersion curves for rotational seismic waves. Complex physical structures are adopted to describe spin and twist effects resulting from the presence of translational and rotational defects in elastic rocks. A seismic space is also assumed to have a complex structure. An earthquake source zone is modeled by a set of equations for interacting fields that is mathematically similar to the noncommutative (anti-) self-dual Yang–Mills equations. Some similarities between dislocations and strings are emphasized, for example, those that exist between surface defects and D-branes in string theories. Dislocations and disclinations are treated as sources for seismic spin and twist fields. By symmetry reduction various soliton equations for seismic spin and twist solitons can be obtained from the set of earthquake source zone equations, which is similar to the noncommutative (anti-) self-dual Yang–Mills equations by symmetry reduction.

Rotational Energy and Angular Momentum of Earthquakes

This chapter briefly presented a few models of rotational motions in the earthquake source. At first, rolling motions were considered and the kinetic energy of rolling was formulated. The second model deals with purely rotational motions. The kinetic energy, work, power, and angular momentum for this model were expressed in terms of earthquake dimensions and the total tectonic slip on the fault. The third model treats rotational motions in the earthquake source as turbulence of grains and blocks between moving tectonic plates. A general approach to the turbulence was discussed. A balance equation for the angular momentum was shown. An angular momentum for a small turbulent eddy was defined.

Chapter 13 – Thermodynamics of Fault Slip

This chapter focuses on the thermodynamic aspects underlying the behavior of faults during earthquake processes. It considers the molecular structure of a fault zone with emphasis on determining a measure of the knowledge, an external observer gains with respect to the occurrence of breaking bonds in the fault zone during an earthquake process. Fault entropy is formulated and related to the seismic moment that gives a physically meaningful description of earthquake size. The chapter also explores stochastic faulting processes instead of deterministic faults when predictions are required that are applicable to computation and measurements. According to information thermodynamics, entropy is a measure of missing information or the lack of knowledge about the molecular structure of the fault zone. It is always positive. Thermal entropy measures ignorance or lack of knowledge about the precise microstates of the molecules in the fault zone, while its macroscopic state is completely described by the seismic moment, shear stresses, temperature, volume, and other macroscopic parameters. The lack of knowledge of the exterior observer about the molecular structure inside a fault is large.

15 - Physics of Earthquakes

This chapter reviews the state of the art of physics of earthquakes and microscopic fracturing. It briefly discusses current knowledge about the classical macroscopic approach to fault zone dynamics with emphasis on the advantages and disadvantages of this formulation. The chapter also examines an elastic continuum medium with defect content. It concludes with discussion of various aspects of the earthquake models and explores how physical effects such as self-organized criticality, chaos, and complexity arise. Fracture proceeds through the nucleation, growth, coalescence, and fragmentation phases. In the microfracturing processes, the microcracks and voids play the role of the main objects. Models of crack nucleation are based on the hierarchical structure of the formation of slip-bands, grain boundary sliding, dislocation pile-ups, dislocation-to-crack transition, and microcrack formation. The formation of dislocation arrays and interactions among the groups of dislocations of opposite signs lead to the coalescence processes. The chapter aims to trace the development of the deformation from its roots at the atomic level to its macroscopic manifestation in earthquake faulting.

Thermodynamics with rotation motions: Fragmentation and slip

Basing on the Asymmetric Continuum Theory, we develop the thermodynamics including fragmentation spin fracture processes; applications for the earthquake source processes are considered. The fracture band model is used to describe a dislocation and disclination superlattice. The Gibbs free energy of defect formation is specified. A dynamic spin fracture criterion was formulated. Consequently, a dynamic model of rock fracture employing dislocations, disclinations, and cracks was constructed to describe slip and fragmentation fracture processes in the earthquake sources.

Twistors as Spin and Twist Solitons

Penrose and Rindler (1986) applied twistors to describe massless spinning particles. They pointed out that twistors can describe twisted photons or charges for massless spin-3/2 fields. Due to the well-known particlesoliton duality, it seems reasonable to relate twistors with spin and twist solitons. We adopt the twistor quantization theory developed by Penrose and Rindler (1986) and employ twistors to describe spin and twist solitons, i.e., quanta of spin and twist energy (cf., Majewski 2006a, b, c, d, e).

Complexity of Rotation Soliton Propagation

Although seismic waves have been studied for many years, their soliton nature has only recently come to wide notice. Deformation solitons propagate along earthquake faults and induce earthquakes. Rotation solitons are generated in earthquake sources and propagate throughout the Earth. The conclusion to be reached from these quite disparate examples is that the research on seismic solitons is essential for investigating the propagation of seismic waves and helps understand mechanisms triggering earthquakes.

Chapter 16 - Anticrack-Associated Faulting and Superplastic Flow in Deep Subduction Zones

This chapter describes microphysics of antidislocation and anticrack formation leading to faulting processes in deep subduction zones. The final stage of faulting is connected with superplastic deformations that have very specific properties. It presents the superplastic deformations in the framework of dynamic theory of irreversible deformations. The concept of antidislocation is also examined. The difference between a regular crack and anticrack is that the crack is empty, but the anticrack is filled out by fine spinel grains. Also, the cracks are directed along the principal compressional stresses, but the anticracks are perpendicular to the principal compressional stresses. Line defects or dislocations are lattice imperfections occurring along a line within the crystal. Dislocations provide the most immediate and widespread connection between microphysical properties and ductile flow of crystals. They are a necessary consequence of consecutive slip. Antidislocation refers to a microscopic deformation such that rows of atoms move in opposite directions and as a result of such a motion the atoms take positions between other atoms and a condensed matter is formed in this region.