Beschreibung
Among seismic waves generated by widely dilferent types of sources, the waves that are the most interest ing and of the longest duration are usually surface waves (which are also called normal waves, interference and channel waves, natural vibrations of layers, etc. ). These waves are distinguished by their dispersion and reso nance, and are used in many investigations - in the determination of the structure of the medium (the existence of surface layers and waveguides), in the determination of the coordinates and properties of the source (in par ticular its energy and mechanism), in the identification of subterranean exploSions, in the mapping of micro-· seisms, in the tracing of storms, etc. Outlines of the wide literature concerning surface waves can be found in [2, 9, 40J. Surface waves can be classed as Rayleigh or Love waves, depending on their velocity and polarization: the displacements of particles in Rayleigh waves are parallel, and the displacements in Love waves perpendicular, to the vertical plane containing the direction of propagation (some variation from this polarization is possible close to the source or in the presence of horizontal inhomogeneities in the medium). The present work is devoted to the calculation and investigation of Love waves in a vertically layered medium. The method used is based on the spectral theory of linear differential operators. ' This method is much more effective than previously applied methods based on the approximation of the medium by a set of homogeneous layers.
Autorenporträt
InhaltsangabeI. The Theory of Love Waves.- §1. Basic Formulas.- 1. Statement of the Problem.- 2. Expressions for Displacements in Terms of the Solution of Two Plane Problems.- 3. Expressions for Displacements in Terms of Characteristic Functions of the.- Corresponding Operators.- 4. An Asymptotic Representation of the Displacement Spectrum.- 5. Modes of Surface Waves and their Phase Velocities.- 6. An Asymptotic Formula for Nonstationary Displacements.- §2. Methods of Calculating the Parameters of Love Waves.- 1. Statement of the Problem.- 2. The Solution of the Problem for Fixed Frequencies.- 3. A Method of Solving the Initial-Value Problem for Eq. (2.3).- 4. The Calculation of Characteristic Values.- §3. The Basic Properties of Love Waves.- 1. Definitions and Basic Formulas.- 2. The Dispersion.- 3. Theoretical Seismograms.- 4. Scaling Laws.- 5. The Principle of Reciprocity.- 6. The Variation of Intensity with Depth.- 7. The Dependence of the Intensity on the Frequency and the Mode Number.- 8. Love Waves in Waveguides.- 9. A Program for the Calculation of Dispersion and Intensity.- II. Love Waves in the Earth's Crust.- §4. Frequency Characteristics of the Medium.- 1. The Fundamental Mode; A Crust without a Surface Layer.- 2. The Fundamental Mode; A Crust with a Surface Layer.- 3. Higher Modes.- §5. Dispersion.- 1. The Fundamental Mode; Crusts without Surface Layers.- 2. The Fundamental Mode; Crusts with Surface Layers.- 3. Higher Modes.- §6. The Theoretical Wave Picture.- III. Love Waves in the Upper Mantle.- §7. Frequency Characteristics of the Medium.- 1. The Fundamental Mode.- 2. Higher Modes.- §8. Dispersion.- 1. The Fundamental Mode.- 2. The Inverse Problem.- 3. Higher Modes.- §9. The Theoretical Wave Picture.- IV. Love Waves and the Parameters of the Source.- §10. Estimates of the Depth of the Focus.- 1. Normal Earthquakes.- 2. Subcrustal Earthquakes.- 3. Features of Higher Modes.- §11. The Determination of the Magnitude M with the Depth of the Focus taken into Account.- 1. The Depth of Penetration of Waves Used in the Determination of Magnitude.- 2. Theoretical Seismograms.- §12. The Azimuthal Intensity Distribution of Love Waves.- Appendix. The Influence of Sphericity, Variation of the Parameters, and Absorption.- §13. The Influence of the Sphericity of the Earth.- 1. Theory.- 2. Calculations.- §14. Derivatives of the Phase and Group Velocities with Respect to the Parameters for the Section.- 1. Theory.- 2. Calculations.- §15. The Influence of Absorption.- 1. Theory.- 2. Calculations.- Literature Cited.
