The propagation of waves along and across the boundary between two media with different characteristic velocities is much more complicated when the source is on or near the boundary than when it is far away and the incident waves are plane. Examples of waves generated by localized sources near a boundary are the electromagnetic waves from the currents in a dipole on the surface of the earth and the seismic waves from a slip event in a fault in the earth's crust like the San Andreas fault in California. Both involve a type of surface wave that is called a lateral wave in electro­ magnetics and a head wave in seismology. Since the two are analogous and the latter is more easily visualized, it is conveniently used here to introduce and describe this important type of surface wave using the data of Y. Ben­ Zion and P. Malin ("San Andreas Fault Zone Head Waves Near Parkfield, CA," Science 251, 1592-1594, 29 March 1991).

1 Historical and Technical Overview of Electromagnetic Surface Waves; Introduction to Lateral Waves.- 1.1 Electromagnetic Waves.- 1.2 Electromagnetic Waves Along Surfaces.- 1.3 Surface Waves in the Field of a Vertical Electric Dipole over the Earth; The Formula of Norton.- 1.4 General Integrals and Approximate Formulas.- 1.5 Numerical Methods with High-Speed Computers.- 1.6 Lateral Waves.- 1.7 Lateral Waves and the Geoelectromagnetic Investigation of the Earth's Crust and Upper Mantle.- 2 Electromagnetic Preliminaries.- 2.1 Maxwell's Equations; Parameters.- 2.2 The Vector and Scalar Potentials; The Electromagnetic Field of a Unit Electric Dipole.- 2.3 The Electromagnetic Field of a Unit Magnetic Dipole.- 2.4 The Reflection and Transmission of Plane Waves at the Plane Boundary Between Electrically Different Media.- 2.5 The Reflection and Transmission of Plane Waves at the Boundary Between Two Lossless Half-Spaces (Case A).- 2.6 The Reflection and Transmission of Plane Waves at the Boundary of a Dissipative Half-Space (Case B).- 2.7 The Reflection and Transmission of Plane Waves Incident from a Lossy Half-Space (Cases C and D).- 3 The Electromagnetic Field of a Unit Vertical Electric Dipole in the Presence of a Plane Boundary.- 3.1 Maxwell's Equations and Their Transforms.- 3.2 Solution of the Transformed Equations.- 3.3 General Integrals for the Field When the Dipole Is in Region 1.- 3.4 Integrated Formulas for the Electromagnetic Field of a Vertical Electric Dipole at the Depth d in Region 1.- 3.5 The Polarization of the Electromagnetic Field of a Vertical Electric Dipole on the Boundary in Region 1; Wave Tilt.- 3.6 The Complete Electromagnetic Field in Region 1 of the Vertical Electric Dipole in Region 1.- 3.7 The Field in Region 2 for the Vertical Electric Dipole in Region 1.- 3.8 Alternative Derivation of the Field in Region 2 for the Vertical Electric Dipole in Region 1.- 3.9 Generalization of the Field in Region 2.- 4 Applications of the Theory of the Vertical Dipole Near The Boundary Between Two Half-Spaces.- 4.1 Limitations of the Theory.- 4.2 Radio Communication over the Surface of the Earth; Electromagnetic Field in Air Due to a Vertical Electric Dipole at Height d in Air.- 4.3 Division of Radiated Power Between Air and Earth Half-Spaces.- 4.4 Communication with Submarines-Unit Vertical Dipole.- 4.5 Communication with Submarines-A Practical Antenna.- 4.6 The Measurement of the Conductivity of the Oceanic Crust with a Vertical Electric Dipole as the Source-Theory.- 4.7 The Measurement of the Conductivity of the Oceanic Crust Using a Vertical Dipole-Comparison of Theory with Measurement.- 4.8 A Note on the Effective Length of the Antenna.- 5 The Electromagnetic Field of a Horizontal Electric Dipole in the Presence of a Plane Boundary.- 5.1 Introduction.- 5.2 Maxwell's Equations and Their Transforms.- 5.3 Solution of the Differential Equations for ?x and B x.- 5.4 The Components of the Electromagnetic Field of the Horizontal Dipole as General Integrals.- 5.5 Integrated Formulas for the Electromagnetic Field in Regions 1 and 2 of the Horizontal Electric Dipole at the Depth d in Region 1.- 5.6 Evaluation of the Integrals for the Electromagnetic Field in Region 1 of the Horizontal Electric Dipole at the Depth d in Region 1.- 5.7 Evaluation of the Integrals of the Field in Region 2 of the Horizontal Electric Dipole at the Depth d in Region 1.- 5.8 Alternative Derivation of the Field in Region 2 of the Horizontal Electric Dipole at the Depth d in Region 1.- 5.9 The Locus of the Poynting Vector and the Depth of Penetration of the Lateral Wave in Region 2.- 5.10 Generalization of the Field in Region 2.- 6 Interference Patterns; Comparison of Approximate Formulas with General Integrals and Measurements.- 6.1 Introduction.- 6.2 Radial Electric Field and Interference Patterns.- 6.3 The Complete Electric and Magnetic Fields.- 6.4 Comparison of Theory with Measurements.- 7 Applications of the Theory of the Horizontal Dipole Near the Boundary Between Air and Earth or Sea.- 7.1 Comparison with the Vertical Dipole.- 7.2 Lateral-Wave Propagation over the Surface of the Earth and into the Ocean-Unit Horizontal Dipoles.- 7.3 The Wave Antenna for Communication over the Earth.- 7.4 Communicating with Submarines with Horizontal Antennas.- 7.5 Lateral Waves from a Horizontal Antenna for Remote Sensing in the Earth or Water.- 7.6 Lateral Electromagnetic Waves from a Horizontal Antenna for Remote Sensing in the Ocean.- 7.7 On the Detection of Submerged Submarines with Lateral Electromagnetic Waves.- 7.8 Detection of Magnetic Field Instead of Electric Field.- 7.9 Determination of the Permittivity and Conductivity of the Earth from Measurement of the Admittance of a Horizontal Antenna.- 7.10 Field of a Horizontal Electric Dipole in the Air over Earth or Sea; Application to FM Communication and Television.- 8 The Measurement of the Conductivity of the Oceanic Lithosphe with a Horizontal Antenna as the Source.- 8.1 The Homogeneous Isotropic Half-Space Model of the Oceanic Lithosphere-Theory.- 8.2 The Measurement of ?2.- 8.3 The Measurement of ?2.- 8.4 Comparison with Measurements.- 8.5 Reflections from an Ideal Reflecting Layer.- 8.6 Interpretation of Measured Data.- 9 Lateral Waves in a One-Dimensionally Anisotropie Half-Space.- 9.1 Introduction.- 9.2 Transform of Maxwell's Equations; Equations for ?x and B x.- 9.3 Solutions of the Differential Equations for ?x and B x.- 9.4 Approximate Integrated Formulas for the Complete Field in Region 1.- 9.5 Comparison with Measurements.- 9.6 Evaluation of the Integrals for the Field in Region 1 over a Homogeneous Anisotropic Region 2.- 9.7 Evaluation of H?1(?, 0), H ?, 0), and Hz1 (?, 0).- 9.8 Three-Dimensionally Anisotropic Region 2.- 10 The Propagation of Lateral Electromagnetic Waves in Air over Vertical Discontinuities.- 10.1 Review of Formulas for the Field in Homogeneous Isotropic Half-Spaces.- 10.2 Formulation of the Problem When the Properties of Region 1 Are Discontinuous.- 10.3 The Scattered Field in Regions 1 and 3.- 10.4 Numerical Evaluation of the Scattered Field; The Total Field.- 10.5 Propagation in the Presence of a Metal Wall in the Air; Induced Current and Scattered Field.- 10.6 Experiments on the Reflection of Lateral Electromagnetic Waves.- 11 The Horizontally Layered Half-Space.- 11.1 Description and Notation; Reflection Coefficients.- 11.2 The n-Layered Half-Space.- 11.3 The Surface Impedance and Reflection Coefficient for an n-Layered Region: Electric Type.- 11.4 The Surface Admittance and Reflection Coefficient for an n-Layered Region: Magnetic Type.- 11.5 The Electromagnetic Field in Region 1 over an n-Layered Half-Space.- 11.6 The Three-Layered Region; General Formulas.- 12 The Three-Layer Problem for Sediment on the Oceanic Crust.- 12.1 Introduction.- 12.2 Integrals for the Components of the Field of a Horizontal Electric Dipole.- 12.3 Approximate Formulas for the Quantity (?1/2)(Q3 -1).- 12.4 Approximate Formulas for the Quantity (?1/2?1)(P3 + 1).- 12.5…