Introduction to seismic travel time methods in anisotropic media

Summary Section 1 (and 11) develops the concepts of the front velocity, the front gradient, the travel time in space and on seismometric profiles, the profile velocity and the profile gradient in connection with the propagation of the fronts of elastic waves in solid isotropic and anisotropic media. The sectional velocity and the sectional gradient are defined in terms of the motion of the curve of intersection of a front with a fixed surface. Section 2 (and 12) relates the coefficients of elasticity of the medium, the front types, and their respective rays. In section 12, the theory of fronts of arbitrary shape and of the corresponding rays for any anisotropic, homogeneous or inhomogeneous solid medium is summarized. In section 3 (and 13), the law of reflection and refraction of fronts on surfaces of discontinuity of arbitrary shape is presented. Sections 4 to 6 (and 14 to 16) treat some elementary applications of seismic travel time methods to homogeneous, uniaxially anisotropic media (=transverse isotropy) in greater detail. In section 4 (and 14), the travel time of a direct front generated by a point source is considered and it is shown how the coefficients of elasticity of the medium can be found based on travel time measurements. The seismic prospection of a plane reflector and of a reflecting boundary of arbitrary shape and position are discussed in section 5 (and 15). In section 6 (and 16), the seismic refraction method is used to locate a plane boundary between a homogeneous, uniaxially anisotropic and a homogeneous isotropic medium, where the boundary is perpendicular or at an arbitrary angle to the direction of anisotropy.