Abstract A strong “refraction branch diffraction,” presumably due to scattering from a lateral heterogeneity on or below the seafloor, has been observed on ocean bottom hydrophone data from the Rivera Ocean Seismic Experiment (ROSE). This arrival is unusual because of its coherence and relatively large amplitude. Finite difference modeling of a number of possible seafloor diffractors and associated lateral velocity variations is presented, which demonstrates the occurrence and characteristics of “refraction branch diffractions.” In general, the half-width of the diffractor must be approximately the same as the seismic wavelength in order to produce a strong diffraction. Velocity gradients present in the models, as well as PS conversion, complicate the wavelength-half-width relationship. Three different models, a hill, a valley, and a subsurface high-velocity block, all produced diffractions of sufficient amplitude to explain the data. There is a hill along the line with approximately the same dimensions as the model hill and it is the proposed source of the diffracted energy in the data. The large models used also clearly demonstrate the existence of phases that are theoretically possible but rarely seen in the marine seismic (geoacoustic) data such as the pseudo-Rayleigh wave and the P and S interference head waves.

Abstract Fermat’s Principle states that for two points A and B in a velocity field, the ray path will be the trajectory between A and B along which the travel time is stationary. For many cases in isotropic media Fermat’s Principle seems intuitively obvious. For example, in a homogeneous, isotropic medium the least time travel path between two points is a straight line. In anisotropic media the results of Fermat’s Principle are less obvious and it is useful to have a rigorous proof. In this “tutorial style” paper we present a proof of Fermat’s Principle for anisotropic elastic media. The proof involves relationships between the slowness and wave surfaces. The slowness surfaces are defined by the determinant ( S ), or equivalently the eigenvalues (G m ), of the Kelvin-Christoffel matrix. The proof is given for both cases.