Seismic velocities in transversely isotropic media

Abstract

When a sedimentary earth section is layered on a scale much finer than the wavelength of seismic waves, the waves average the physical properties of the layers; a seismic wave acts as if it were traveling in a single, transversely isotropic solid. We compute the velocities with which P‐waves, SV‐waves, and SH‐waves travel in transversely isotropic solids formed from two‐component solids and find the corresponding moveout velocities from [Formula: see text] plots. The combinations studied are sandstone and shale, shale and limestone, water sand and gas sand, and gypsum and unconsolidated material, one set of typical physical properties being selected for each component of a combination. A reflector at 1524 m and a geophone spread of 0–3048 m are assumed. The moveout velocity for an SH‐wave is always the velocity for a wave traveling in the horizontal direction. The P‐wave moveout velocity found from surface seismic data can be anywhere from the vertical P‐wave velocity to values between those for vertical and horizontal travel; the actual value depends on the elastic parameters and the spread length used for velocity determination. If the two components of the solid have the same Poisson’s ratio, the velocity from surface‐recorded data is the vertical P‐wave velocity. For this case, SH‐wave anisotropy can be computed. SV‐wave data usually do not have hyperbolic time‐distance curves, and the moveout velocity found varies with spread length. Surprisingly, the water sand‐gas sand combination gives a medium with negligible anistropy. A two‐component combination of gypsum in weathered material gives rise to [Formula: see text] plots that seem to explain the unusual behavior of near‐surface SV‐waves seen in field studies reported by Jolly (1956).