Normal mode theory is applied to investigate the phenomenon of refraction along an embedded highspeed layer. At any single frequency an infinite number of normal modes exist, each of which is characterized by some propagation constant. The real and imaginary parts of the propagation constant respectively specify the phase velocity and attenuation constant for the disturbance. It is shown that at low frequencies both a symmetric and an antisymmetric unattenuated mode exist. At higher frequencies, these modes transform into attenuated modes which continually radiate energy from the layer into the surrounding medium. Some computed properties of the symmetric attenuated mode for a specific set of elastic parameters are consistent with model seismic studies. The phase velocity curve exhibits a distinct plateau region for wavelengths in the vicinity of three times the layer thickness. In this region the refraction velocity corresponds to that of extensional waves in a thin plate while the attenuation is approximately 8 db per wavelength.
It seems that the simple concept of group velocity has little physical meaning in this study. Group velocities greater than the P-wave velocity are obtained and cannot possibly correspond to the velocity with which energy is propagated.
Figures & Tables
Seismic Refraction Prospecting
The seismic method is divided into reflection and refraction techniques, based on whether or not a wave undergoes a reflection at the extent of its travel. Thus, while most refracted events have not been reflected, most reflected events have been refracted, because a refraction occurs across any velocity interface in accordance with the simple and basic Snell’s law. This law states that the sine of the angle of incidence is to the sine of the angle of refraction as the velocity on the first side of the interface is to the velocity on the second side of the interface.
Where the refraction angle is large, and not near to zero as it is in the case of reflection work, there are many considerations concerning the geometry of the raypath that have to be made in refraction interpretation. Basically, the papers in this volume describe various techniques for separating out special raypath solutions and making approximations that give us a structural geologic picture from the study of these approximations or specializations.
The following factors are of extreme importance in refraction surveying’ 1) Distance’ Surveying must be accurate in order to make correct depth determinations of the refractor by the use of the refraction method. 2) Velocity’ The velocity of the various horizons, through which the refracted wave passes, must be known if an accurate structural picture is to be determined. Many of these velocities can be determined from the refraction data, and, in fact, the refraction method is a good means of establishing many of the velocities needed for these calculations. 3) Time’ Accurate time information is a prerequisite, although this is no more the case in refraction than in reflection work. In most instances, refraction information is to be recorded to the nearest 1/1,000 sec for exploration purposes.
The distance parameter will be discussed first. In many surveys the distance between the shot and receiver may be extremely long (25 to 50 miles), and the requirement for accuracy is just as vital as if this distance were very short (a few hundred feet). Because of the differential velocities involved, distance errors can cause errors in depth greater than the distance errors themselves. For somecases, in the experience of the editor, the depth error may be three times the distance error. The velocity is very critical in refraction information. Of particular important is the refractor velocity, which is often used to determine the time to be subtracted from the total time path to determine that amount of time which is near verticalor can be converted to a vertical path time.