A General Wavefront Method

Published:January 01, 1967
Abstract
Wavefront systems may be divided into two broad classes, radiating (point source) and directed (line source). Radiating systems may be constructed for any point on the section when velocity distribution is known; directed wavefront systems are reconstructed from observed timedistance data and a knowledge of overburden velocities.
The General Wavefront Method reexamines hitherto separately presented and timetested classical techniques, together with certain novel and special applications, and shows that all are related by a single basic concept: an observed or deduced traveltime may be distributed between two appropriate wavefront systems, A and B, yielding a locus of general solutions and/or specific solutions. Depending on the particular problem various combinations of radiating and/or directed wavefronts are employed. The resulting easily constructed loci are related to curves of the simplest types; straight lines, circles, parabolas, hyperbolas, ellipses, and ovals, which in turn have a simple relationship to the desired interfaces (i.e., intersect on interface or are tangential to it).
Complex problems of the kind encountered in the field are readily resolved by progressive reduction to simplest terms. Thus field cases, including multiple layers, highrelief structures involving penetration, faulting with attendant diffraction, and unusual travel paths, accelerating overburden velocities, etc., may all be handled on a routine basis.
The usual sources of overburden velocity information are evaluated from the point of view of usefulness for the refraction method and particularly for wavefront interpretation.
In addition, recording techniques incorporating existing wells into refraction surveys are presented as part of useful wavefront refraction lore.
Figures & Tables
Contents
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.