Outline of a System of Refraction Interpretation for Monotonic Increases of Velocity with Depth

Published:January 01, 1967
Abstract
In the early 1930's, Dr. Evjen wrote a treatise on “The Geometry of Refraction and Reflection Shooting” which to this day remains a classic in its field. Most of the seismologists of the Shell Companies over the entire world have learned part of their trade from this treatise. The book was released to Dr. Evjen after he left the service of Shell, but circumstances have prevented him from publishing it, wholly or in parts. It was, therefore, an honor as well as a genuine pleasure for this writer to condense, with Dr. Evjen's permission, one of the chapters of the book. It deals with monotonic increases of velocity with depth in a way which is entirely satisfactory from both the practical and the theoretical points of view.
 V_{1} =
velocity at the surface.
 V_{z} =
velocity at depth Z.
 q =
dimensionless constant.
 L =
a constant with the dimension of length.
 T, X =
time and distance on a timedistance curve.
 T, x=
time and horizontal distance from shotpoint to any point on a trajectory.
 i =
angle between raypath and vertical at any point of path.
 i_{1} =
value of i at surface.
 U =
dX/dT= V_{1}/sin i_{1} = V_{z}/sin i = reciprocal of slope of T–X graph.
 Z =
depth below datum.
 ds =
element of raypath.
A velocity distribution or a family of velocity increases with depth must fulfill two requirements—integrability of the time and distance integrals and ease of construction of the trajectories. Although many velocity
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.