often called exponential-with-time. Both the resulting ray paths and wave 

 fronts are circular. 



Used to a lesser extent than the linear-with-depth function is a linear- 

 with-time velocity distribution, V — V + ar, in which a is an acceleration 

 constant. Since in terms of depth this function becomes V = W 2 + 2az, it is 

 also known as parabolic-with-depth. The resulting travel paths are cycloidial 

 while the wave fronts are anonymous ovals. 



The popularity of the linear-with-depth velocity function over the last 

 20 years stems from the relative ease of wave-front chart construction once the 

 constants, V and k, have been established. The determination of these constants 

 is somewhat involved (Legge and Rupnik, 1943). In contrast, the constants 

 of the linear-with-time are easy to find whereas chart preparation is laborious. 

 Specialized analog computers have been built to relieve this tedious chore 

 (Musgrave, 1952). Digital computers have so reduced the hours of calculations 

 that wave-front charts may be produced for every few shotpoints in areas of rapid 

 lateral variation of velocity. 



Velocity distribution data are obtained by several techniques. The 

 method of long-reflection profiles was the first to be employed and is still 

 very useful in undrilled regions or in areas requiring close lateral control 

 of velocity. When shot across a common centerpoint and along dip azimuth, 

 a long reflection profile yields data which relate to average velocity as 

 V = \/d(x 2 ) I 'd(T 2 ) cos <f> where d(x 2 ) /d(T 2 ) is the inverse slope of a T 2 versus 

 x 2 plot. In areas where no special effort has been made to secure velocity infor- 

 mation, a statistical treatment of data available from a suite of ordinary reflection 

 records results in velocities which are averaged over the prospect. 



Two other methods of velocity measurement are in current use, both of 

 which require a deep well bore. The first, called well-velocity shooting, has been 

 employed for many years. It consists of lowering a special seismometer into 

 the bore hole, stopping it at numerous depths and shooting at the surface. 

 Time-depth data are thus obtained from which the general velocity distribution 

 is determined and a velocity function may be calculated. Well-velocity shooting 

 is a combined effort involving a seismograph crew to shoot and take the 

 records and a well-logging crew to lower the seismometer into the bore hole. 



A few years ago, equipment was designed to make a continuous-velocity 

 log of the formation penetrated by the bore hole (Summers and Broding, 1952; 

 Vogel, 1952). A typical subsurface tool comprises an elastic pulse transmitter 

 separated from a pulse receiver by an acoustic insulator. As the transmitter 

 emits a pulse into the bore hole wall, it simultaneously transmits a time break 

 up the logging cable. When an elastic pulse reaches the receiver, another signal 

 is sent up the logging cable whose arrival time is compared with the correspond- 

 ing time break. This sequence of events is repeated perhaps 20 times per second. 

 Since the distance separating the transmitter and receiver is fixed, the velocity 



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