SEISMIC METHODS 681 



make an explicit calculation possible, the process of making this computa- 

 tion for each reflection is too cumbersome to be practical in the routine of 

 seismograph work. To facilitate the speed of computation of the dip 0, the 

 horizontal distance H, and the vertical distance Z, various forms of com- 

 puting charts, slide rules, and machines have been developed which make 

 use of these fundamental Equations 2)7 and 39. f 



Basic Assumptions 



A completely rigorous calculation of each reflection requires a thorough 

 knowledge of the wave velocities in the media between the reflecting beds 

 and the surface. Since the chief purpose of reflection shooting is to obtain 

 a subsurface map of geological structure without the expense of drilling 

 numerous deep holes, wherein exact measurements could be made, the 

 velocity data necessary for a rigorous calculation are rarely known in 

 detail. In some cases velocity data are obtainable from a few scattered 

 points, such as deep wells, which far too often were drilled entirely outside 

 the immediate area of the contemplated reflection survey. In a majority 

 of cases, the velocity data used are approximations or estimates based on 

 the best available data or background experience. 



As a result of the experience gained in collecting a relatively large 

 amount of velocity data from many areas where measurements have been 

 taken, two very significant generalizations have been made : ( 1 ) the velocity 

 increases generally with depth, and (2) the lateral variations of seismic 

 velocity, though present, may be assumed to be small. Thus it is usual to 

 neglect the lateral velocity variation and to use the same velocity-depth 

 function throughout any one area. This assumption greatly simplifies the 

 computation of reflection data. The theoretical obstacles to the computation 

 of these data would be great indeed if the seismic velocity must be described 

 by three spacial coordinates instead of only one. 



Most modern computing methods are based upon these assumptions, 

 which is equivalent to saying that the same velocity expression can be used 

 for all angles of reflecting beds and for all shot-points in any one area. 



Continuous Velocity-Depth Functions, — In order to make use of 

 the basic equations 37 and 39 it is necessary to obtain a knowledge of the 

 seismic wave velocity in the area to be prospected. There are several 

 methods of ascertaining this data. The most accurate method is well- 

 shooting, but if no wells are available the velocity may be measured by use 

 of either the refraction or reflection methods. These measurements will be 

 treated under separate headings. The determination of vertical velocities 

 from reflection seismograph observations is discussed by Gardner,^ utilizing 

 specially grouped arrangements of shot-points and detectors to minimize 

 the errors in measurement. 



t The development of these equations has been prepared largely from the work of R. W. Raitt 

 in 1935. A similar analysis is given by Haskell and Widess, Geophysics, Vol. 5, No. 2, April, 1940. 



t L. W. Gardner, "Vertical Velocities from Reflection Shooting," Geophysics, Vol. XII, No. 2, 

 April, 1947, pp. 221-228. 



