SEISMIC METHODS 713 



The most effective relative orientation of spreads for determination 

 of true dip is one in which the spreads are at right angles to each 

 other. In this case, the magnitude of the maximum gradient is equal 

 to the square root of the sum of the squares of the component gradients, 

 and its direction makes an angle with the direction of one of the spreads 

 which is proportional to the inverse tangent, or cotangent, of the ratio 

 of the component gradients. 



After the magnitude and direction of the maximum gradient have 

 been obtained, the gradient is expressed in terms of AT by means of 

 Equation 69. The AT thus found is then inserted in Equation 21. 



sin ^ = ^ F (70) 



where — — - = — - — of Equation 21. 



S ax 



It is customary to locate shot-points along a straight line ("shot- 

 point line") in order to gain approximately a vertical cross-sectional 

 view of the geologic strata. When cross dip, i.e., dip normal to the shot- 

 point line, is small or constant, a close approach to a vertical section may 

 be obtained. Because dip data along a line may be treated more readily 

 than data in scattered directions, stress is sometimes given to line spreads, 

 and cross spreads at some of the shot-points on the shot-point line are 

 omitted. 



Rigorous interpretation of dips over a prospect can be achieved by 

 time gradients. In dip shooting, time gradients alone are determined and 

 the process of preparing an equivalent time horizon is similar to that of 

 preparing a contour map from a knowledge of dip only; that is, an equiva- 

 lent time horizon is obtained by running time phantoms incorporating the 

 time gradients. The time maps would be converted to space maps by 

 measuring maximum time gradients and applying the equation (70) 

 already established for true dip. 



In general, however, the data from seismograms are converted into 

 space coordinates long before a space map is drawn up in order that direct 

 space information on a prospect may be furnished during the course of 

 the survey. 



The usual procedure is to utilize the time gradients determined along 

 the line spread as though they were maximum gradients and to plot space 

 coordinates computed from these time gradients on a vertical section 

 through the shot-point line. The degree of approximation implicit in a 

 vertical section of this sort depends on the magnitude of cross dip and its 

 change along the section. 



From geometric considerations, it is apparent that because the tangent 

 of dip is a gradient of depth, the tangent of true dip of a sloping 

 plane is related to the tangents of the component dips in exactly the 

 manner that the maximum time gradient is related to its components. 



