712 



EXPLORATION GEOPHYSICS 



section of the rays with the ground surface and drawing a smooth curve 

 through the plotted points. 



Vector Composition of Reflection Time Gradients. — In general the 

 direction of the true dip of the underground strata is seldom known before 

 the shooting, and therefore the instrument spread will be found oriented 

 obUquely with respect to the true dip of the reflecting bed. The resulting 

 problem of dealing with components of dip as related to the AT obtained 

 with spreads oriented at an angle to the true dip is somewhat involved 

 when exact solutions are desired. The problem may be simplified by pro- 

 ceeding with computations on the assumption that the component of dip 

 of the reflection bed in the direction of the spread is related to the AT 

 recorded at that spread by the equations derived for spreads along the 

 direction of the true dip of reflecting bed. 



A more exact solution can be obtained as follows : At a given point 

 on the ground surface, a spread in the direction of maximum gradient 

 of reflection time will be oriented along true dip, while a spread in 

 the direction of zero gradient or constant reflection time will be oriented 

 along strike. Furthermore, because the gradient of any scalar quantity 

 is a vector, the component of the time gradient in any direction is 

 obtained by the usual procedure for resolving vectors. Hence, if the 

 maximum gradient of the reflection time at a point P on the ground sur- 

 face is (dT/dx) Pmax, and is directed, for example, due north, the magni- 

 tude of the gradient at a bearing ^ is : 



\dxjp„ 



cos <^ 



The vector property of the time gradient is applied in the following 

 manner. Draw two lines radiating from point 0, each in the direction in 

 which the time gradient was determined from dip reflection shooting. 

 (Figure 436.) Choose a convenient unit of length and mark oflf lengths 

 equal to the magnitude of the corresponding time gradient. Strike ofif 

 normals to the vectors at their tips. The intersection of these normals 



establishes the point of the maxi- 

 mum gradient vector ; that is, the 

 length of the vector delimited by the 

 point and the intersection of the 

 normals is proportional to the mag- 

 nitude of the maximum gradient 

 and its direction is parallel to that 

 of the maximum gradient. The mag- 

 nitude and direction of true dip 

 is thus obtained from the deter- 

 mination of values of AT in two 



-Composition for maximum reflection ,i,v„„f:^„o 

 time gradient. GirCCnonS. 



Fig. 436. 



