350 EXPLORATION GEOPHYSICS 



explained by referring to Figure 202 and its accompanying legend. A 

 closed traverse is passed through stations 1, 2, 3, 4 and 5, station 1 being 

 chosen as the base station. At each station, a vector is constructed which 

 has a length proportional to the magnitude of the observed gradient at that 

 station and a direction parallel to the direction of the observed gradient. 

 Next, the gradient vector at each station is projected on the closed traverse 

 and the magnitude of the component along the traverse is computed. (Com- 

 ponent vectors having the same direction as that in which the traverse is 

 traced are taken as positive, and those having the opposite direction are 

 taken as negative.) The next step is to determine average values of the 

 components by adding components corresponding to two adjacent stations 

 and dividing by two. For example, the average value of the components 



corresponding to stations 1 and 2 is — , 4 being the component of the 



gradient at station 1 along the traverse (1, 2) and 16 the component at 

 station 2 along the same traverse. 



Computing the average value of the gradient component along a particular direc- 

 tion (specifically, the direction connecting two stations in the closed traverse) is 

 equivalent to assuming that the gradient or change of gravity per unit length is uni- 

 form along the line connecting the stations. With this simplifying assumption, the dif- 

 ference in gravity values between two such stations can be readily computed merely by 

 multiplying the average gradient component by the distance between the two stations. 

 Thus, in Figure 202, it is assumed that the gravity anomaly at station 1 (base station) 

 is zero. The anomaly at station 2 is equal to the distance between stations 1 and 2 

 times the average gradient component = 30,000 cm. • 10£/cm. = 300,000 E. 



It is now necessary to adjust the gravity differences for error in closure. For zero 

 error in closure, the sum of the differences in gravity (column 5) between the stations 

 in a complete cycle of the closed traverse would be equal to the anomaly of the base 

 station — zero in our example. However there is an error in closure of 180,000 Eotvos 

 units or .18 milligals. The error is positive, and to correct for it the fraction of the 

 total error corresponding to the probable error made between each set of two stations 

 must be subtracted from the difference in gravity between the particular set of two 

 stations. Any error made in difference of gravity between stations is proportional to 

 the distance between the stations, since the gradient of gravity between them has been 

 assumed constant. 



Thus the fraction of the total error to be applied as a correction to the gravity 



difference between two stations must be proportional to the distance between them. 



This fraction can now be seen to be the ratio of the distance between any two stations 



. ^ . 30,000 



to the total distance of the closed traverse. The correction for station 2 is — , . ^ ^^q 



• 180,000 = —40,000 (approximately). The corrected difference, therefore is 300^000 

 - 40,000 = 260,000 E. 



The sum of the corrected differences (column 6) should now be zero, since the 

 closure error has been corrected. Had the exact corrections for each station been used 

 rather than the approximations (e.g., exact correction for station 2 is 38,570), the 

 closure error would have been entirely corrected. As it is, an error of 10,000 Eotvos 

 units or .01 milligals allows accuracy which is quite sufficient for normal work. 



The differences in columns 5 and 6 are, of course, relative to the base station (1). 

 Column 7 is the sum of the corrected differences — converted into milligals — up to each 

 particular station relative to the base station (proceeding consistently along the closed 

 traverse from the base station). 



