EVALUATING THE ACCURACY OF A GRAVIMETRIC SURVEY 



147 



Errors Due to Non-Linearity of the Field (e^^, (5,-^) 



The values e^^ and d^^ are functions of g, a and p. However, we do not 

 know an exact form of the function g — g (x) (to simpHfy we will consider 

 a field along the profile). It remains, therefore, to approximate the field g{x) 

 from its discreet values at the observation points. A check of the various 

 methods of approximation showed that the simplest and most convenient 

 is the parabolic interpolation. 



X, km 



The paraboHc interpolation can be carried out by various methods. The 

 most obvious way is to draw a parabola through three observation points. 

 This method leads to very simple expressions for s^^ and 5,-^. However, it 

 necessitates finding the mean square values of the differences of the first 

 and second order for the observed field. 



^10 = (82- gi) and A^ = {gs-g2)-ig2-gi)- 



This involves considerable expense in time. For detailed surveys this method 

 is probably the best. As regards the surveys of a regional and exploratory 

 nature, a much simpler method of parabolic interpretation can be used. 

 The usually observed field consists of a succession of maxima and minima 

 of gravity. Let us assume that by measurements the mean arithmetical 

 values g-Q and Zq have been found, so that 2gQ is the mean value for the 

 differences in gravity of the neighbouring maxima and minima and 21q is 

 the mean distance between them. Given a parabohc law for the change in 



