THE AMERICAN ASSOCIATION OF PETROLEUM GEOLOGISTS 
TRANS. SOCIETY PETROLEUM GEOPHYSICISTS, VOL. V (MARCH, 1935), PP. 161-179, 7 FIGS. 
THE RAPID ADJUSTMENT OF OBSERVATIONS IN A 
NETWORK OF GEOPHYSICAL STATIONS BY THE 
METHOD OF LEAST SQUARES! 
E. LANCASTER JONES* 
London, England 
ABSTRACT 
‘A frequent problem in geodesy and geophysics concerns the adjustment of a set 
of values for a physical magnitude at a number of stations. The values are obtained 
from other observed magnitudes by computations involving the geometrical] links of the 
station network, and there is ambiguity on account of the multiplicity of connections. 
Since the magnitude desired is single-valued at each station, the values obtained are 
usually adjusted by the method of least squares. Where the number of stations is large 
and the network is complex, the normal equations for least-square adjustment are very 
numerous and their solution by standard procedure is tedious. The paper develops a 
method of establishing the normal equations, and solving them by successive approxi- 
mations, which is simple, rapid and satisfactory in practice, and is applicable to any 
network, however large and complex. Although particular attention is focused on the 
problem of obtaining isogams from observations of gravity gradients in applied geo- 
physics, the method has obvious applications in other fields where the mathematical 
conditions are similar. 
§1. INTRODUCTION 
In many branches of geodesy and geophysics, observations of 
physical magnitudes are made at a series of stations which form a 
network of triangles or polygons. From these measured magnitudes 
it is frequently desired to compute the values of other magnitudes 
at the stations concerned. By reason of the relationship between the 
observed and computed magnitudes, and the geometry of the net- 
work, it usually happens that there is ambiguity in the final values 
attained, and it is customary to apply the method of least squares 
to resolve the ambiguity. 
A particular example occurs in applied geophysics in the com- 
putation of isogams fromm observations of the gradients of gravity at 
stations of the network. The difference in gravity ga—ga at two sta- 
tions A, B of the network may be obtained by taking any path 
formed of straight lines joining adjacent stations between A and B, 
assuming that the average gradient of gravity along the rectilinear 
* The Science Museum, South Kensington. 
1 From Proc. Phys. Soc. London, Vol. 45 (November 1, 1933), PP- 792-807. Re- 
printed with the permission of The Physical Society of London and the author. Com- 
municated by Professor A. O. Rankine, July 28, 1933. 
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