SECT. 1] GRAVITY AT SEA 153 



as any when the surveying ship makes a single pass through a relatively un- 

 surveyed area. In this case the only precise bathymetric information is that 

 along the ship's track, and a two-dimensional assumption is as good as any 

 other. 



Kukkamaki (1954) has derived an expression for the attraction of a vertical 

 line mass at a point as a function of the heights of the upper and lower limits 

 of the mass and distance from the point. The topography may be put on cards 

 as the average height of squares or as spot heights on a regular grid 

 and Kukkamaki's expression may be integrated numerically over any required 

 area with the aid of some method such as Simpson's rule. Alternatively, Talwani 

 and Ewing (1960) have described a method based on an expression for the 

 attraction of a horizontal lamina with a polygonal boundary at an external 

 point. The topographic contours are approximated by polygons and the attrac- 

 tion of the water-mass computed by integration over the laminas bounded by 

 the actual and interpolated contour lines. A modification can be made to take 

 account of the earth's curvature. 



Most major topographic features are compensated isostatically ; that is to 

 say the mass per unit area over the Earth's surface remains constant, the surface 

 excesses of mountain ranges and high plateaus and the deficits of ocean basins 

 being cancelled by compensating masses at depth. Several hypotheses have 

 been proposed to describe the compensating masses in detail. The variation of 

 gravity at sea-level can be computed from the topography and the compensating 

 masses distributed according to any one of these hypotheses. The difference 

 between the actual value and this computed value is known as the isostatic 

 anomaly. There are as many different types of isostatic anomaly as there are 

 isostatic hypotheses. None of the hypotheses is particularly realistic in view of 

 present knowledge, and the chief use of the isostatic anomaly is that it usually 

 varies more slowly than the free-air or Bouguer one. Hence, in an area of very 

 sparse data, the isostatic anomalies are more likely to be typical of the whole 

 area than any other. They also make it very easy to see quickly whether an area 

 is in isostatic equilibrium and it should be easy to compute by a high-speed 

 computer once the topography is in a form suitable for computation of the topo- 

 graphic corrections. The most realistic isostatic hypothesis, and that which 

 generally gives the smallest and most slowly varying anomalies, is the Airy- 

 Heiskanen system for a normal crustal thickness of 30 km. This is now the most 

 generally adopted system. 



A map of topographically corrected gravity anomalies shows the presence of 

 hidden mass excesses and deficits. It is not usually possible to make a unique 

 interpretation of this anomaly pattern, though it is always possible to compute 

 the gravitational attraction of an assumed structure and to compare this with 

 the observed anomalies. An otherwise acceptable solution to a structural 

 problem may be rejected on gravitational grounds, but the structure deduced 

 from a gravity profile usually contains a number of additional assumptions. 

 This ambiguity is usual in geophysical methods and, for this reason, interpreta- 

 tions are very much more trustworthy when based on several different types of 



