360 EXPLORATION GEOPHYSICS 



and depth to the structure which gives the observed gravity effects. The 

 quantitative, and very rarely used, procedure is as follows : t A tentative 

 cross section as suggested by visual inspection of the results is sketched. 

 This tentative structure is split into blocks, as shown in Figure 208, 

 and the gravity effects are calculated block by block. The calcula- 

 ted anomalies are then compared with the observed anomalies. In 

 order to make the observed and computed anomalies agree, it usually will 

 be necessary to add and subtract blocks from the cross section and repeat 

 the calculations for each addition or subtraction. This procedure is ex- 

 tremely tedious ; for example, 3 months of steady calculations of this sort 

 were required to obtain a satisfactory structural picture of the Hoskins 

 Mound Salt Dome, Brazoria County, Texas. The time element, therefore, 

 precludes any appreciable practical use of these interpretative methods. 



Short-Cut Methods.f — The most extensive development of these meth- 

 ods has been done by Karl Jung t who has devised formulas and graphical 

 methods for the recognition of certain simple bodies and the determination 

 of their depths and dimensions. Jung utilizes the abscissas of the nu- 

 merical maxima and minima of the gradient and differential curvature 

 profiles. With the exception of the sphere, the geologic bodies covered by 

 the Jung formulas and graphical methods are assumed: (a) to be infinite 

 at right angles to the vertical plane of the cross section, (b) to have a 

 cross section of simple geometric shape, (c) to be homogeneous in den- 

 sity, and (d) to be surrounded by a homogeneous medium. The methods, 

 therefore, have two obvious limitations : ( 1 ) In general, the abscissa of the 

 point of maximum gradient or differential curvature cannot be determined 

 with great accuracy. (2) Most geologic structures and ore bodies cannot 

 be treated as infinite at right angles to the plane of the section ; also, their 

 gravity effects do not correspond to those of bodies having a simple geo- 

 metric cross section. 



Graphical Methods. — These methods utilize sets of standard graphs, 

 each graph representing a vertical section along a line of symmetry. In 

 constructing these graphs, formulas of the type 115 to 128 are employed. 

 For example, graphs are based on formulas 119 and 121 when infinite 

 prisms are used as the building blocks and on formulas 123 and 124 when 

 finite prisms are used. In one convenient standard set, the following rela- 

 tions are assumed. Depth to top : depth to bottom : length of each prism 

 = a: b: c, where the ratio a: b is retained constant and c is varied. ff Graphs 

 constructed according to this formula correspond to anticlines. (A com- 

 plete discussion of the graphical method is given by Barton in the article 

 cited.) 



t Barton, loc. cit. 



t Karl Jung, "Die Bestimmung von Lage und Ausdehnung einfacher Massenformen unter 

 Verwendung von Gradient und Krummung's Grosse," Zeit. fur Geophysik, 1927, Vol. 3, p. 257. 

 tt D. C. Barton, loc. cit. 



