Isostasy and its Meaning

The theory of isostasy supposes that, in regions which have not been disturbed recently, each vertical column of the earth's crust with a certain minimum radius and extending to a depth of about IOO km has approximately the same mass. To find the deviation from this approximation in a given region, the density must be assumed as a function of depth. Such assumptions used at present for calculations are discussed critically. The resulting errors are greater than it is normally beleaved; errors in the calculated isostatic gravity anomalies exceeding ten milligals must be expected in certain regions. Systematic errors result from the usual assumption in routine calculations that the mean density in the earth's crustal layers under the bottom of the Pacific and in the continental areas is the same, and that in both the difference between the density of the layers above about 3 0 km and the layers below this depth is 0.6. The processes producing and maintaining isostatic equilibrium are discussed. In the theory of isostasy it is assumed that in regions that have not been disturbed recently each vertical column of the earth's crust with a given radius (at least, say, 10 km) and extending down to a sufficient specified depth (apparently at least 60 km), has approximately the same mass, regardless of the surface condition (continental or oceanic) or of the surface elevation of the region. Since this hypothesis is an ap roximation, the question cannot be raised w \ ether the theory of isostasy is true or false, but how good the approximation is in a given region. In addition to the use of deflections of the vertical, for which too few observations are Contribution No. 504, California Institute of Technology, Division of the Geological Sciences, Pasadena, California. available, there are two ways to approach t h i s uestion. The first is, to use observations of t x e density and distribution of rocks in the earth's crust and of gravity at the earth's surface and to calculate the residuals (the so-called gravity anomalies) against an assumed equilibrium condition; the second is to consider the processes involved in establishing isostasy. Neither provides an answer with the desired precision, since each requires certain assump tions which are not as well founded as is commonly believed. For the first approach it is necessary to observe gravity at as large a number of points on the earth's surface as possible, and to calculate under various assumptions regarding the structure of the earth's crust their deviation from gravity values theoretically to be ex2 B. G U T E N B E R G pected, if hydrostatic equilibrium exists at an assumed depth. Thus, these calculations must be based on hypotheses regarding the density in the various crustal layers as well as on the thickness of these layers. Two fundamental hypotheses have been used which are based on two extreme assumptions (for historical references, see e.g. BOWIE 1931). For the first, PRATT supposed that all crustal columns begin at a discontinuity which has the same depth for the whole earth, that within each such column the density is constant, and that the differences in elevations of the earth‘s crust are compensated by different densities in the various crustal columns. The assumed discontinuity is called “depth of compensation”. The product of the density d of the column and the surface elevation h above the depth of compensation is the same everywhere: