SVENSKA GEOFYSISKA FORENINGEN

VOLUME I, NUMBER 3 Te I L u s AUGUST 1949 A QUARTERLY JOURNAL OF GEOPHYSICS

Isostasy and its Meaning

By B. GUTENBERG, California Institute of Technology1

(Manuscript received June 25, 1949)

Abstract

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 30 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 available, there are two ways to approach this in regions that have not been disturbed re- uestion. The first is, to use observations of cently each vertical column of the earth's crust tx e density and distribution of rocks in the with a given radius (at least, say, 10 km) and earth's crust and of gravity at the earth's surface extending down to a sufficient specified depth and to calculate the residuals (the so-called (apparently at least 60 km), has approximately gravity anomalies) against an assumed equili- the same mass, regardless of the surface condi- brium condition; the second is to consider the tion (continental or oceanic) or of the surface processes involved in establishing isostasy. elevation of the region. Since this hypothesis Neither provides an answer with the desired is an ap roximation, the question cannot be precision, since each requires certain assump raised w\ ether the theory of isostasy is true tions which are not as well founded as is com- or false, but how good the approximation is monly believed. in a given region. For the first approach it is necessary to In addition to the use of deflections of the observe gravity at as large a number of points vertical, for which too few observations are on the earth's surface as possible, and to cal- culate under various assumptions regarding Contribution No. 504, California Institute of Tech- nology, Division of the Geological Sciences, Pasadena, the structure of the earth's crust their deviation California. from gravity values theoretically to be ex- 2 B. GUTENBERG pected, if hydrostatic equilibrium exists at an assumed that there is sufficient “plasticity” assumed depth. Thus, these calculations must somewhere in the outer part of the earth to be based on hypotheses regarding the density make “isostatic” adjustment possible. in the various crustal layers as well as on the There can be little doubt that neither the thickness of these layers. Two fundamental PRATTnor the AIRYhypothesis is completely hypotheses have been used which are based accurate. In most regions the actual conditions on two extreme assumptions (for historical are probably better approximated by the references, see e.g. BOWIE1931). For the AIRYhypothesis than by PRATT’S.(See GUTEN- first, PRATTsupposed that all crustal columns BERG 1927 and HEISKANEN1936). The con- begin at a discontinuity which has the same dition for isostasy is approximately given by depth for the whole earth, that within each such column the density is constant, and that a az = constant (3) the differences in elevations of the earth‘s 0 crust are compensated by different densities regardless of the locality; the density d is a in the various crustal columns. The assumed function of the depth, different from region discontinuity is called “depth of compensa- to region, z is the elevation above a level at tion”. The product of the density d of the which approximately hydrostatic equilibrium column and the surface elevation h above the can be assumed, say about IOO km below sea depth of compensation is the same everywhere: level, and h is the value of z at the earth‘s surface. dh = constant (1) There have been various ways by which the mechanism of isostasy and the deviations of The other extreme assumption is that of the actual from assumed ideal conditions have AIRYwho assumed that all blocks near the been investigated. In the early attempts (see surface have the same density and “float” in e. g. HEISKANEN1936) it had been believed the deeper material, like icebergs are floating that the best approximation to the actual in water. If we denote by d, the density of the conditions could be found by assuming a deeper material in which the crust is floating, variety of density distributions and calculating by d, the density of the floating material, by the resulting gravity anomalies; that assump- the distance of the bottom of the floating h, tion was considered the most likely, which material from an arbitrary depth, which must gave the smallest anomalies. More recently be at or below the level of the deepest part (HEISRANEN1948) the assumption has been of the floating material, and by h2 the thick- considered best which gives the least effect of ness of the floating material, then the AIRY elevation on the residuals in a given area. hypothesis can be expressed the following by Finally, HEISKANEN(1936) calculated residuals equation: assuming the probable thckness of the layers dl h, + d, h, = constant as they have been found from seismological (4 evidence and combining them with probable AIRYassumed that d, and d, do not depend on values of the density in these layers. This the locality under consideration but locally type of reduction, which is occasionally re- different values of d, are indicated by the ferred to as “HEISRANENmethod”, certainly is observations (Table I) and are to be expected preferable to any other. Unfortunately, it for geophysical reasons. requires a large amount of work for the calcula- In addition to his idea concerning the me- tions. chanism by which isostasy is maintained, (but Recently the tendency prevails to use still not as a prerequisite to it), PRATTassumed that more uniform assumptions for the whole the difference in density in the various parts earth and to apply them to routine reductions of the earth‘s crust depends on the amount of of the fast increasing body of data, rather than contraction at the time when the material make for each region such individual assump- solidified, thus explaining the smaller density tions which seem to be most probable for the of high mountain areas. This idea of PRATTis local tectonic structure down to a depth of at generally considered as incorrect. On the least 60 km. Thus, it has been proposed re- other hand, in the AIRYtheory it must be cently (HEISKANEN1948 a) to use not only the ISOSTASY AND ITS MEANING 3 same mean densities of 2.67 for the u per la ers, Table I1 and of 3.27 for the “sima” regar ess o the Average thickness of layers in the earth’s crust &P with a given velocity of longitudinal earthquake crustal structure-continental, Atlantic or Paci- waves (all data approximate with relatively large fic-but, in addition, to suppose everywhere local variations). the same “thickness of the crust” of 30 km (corresponding to a region where the surface Thickness of layers, including is at sea level). If this suggestion is carried out, sediments, in km a faster calculation of “isostatic gravity Region With velocity of anomalies” will be possible, and outlines of longitudinal waves of Both areas with large anomalies will become avail- s1/2-61/4 able more s eedily; however, increased errors kni/sec. in the dcuP ated anomalies must be expected. Conclusions based on differences of the order Northwest Europ 27 small of 10 milligals, especially in comparing values Black Forest . . . 16 16 in oceanic areas with those in continental Central Alps . . . 30 25 regions must be expected to become even more Central Asia . . . 30 20 doubtful than at present; unnecessary great Southern Californi coastal...... 18 18 36 uncertainties in the calculated isostatic gravity Central Californi anomalies result from supposing everywhere coastal ...... I0 22 32 densities of 2.67 and 3.27 in the “floating” and Sierra Nevada . . 20 40 60 “supporting” layers respectively, regardless of Eastern North America . . . . . I0 the tectonic structure in the region involved. 30 40 New Zealand. . . I2 I8 30 There is little doubt that the density of the Atlantic Ocean . sediments 20? 20? surface layers in the continents is noticeably Pacific Ocean. . . sediments small ? small ? smaller than that of the corresponding crustal layers in the oceans. Data, according to The density of rocks in these layers, as detei- WASHINGTON(1922), are given in Table I. mined from laboratory samples under pressure of I atmosphere, varies from about 2.65 in Table I granites, 2.7 in granodiorites and also in the Average densities according to WASHINGTON Basement Complex in Finland, to 3.0 in a without, b with water content, n number of analyses. gabbro, which by many is considered charac- teristic for the deeper layers of the “floating” Average density material. The densities of rocks which are Region possibly characteristicof the layer “supporting” b the crust, such as peridotite, yroxenite and dunite, are about 3.2 to 3.3. TR us, in the con- North America . . 2.78 2.73 1,709 tinental areas, the difference in density between South America . . 2.78 2.73 138 the “floating” and “sup orting” material ma Europe ...... 2.19 2.73 1,985 well be only of the ifference of 0.6, whic Africa ...... 2.78 0 1 2.72 223 is assumed for practically all gravity calcula- Australia...... 2:s I 2.75 287 Atlantic ...... 2.89 2.81 56 tions, and still less in areas with “Pacific Pacific...... 3.09 3.01 72 structure”. The effect of pressure on the density can be assumed to be the same for both layers, Table I shows, in addition, that in all as a first approximation. probability, even in the continents, the density It does not seem unlikely that the assump- assumed for the crustal ,a ers is too small, con- tion of a difference in density of the two sidering the fact that va’i ues assumed for the layers of 0.6 throughout the world results in gravity calculations have to represent not only systematic errors which affect especially cal- the density of the uppermost surface layers, culations of gravity anomalies for the oceans. but also of the deeper more basic and heavier This may well be one of the reasons for the layers down to the material in which the upper finding from gravity observations that the layers are “floating”. Their approximate equatot- can be represented in second ap- thickness is given in the last column of Table 11. proximation by an ellipse with the short 4 B. GUTENBERG and long axes pointing towards the con- that in the earth’s crust the relaxation time, tinental and oceanic areas of the earth’s that is the time during which a given devia- crust respectively and differing by roughly tion from equilibrium is reduced to I/e by 300 meters. flow processes, is of the order of 10,000years. As a consequence of the inaccuries of the No exact figure can be given for specific assumptions, the calculation of isostatic gravity layers, especially since the effect of the crustal

Table 111 Isostatic gravity anomalies Ag in milligal after HEISKANEN (1936). a) Using PRATT’S reduction method, depth of compensation T km. b) AIRY’S method, “thickness of thc crust” D km. c) HEISKANEN’S method, using geophysically determined data on the crustal layers.

I I Method of reduction Region la a Ib b

87 stations in plains, USA ...... + 8 85.3 + 7 113.7 + 6 60 20 mountain stations, USA...... + 18 85.3 + 9 113.7 -10 77 - 27 coastal stations, USA ...... + 3 85.3 I 113.7 - 4 77 23 coastal stations, Pacific, USA.. -20 113.7 -20 60 12 stations, Caucasus . , ...... + 47 156.3 + 61 113.7 + 28 77 10 stations, Alps ...... + 31 85.3 -k 18 113.7 -14 77 anomalies involves errors which are far layers on this process is not known well greater than the errors in the observations. enough. However, since deep focus earthquakes Gravity observations frequent1 are accurate occur down to a depth of about 700 km, to better than I milligal. On t rl e other hand, strain must be able to accumulate down to under favorable circumstances the calculated this depth; and the relaxation time in these gravity anomalies may be uncertain by 10 layers must be expected to be at least of the miiligals or more, especially in mountain order of IOO years. It may well be that at a areas. Table 111 gives selected data after HEISKA- de th of about 700 km, the relaxation time NEN (1936). Stdl greater differences are to be fPa1 s below the critical limit at which flow found in hs tabulations for more extreme processes become so fast that they prevent values of the supposed depth of compensa- accumulation of strain large enough to pro- tion; in addition, the anomalies calculated duce a break. by the AIRYmethod correspond to the same The speed of flow-processes is frequently mean density of the surface layers everywhere, characterized by the “coefficient of viscosity” and other assumptions will increase the dif- 17, defined by ferences between the results. The belts of large negative and large positive 17 =w (4) anomalies stand out regardless of the method of reduction under reasonable assumptions. where p is the coefficient of rigidity (about These belts of large gravity anomalies coincide 5 x 1011 dynes/cmZ in the layers under con- almost everywhere with belts of earthquakes sideration) and z the time of relaxation. The (GUTENBERGand RICHTER1949). There is no coefficient of viscosity corresponding to a doubt that they are actually regions in which time of relaxation of 10,000and 100 years is tectonic processes are going on, disturbing consequently of the order of IO23 and 1021 continuously the isostatic equilibrium. There poises respectively. It cannot be ap reciably is some indication from the post-glacial uplift below the latter value at depths Bown to ISOSTASY AND ITS MEANING 5 700 km, if the hypotheses involved in the of flow rocesses in the interior of the earth is preceding calculations are correct. practicalf y nil. At present there is no the0 The second method for investigating the available which applies to such processes. A7 mechanism of isostasy is to consider the that is known are results of a relatively few structures and the processes involved. In experiments on rock under high pressures or Table I1 a summary is given of the approximate temperatures (rarely both), which have led to thickness of layers in several regions from empirical descriptions of such processes. The seismic data published b various seismologists. “constants” involved are functions of time On the other hand, resu Kts found from isostatic and a variety of hysical conditions. Processes calculations (HEISKANBN1948 a, 1948 b) in- at the surface o P the earth, which are rather dicate that the “thickness of the crust” for a slow compared with the time of relaxation of region with the surface at sea level is in ge- roughly 10,000 years, such as sedimentation neral about 30 km and at greater depth under and erosion, do not lead to large gravity ano- mountain ranges. The combined results can malies or deviations from e uilibrium. Where be inter reted as meaning that down to a processes have a much hig1 er speed, gravity depth o P at least 60 km there are relatively anomalies must be expected, and vice-versa. large differences in density between the various If these processes stop, as, for example, in parts of the earth. This does not mean ne- melting of ice or accumulation of ice in cessarily that contemporary flow processes laciated areas, these areas gradually approach within this depth range produce approximate [Yd rostatic equilibrium again. eqdbrium. At present, noticeable flow The earth’s crust as a whole is not in hydro- processes may be limited to distinctly greater static equilibrium. However, there is no doubt depths. It must be considered that the speed of that there are large tectonically uiet areas in flow-processes in a given region was probably which the material at a depth of a1 out 100km appreciable higher at times when mountains is not very far from hydrostatic equilibrium. were forming there under much greater The combination of these facts is what we call stresses and hi her temperatures than today, “isostasy”. One of our major aims must be to and that pro% ably the “roots of moun- find deviations from hydrostatic equilibrium tains” originated simultaneously with the in the various regions of the earth with much mountains. higher accuracy than at present. Unfortunately, our theoretical knowledge

REFERENCES

BOWIE,W., I93 I : Isostasy. Physics of the earth, vol. 3, HEISKANEN.W., 1948 a: Report on Isostasy. Intern. Nat. Res. Council, Washington, D. C., No. 78, Union 3f Geophys. and Geod., Oslo. pp. 103-11s. -, 1948 b: Lectures at Pasadena, December 1948. GUTENBBRG,B., 1927: Die Bedeutung der Isostasie. See also: On the interpretation of the gravity ano- Gerlands Beifr. z. Geophysik, 16: pp. 396-403. malies. Geol. Soc. Amer. Bull., (in press). GUTENBERG,B. and RICHTER,C. F., 1949: Seismic- MEINESZ,VENING F. A., 1933: Ergebnisse der ity of the Earth and Associated Phenomena. Prince- Schwerkraftbeobachtungen auf dem Meere in den ton Press. Jahren 1923-1932. Ergebnisse der Kosmischen Phy- HEISKANEN,W., 1936: Das Problem der Isostasie. sik. 2: pp. 153-212. Hnndbuch der Geophysik, vol. I, pp. 878-951. WASHINGTON,H., 1922 : Isostasy and rock density. Berlin. Geol. Soc. Amer. Bull, 23: pp. 372-410.