• 

DEPARTMENT OF THE INTERIOR 

UNITED STATES GEOLOGICAL SURVEY 

GEORGE OTIS SMITH, DniECTOR 

PROFESSIONAL PAPER 85-C 

IN~rERPRE~rA,-fiON· OF ANOMALIES OF 

GRAVI,_l-,Y 

BY 

GROVE KARL GILBERT 

• F'ublislle<l December 18, 1913 

PART C OF PROFESSIONAL PAPER 85, "CONTRIBUTIONS 

TO GENERAL GEOL9GY, 1913" 

WASHINGTON 

GOVERNMENT PRINTING OFFICE 

1913 
CONTENTS. 

Page. 

The anomalies.. . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 

Interpretation by imperfect isostatic adjustment........................................................... 30 

Interpretation by vertical heterogeneity of crust. .............................. ·. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 

Interpretation by variation of depth of compensation ....................... : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 

Geologic relat~ons of anomalies............................................................................ 32 

The locus of adjustment .............. , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 

Interpretation by nucleal heterogeneity................................................................... 35 

Review and conclusion.................................................................................... 36 

ILLUSTRATIONS. 

'Page. 

PLATE IV. Map of the United States showing lines of equal anomaly of gravity ........ "..................... 32 

FIGURE 7. Hypothetic relation of density anom~lies to densities and to depths....... . . . . . . . . . . . . . . . . . . . . . . . . 31 

II 
INTERPRETATION OF ANOMALIES OF GRAVITY. 

By GROVE KARL GILBERT. 

THE ANOMALIES. 

A by-product of the adjustment of primary triangulation for the United States was the 

deternrination of the defle.ction of the vertical at 765 stations.1 In discussing these deflections 

:Hayford introduced the hypothesis of isostatic compensation, with the result that the deflections were "thereby reduced to less than one-tenth of the mean values which they would have 

if no isostatic compensation existed." 2 The particular form given to the hypothesis was this: 

At son1e depth below the horizon of sea level, called the depth of compensation, the stresses due 

to gravity are ·uniform. Each unit vertical column above the horizon of con1pensation contains the sam~ mass, 3 the product of the length of the column by its mean density being the 

same in all places, or the variation of length associated with topographlc relief being compensated by reciprocal variation of n1ean density. In the adjustment of the deflections of the vertical various assumptions were made as to t:p_e depth at whlch compensation is. complete, and 

the depth yielding .the best adjustment was found to be 122 kilometers. 1 • 

liayford and Bowie, in discussing the determinations of gravity at stations in the United 

States, use<;l the same hypothesis of isostatic adjustment and adopted from I-Iayford's earlier 

work the estimate of 122 kilometers as the depth of compensation. For each of 124 stations 

at which the intensity of gravity had been measured they computed the attractive influence 

not n1m·ely. of the elements of the neighboring topography, but of the topographic elements of 

the entire earth, and the whole computation was made subject to the isostatic hypothesis. 

The attractive influence thus deduced .was added (algebraically) to the value of gravity appropriate to the latitude and altitude of the station, giving a theoretic or computed value, whlch 

was then compared with. the value obtained by observation. The difference-observed minus 

computed-is called the local anomaly of gravity. The mean of the 124 anomalies is 0.020 

dyne. Tills is approximately one-fourth as large as the mean of anomalies obtained without 

the introduction of the isostatic hypothesis. . 

The success of the hypothesis in reducing anomalies of the vertical and anomalies of gravity 

is held-properly, as I think-to show that isostatic adjustment in the earth's crust is nearly 

perfect. Taking the outstanding or ·residual anomalies as 1neasures of the approximation to 

1 ~l'ho papers to which tho present article refers are as follows: . 

Hayford, J. F., 'l'ho figure of the earth and isostasy from measurements in tho United States, U.S. Coast and Geodetic Survey, Washington, 

HI09; Supplementary investigation in 1909 of the figure of the earth and isostasy, U. S. Coast and Geodetic Survey, Washington, 1910; 'l'ho relations 

of Isostasy to geodesy, geophysics, and geology, Science, new ser., vol. 33, pp. 199-209, 1911. 

Hayford, J. F., and Bowie, 'Villiam, The effect of topography and isostatic compensation upon the intensity of gravity, U.S. Coast and Geodetic Survey Special Pub. No. 10, Washington, 1912. 

Howle, William, Effect of topography and isostatic compensation upon the intensity of gravity, U. S. Coast and Geodetic Survey Special Pub. 

No. 12, Washington, 1912; Some relations between gravity anomalies and tho geologic formation(s] in the United States, Am. Jour. Sci., 4th sor., 

vol. 33, pp. 237-240, 1912. 

Spencer, J. ,V., Relationship between terrestrial gravity and observed earth movements of eastern America, Am. Jour. Sci., o<tth sor., vol. 

35, pp. 5(11-573, 1913. 

2 Figure of tho earth and isostasy, p. 175. 

a Mass is the term employed by Hayford, and his usage has been followed in the present paper. In strictness weight is the quantity with 

which isostasy is concerned, and the substitution or mass for weight in the analyses involves the assumption that gravity is uniform from top to 

bottom of tho zone of compensation. It is, in fact, about 1 per cent greater Rt tbe depth of 122 kilometers than· at tho surface. Tho numerical 

errors possibly entailed by the substitution are negligible. 

12807°-13 29 
30 CONTRIBUTIONS TO GENERAL G~OLOGY, 1913. 

perfect adjustment, the authors state that the mean anomaly in the vertical corresponds to the 

mass of a rock layer 250 feet thick, and the mean anomaly in gravity to a rock layer 630 feet 

thick. 1 

Each measurement of the intensity of gravity is of course affected by an error. The corresponding computed intensity is also affected by an error. Their difference, the anomaly, is the 

algebraic sum of the two errors .. The average error of the observed values of gravity is demonstrably small, so that the anomalies differ little from the errors of the computed values. The 

error of a computed value is not all from a· single source. Part of it comes from the data used, 

such as the altitude, the mean density of fhe surface rock, and especially the configuration of 

the surrounding topography; another part comes from the methods of computation, which were 

somewhat shortened for the sake of economy;_ and a third part comes from assumptions connected with the specific hypothesis of isostatic compensation. The authors cited discuss these. 

classes of error with care and reach the conclusion that all are small in comparison with those 

, arising from the assumptions. 2 An attempt to interpret the anomalies may therefore properly 

include the consideration of their relations to various assumptions. 

INTERPRETATION BY IMPERFECT ISOSTATIC ADJUSTMENT. 

The explicit general assumption as to compensation is that the excess of mass in any crustal 

column due to its projection above sea level is exactly compensated by defect in density uniformly distributed from the surface to a depth of 122 kilometers; and that defect of mass in any 

unit column beneath the ocean is similarly compensated by excess of density (with due allow-

. ance for the mass of the overlying water). This general assumption includes the more specific 

. assumptions (1) that the compensation is perfect, (2) that the compensatory defect or excess 

is uniformly distributed through the· column, (3) that the depth of compensation,-122 kilometers, 

is not subject to v&riation from place to place. To these may be added an implicit assumption 

of which there will be occasion to speak on a later page. The inexactness of the three assumptions is explicitly and fully recognized by the authors cited,3 but their discussion gives prominence only to the inexactness of the first. In a general way they 'interpret the anomalies as due 

to uncompensated local excesses or defects of mass in the crustal layer, or, ill other words, to 

imperfection of isostatic adjustment. The present paper will consider the pos~ibilities of interpretation connected with the other specific assumptions. . . 

INTERPRETATION BY VERTICAL .HETEROGENEITY OF CRUST. 

In place of the assumption that the vertical distribution· of compensatory density difference 

is uniform, let us assume that it is subject to the same variation as is the assumed horizontal 

distribution of compensatory density difference. In each case the compensatory element of 

density is but a small fraction of the entire density. 

The topographic relief most intimately associated wit~ the gravity stations is that of 

the United States. The mean altitude of the United States, as given by the authors, is 2,500 

, . feet, or 762 meters; and the compensatory--·· Q<)rrection to density for . + 762 meters is 

- 762 X 2

·

67 = -0 0167 The compensatory correction for neighboring oceanic topography is 122,000 . . . 

positive, and its average is.'coordinate in amount. The value 0.0167 may serve as a rough 

estimate of the average departure in density which was assumed :i.t1 computing corrections for 

topography. An alternative estimate may be based on the topographic relief of the entire 

globe. Again, using the level of the ocean surface as a horizon of reference, making due allowance for the partial compensation given by the.mass of the water, and combining positive and 

negative corrections irrespective of sign, we have 0.0381 as the resulting value of the average 

departure in density. Neither mode of estimation is entirely satisfactory, but together ~hey 

I This figure applies to 122 instead of 124 anomalies. By omitting two aberrant anomalies the mean is reduced from 0.020 to 0.018. See Special 

Pub. No. 12, p. 23. 

2 Special Pub. No. 10, pp. 88-94. 

a Idem, p. 11. 
INTERPRETATION OF ANOMALIES OF GRAVITY. 31 

yield an order of magnitude; and an intermediate value, 0.025, will be accepted as sufficiently 

precise for the present purpose. In order to discuss the effect of a vertical variation of density 

cqordinat~ in amount with the postulated horizontal variation, it will be assumed that the 

average deviation of the density of any large portion of the crustal column. from its normal 

·is 0.025. · · · 

In: the diagram, figure 7, vertical distance represents depth below the earth's surface, A 

corresponding to the surface and B to the level of compensation, 122 kilometers below. IIorizontal distances, measured from AB as origin, represent density. The line OD arbitrarily 

repr,e~ents the normal curve of density in relation to depth. The nature. of the curve within 

the zone of compensation is un~own, and its form has no importance 'in the present connecti~n. 

The shaded area GE expresses the· assumption that in a particular locality the upper half of 

the zone is characterized by a uniform defect of density, and the shaded are~ D F expi·esses 

the assumption that in the same locality the lower half of the zone is characterized by an excess 

of density of the same amount. The widths of the areas oorrespond by· scale to departures 

of 0.025. Tha introduction of these departures in density does not affect the total mass of 

the unit column, but it does affect the intensity of gravity at the top of the column. The 

trac.t of defic~ency being· nearer to the surface than the. tract of excess, the loss of attraction 

exceeds the gain and there is a net reduction of tb.e intensity of gravity. · 

To obtain numerical results it is necessary to assume horizontal as well as vertical dimensions for the bodies of rock affected by abnormality of density, and computations are facilitated 

by giving each ideal body the .form of a right cylinder, the one resting on the other. The 

radius of the cylinders is assumed as 61 kilometers (one-half of the depth of the level of compensation); the assumed defect in density for the upper 

cylinder and the assumed excess for the lower are each 0.025; 

a.nd the station on which their influence is computed is J'------01 D 

·assumed to be at the cetlter of the upper face of the upper 

.cylinder. 'l'he computed influence 1 of the defect in· density 

on gravity at the station is -0.0375 dyne; that of the excess 

is + 0.0115 ·dyne; and their algebraic sum is -0.026 dyne. 

If h f d · · · h b d d h d f FIGURE 7.-Hypothetic relation of density anom- t e excess o ens1ty IS m t e upper o Y an t e e ect al.ies to densities and to depths. 

in the lower, the effect. on surface gravity is + 0.026 dyne. 

These quantities are to be compared with the mean anomaly for the systen1 of gravity stations,. 

·which is 0.020. dyne. 

Thus it appears that the same moderate assumptions as to variation of density which 

: llayford and Bowie apply to horizontal relations in discussing isostatic compensation yield, 

·if applied to vertical relations,: departures in gravity intensity of the same order of magnitude 

a.s the outstanding anomalies found after making allowance for isostatic compensation. 

From this I infer that the anomalies may be in part due to irregularities in the vertical dis-

. tribution of densities, or that such irregularities are competent, alike in the nature of their 

·influence and in its possible amount, to cause such anomalies of gravity as have been discovered. 

INTE,RP:RETAT~ON BY VARIATION OF DEPTH OF COMPENSATION. 

Let us now consider the effect of rernoving the restrictive assumption .which makes the 

depth of compensation uniform at all points. In Hayford's discussion of deflections of the ver-

. ticnJ separate cdmputations are made for ten divisions of the United States, and the results of 

·.~pese computations lead· to the conclusion "that ·while there are indications that the depth of 

compensation is greater in the eastern and central portions of the United States than in the 

·,~r_es~~~·n portion, the evidence is not strong enough .to prove that there is a real difference in 

depth of compensation in the different regions;" 2 but the authors of the papers on gravity use 

only the assumption of uniformity. In view of the recognized heterogeneity of crustal material 

h appears· to me both possible and probable ·that the· depth at which material is sufficiently 

mobile to effect isostatic adjustlnent is subject not only to regional but to ·highly localized 

1 Computed by means of a formula given by Hayford and Bowie in Special Pub. No. 101 p. 17. 2 Figure of the earth and isostasy, p. 143. 
32 CONTRIBUTIONS TO GENERAL GEOLOGY, 1913. 

variation. To obtain an idea of the quantitative relations between local variation of the qepth 

of compensation and resulting variation of gravity, I have postulated a circular tracthaving a 

radius of 61 kilometers and having such topographic relief that the compensatory density, for a 

depth of 122 kilometers, is - 0 025. Then I have introduced various changes in the postulated 

depth of compensation, with corresponding changes in the compensatory density, and computed the effect on local gravity. The change in intensity of gravity corresponding to 40 per 

cent increase in the depth of compensation is -0.0161 dyne; the change corresponding to 40 per 

cent decrease is + O.Oi25 dyne. These quantities are to be compared with the mean anomaly 

of-gravity, 0.020 dyne. The resulting figures would be somewhat but not greatly different if 

the computations were applied to an area several times larger. ' 

The general fact appears to be that local variations of the depth of compensation are competent to cause anomalies of gravity, but that ':ery large variations would be necessary to pro~ 

duce such anomalies as have been observed. To explain in this way the.greatest of the anomalies 

it would be necessary to assume that the zone of compensation is many times as deep at some 

places as at others. While such a condition may not be impossible, the geodetic results indicate 

that it is highly improbable; and I am disposed to regard variation in depth of compensation 

as decidedly less available in interpreting anomalies than variation in the vertical distribution 

of densities. · 

GEOLOGIC RELATIONS OF ANOMALIES. 

To exhibit the geographic distribution of anomalies the authors cited have drawn lines o'f 

equal anomaly on a map of the United States; 1 and these lines are reproduced in Plate IV. 

The contour interval is 0.01 dyne, and areas of plus anomaly are distinguished from areas of 

minus anomaly by shading. The positive and negative anomalies are not indiscriminately 

mingled, as should be expected if the anomalies had the character of accidental errors, but fall 

into groups. Large districts of plus anomaly appear and other large districts of minus anomaly. 

Thi·s effect is undoubtedly heightened by the fact that the distances between stations are large, 

but is not created thereby. A comparison of parts of the map controlled by numerous stations 

with parts controlled by few and a comparison of this map based on 124 st·ati.Qns with an earlier 

map bas(3d ori 87 stations leave no question in my mind that there is a veritable areal grouping 

of the anomalies. With the multiplication of gravity stations the courses of the lines will be 

modified, and contrasted areas will become more clearly defined, but the type of the future 

map is shown by the one we now have. · 

The anomaly .map is in some way an expression of subterranean structure, for it tells of the 

distribution of mass. As the subterranean structure is a produ~t of the earth's history, the 

distribution of anomalies has a historical significance. To determine the nature of this significance is a problem in interpretation: . 

Bowie 2 has classified the anomalies according to the geologic formations occurring at the 

stations to which they pertain, thus in effect attempting a correlation between the map of anomalies and the geologic map, but the correspondences are not important. By a series of computations he shows that such local excesses or defects of mass as may be ascribed to the densities 

and ,volumes of formations visible at the stations are not at all adequate to explain the 

anomalies. 

Hayward and Bowie have compared the anomalies with areas of large recent unloading of 

the crust by erosion and with areas of large recent loading by deposition, but have not found 

such correspondence as to support the hypothesis of cause and effect; 3 and a similar negative 

result followed an attempt to correlate anomalies with the loadings and unloadings of certain 

districts by the ice of glacial time. 4 Spencer 5 emphasizes the fact that there are large plus 

anomalies within the region once covered by the Laurentian ice sheet and regards it as proof 

i Special Pub. No. 12, illustration No.2. 

2 Am. Jour. Sci., 4th ser., vol. 33, pp. 237-240, 1912. See also U.S. Qoast and Geodetic Survey Special Pub. No. 10, pp. 113-117, 1912. 

s Special Pub. No. 10, p. 112. : 

4 Idem, p. 116. 

5 Am. Jour. Sci.; 4th ser., vol. 35, pp. 569-570, 1913. 
U. S. GEOLOGICAL SURVEY 

-. ...._ __ ___ 

---------.r-

./ -:------

1 I -------.. ....___ 

MAP OF THE UNITED STATES SHOWING LINES OF EQUAL ANOMALY OF GRAVITY. 

Areas of plus anomaly are shaded. Contour interval, O.Ql dyne. Gravity stations are indicated by dots. 

PROFESSIONAL PAPER 85 PLATE IV 

r\ . 

I 

... ~ v -- \ \ 
·.J., INTERPRETATION OF ANOMALIES OF GRAVITY. 33 

that the rising of that region after the removal of the ice load was not caused by the re~oval 

of load. 

In the drawing of inferences from the relations of anomalies to loading and unloading 

much depends on the mode of interpreting anomalies; and, conversely, the relations of anomalies to loading and unloading may be used as tests of modes of interpretation. In a general 

way the continental shelves have long been ·areas of loading and adjacent land districts have 

been areas of unloading. To whatever extent isostatic compensation for this loading and 

unloading has been imperfect, to whatever extent the readjustment lags behind the disturbance of equilibrium, there should be an excess of mass. under the submerged shelf and a 

deficiency under the land .. Under the hypothesis of interpretation which correlates excess 

of mass with plus anomalies and defect of mass with minus anomalies we should expect to 

find, as a general fact of the anomaly map, au anomaly gradient from ocean to laud in 

coastal regions. Such a gradient is, in fact, found between Boston, Mass., and Trenton, 

N. J., and between Florida and the Rio Grande, the two stretches comprising one-third of our 

coast; but the gradient is unequivocally oceanward between Delaware and Florida, and 

elsewhere its direction is parallel to the coast. The Appalachian belt south of the region of 

glaciation has been practically free from. loading during two geologic ages and has been 

unloaded to the extent of many thousands of feet of rock. Isostatic adjustment may be supposed to have added mass in compensation for the unloading, or for part of it, but may not 

plausibly be supposed to have overcompensated so as to create an excess of mass. ·Nevertheless, there are large plus anomalies in that belt, and their existence evidently creates a 

difficulty in interpreting plus· anomalies as due to crustal excess of mass. The dis.trict of 

greatest loading in recent time is the Delta of the Mississippi, and if isostatic adjustment has 

not fully kept pace with the loading there should be in this district a local excess of mass. 

The fact that the local anomaly is minus instead of plus calls in question the mode of interpretation which infers crustal defec.ts of mass from minus anomalies. 

The hypothesis that certain Pleistocene sinkings and risings of the land were caused Ly 

the associated additions and removals of ice load is in general accord with the theory of 

isostatic adjustment. If it is true that the crust became approximately adjusted to the last 

loading and that the subsequent deformation, of which we have record in the inclined shores 

of glacial lakes, was caused by a readjustment during and after the final unloading, then 

there should be no excess of mass in the readjusted or readjusting area. Because there is 

a tract of plus anomaly within this area Spencer discredits the hypothesis of deformation 

through unloading, but the fact may equ'ally 'be used to discredit the hypothesis underlying 

· his mode of interpreting anomalies. 

In all these cases involving loading or unloading the hypothesis that the anomalies 

represent imperfect compensatio~ and imperfect adjustment yields results which are unsatisfactory because they are opposed to plausible expectation, and the expectation is plausible 

because it is founded on the theory-we need no longer call it the hypothesis-of isostatic 

adjustment. In all these cases the distribution. of anomalies may be reconciled with ratio~al 

expectation by assuming local irregularities in the vertical distribution of densities, and the 

irregularities thus assumed need b~ only of the order of magnitude of those irregularities in 

horizontal distribution of densities which· have been assumed in the reduction of the geodetic 

observations. . 

In my opinion these conside~ations connected With phenomena of loading and unloading 

serve to show that the anqmalies may not properly be interpreted as due exclusively to crustal 

excesses and defects of 1nass existing be~ause of imperfection of isostatic adjustn1ent. Some 

additional mode of interpretation must be admitted, and at least one other mode, that connected with irregularities in the ver~ical density gradient, appears to be both qualitatively 

and quantitatively competent. 

If the two modes of interpretation are accepted as coordinate, it becon1es possible to extend 

the conclusion of Hayford and Bowie as to the perfection of isostatic adjustment. The one 

mode of interpretation, if used exclusively, yields. an average imperfection of adjustment 
34 CONTRIBUTIONS TO GENERAL GEOLOGY, 1913. 

measured (positively or negatively) by the weight of a layer of rock 630 feet thick; the other, if 

used exclusively, implies no imperfection of adjustment. Ariy combination of the two yields 

the conception of ·an adjustment more nearly perfect than would be implied by the measure of 

630 feet of rock. 

If vertical 'irregularity of density were to be accepted as the exclusive cause of gravity 

anomaly, the map of gravity anomaly would become (approximately) a map of vertical density 

anomaly, each area of minus gravity anomaly being replaced by an. area in which departures 

from the norm~l density gradient of the crust are negative near the .surface and positive below 

and each area of plus anomaly by one in which density departures are positive near. the surface 

and ·negative below. Such a change would remove the problem of interpret~tion to a new 

position, by raising the question of the origin of the anomalies in density. Giving attention 

to this new question, I have been led to the suggestion that a competent cause for the peculiarities of density distribution would be apt to find expression also in the greater facts of the 

structure of the continent. Among those greater facts1 so far as we are able to read them in 

the visible structure and physiography, are (1) the Appalachian-Ozark belt of corrugation and 

(2) the strong contrast, farther west, between a cordilleran region of strong orogenic disturbance 

and a plains region of relative freedom from disturbance; and I have studied the relation of 

these features to the features of the anomaly map. The correspondences are so slight that they 

may be regarded as accidental, and the general rela:tion is that of independence and discordance. 

The result is of limited sigJ?.ificance because the visible structure elements may constitute but 

' a small fraction of the structure of the crust, but so far as it goes it fails to support the 

hypothesis that the anomalies of gravity are due exclusively to anomalies in the vertical 

distribution of density within th~ crust. 

THE LOCUS OF ADJUSTMENT. 

. ' 

Hayford has given an analysis of the general mechanics of isostatic readjustment when the 

isostatic equilibrium has been disturbed by erosion and deposition.~ The analys.is reveals 

stresses tending to cause an undertow within the crust, and adjustment is ascribed by Hayford 

to the undertow. My own conception of the process of adjustment accords with these features 

of his analysis, but adds· the idea of relative mobility as an important condition in determining 

the place of underflow and the perfection of the adjustment. 

Now that the argument from tides has been efficiently supported by that from the speed 

of earthquake waves, we may accept with. confidence the doctrine of the high rigidity of the 

earth's nucleus. The theory of high rigidity acc·ords also with the fact of high density, provided 

the nucleal materials are similar to the crustal, for with sufficient compression the v~cosity of 

even the most mobile fluids become high rigidity. Immobility at all depths below that of 

compensation is either explicitly or implicitly assumed by Hayford a.nd Bowie·. 

On the other hand, there is much _geologic evidence of mobility somewhere below the 

surface. Part of this evidence is volcanic. The continuous or: secular relations of pressure, 

temperature, and density in the subterranean region from which liquid rock rises at intervals 

may be assumed to be· such that moderate change of condition either induces liquefaction or 

else so lowers the density of rock already liquid as to render it eruptible; and such a balancing of conditions implies some sort of mobility. Other evidence is diastrophic. In sorp.e 

·regions, ·such as the Appalachian, overthrusts. and folds testify to great reduction in the 

horizontal extent of rocks near the surface, the reduction having been accomplished in a 

small fraction of geologic time. If the subjacent portion of the nucleus had been correspondingly forced into narrower space there would have resulted an enormous mountain range, but 

the actual uprising was of moderate amount. Plausible explanations of the phenomena necessarily include horizontal .movements of the upper rocks: without corresponding movements of 

the nucleus and thereby imply mobility in. an intervening layer. In certain -block-mountain 

districts of the West the. master faults are antithetic in type to the overthrust and demon- 1 

1 Science, new ser., vol. 33, p. 202, 1911. 

.• 
J. 

INTERPRETATION Ol!., ANOMALIES OF GRAVITY. 35 

strate pronounced extension of the upper part of the crust. The nucleal tract beneath could 

not share in this extension without creating an enormous depression, which does not exist; 

and the interpretation of the phenomena involves horizontal shear in material more mobile 

than the visible upper rocks. 

The conception thus engendered, of a relatively mobile layer separating a less mobile layer 

above from a nearly immobile nucleus, appears to me in full accord with the. evidence which 

geodesy affords of isostatic adjustment. 1;he geodetic "depth of compensation·" ·agrees with 

such suggestions as to the position of the horizon of maximum mobility a.s might be afforded 

by the volcanic and diastrophic phenomena. The existence of a horizon of mobility accords 

with the inference of approximate perfection of isostatic adjustment. · 

It is not necessary to supp.ose that the degree of mobility at the horizon of mobility is 

that of a liquid at the surface. When such mobility is attained by any but the densest rocks 

eruption takes place. It is not necessa1;y to think of the degree of mobility as uniform, either 

from place to place or from time to time. Its place variation would naturally be coordinate 

with that of rock types, and its time variation coordinate with epochs of elevation and subsidence. Neither should the depth of the horizon of maximum mobility be thought of as uniform. 

INTERPRETATION BY NUCLEAL HETEROGENEITY. 

The inner earth is the inalienable playground of the imagination. Once it contained the 

forges of blacksmith gods; or it was the birthplace of our race, or the home or prison of disembodied spirits. Later Symmes hollowed from it a vast habitable empire, concave like the 

world of Koresh. Science now claims exclusive title but holds it chiefly for speculative purposes; 

and the freedom of speculation practically recognizes but two limitations: The inner earth is 

dense, and it is rigid. As to all other properties opinion is untrammeled. 

It is my own view that the inner part of the nucleus is not merely hot, but very hot. If 

the law of compression by pressure and the law of expansion by heat, as we know them at the 

surface, apply equally to the nucleus, then the mean temperature of the earth must be enornlous in order to afford a mean density so low as 5.6. An enormous temperature implies 

an enormous store of heat. This is the source of the energy involved in the hypogene activities of the earth, and it is fed to the crustal region by conduction. If the earth were composed of homogeneous shells diversity_ of crustal activity would depend on outside conditions 

only and would be connected with latitude. In fact, however, the diversity of crustal activity 

is largely independent of latitude. It is in part related to visible diversity of crustal material, 

but in larger part it appears unrelated to things visible. Deformation sometimes shows or 

seems to show dependence on erosion and deposition, but any such scheme of causation yields 

a running-down process and fails to account for the perpetual initiative of geologic activity 

through the ages. The deformations whic~ have not only developed but perpetually remodeled 

the continents have a source below the surface. Their method probably involves reactions 

between temperature, pressure, and the physico-chemic constitution of rocks, but these reactions, like the superficial reactions, yield running-down processes and do not afford a fundamental explanation of crustal activity. The factor to which I appeal is primordial heterogeneity of earth material, a heterogeneity. which gives diversity to the flow of heat energy 

and to the physical and chemic changes of crustal regions. It does not seem sufficient that the 

crust be heterogeneous; there should be heterogeneity also below the horizon of mobility. 

Under this speculative view of the earth's constitution the anomalies of gravity may be in 

part occasioned by tracts below the level of con1pensation which are characterized by exceptional 

density. It nppears to me quite possible that underflow in a mobile layer might effect a practically perfect adjustment for differences in density above the layer, so as to bring crustal 

densities and crustal relief into harmony, and yet l~ave.uncmnpensated the differences in density 

of the i1ucleus. 

To obtain so1ne idea tts to the quantitative ability of nucleal heterogeneity to modify gravity, 

let us assume that abnormalities of d.ensity are us great in the nucleus as in the crust. Le.t. us 
36 CONTRIBUTIONS TO GENERAL GEOLOGY, 1913. 

assume that just below the horizon of compensation is a nucleal tract in which the abnormality 

of density is ±0.025, and that the form and dimensions of the tract are those of a right·cyllnder 

with height and radius each equal to 122 kilometers. The computed attraction of the nucleal 

abnormality of mass, exerted at a gravity station situated directly above the center of the 

cylindric tract, is ±0.023 dyne; and this is of the same order of magnitude as the mean anomaly 

of gravity, 0.020· dyne. The influence of such an abnormality of mass would have its mau'\:i-

,mum .at. the station and would diminish with increasing distance from the station, the genertt.l 

result being a hill or a hollow on the contour map of anomalies of gravi~y. 

The mode of interpreting gravity anomalies which appeals to nuclear heterogeneity is 

applicable not only to those anomalies which encounter difficulty in dealing with districts of 

loading and unloading, but also to those grouped anomalies whose areas and· contours exhibit 

independence of all visible geologic structure. It seems, in fact, to. be competent to account 

for all anomalies except such as exhibit very steep gra,dient. On the· other hand, if the devel.. 

opment of the subject shall show that there are anomalies which can be explained in no other 

way, the existence of such anomalies may constitute evidence of nucleal heterogeneity. 

Hayford and Bowie, by ignoring the possibility of nucleal density anomalies, implicitly 

assume isostatic adjustment in the nucleus, such an adjustment as would exist in a nucleus 

composed of concentric homogeneous shells. The alternative interpretation of gravity anomalies just outlined is founded on the supposed inexactness of that assumption. 

REVJ;EW· AND CONCLUSION. 

The mean density ·of the earth is about twice the average density of earth material at the 

surface. In a general way density increases from the surface downward. If the density gradient 

were everywhere the same the earth might be described as composed of concentric layers, each 

homogeneous as to density. 'fhe actual departures from such an equable arrangement may be 

called anomalies of ·density. Anomalies of density systematicall}7 related to topographic relief 

have been .assumed by Hayford and Bowie in computing theoretic gravity at each gravity 

station, the difference between the theoretic gravity and observed gravity being the local anon1aly 

of gravity. An anomaly of gravity (except as affected by errors of observation, etc.) is caused 

by anomalies of density other than those systematically introduced into the computations. 

Hayford and Bowie's system of density anomalies is one which assumes isostatic equilibrium 

at a depth of 122 kilometers. The distribution of the additional anomalies of density necessary 

to account for the anomalies of gravity is unknown. So· many different distributions seem 

possible· that the actual distribution may not be det.er1ninable. One suggested distribution 

(Hayford and Bowie) includes only horizontal variation and restricts yariation to the. crustal 

region. It involves moderate imperfection of isostatic equilibrium. at the depth of 122 kilometers, and it encounters difficulties when applied .to the anomalies .of regions which have 

recently gained or lost mass through loading or unloading. A second suggested distribution, or· 

element of distribution, involves vertical variation within the crustal region. Taken by itself 

it seems equally competent with the first, and it does not involve .the same imperfection of 

isostatic equilibrium. A third suggestion, coordinate with the others in that it is quantitatively, adequate, is that the additional anomalies of density are not confined to the crustal 

region but occur also at depths greater than 122 kilometers and below the region of isostatic 

~djustment. A fourth suggestion, that the distribution of the additional anomalies of density 

is connected with variation in the depth of the horizon of adjustment, may supplement either 

of the others but is not by itself sufficient to account for the anomalies of gravity. 

Volcanic phenomena and phenomena of crustal shortening and crustal extension indicate a 

horizon of relative mobility above the rigjd nucleus. To whatever extent a subcrustallayer is 

mobile the means are furnished for approximately perfect isostatic adjustment at that level. It 

is inferred· that the actual adjustment is more nearly perfect than would be indicated by the 

geodetic data if those data were interpreted according to the first of the above-mentioned 

suggestions. The geologic evidence in favor of a mobile layer combines with the evidence from 

J. ... 
INTEUPRETATION OF ANOMALIES OF GRAVITY. 37 

approximate isostasy despite surface transfers of load to show that the anomalies of gravity are 

not due chiefly to uncmnpensated ex<?esses and deficiencies of mass in the crUBt; and I incline 

to the view that the hypothesis which so interprets them is one of the least probable of the 

four suggested. 

The second and third suggested interpretations-that by vertical arrangements of anomalies 

of density within the crust, and th~t by anomalies of density below the horizon of isostatic adjustment-are not competitive, and each may prove to have its field of application. The second has a sound basjs, for vertical variation of density in the crust is demonstrated as far down 

as the som:·ces of volcaujc eruption. The third has perhaps no more than a presumption in 

its favor. The failure of anomalies of gravity to group themselves in harmony with-large features of crustal structure n1akes it easy to think that their grouping may be related to nucleal 

structure. When the 1nultiplication of gravity stations shall have relieved some of the broad 

areas of the anomaly map from their present vagueness, the groupings may be found more 

significant than they seem at present. Crustal diversity may be to an important extent a product and record of the geologic. chapter of eart~ history. Nucleal diversity, if it exists, belongs 

to pregeologic chapters. -

Starting with geodetic and topographic data and assuming certain uniformities, Hayford 

and ;Bowie have demonstrated isostasy and developed a gravity anomaly map. The map 

contains a body of observational data coordinate with the geodetic and topographic. By a 

future mathematical discussion which ·treats the three bodi~s of data together and which 

recognizes alternative interpretations of the anomalies of gravity it may be possible to practically demonstrate the meaning of the anomaly map .. At present the map seems to express 

chiefly an effect of heterogeneity jn the nucleus and an effect of irregularity in the vertical 

distribution of densities within the crUBt. 

0