Gravity anomalies

Gravity anomalies are variations in expected values of measured gravity at specific locations and elevations on the earth. Gravity anomalies reveal changes in the density of rocks in the subsurface and were the first evidence for the existence of mountain roots and the differences between oceanic and continental crust.

Gravity Variation Factors

A gravity anomaly is a departure from the expected value of the acceleration of gravity at any point on the earth's surface. In general, such departures are small compared to the total gravity of the earth, which averages 980 centimeters per second squared. The actual value varies as a function of latitude and elevation. This variation occurs because the earth is not a perfect sphere but a spheroid of revolution. The equatorial radius is 6,378 kilometers, 21 kilometers longer than the polar radius of 6,357 kilometers. Since gravity decreases over distance, the gravity at the equator is less than that at the pole. Added to this is the effect of the earth's rotation. Together, these effects lead to gravity values of 978.0490 centimeters per second squared at the equator and 983.2213 centimeters per second squared at the pole, with a value for any latitude between predicted by a simple formula. Latitude explains the largest variation in gravity values of the earth. A second major effect results from elevation, which brings about a decrease in gravity of approximately 0.094 centimeter per second squared for every thousand feet of elevation above sea level.

The gravity at two points on the earth's surface will depend on latitude and elevation effects and on the densities of the rocks beneath the two points. The densities are of particular interest to the geophysicist. To evaluate these densities, the gravity values measured at two points on the earth's surface must be corrected for the latitude and elevation effects.

Free-Air and Bouguer Anomalies

The correction for the shape and rotation of the earth is made with the simple formula mentioned previously and reduces the effect of the latitude difference to zero. After this correction has been made, differences in gravity measured at two points may be attributed to differences in elevation and variations in the density of the underlying rocks. The correction for elevation is made relative to sea level and may be divided into two parts. The first involves the effect of being farther from the center of the earth as a result of the elevation. This correction is called the free-air correction, because it corrects the effect of distance as if there were only air between the point on the surface of the earth and sea level. The second part of the elevation correction involves the subtraction of the effect of the slab or rock between the surface and sea level. This latter correction is termed the Bouguer correction.

Gravity values corrected for latitude and incorporating the free-air correction are termed the free-air gravity or free-air anomaly. Gravity values corrected by latitude and by free-air and Bouguer corrections are called the Bouguer gravity values or Bouguer anomaly. Bouguer gravity values may also involve corrections for irregular topography and the curvature of the earth.

Rock Density

After the measured gravity values have been corrected, all differences caused by latitude, elevation, and topography have been removed mathematically, and the residual gravity anomalies reflect the lateral changes in rock density at depth. These gravity anomalies are typically small, usually less than 0.2 centimeter per second squared or 200 milligals—representing the differences between measured and ideal gravity values.

The value of the anomaly is related directly to a surplus or deficiency in mass in the subsurface. The effect of this mass difference is related to the acceleration of gravity by Isaac Newton's equation δg = GδM/r², where δg is the difference in gravity values over what is expected, G is the universal gravitational constant, r is the distance from the anomalous mass to the point on the surface of the earth where the gravity is measured, and δM is the increased or decreased mass.

This mass is usually expressed as the product of the change in density (δσ) times volume, or δM = δσ × V. The density difference is the physical property of the rocks in the subsurface that causes the gravity anomaly. The amplitude and wavelength of the anomaly are caused by the size of the density contrast, the size and shape of the body, and the depth of the body.

This relationship can be illustrated by use of the simplest shape that may cause a gravity anomaly: a sphere. The figure shows spheres of different densities and sizes that are buried at different depths and the gravity anomalies associated with them. The anomalies have a maximum amplitude directly above the centers of the buried spheres, and the amplitudes decrease away from the bodies. In the figure, the horizontal axis marks distance in kilometers right and left of the center of the spheres, and the vertical axis marks the anomaly amplitude in milligals. In the first panel, three spheres are buried with their centers at the same depth of 20 kilometers. Most of the rocks in the area have a density of 2.7 grams per cubic centimeter; this value represents the background value of density in the example. Sphere A has a radius of 10 kilometers and a density of 2.9 grams per cubic centimeter, giving a positive density contrast, δσ, of 0.2 gram per cubic centimeter. The excess mass causes a positive gravity anomaly with a maximum amplitude of 13.97 milligals. The second sphere, B, has a density of 3.12 grams per cubic centimeter, a density contrast of 0.42 gram per cubic centimeter, and a 10-kilometer radius, causing a maximum anomaly value of 27.24 milligals. The third sphere, C, has a density of 3.12 grams per cubic centimeter but is smaller, with a radius of only 8 kilometers. This sphere causes an anomaly of 13.95 milligals. Even though sphere C has the same density as sphere B, its size, and therefore its mass, is less, and the resulting anomaly is less.

Comparison of anomalies A and C shows them to be nearly identical. This occurs even for bodies of different densities when the product of volume and density yields the same mass. Note that the half-width of anomalies A, B, and C are all the same, with a value of 16 kilometers. This occurs because the center of mass of all three spheres is buried at 20 kilometers.

In the figure's second panel, spheres D and E are the same sizes and densities as A and B, respectively, but are buried at 28 kilometers depth. The amplitudes of each anomaly are diminished as a result of the greater distances to the bodies. Furthermore, the wavelengths and the half-widths of the anomalies are increased. Here, the half-widths are approximately 21 kilometers. This example shows that a pair of anomalies such as A and E with approximately the same amplitude will have different wavelengths or half-widths if the bodies causing the anomalies are at different depths.

The last sphere is buried at a depth of 40 kilometers with a radius of 20 kilometers and a density contrast of 0.2 gram per cubic centimeter. The maximum amplitude of the anomaly is 27.94 milligals, close to the amplitude of sphere B, but the half-width of the anomaly is 31 kilometers, nearly twice that of anomaly B.

While most rock bodies do not approximate spherical shapes, the above relationships show several general principles of gravity interpretation. The anomaly occurs because of an excess (or deficit) of mass in the subsurface. The amplitude is controlled by the density, size, and depth of occurrence of the rock body. The wavelength and half-width are related to the depth of the body. The longer the wavelength and half-width, the greater the depth of the source of the anomaly.

More complexly shaped geologic bodies cause more complex anomalies, and more complex equations are used to describe them. Shapes often used to simulate geologic bodies include cylinders, slabs, and three-dimensional prisms. The power of the gravity method involves the use of equations to calculate an anomaly that matches as closely as possible the gravity values measured in the field. The match allows the scientist to infer much about the character of rocks at depth.

Determining Rock Density

Gravity anomalies show the density variations in the subsurface related to the occurrence of specific rock types. Practically, these variations must involve a lateral change in density from one place to another. Geologists and geophysicists try to understand the variation in terms of specific rock types. The densities of rocks vary as a function of composition, mineralogy, the occurrence of open spaces, and physical conditions such as temperature and pressure. Among sedimentary rocks, sandstone has a density range of 2.35-2.55 grams per cubic centimeter; shale, 2.25-2.45; limestone, 2.45-2.65; and loose sand, 1.90-2.00. Igneous rocks include granite, with a density range of 2.60-2.80 grams per cubic centimeter; gabbro, 2.85-3.10; and peridotite, 3.15-3.25. Metamorphic rocks include the following density ranges: granite gneiss, 2.60-2.70; schist, 2.70-2.90; amphibolite, 2.80-3.10; eclogite, 3.30-3.45; and marble, 2.70-2.75.

Using these data, one can get an idea of the rocks that are likely to cause a positive or negative gravity anomaly. If one were to rely only on these figures in interpreting rock types from gravity data, however, one would find a great many possibilities because of the overlapping of density ranges for different rock types. Thus, a limestone may have a density similar to that of a granite or a gneiss. For this reason, the geophysicist must be guided by what is known about the geology in the area being studied and by careful measurements of the actual densities for rocks from outcrop or drill holes in the region.

Gravity Modeling

The boundaries of the shapes of the rock bodies, which are mathematically determined by gravity modeling, are interpreted as having a geologic significance. Thus, these boundaries, representing the contact between rocks of different densities, may be interpreted as faults, intrusive contacts, unconformities, or normal depositional contacts, depending on what else is known about the geology.

By tracking changes in acceleration as a satellite orbits a planetary body, space scientists are able to map variations in the gravity field. These observations led to the discovery of lunar mascons (apparent mass concentrations in the lunar near-surface rocks). Mascons were eventually determined by gravity modeling to be caused by relatively thin layers of dense basalt pooled in large lunar basins mirrored by upward migration of dense mantle material. Gravity maps have been constructed for Mars and Venus by satellite measurements as well.

Gravity Anomaly Patterns

The largest differences in gravity occur as gravity anomalies between the ocean basins and the large continental masses. Ocean basins have positive gravity values, related to the dense rocks that underlie the oceans. Continents, by comparison, have negative Bouguer gravity values, which reveal that thick sections of low-density rock occur beneath the continents. The twin GRACE (Gravity Recovery and Climate Experiment) satellites launched in 2002 have produced large-scale anomaly maps from slight changes in their relative orbits. While the twin GRACE satellites ended their mission in 2017, their work was continued by the GRACE Follow-On (GRACE-FO), launched in 2018. In 2024, NASA announced plans to continue the program with the GRACE-Continuity, or GRACE-C, scheduled to launch in 2028.

The relationship between the density of underlying rock and elevation is a very general one that applies to most areas of the earth. As early as 1850, measurements had shown that mountains were underlain by rocks less dense than those underlying the surrounding lowlands. The relationship was explained by two models. The first was that continents and mountains were high because they were underlain by thicker sections of low-density rocks. Seismic data on the depths to the base of the continental crust have confirmed this model in most places. The second model suggested that mountains were high relative to lowlands because mountains are less dense than the rocks under the lowlands. This relationship has also been verified in a number of areas and does explain the lower elevations found in some rift valleys.

Scientists have found that the patterns of gravity anomalies in a large area may give a distinctive grain or “fabric” to regions on the continents. The patterns in a particular region may involve a series of positive and negative anomalies of a certain amplitude aligned in a particular direction. Adjacent regions may have groups of anomalies of different amplitudes, wavelengths, or orientations that contrast with one another in the same way that the different sections of a quilt stand out against one another. The distinctive regional character of gravity in many places allows geologists to divide the crust into provinces. Other geologic observations and age determinations have shown these provinces to be pieces of crust that were assembled over time to make the continents.

Geophysical Applications

Gravity anomalies are a major source of geophysical understanding of the earth, but there are uncertainties in the interpretation and modeling of gravity data. These uncertainties are lessened by the use of geologic information and other geophysical survey techniques. Magnetic, electrical, or seismic data can provide additional information about the depth, size, and shape of the body in the subsurface. Knowledge of these variables improves the scientist's ability to define rock density and the rock type.

Gravity anomalies have helped to define the compositional and structural differences between oceanic and continental crust and the crustal thickening that occurs under mountain ranges. The patterns of gravity anomalies also reveal the internal structure of continents and the stages of continental development. The occurrence of gravity anomalies associated with the oceanic trench systems and island areas likewise attest to the dynamic character of these features and constitute evidence for the theory of plate tectonics.

Economic Applications

Of major importance is the application of gravity anomalies to natural resource discovery and evaluation. Many economically important features are related to changes in rock density and are detectable using gravity measurements. Lateral changes in density may occur in areas where anticlines or faulting have formed traps for oil and gas. These features may cause either positive or negative anomalies. One of the most successful of these applications is in the energy industry, where a large number of producing fields are related to thick, intrusive masses of salt called salt domes. The low-density salt moves upward in the sedimentary section, creating folds and faults that are excellent traps for oil and gas. The negative gravity anomalies associated with the salt domes have been used to locate pools of oil and gas in this geologic environment.

A second application of economic importance is in the location and evaluation of groundwateraquifers in certain parts of the country. Aquifers are often found where Quaternary (about 2 million years to the present) sand and gravel deposits are especially thick. Since the density of sand and gravel is much less than that of rock, thick sections cause negative gravity anomalies proportional to aquifer thickness. Information from gravity surveys may thus be useful in land-use planning and development.

Principal Terms

amplitude: the positive or negative value (intensity) of an anomaly as measured against the background values in the region

Bouguer gravity: a residual value for the gravity at a point, corrected for latitude and elevation effects and for the average density of the rocks above sea level

density: the mass of a specific volume of a given material

free-air gravity: a residual value for the gravity at a point, corrected for latitude and elevation effects; this value allows the scientist to determine differences in the densities of subsurface rocks

half-width: the distance over which the amplitude of an anomaly falls from its maximum value to half the maximum amplitude

isostasy: the concept of balance by which continental and oceanic crust are “floating” on the denser substrate of the mantle

milligal: the basic unit of the acceleration of gravity, used by geophysicists in measurement of gravity anomalies equal to 0.001 centimeter per second squared

wavelength: the distance over which an anomaly rises to its maximum amplitude and falls again to background values

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