Gravity anomaly
The gravity anomaly at a location on the Earth's surface is the
Different theoretical models will predict different values of gravity, and so a gravity anomaly is always specified with reference to a particular model. The Bouguer, free-air, and isostatic gravity anomalies are each based on different theoretical corrections to the value of gravity.
A gravity survey is conducted by measuring the gravity anomaly at many locations in a region of interest, using a portable instrument called a
Definition
The gravity anomaly is the
Gravity anomalies were first discovered in 1672, when the French astronomer Jean Richer established an observatory on the island of Cayenne. Richter was equipped with a highly precise pendulum clock which had been carefully calibrated at Paris before his departure. However, he found that the clock ran too slowly in Cayenne, compared with the apparent motion of the stars. Fifteen years later, Isaac Newton used his newly formulated universal theory of gravitation to explain the anomaly. Newton showed that the measured value of gravity was affected by the rotation of the Earth, which caused the Earth's equator to bulge out slightly relative to its poles. Cayenne, being nearer the equator than Paris, would be both further from the center of Earth (reducing the Earth's bulk gravitational attraction slightly) and subject to stronger centrifugal acceleration from the Earth's rotation. Both these effects reduce the value of gravity, explaining why Richter's pendulum clock, which depended on the value of gravity, ran too slowly. Correcting for these effects removed most of this anomaly.[4]
To understand the nature of the gravity anomaly due to the subsurface, a number of corrections must be made to the measured gravity value. Different theoretical models will include different corrections to the value of gravity, and so a gravity anomaly is always specified with reference to a particular model. The Bouguer, free-air, and isostatic gravity anomalies are each based on different theoretical corrections to the value of gravity.[5]
The model field and corrections
The starting point for the model field is the International Reference Ellipsoid, which gives the normal gravity gn for every point on the Earth's idealized shape. Further refinements of the model field are usually expressed as corrections added to the measured gravity or (equivalently) subtracted from the normal gravity. At a minimum, these include the tidal correction △gtid, the terrain correction △gT, and the free air correction △gFA. Other corrections are added for various gravitational models. The difference between the corrected measured gravity and the normal gravity is the gravity anomaly.[6]
The normal gravity
The normal gravity accounts for the bulk gravitation of the entire Earth, corrected for its idealized shape and rotation. It is given by the formula:
The tidal correction
The Sun and Moon create time-dependent tidal forces that affect the measured value of gravity by about 0.3 mgal. Two-thirds of this is from the Moon. This effect is very well understood and can be calculated precisely for a given time and location using astrophysical data and formulas, to yield the tidal correction △gtid.[8]
The terrain correction
The local topography of the land surface affects the gravity measurement. Both terrain higher than the measurement point and valleys lower than the measurement point reduce the measured value of gravity. This is taken into account by the terrain correction △gT. The terrain correction is calculated from knowledge of the local topography and estimates of the density of the rock making up the high ground. In effect, the terrain correction levels the terrain around the measurement point.[9]
The terrain correction must be calculated for every point at which gravity is measured, taking into account every hill or valley whose difference in elevation from the measurement point is greater than about 5% of its distance from the measurement point. This is tedious and time-consuming but necessary for obtaining a meaningful gravity anomaly.[10]
The free-air correction
The next correction is the free-air correction. This takes into account the fact that the measurement is usually at a different elevation than the reference ellipsoid at the measurement latitude and longitude. For a measurement point above the reference ellipsoid, this means that the gravitational attraction of the bulk mass of the earth is slightly reduced. The free-air correction is simply 0.3086 mgal m−1 times the elevation above the reference ellipsoid.[11]
The remaining gravity anomaly at this point in the reduction is called the free-air anomaly. That is, the free-air anomaly is:[12]
Bouguer plate correction
The free-air anomaly does not take into account the layer of material (after terrain leveling) outside the reference ellipsoid. The gravitational attraction of this layer or plate is taken into account by the Bouguer plate correction, which is −0.0419×10−3 ρ h mgal m2 kg−1. The density of crustal rock, ρ, is usually taken to be 2670 kg m3 so the Bouguer plate correction is usually taken as −0.1119 mgal m−1 h. Here h is the elevation above the reference ellipsoid.[13]
The remaining gravity anomaly at this point in the reduction is called the Bouguer anomaly. That is, the Bouguer anomaly is:[12]
Isostatic correction
The Bouguer anomaly is positive over ocean basins and negative over high continental areas. This shows that the low elevation of ocean basins and high elevation of continents is compensated by the thickness of the crust at depth. The higher terrain is held up by the buoyancy of thicker crust "floating" on the mantle.[14]
The isostatic anomaly is defined as the Bouger anomaly minus the gravity anomaly due to the subsurface compensation, and is a measure of the local departure from isostatic equilibrium, due to dynamic processes in the viscous mantle. At the center of a level plateau, it is approximately equal to the free air anomaly.[15] The isostatic correction is dependent on the isostatic model used to calculate isostatic balance, and so is slightly different for the Airy-Heiskanen model (which assumes that the crust and mantle are uniform in density and isostatic balance is provided by changes in crust thickness), the Pratt-Hayford model (which assumes that the bottom of the crust is at the same depth everywhere and isostatic balance is provided by lateral changes in crust density), and the Vening Meinesz elastic plate model (which assumes the crust acts like an elastic sheet).[16]
Forward modelling is the process of computing the detailed shape of the compensation required by a theoretical model and using this to correct the Bouguer anomaly to yield an isostatic anomaly.[17]
Causes
Lateral variations in gravity anomalies are related to anomalous density distributions within the Earth. Local measurements of the gravity of Earth help us to understand the planet's internal structure.
Regional causes
The Bouguer anomaly over continents is generally negative, especially over mountain ranges.
More generally, the Airy isostatic anomaly is zero over regions where there is complete isostatic compensation. The free-air anomaly is also close to zero except near boundaries of crustal blocks. The Bouger anomaly is very negative over elevated terrain. The opposite is true for the theoretical case of terrain that is completely uncompensated: The Bouger anomaly is zero while the free-air and Airy isostatic anomalies are very positive.[15]
The Bouger anomaly map of the Alps shows additional features besides the expected deep mountain roots. A positive anomaly is associated with the Ivrea body, a wedge of dense mantle rock caught up by an ancient continental collision. The low-density sediments of the Molasse basin produce a negative anomaly. Larger surveys across the region provide evidence of a relict subduction zone.[20] Negative isostatic anomalies in Switzerland correlate with areas of active uplift, while positive anomalies are associated with subsidence.[21]
Over mid-ocean ridges, the free-air anomalies are small and correlate with the ocean bottom topography. The ridge and its flanks appear to be fully isostatically compensated. There is a large Bouger positive, of over 350 mgal, beyond 1,000 kilometers (620 mi) from the ridge axis, which drops to 200 over the axis. This is consistent with seismic data and suggests the presence of a low-density magma chamber under the ridge axis.[22]
There are intense isostatic and free-air anomalies along island arcs. These are indications of strong dynamic effects in subduction zones. The free-air anomaly is around +70 mgal along the Andes coast, and this is attributed to the subducting dense slab. The trench itself is very negative,[23] with values more negative than −250 mgal. This arises from the low-density ocean water and sediments filling the trench.[24]
Gravity anomalies provide clues on other processes taking place deep in the
Local anomalies
Local anomalies are used in
At scales between entire mountain ranges and ore bodies, Bouguer anomalies may indicate rock types. For example, the northeast-southwest trending high across central New Jersey represents a graben of Triassic age largely filled with dense basalts.[28]
Satellite measurements
Currently, the static and time-variable Earth's gravity field parameters are being determined using modern satellite missions, such as
Large-scale gravity anomalies can be detected from space, as a by-product of satellite gravity missions, e.g., GOCE. These satellite missions aim at the recovery of a detailed gravity field model of the Earth, typically presented in the form of a spherical-harmonic expansion of the Earth's gravitational potential, but alternative presentations, such as maps of geoid undulations or gravity anomalies, are also produced.
TheSee also
- Gravimetry
- Gravity anomalies of Britain and Ireland
- Indian Ocean Geoid Low
- Magnetic anomaly
- Mass concentration (astronomy)
- Physical geodesy
- Vertical deflection
References
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- ^ Lowrie 2007, p. 65.
- ^ Lowrie 2007, p. 44.
- ISBN 9780199653065.
- ^ Lowrie 2007, pp. 77–78.
- ^ Lowrie 2007, pp. 65–66.
- ^ Lowrie 2007, p. 54.
- ^ Lowrie 2007, p. 77.
- ^ Lowrie 2007, p. 79.
- ^ Lowrie 2007, pp. 79–80.
- ^ a b Lowrie 2007, pp. 83–84.
- ^ Lowrie 2007, p. 80.
- ISBN 9781405107778.
- ^ a b Kearey, Klepeis & Vine 2009, pp. 45–48.
- ^ Lowrie 2007, pp. 103–104.
- ^ Kearey, Klepeis & Vine 2009, p. 46.
- ^ a b Lowrie 2007, p. 95.
- .
- ^ Lowrie 2007, p. 97.
- ^ Lowrie 2007, p. 103–105.
- ^ Lowrie 2007, pp. 97–99.
- ISBN 0314921958.
- ^ Lowrie 2007, p. 99.
- .
- .
- ^ Monroe & Wicander 1992, pp. 302–303.
- ^ Herman, G.C.; Dooley, J.H.; Monteverde, D.H. (2013). "Structure of the CAMP bodies and positive Bouger gravity anomalies of the New York Recess". Igneous processes during the assembly and breakup of Pangaea: Northern New Jersey and New York City: 30th Annual Meeting of the Geological Association of New Jersey. New York: College of Staten Island. pp. 103–142. Retrieved 29 January 2022.
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Further reading
- Heiskanen, Weikko Aleksanteri; Moritz, Helmut (1967). Physical Geodesy. W.H. Freeman.