Gravity and Magnetics Terms for the 4th Edition of the SEG encyclopedic Dictionary

* absolute gravity: The absolute acceleration of the Earth's gravity field as opposed to relative gravity such as gravimeters measure.

ac demagnetization: Alternating-field demagnetization; see demagnetization .

* aclinic line: Magnetic equator (q.v.).

Adams-Williamson equation: An equation to determine the density of the Earth as a function of radius. See Fowler (1990: 108-109).

aerogravity: Measurements of the Earth's gravity field in a moving airplane, blimp, or helicopter. Requires precise measurement of location and height, velocity vector, and plane attitude. Compensation to get free-air gravity includes (a) vertical acceleration correction to compensate for aircraft vertical motion, (b) horizontal acceleration correction to compensate for course changes or turbulence, (c) gravimeter platform velocity (Eötvös correction), (d) aircraft elevation above sea level (free-air correction), (e) latitude correction, (f) low-pass filtering to remove residual noise. See also gravity survey resolution.

* aeromagnetic: Involving magnetic measurements made from an aircraft. A fixed-wing survey uses sensors mounted on the aircraft, sometimes in a towed bird 50-100 m below and behind the aircraft. Sensors are also mounted in helicopters. Surveys are usually flown at constant elevation above sea level, but sometimes drape surveys (q.v.) are flown at a constant elevation above the somewhat-smoothed surface.

aeromagnetic gradiometer: See gradiometer.

aeromagnetic survey specification: Parameters include (a) scheduling (sequence, duration), (b) area information (location, extent), (c) line spacing (traverse, control/tie lines), (d) line direction, (e) line length, (f) altitude (or drape), (g) sample interval, (h) base station magnetometer, (i) positioning information.

airborne gravity: See aerogravity .

* airborne magnetometer: Device used to measure variations in the Earth's magnetic field from an aircraft. See magnetometer .

aircraft signature: :The effect of the aircraft on magnetometer measurements. See compensation test.

* Airy hypothesis: The isostatic conceept that the thickness of crustal blocks of constant density varies so that the thicker parts ride higher; thus mountainous areas are compensated by deep roots extending to 50-60 km and deep ocean basins by antiroots at 6-8 km. See Figure I-6 and isostasy:

* alternating-field demagnetization: See demagnetization .

* analytic signal: 1. For a signal such as f(t), see Hilbert transform . 2. The analytic signal A of a potential field F is

A(x,y,z) = F(x,y,z) - jH(x,y,z),

where H(x,y,z) is the Hilbert transform of F(x,y,z) and j = (-1)^-1/2.

A(x,y,z) = i dF/dx + j dF/dy + k dF/dz,

where i,j,k are unit vectors in the x,y,z directions. The analytic signal amplitude (also called the envelope) is

|A| = |[(dF/dx)² + (dF/dy)² + (dF/dz)²]^1/2 |.

An enhanced analytic signal A_n refers to higher-order vertical derivatives :

A_n = i d(dⁿF/dz ⁿ)/dx + j d(dⁿF / dz ⁿ)/dy + k d(dⁿF/ dz ⁿ)/dz.

See also analytic signal method .

analytic signal method: A processing method for potential field data, also called the total gradient method. Used for defining the edges of density or magnetization anomalies in terms of spatial derivatives in orthogonal directions. See also analytic signal . See Debeglia and Corpel,1997; MacLeod, Jones, and Dai, 1993; Roest, Verhoef, and Pilkington, 1992.

* anhysteretic remanent magnetization: The magnetic state of a sample which has been subjected to a constant magnetic field while a supplemental decaying alternating field has been progressively reduced to zero. This procedure removes isothermal remanent magnetization.

* antiferromagnetism: Property of certain magnetic atoms which makes sublattices take an antiparallel ordering of spins (i.e., oriented opposite to each other), such that no net magnetization is observed. Compare ferromagnetism and ferrimagnetism .

* archeomagnetism: Study of the Earth's magnetism during historical times. See paleomagnetism.

* artificial magnetic anomalies: Non-geologic anomalies. See cultural magnetic anomalies .

automated depth estimation: Programs to automatically scan digital profiles or maps to estimate the depth of magnetic, gravity, etc. source bodies. Methods include Naudy's method, Phillips' method, analytic signal method, Werner filtering (Werner deconvolution) (q.v.). See also depth rule . See Cowen and Cowen, 1991; Thurston and Smith, 1997.

* Bartlett window: A triangular window; see Fig. W-11.

BHGM: Borehole gravimeter (q.v.).

Blakely-Simpson method: An automated program that compares each grid point with eight surrounding points to locate maxima by interpolating a second-order polynomial.

Bott-Smith method: The depth of a gravity source h = 0.86 g_max/(dg /dx)_max, where g_max is the maximum gravity anomaly value and (dg /dx)_max is its maximum slope. Also called Smith rule. See depth rule.

borehole gravimeter: A remote reading gravimeter which can be lowered in a borehole. The difference between the gravity readings at two different depths gives the apparent density r (in g/cm3) between the depths:

r = 3.686 - 128.5 ∆g/∆h1 = 3.686 - 39.18 ∆g/∆h ² ,

where ∆g is the gravity difference in mGal, ∆h₁ is the depth difference in meters, and ∆h₂ the depth difference in feet.

borehole gravity gradiometer: A measurement of the vertical gradient of gravitational acceleration. Usually measured indirectly by taking the difference between borehole gravity measurements at two depths.

* Bouguer anomaly: (boo ger' or bo gar') 1. The value obtained after latitude correction, elevation correction (including both free-air and Bouguer corrections), and (usually) terrain correction have been applied to gravity data. The Bouguer gravity field is not the same as the field which would have been observed at the datum elevation, because the shape of anomalies due to remaining density irregularities still are appropriate to the elevation of measurement rather than to those of the datum elevation. Also called Bouguer gravity. 2. Sometimes, a departure from smoothness in the contours on a map showing Bouguer values (i.e., a residual in Bouguer anomaly values). Named for Pierre Bouguer (1698-1758), French mathematician who tried to determine the figure of the Earth. See Chapin, 1996.

* Bouguer correction: 1. A correction to gravity data because of the attraction of the rock between the station and the datum (often sea level) or, in the case of stations below the datum elevation, for rock that is missing between the station and datum. The Bouguer correction is 0.041 92 ^rh mGal, where r is the specific gravity of the intervening rock and h is the difference between the station and datum elevations in meters (or 0.012 78 ^rh mGal if h is in feet). Regional studies sometimes assume r = 2.67 g/ cm₃. Also cvalled slab correction. 2. In surface-ship gravity data, the Bouguer correction replaces the sea water with rock, and r is the difference in specific gravity of the replacement rock and that of sea water.

* Bouguer plate: An infinite slab of finite thickness h and density r(g/cm³); its gravity effect is 0.041 85 rh mGal if h is in meters.

Bouguer spherical cap: The Earth segment that includes rocks above datum (usually sea level) out to 166.735 km. The sum of the ordinary Bouguer correction and the Bullard B corrrection (q.v.)..

Bullard B (earth curvature) correction: An adjustment to the Bouguer correction which accounts for the Earth's curvature rather than a planar slab. See LaFehr, 1992.

center of gravity: (1) If all the mass of a body were concentrated at this single point, the gravity effect would be the same as for the mass distributed throughout the body. (2) Used for other types of data, e.g., the distribution of CMP points within a seismic bin.

* cesium magnetometer: (se' ze ∂m) A type of optically-pumped magnetometer (q.v.). Sensitivity to 0.001 nT. Also spelled caesium.

* chemical remanent magnetism (CRM): See remanent magnetism .

chessboard method: A potential field continuation method for converting level-flown data to drape-flown and vice-versa. Level-flown data are continued to a series of levels that span the drape range, giving a set like stacked 3-D chessboards; interpolation is carried out vertically to give drape profiles.

compensation test: Aircraft maneuvers to derive compensation coefficients to correct for the effects of the aircraft on magnetometer measurements. At high altitude the aircraft flies in different directions (heading test) and undergoes oscillating pitch, roll, and yaw of 5-10o to determine a figure of merit, which should be <1-2 nT. A new figure of merit has to be determined with each change of aircraft configuration. If towing a bird, the aircraft also flies over an anomaly in opposite directions to determine the offset that direction makes (lag test).

complex gradient: The resultant of vertical and horizontal gradients. Especially used in interpreting dikes from magnetic data.

contact: A boundary (often a fault) between two blocks of different susceptibilites/densities.

* continuation: Determining a field over one surface from measurements of the field over another surface (specifically, at another elevation). The field at the elevation z , F(x,y,z) can be found from the field on the surface, F(x',y',0) . Where the surfaces are horizontal and no sources intervene, the upward continuation relation (an application of Green's theorem) is Interchange of the two fields in this equation gives the downward continuation relation. See Peters (1949) and downward continuation . See also Telford et al., 1990, §2.6.7, 3.7.5; and Pawlowski, 1995.

cosine correction: Multiplying an anomaly that is not perpendicular to a profile by the cosine of the angle between the anomaly orientation and the normal.

crossovers: Line intersections.

* cultural magnetic anomalies: Local magnetic anomalies caused by man-made features such as transmission lines, electric railways, steel drill casing, pipelines, etc. Generally of short wavelength. Also called artificial magnetic anomalies.

* Curie depth: The depth in the earth at which the Curie point (q.v.) is reached, of the order of 30 km. Named for Pierre Joliot-Curie(1859-1906), French physicist.

* Curie point: The temperature at which a material loses its ability to retain magnetism, that is, where it changes from ferromagnetic to paramagnetic behavior. Below this temperature atoms interact so that their magnetic moments couple and behave collectively. At the Curie temperature the atom's thermal energy equals the coupling energy, and above this temperature the atomic magnetic moments are not coupled and the substance behaves paramagnetically. The Curie temperature of most rocks is approximately 550°C, which is usually reached at 30-40 km depths. The analogous point with antiferromagnetic materials is the Neel point.

* Curie's law: Magnetic susceptibility is inversely proportional to the absolute temperature. This law applies where dipoles are far enough apart that their interaction is small, as in solutions of paramagnetic salts. In paramagnetic solids the susceptibility is inversely proportional to the difference between the temperature and the Curie point, this latter fact being called the Curie-Weiss law.

* Curie-Weiss law: See Curie's Law .

curvature correction: Correction to gravity data to compensate for Earth curvature because the Bouguer correction assumes a planar slab. See Bullard B correction.

* curvature of gravity: A vector calculated from torsion-balance data indicating the shape of an equipotential surface. It points in the direction of the longer radius of curvature.

* declination: 1. The angle between geographic north and magnetic north. 2. The angle between the celestial equator and a celestial body. Differs from celestial latitude.

* degaussing: (de gous' ∂ng) Demagnetization (q.v.).

* demagnetization: 1. A method for determining the stable component of remanent magnetization by partial demagnetization and removal of components with low coercive force. The specimen is placed in a space with nulled field (such as produced with Helmholz coils) and then subjected to an alternating magnetic field which is reduced gradually by decreasing the current of the field coil or by removing the specimen from the coil. 2. Reducing the magnetic field to zero to effect complete demagnetization to clean magnetic tape (remove the data stored on it) so that the tape can be reused. A tape may be rotated during the demagnetization to remove the effect of the Earth's magnetic field. Also called alternating-field demagnetization and degaussing.

* density: 1. Mass per unit volume. Commonly measured in g/cm3 or kg/m³, often without the units being expressed explicitly. Bulk sedimentary-rock densities vary mainly because of porosity and are generally in the range 1.9-2.8 g/cm³. 2. Frequency of occurrence. 3. The equivalent position of a color on a gray scale. See Figure C-6a. 4. A measure of the degree of blackening of an exposed photograph after development.

* density contrast: The difference in density between two formations or rock units. Lateral density contrasts are responsible for lateral changes in the Earth's gravity.

* density log: A well log which records formation density. The density-logging tool consists of a gamma-ray source (e.g., Cs137) and a detector so shielded that it records backscattered gamma rays from the formation. This secondary radiation depends on the density of electrons, which is roughly proportional to the bulk density. The compensated density-logging tool (FDC) includes a second detector which especially responds to the mud cake and small borehole irregularities; its response is used to correct the readings of the main detector. See Figure D-3. Sometimes called gamma-gamma log. Compare nuclear cement log and photon log .

* density profile: A line of gravity readings taken over a topographic feature having appreciable relief that is not associated with density variations or structure, the object being to determine the best density factor for elevation corrections. The most appropriate density is the one that minimizes the correlation of gravity values with elevation. Method devised by L. L. Nettleton. See triplets and Telford et al. (1976, p.28-30).

* depth rule: A rule relating the depth of a body to a feature of anomaly shape. Depth rules apply to specific source shapes; see Figure D-7. 1. Rules used in gravity interpretation include (a) half-width rules (the half-width being half the width at half the anomaly amplitude): for point masses, depth = 1.3 half-width and for horizontal line masses, depth = half-width. (b) For faults, half the width between points where the anomaly is one-quarter and three-quarters amplitude; (see Figure H-1). 2. Rules used in magnetic interpretation include (a) the straight-slope-measurement rule (q.v.); (b) the Peters' rule for dikes, depth = 5/8 of the horizontal distance between points where the slope is half the maximum slope; (c) the Tiburg rule for magnetic poles, depth = 2/3 of the horizontal distance at half the maximum amplitude; (d) the Hannel rule for magnetic poles, depth = half of the horizontal distance at a third the maximum amplitude; (e) the Thalen rule, the depth of a magnetic source is 0.7 the horizontal distance between maxima and minima; and other such rules. See also automated depth estimation and radial power spectrum..

depth slicing: A filtering technique used to isolate anomalies based on wavelength criteria. Used to determine the depths of gravity and magnetic sources. See Ruder, 1997.

* derivative map: A map of one of the derivatives of a potential field, usually the second vertical derivative. The objective of a derivative map is to emphasize short wavelength (high frequency) anomalies. Second derivative maps are based on Laplace's equation:

∂²f/∂z² = -(∂²f/∂x² + ∂²f/∂y²).

The horizontal derivatives, ∂²f/∂x² and ∂²f/∂y², are usually estimated by finite difference methods from values measured at gridded points on a map, often using a residualizing template based on polar representation of the Laplacian or by two-dimensional convolution with such a template.

* detrital remanent magnetism (DRM): See remanent magnetism .

diagenetic magnetite: A magnetic mineral formed as a replacement mineral by hydrothermal alteration. Sometimes formed by hydrocarbon seepage.

DiaMag™: A helicopter-bourne magnetic horizontal gradiometer system used for diamond and gold exploration. Trademark of High-Sense Geophysics Ltd.

* diamagnetic: (di, ∂ mag net' ik) Having net negative magnetic susceptibility and a permeability less than that of free space (less than unity in the cgs system). The motion of an electron about a nucleus produces a miniature circular current whose magnetic-moment vector precesses around an applied external field. This additional periodic motion produces a magnetic moment opposite in direction to the applied field. Diamagnetic effects in the Earth's field rarely exceed one nanotesla. The strongest diamagnetic anomalies are probably due to salt domes. Compare paramagnetic and ferromagnetic .

* dike: 1. A tabular body which is longer vertically than in other dimensions (as opposed to a slab). Vertical and dipping dike models are commonly used in potential field calculations. 2. Igneous rock that cuts across adjacent rock. Also spelled dyke. See Figure M-10.

* diurnal variation: Daily fluctuations, for example, those of the geomagnetic field related principally to the tidal motion of the ionosphere (involving amplitude and phase variations with season and latitude by as much as 100 nT). Also called diurnals. Records from a stationary magnetometer are used for their removal from aeromagnetic data.

* dot chart: A chart used to compute the theoretical gravity (or other potential) effect of a mass distribution; see Figure D-19. A dot chart is superimposed on a scale cross-section of the mass; the number of dots which fall within the mass outline multiplied by the anomalous density is proportional to the gravity effect at the origin of the chart. The chart is then moved to a different position on the outline and the number of dots counted again to give the effect at another point, and so on for every point for which the gravity value is to be determined. Most charts assume that the mass distribution extends to infinity perpendicular to the plane of the chart and end corrections have to be applied to remove this restriction. Also called graticule.

* double Bouguer correction: 1. The Bouguer correction (q.v.) to sea level for measurements made on the ocean floor involves a correction to replace the upward attraction of the sea water above the meter with the replacement density of rock. 2. Corrections for measurements made in mines or in boreholes, usually involving measurements made both above and below a layer.

* downward continuation: 1. The process of determining the value of a potential (e.g., gravitational) field at a lower elevation from values measured at a higher elevation, based on the field continuity. A potential field is not continuous across the boundaries of anomalous masses. As the depth from which an anomaly originates is approached, its potential field expression becomes sharper and tends to outline the mass better until the depth of the mass is reached; beyond this point the field computed by continuation becomes erratic. Noise in the data often precludes successful application. See continuation . 2. Calculating over a surface at depth the values of any quantity that can be determined from shallower measurements. Often refers to calculating the seismic wavefield at depth, as is done in finite-difference migration.

* drape survey: An airborne geophysical survey flown at a constant distance above the somewhat-smoothed surface rather than at a constant elevation above mean sea level.

* drape flown: Delete

dyke: See dike .

dynamic gravity: Gravity measurements made from a moving platform, such as a surface ship at sea or an aircraft.

* Earth's gravity field: The field varies from about 978 000 mGal at the equator to 983 000 at the poles. See International gravity formula and gravitational constant .

* Earth's magnetic field: See magnetic field of the Earth and normal magnetic field .

* elevation correction: 1. The correction applied to reflection or refraction arrival times to reduce observations to a common reference datum. 2. In gravity, the sum of the free-air and Bouguer corrections. The elevation correction is obtained by multiplying the difference between station and reference elevation by the elevation correction factor (ECF):

ECF = (0.09406 - 0.01278 r) mGal/ft = (0.3086 - 0.04192 r) mGal/m,

where r = density in g/cm3.

* elevation correction factor (ECF): See elevation correction .

enhanced analytic signal: See analytic signal.

* Eötvös effect: The vertical component of a Coriolis acceleration observed when measuring gravity while in motion. The meter's velocity over the surface adds vectorially to the velocity due to the Earth's rotation, varying the centrifugal acceleration and hence the apparent gravitational attraction. The Eötvös correction E in mGal for a meter whose speed is V knots at an azimuth angle a and latitude f is E = 7.503 V cos f sin a + 0.004154 V ².

The Eötvös uncertainty dE in terms of direction uncertainty da and speed uncertainity dV is

dE = (7.503 V cos f cos a da + (7.503 cos f sin a + 0.008308 V )dV .

See Glicken (1962). Named for Baron Roland von Eötvö (1848-1919), Hungarian physicist.

* Eötvös unit (EU): (et' vos) A unit of gravitational gradient or curvature; 10^-6 mGal/cm.

equivalent layer: A single layer containing gravity or magnetic sources that yields the same gravity or magnetic field as the actual distribution of sources.

Euler deconvolution: Euler method (q.v.).

Euler's homogeneity equation:

(x - x_o ) dF/dx + (y - y_o ) dF/dy + (z - z_o) dF/dz = N (B - F ),

where (x_o, y_o, z_o) is the source location whose magnetic field F is measured at (x, y, z); B is the regional value of the total field; and N is Euler's structural index. N is a measure of the rate of field change with distance; e.g., the magnetic field of a sphere falls off as the cube (N = 3), of a pipe as the square (N = 2), of a thin dike linearly (N = 1), of a semi-infinite body, not at all (N = 0). An Euler depth estimate increases with increased N . Real bodies are simulated by a superposition of simple bodies.

Euler method: A procedure applied to profile or map data to solve Euler's homogeneous equation (q.v.) for the locations and depths of sources for an assummed Euler structural index. Each calculation is run for different window lengths to obtain solutions for differernt depths. At a valid depth values cluster together; a fault might be indicated by a vertical alignment. Calculations are often automated with gridded data. Also called Euler deconvolution. See Reid, Allsop, Ganser, Millet, and Somerton, 1990; Harris, Jessel, and Barr, 1996.

Euler's structural index: See Euler's homogeneity equation.

external magnetic field: See solar wind.

fabric: The spatial configuration of features (trends) characterizing a region. Also called grain and signature.

faulted slab: A semi-infinite slab (plate) of uniform thickness, common in potential-field modeling.

faye anomaly: Free-air gravity anomaly.

* Faye Delete

* ferrimagnetism: Property of some spinel-structured ferrites which show both ferromagnetic and antiferromagnetic properties because ionic interactions favor both parallel and antiparallel alignments of group (domain) magnetic moments. Ferrimagnetic substances include distinct ferromagnetic sublattices which couple antiferromagnetically so that the observed magnetism is the difference.

* ferromagnetic: Having positive and relatively large susceptibility and generally large hysteresis and remanence. In ferromagnetic materials the atoms interact and atomic magnetic moments couple so that groups of atoms (domains) behave collectively and orient in a parallel configuration. As the temperature of such materials rises to the Curie point, the thermal energy of the atoms becomes sufficient to overcome the coupling energy and the material behaves paramagnetically. See also diamagnetic and paramagnetic .

* fish: 1. A sensor that is towed in the water, such as a side-scan sonar sensor. A magnetometer fish is typically towed 200-300 m behind a vessal at a depth of 15-20 m. 2. An object left in the borehole during drilling or workover operations that must be recovered before work can proceed.

* fluxgate magnetometer: An instrument capable of detecting changes in the magnetic field of the order of 0.2 nanostesla. See Figure F-13. The magnetometer measures the magnetic field component along the axis of its core and must be oriented with the field if the total intensity is to be measured. With the Gulf magnetometer this is accomplished by using three mutually perpendicular fluxgate instruments and servomechanisms which vary the orientation to minimize the magnetic field in two of these directions, thus maximizing the field for the third. Compare proton magnetometer , optically pumped magnetometer , and Squid cryogenic magnetometer .

flying surface: The flight program for terrain surveys.

* free-air anomaly: Gravity data which have been corrected for latitude and elevation (free-air correction, q.v.) but not for the density of the rock between the datum and the measurement elevation (Bouguer correction). Measures the attraction because of the mass of the subadjacent earth. Also called free-air gravity.

* free-air correction: 1. A correction because a gravity measurement was made at a different distance from the center of the Earth than the datum. The correction is

0.308 768 - 0.000 440 sin2f - 0.000 000 1442 h mGal/m,

where f is the latitude and h is elevation above the ellipsoid. Usually only the first term is used, 0.3086 mGal/m or 0.09406 mGal/ft. 2. In Turam, normalizing a ratio of successive measurements by dividing by the ratio of the calculated free-space vertical magnetic field. Compare normal correction .

free-fall gravimetry: Measuring the absolute gravity by timing the free fall of a weight in a vacuum.

FTG technology: Gravity methodology developed for use in Trident submarines that provides super-high sensitivity. FTG stands for full tensor gravity.

Fuller filter: A moving-average space-domain convolution. See Fraser, Fuller and Ward, 1966.

full tensor gradient (FTG): A nine-component symmetric tensor which defines the rate of change of the three components of a potential-field gradient:

| F_xx F_xy F_xz |

| F_yx F_yy F_yz |

| F_zx F_zy F_zz |.

For the field F, the rate of change in the j direction of the gradient in the i direction is Fi j .

* Gal: A unit of acceleration or of gravitational force per mass, used in gravity measurements. One Gal = 1 cm/s² = 10^-2 m/s² = 10^-2 newton/kg. The Earth's nominal gravity is 980 Gal. Named for Galileo Galelie (1564-1642), Italian physicist.

* gamma (g: A unit of magnetic field equal to one nanotesla, the preferred SI name. 1 gamma = 10^-5 gauss = 10^-9 tesla.

* gauss (G): (gous) The cgs-emu unit of magnetic induction (or flux density) B. It is a measure of the number of magnetic lines of force per unit area. 1 gauss = 1 maxwell/cm² = 10⁵ gamma = 10^-4 tesla = 10^-4 weber/m₂. "Gauss" is also used in the cgs system as a unit for magnetization, or dipole moment per unit volume. In cgs units, a magnetizing force (in oersteds) gives rise to a flux density or field (in gauss), with the values being equal in magnitude if in free space. Named for Karl Friedrich Gauss (1777-1855), German mathematician and natural philosopher.

* Gauss's theorem: The total flux f through any closed surface is equal to 4πk times the source strength m enclosed by the surface:

f = 4πkm = g . ds = ÚÚ —U . ds = ÚÚÚ —. g dv = 4πk ÚÚÚ r dv .

[ÚÚ is surface integral, ÚÚÚ is vol;um,e integral]

ds is a vector surface element and dv a volume element. (The 4π is often deleted in the mks system.) k is a constant which depends on the units of measure. This can also be expressed in terms of the flux density or field strength g, the source density r, and the potential U . f may be electrical flux if m is electrical charge; in the mks system, f is in webers if m is in coulombs and k ª 9 x 10₉. Or f may be gravitational flux if m is mass, in which case k = -g, where g is the gravitational constant. Or f may be magnetic flux if m is magnetic pole strength. Also called Gauss's law: The equality between the surface and volume integrals involving g is also called the divergence theorem.. This theorem postulates the inherent non-uniqueness of potential fields.

* generalized reciprocal method (GRM): A refraction interpretation method that is a generalization of the plus-minus method (q.v.). Based on determining the critical distance, i.e., the point where head waves leave the refractor when shooting in opposite directcions It takes into account non-coincidence of the stations used for calculating plus values. See Palmer (1979).

Geodetic Reference System 1967 (GRS67): The gravity field is given by

g = 978 031.846(1 + 0.005 278 895 sin2f + 0.000 023 462 sin4f) mGal.

This gives the correction for latitude f as

1.3049 sin 2f mGal/mile = 0.8108 sin 2f mGal/km.

* geomagnetic field: See magnetic field of the earth .

* geomagnetic pole: The north or south magnetic poles, the projection onto the surface of the poles of the geocentric dipole that best accounts for the Earth's magnetic field. See magnetic field of the Earth and compare magnetic dip poles.

* geomagnetic reversal: Change in the polarity of the Earth's magnetic field from its present polarity. This has occurred a number of times in the Earth's history and provides a method for age dating; see magnetochronology.

* Geosat: An Earth satellite funded by the U.S.Navy. A high-resolution radar altimeter measures the geoid, sea waves, sea ice, etc.

Goussev filter: A space-domain operator that calculates the scalar difference between the total magnetic-field gradient and its horizontal component.

* gradient: (gra' de ∂nt) 1. The first derivative (or rate of change of one variable with respect to another variable, often with respect to distance). For example, the change in gravity, temperature, magnetic susceptibility, or electrical potential with respect to horizontal or vertical distance. Sometimes measured with a gradiometer (q.v.). 2. The operation which finds the gradient from a potential function:

Gradient of U = grad U = —del U = i ∂U /∂x + j ∂U /∂y + k ∂U /∂z ,

where i,j,k are orthogonal unit vectors in a rectangular coordinate system. See Figure C-13c for expressions of the gradient in cylindrical and spherical coordinates. 3. A component of the gradient in an arbitary direction, as the horizontal gradient of the magnetic field. See also full tensor gradient .

gradient dip estimation: A method of estimating dip q of a contact based on the distance d between the maxima of the total gradient and that of its horizontal component: d = h cot q, where h is the depth of the contact.

* gradiometer: (grad' ∂ om, ∂t ∂r) A method for measuring a component of the gradient of a potential or electromagnetic field. 1. An arrangement of two magnetometers (or gravimeters), one above the other, so that the difference in their readings is proportional to the vertical gradient of the magnetic (gravity) field, or of magnetometers on opposite wingtips amd in a tail stinger of an aircraft, so that differences in their readings is proportional to the horizontal gradients of the magnetic field, or some similar arrangement. The direction with respect to the Earth's magnetic field is a factor in interpretatrion. 2. A three-arm torsion balance that is sensitive to gravity gradients but not to curvature.

grain: The spatial configuration of features (lineations, trends) characterizing a region. Also called fabric and signature.

* graticule: (grat' ∂ kyool,) 1. A template for graphically integrating gravity or similar data. See also dot chart and zone chart . 2. A grid network such as lines representing parallels and meridians on a plotting sheet.

* gravimeter: (gr∂ vim' i t∂r) An instrument for measuring variations in gravitational attraction; a gravity meter. Most gravimeters are of the unstable or astatic type. The gravitational force on a mass in the meter is balanced by a spring arrangement. A third force is provided which acts when the system is not in equilibrium; it intensifies the effect of changes of gravity and increases the sensitivity of the system. Usually a zero-length spring is used; it has a stress-strain curve which passes through zero length when projected back to zero strain. See Figure G-5.

* gravitational constant: The proportionality constant g in Newton's Law of Universal Gravitation: the gravitational force F between two point masses m₁ and m² can be related to the distance r between them:

F = g m₁m₂/r² ;

g has the value 6.670 x 10-11 newton.m²/^kg2. The force is a vector directed toward the attracting mass. The gravitational field g (also a vector, often called the acceleration of gravity) is the force per unit mass (measured by the force on the mass m₁ in the gravimeter):

g = F/ m₁ = g m₂/r² ;

g is the vector sum of the effect of the all other masses (e.g., the masses in the earth).

* gravitational potential: The negative of the work required to move a unit mass from infinity to a given point against gravitational forces. In the field of a point mass m a distance r away, this is g m/r , where g is the gravitational constant. Also called Newtonian potential.

* gravity: The force of attraction between bodies because of their masses. Usually measured as the Earth's gravity field which varies from about 978 000 mGal at the equator to 983 000 at the poles. See International gravity formula and gravitational constant .

* gravity anomaly: 1. The difference between the gravity which is observed and that expected from a model. 2. Bouguer anomaly (q.v.). 3. Free-air anomaly (q.v.).

* gravity meter: Gravimeter (q.v.).

* gravity reduction: Applying Bouguer, free-air, isostatic, latitude, and/or terrain corrections to gravity measurements.

* gravity standard: The International Gravity Standardization Network 1971 (IGSN71) is now standard. See International gravity formula and Woolard (1979).

* gravity survey: Measurements of the gravitational field at various locations over an area of interest. The objective in exploration work is to associate variations with differences in the distribution of densities and hence of rock types. Occasionally the whole gravitational field is measured (as with free-fall equipment or a pendulum), occasionally derivatives of the gravitational field (as with a torsion balance), but usually it is the difference between the gravity field at two points that is measured (as with a gravimeter , q.v.). Gravity data usually are displayed as Bouguer or free-air anomaly maps.

gravity survey resolution: Goussev and Peirce (1999) give the values and required resolution in table GG.

* gravity unit: A unit of gravitational acceleration, equal to 0.1 mGal or 10^-6 m/s².

* grid effect: 1. Systematic error introduced in interpolating values at grid points where observations have not been made. Such errors may create false anomalies along certain orientations. 2. False anomaly trends which may be created when grid residual maps are made with templates which are not azimuthally symmetrical.

* grid residual: A method of emphasizing anomalies of a certain size in a potential-field map. A grid (usually square or trigonal) is drawn on a contour map and values are determined at the grid intersections by interpolation. The residual at a grid intersections is the value at that point less the average at other intersections a fixed distance away. Averages at several distances may be used and weighted to approximatethe second vertical derivative or other functions. The process of making grid residuals is also called map convolution (a two-dimensional convolution) because it represents map data convolved with a residualizing operator (or template). See also residualize .

* grid smoothing: Smoothing sharp irregularities in potential-field measurements such as arise from very shallow disturbances. A grid is drawn on a contour map and the average of values a fixed small distance away is taken as the smoothed value at the grid intersection.

Griffin method: Determining the regional by averaging around a circle centered at a station.

GRS67: Geodetic reference system (q.v.).

* g.u.: Gravity unit; 0.1 milligal.

* Gulf magnetometer: A type of fluxgate magnetometer (q.v.).

* half width: Delete

half width method: A method of estimating the depth to a gravity or magnetic source from anomaly shape. Depending on the model, the half-width is (a) half the width of an anomaly at half the maximum (or minimum) value, or (b) half the width between points where the anomaly is one-quarter and three-quarters amplitude. The depth to the center of a horizontal cylinder is given by (a), to the center of a spherical mass by 1.3 (a), to the center of a spherical magnetic sphere by 2.0 (a), to the mass center of a thin semi-infinite slab (fault anomaly) by (b). See also depth rule and Fig. H-1b.

* halo: Delete

* halo effect: 1. Many residual and second-derivative methods produce a ring or halo of opposite sign around an anomaly, reflecting the opposite field curvature around the periphery of the anomaly. Halos do not represent separate anomalous masses. Halos can be reduced or eliminated by biasing. 2. A ring anomaly, claimed to be characteristic of certain electromagnetic or geochemical effects of structures or hydrocarbon accumulations.

* Hammer chart: A template for making gravity terrain corrections. See Hammer (1940).

* Hannell rule: (han' ∂l) See depth rule .

* harmonic function: A function that satisfies Laplace's equation (q.v.), has continuous single-valued first derivatives, and has second derivatives. It repeats after successive equal intervals of the arguments.

* Hayford modification: The isostatic hypothesis that the pressure is balanced at the "depth of compensation". See isostasy. Named for John Filmore Hayford (1868-1925), American geodesist.

Heiskanen modification: The isostatic hypothesis that lithosphere density varies but 2/3 of the topography is compensated with roots. See isostasy.

helicopter gravity: See aerogravity and Heligrav. Helicopters are sometimes used merely for transport.

helicopter magnetics: See aeromagnetic.

Heligrav™: An automated gravity meter is lowered to the ground from a hovering helicopter. Trademark of Scintrex Ltd. See Seigel and McConnel (1998).

* herringbone: (her' ∂ng bon,) A pattern of systematic deviation of contours on a contour map produced when one line of data is systematically mislocated or has systematic bias. See Figure H-3.

high-resolution aeromagnetics (HRAM): More properly called high-precision aeromagnetics, this refers to surveys flown at low terrain clearance (80-150 m) with close line spacing (100-500 m) recorded with a high-sensitivity magnetometer (0.001-0.005 nT) at high sample rates (0.1-0.25 s) using a high-precision positioning system (usually differential GPS).

* hysteresis: (his, t∂ re' sis) 1. A phenomenon exhibited by a system or material in which response depends nonlinearly on past responses. The system will not return to the original state after a property has been changed when the cause of the change has been removed. 2. Especially the effect where the magnetization produced by an applied field lags behind the field; see Figure H-9. This involves energy loss. When the applied field returns to zero, the residual magnetism is called remanent magnetism. The magnetic field intensity required to reduce the remanent magnetization to zero is the coercive force.

* IGRF: International geomagnetic reference field (q.v.).

* IGSN71: International Gravity Standardization Net (1971) (q.v.).

* inclination: 1. The angle between a line's direction and the horizontal; e.g., magnetic inclination is the angle at which magnetic lines of force dip. 2. The dip of a plane (bed, fault, or other tabular body) measured from the horizontal. The attitude of the plane may be characterized by the direction of a normal to the plane and the plane's inclination is the angle betweenthe normal and vertical. 3. The angle between the orbital plane of a satellite and the Earth's equatorial plane.

* index factor: A constant which, when multiplied by certain measurements made on potential-field anomalies, gives an estimate as to the maximum depth at which the anomalous mass could be located). Used in magnetic and gravity interpretation. See depth rule .

* inflection-tangent-intersection (ITI) method: A magnetic interpretation method that involves measuring a number of shape features on a profile across a magnetic anomaly and making the best fit of these measurements to theoretical values for a vertical dike. Both distance and amplitude measurements may be made, as shown in Figure I-4. Also called Naudy method. See Naudy (1971).

instantaneous amplitude: The amplitude of the envelope of an oscillatory signal.

* intensity of magnetization: Magnetic moment per unit volume (occasionally, per unit mass). Includes induced and remanent components.

* International Geomagnetic Reference Field (IGRF): A long wavelength regional magnetic-field model and expected secular changes are determined by an international committee about every five years (e.g., 1965, 1975, 1980). The model consists of spherical harmonics. The IGRF is subtracted from observed data to determine the local field.

* International Gravity Formula: Theoretical gravity (as of 1987) is

978 032.68 (1 + 0.001 931 851 386 39 sin²f)

(1 - 0.006 694 379 990 13 sin²f) mGal,

where f is the latitude. Older versions are:

1930: 978 049.0 (1 + 0.005 288 4 sin²f - 0.000 005 9 sin²2f) mGal,

1967: 978 031.8 (1 + 0.005 302 4 sin²f - 0.000 005 8 sin²2f) mGal.

GRS67 : 978 031.846 (1 + 0.005 278 895 sin²f + 0.000 023 462 sin⁴f) mGal.

See latitude correction .

* International Gravity Standarization Net (IGSN71): The accepted reference frame for gravity measurements. Supercedes the Potsdam System which was defined by pendulum measurements in 1906. See Woolard (1979)

* intrabasement anomaly: A local anomaly caused by variation of magnetic polarization within the basement complex. Generally the depth to the bottom of such a body is more than twice the depth to its top.

* IRM: Isothermal remanent magnetization. See remanent magnetization .

* isoanomaly: A line on a map connecting points of equal anomaly, used especially for maps showing magnetic or gravity anomalies; also spelled isanomaly.

* isocline: Line of equal magnetic inclination.

* isogal: Line of equal gravity anomaly.

* isogam: Line of equal magnetic intensity.

* isogon: Line of equal magnetic declination.

isomagnetic maps: Maps (charts) showing the elements of the geomagnetic field.

* isostasy: (i sos' t∂ se) The gravitational balance of large portions of the earth's crust as though they were floating on a denser underlying layer (the asthenosphere). Isostasy accounts for major topography. (a) The Pratt hypothesis assumes density variations so that areas of less-dense crust rise topographically above areas of more-dense (see Figure I-6). The (b) Hayford modification requires that the pressure be balanced at the "depth of compensation". (c) The Airy hypothesis varies the thickness of crustal blocks of constant density so that the thicker parts ride higher; thus mountainous areas are compensated by deep roots extending to 50-60 km and deep ocean basins by antirootsat 6-8 km. (d) The Heiskanen modification permits density to vary but compensates 2/3 of the topography with roots. (e) The Vening Meinesz hypothesis allows some of the balance to be accommodated laterally by the surrounding region rather than in the vertical direction only. The radius of regionality specifies the size of the region over which compensation is distributed; it is of the order of 200 km.

isostatic anomaly: The result of applying the isostatic correction (q.v.) to Bouguer anomaly data,

* isostatic correction: A correction to gravity data to compensate for lateral density or thickness variations between large blocks of the Earth's crust. The correction assumes an isostatic model; it is made from elevation and water-depth data using zone charts. See Heiskanen and Vening Meinesz (1958, p.159-170).

* isostatic rebound: Isostatic adjustment after removing or imposing a stress. From sea-level changes attributed to the melting of Pleistocene continental glaciers, the isostatic-rebound relaxation time is of the order of 4000 years, corresponding to a viscosity of 4 x 1022 poise.

* isothermal remanent magnetism (IRM): See remanent magnetism .

Jacobsen filter: A spectral-domain operation based on upward continuation. Also called a separation filter. See Cowen and Cowen (1993).

* K-index: A measure of the average intensity of magnetic disturbances in time, such as magnetic storms, but excluding diurnal and lunar time variations.

Koefoed method: A 2-D method of estimating the depth of a magnetic source based on the horizontal distance between points 1/2 and 3/4 of the maximum anomaly value.

* Koenigsberger ratio (Q ): (ka' nigs ber, g∂r) The ratio of the remanent magnetization to the induced magnetization (product of susceptibility and the Earth's magnetic field strength). See Hood (1964).

* lag: 1. A difference in the time of two events. 2. A delay in the arrival time of seismic events. Lagging refraction or reflection arrivals may indicate subsurface structure or delay caused by weathering variations, phase shifts in filtering, shothole fatigue, etc. Negative of lead. 3. The phase angle by which the current is behind the emf in an inductive circuit. 4. The time delay between the breaking of the bridgewire in a detonating cap and the resulting explosion. 5. To be behind. 6. The distance an aerosurvey bird is behind the aircraft, where location is determined.

lag test: Determining how far a bird sensor is behind the towing aircraft by flying in opposite directions over a distinctive feature (such as a large iron bridge for aeromagnetics).

* Laplace's equation: (la plas') A differential equation which describes certain behavior at points in free space. The Laplacian del²U of a potential function U vanishes in space which contains neither sources nor sinks. (— is the operator "del".) In rectangular coordinates,

—²U = ∂²U /∂x² + ∂²U /∂y² + ∂²U /∂z² = 0.

Gravity, magnetic, electrical, electromagnetic fields obey Laplace's equation in free space. See Figure C-13c for the Laplacian in cylindriocal and spherical coordinates. Compare Poisson's equation . Named for Pierre Simon Laplace (1749-1827), French mathematician.

* Larmor frequency: (lar' mor) The frequency with which gyromagnetic moments precess in a magnetic field. Atoms and nuclei possess magnetic moments because of their spin and precess like small gyroscopes about the direction of an externally-applied steady magnetic field (such as the Earth's field). Radio-frequency energy at right angles to the steady field will be absorbed because of resonance when the RF-frequency equals the precession frequency. This principle is involved in proton-resonance and optically pumped magnetometers and in the nuclear-magnetism log (q.v.). Named for Sir Joseph Larmor (1857-1942), English mathematician.

* latitude correction: 1. A correction to gravity data because of (a) variation in centrifugal force resulting from the Earth's rotation, as the distance to the Earth's axis varies with latitude f, and (b) variation of the Earth's radius because of polar flattening. The Geodetic Reference System 1967 (GRS67) gives

g = 978 031.846(1 + 0.005 278 895 sin²f + 0.000 023 462 sin⁴f) mGal.

The latitude correction amounts to

1.3049 sin 2f mGal/mile = 0.8108 sin 2f mGal/km.

2. A gyrocompass correction for the rotation of the horizontal north vector as a function of latitude. (The horizontal north vector is tangent to the Earth and hence the rotation is the result of Earth curvature.) 3. The north-south correction to magnetic data to remove the Earth’s normal field.

line of force: A curved line in a three-dimensional potential field such that a tangent anywhere along the line is in the direction of the force on a charge (pole, mass, etc.) at that location. Perpendicular to every equipotential surface The density of lines of force is called the flux density or field strength. Used in connection with electric fields, magnetic fields, gravitational fields, etc. See Gauss law.

* magnetically quiet: Having ambient magnetic variations less than tens of nanoteslas.

* magnetic anomaly: The difference between observed and theoretical or predicted magnetic values. A residual magnetic anomaly is the anomaly which remain after removal of the longer wavelength regional. The shape of a magnetic anomaly depends on (a) the geometry of a body, (b) the magnetic inclination, (c) the direction of the Earth's magnetic field with respect to the direction of the line of observations, and (d) the direction and intensity of the body's remanent magnetism. 

* magnetic artifacts: See artificial magnetic anomalies .

* magnetic basement: The upper surface of extensive crystalline rocks having magnetic susceptibilities which are large compared with those of sediments. Often but not necessarily coincident with the geologic basement that is the surface beneath which sedimentary rocks are not found. Generally excludes magnetic sediments, thin volcanic and other high-susceptibility rocks intruded into the sedimentary section, but thick volcanic rocks in the sedimentary section might be classed as magnetic basement where the magnetic effects of deeper bodies would not be resolvable.

* magnetic cleaning: Removing the "soft" secondary magnetization of a sample so the "hard" primary magnetization can be studied. See demagnetization .

magnetic compensation: Correction for the static and dynamic effects of the survey aircraft, often performed by an onboard computer

magnetic data correction: Corrections include compensation for (a) irregular solar micropulsations and magnetic storms, (b) diurnal and secular variations, (c) instrument drift, (d) flight elevation, (e) location errors and misties, (f) the International Geomagnetic Reference Field (IGRF) (q.v.). A long wavelength regional magnetic-field model and expected secular changes are determined by an international committee about every five years (e.g., 1965, 1975, 1980). The model consists of spherical harmonics. The IGRF (q.v.) is subtracted from observed data to determine the local field. (g) inclination and declination, (h) cultural effects. Not all these corrections are applied nor in this sequence.

* magnetic dip: Magnetic inclination; see inclination .

magnetic dip poles: See magnetic field of the Earth:

* magnetic dipole: 1. One ampere flowing in a circular coil of area 1 m². For two magnetic poles of strength p separated by an infinitesimal distance Dx , the dipole strength is p Dx . 2. A source of electromagnetic energy created by an alternating current in a single or multiturn loop carried from an aircraft or laid out on the ground. 3. The magnetically polarized nature of rocks and ore bodies.

* magnetic disturbance: Magnetic storm (q.v.).

* magnetic equator: The line on the surface of the Earth where a magnetic needle remains horizontal, that is, where magnetic lines of force are horizontal. Local field irregularities are often ignored. Also called the aclinic line.

magnetic fault identification cube (MaFIC): A 3-D volume of magnetic sources calculated by an automated depth estimation (q.v.).

* magnetic field: The space through which influence on a magnet is exerted. The torque at any point in space which would tend to orient a current-carrying coil or magnet if located at that point. A vector quantity also called the magnetic flux density or the magnetic induction and symbolized by B. The unit of measure for B in the SI and mks systems is the tesla and in the cgs system the gauss or gamma (1 tesla = 1 weber/m2 = 1 newton/amp.m = 104 gauss = 104 maxwell/cm2 = 109 gamma). B is given in terms of the force dF produced on a small element of length dl which is carrying a current I :

d F = I dl x B.

B is related to the magnetizing force H by a constant of the medium called the permeability m:

B = m m_o H.

The unit of measure for H in the SI and mks systems is ampere turns per meter and in the cgs system, the oersted (1 ampere turn per meter = 4π10^-3 gilbert per centimeter). m_o is the permeability of free space; m_o = 4π10^-7 weber per ampere meter in SI units and 1 gauss per oersted in cgs units. B can also be expressed as

B = m_o (H + M) in SI units,

B = m_o (H + 4πI) in cgs units,

where M and I are the magnetization and intensity of magnetization. A magnetic field whose magnitude is given by the inverse-square law surrounds a magnetic pole, and a magnetic field given by Ampere's law surrounds an electric current. H is sometimes called the magnetic field. See Figure M-1.

* magnetic field of the Earth: The Earth's magnetic field is often represented by a dipole at the Earth's center. The projections of this dipole onto the Earth's surface are the geomagnetic poles. A better representation of the Earth's field is given by a dipole about 400 km from the center. The locations where the magnetic dip is 90∞ are called the magnetic dip poles; they do not coincide with the geomaagnetic poles. The portion of the Earth's field not representable by a dipole is called the non-dipole field. Time-varying components of the Earth's field are shown in Figure M-2. See also normal magnetic field .

* magnetic flux: The flux through a surface is the integral over the surface of the normal component of the magnetic induction; expressed in webers in SI units or in maxwells in cgs units (1 weber = 10⁸ maxwells). See Gauss's theorem.

magnetic gradiometry: Measuring gradients of the magnetic field in different directions. This has three possible advantages over measuring the field itself: (a) it reduces noise due to temporal field changes, (b) enhances shallow anomalies, and (c) improves lateral resolution. See gradiometer.

* magnetic inclination: See inclination .

* magnetic induction: See magnetic field .

* magnetic intensity: Magnetic-field strength; see magnetic field .

* magnetic interpretation methods: The objective of magnetic data interpretation usually is to locate anomalous magnetic material, its depth, dimensions, and magnetization. Most petroleum search use of aeromagnetics involves determining the depth to the top of anomalous bodies (and thereby inferring the depth to magnetic basement) and the preparation of a contour map of the magnetic basement from the results. Inverse solutions involve various auxilliary conditions in order to achieve a solution. Various shape measurements are made on magnetic profiles or maps and used in conjunction with depth rules (q.v.). Two- dimensional convolution operations such as calculation of a second-vertical-derivative map, downward continuation, or reduction to the pole sometimes are used to help locate anomalous bodies and determine their shape. Sometimes interpretation involves comparison with the fields over known areas or comparison against the fields of model anomalies shown in a catalog of master curves. The most common magnetic interpretation models are a dipping-dike and vertical prism for intrabasement bodies and a thin magnetic layer for structural features. Iterative methods involve calculating the field which a model would produce, comparing it with the observed field, and then iterating until a satisfactory degree of fit between model field and observed field is achieved.

* magnetic latitude: 1. The angle of magnetic inclination determined on a smoothed regional basis rather than locally at a point. 2. The angle having a tangent equal to half that of the magnetic dip.

* magnetic meridian: The direction of the horizontal component of the Earth's magnetic field; the direction of magnetic north.

* magnetic moment: Magnetic dipole (q.v.).

* magnetic permeability (m): The ratio of the magnetic induction B to the inducing field strength H; denoted by the symbol m:

m = B /m_oH .

m_o is the permeability of free space = 4π10^-7 weber per ampere meter (or henries per meter) in SI system, and 1 gauss per oersted in the cgs system; permeability m is dimensionless. The quantity mmo is sometimes considered the permeability (especially in the cgs system).

* magnetic polarization: Magnetization (q.v.).

* magnetic pole: 1. One of the two points near opposite ends of a magnet toward which the magnetic lines of force are oriented and concentrated. If the magnet is permitted to rotate about its center, the pole which points in the direction of the Earth's north magnetic pole is the north-seeking or positive pole; the other pole is the south-seeking or negative pole. Different from magnetic dip pole. See magnetic field of the Earth . 2. The pole strength of a magnetized bar of cross-section A perpendicular to the magnetization M is MA . See Figure M-1.

* magnetic potential: The product of the current and the solid angle subtended by a coil divided by 4π (a sphere subtends the angle 4π). If there are several coils, their individual magnetic potentials (which are scalars) are added. The magnetizing force H is the negative gradient of the magnetic potential, a scalar representing the work done against the magnetic field to bring a unit magnetic pole to the point. A is a vector field whose curl gives the magnetic induction.

magnetic quiet zone: The Cretaceous period from the Aptian through the Santonian (124 to 83 Ma) during which no reversals of the Earth's magnetic field occurred, so that ocean-basin magnetic stripes are absent.

* magnetic resonance: Interaction between the magnetic moments (electron spin and/or nuclear spin) of atoms with an external magnetic field. Magnetic resonance is basic to the operation of the proton-resonance magnetometer and optically-pumped magnetometer (q.v.). See also nuclear-magnetism log and Larmor frequency .

* magnetic signature: The shape of a magnetic anomaly.

* magnetic storm: A period of rapid, irregular, transient fluctuations of the magnetic field which are greater in magnitude, more irregular, and of higher frequency than diurnal variations. These occur most commonly during unusual sunspot activity as a result of bombardment of the Earth by high-energy particles from the sun. Magnetic storms commonly have an amplitude of 50 to 200 nanoteslas, occasionally thousands of nanoteslas, and their duration is often several days. Magnetic prospecting has to be suspended during magnetic storms.

* magnetic survey: Measurements of the magnetic field or its components (such as the vertical component) at a series of different locations over an area of interest, usually with the objective of locating concentrations of magnetic materials or of determining depth to basement. Differences from the normal field are attributed to the distribution of materials having different susceptibility.

magnetic survey resolution: Goussev and Peirce (1999) give the table MM for required resolution:

* magnetic susceptibility: A measure of the degree to which a substance may be magnetized; the ratio k or k' of the magnetization M or I to the magnetizing force H that is responsible for it:

k H = M in the SI system,

k' H = I in the cgs system,

The susceptibility is dimensionless but of different magnitude in the two systems:

k = 4πk' .

The susceptibility is related to the magnetic permeability m

k = m - 1,

k' = (m - 1)/4π.

Susceptibility in cgs units in sometimes measured in units of 10^-6 ("micro-cgs"). Rock susceptability usually ranges from 0 to 0.01 cgs units (0 to 10 000 micro-cgs).

magnetic vector potential: See magnetic potential.

* magnetization: Magnetic moment per unit volume (occasionally per unit mass), a vector quantity. Also called magnetic polarization or intensity of magnetization. Designated by symbols M or I. A measure of the effect of the medium on the magnetic field B when subject to a magnetizing force H:

B = m_o (H + M) in SI system,

B = H + 4πI in cgs system,

where m_o is the permeability of free space. The proportionality between magnetization and H is the magnetic susceptibility (q.v.), k or k' .

* magnetizing force (H): A measure of the influence of a magnet in the surrounding space. See magnetic field and Figure M-1.

magnetochronology: Change in the polarity of the Earth's magnetic field from its present polarity. This has occurred a number of times in the Earth's history and provides a method for age dating; see geomagnetic reversal:

* magnetohydrodynamic theory: The theory that coupling between the mechanical and electrodynamic forces in the fluid core is responsible for the Earth's main magnetic field.

* magnetometer: An instrument for measuring magnetic-field strength. Ground magnetometers sometimes measure the vertical or horizontal components of the magnetic field, sometimes the total field. Most airborne magnetometers are of three types: (a) fluxgate , (b) proton-resonance , or (c) optically pumped (see individual entries); all measure the total-field intensity. Cesium magnetometers measure the absolute field to 0.001 nT accuracy. Vector and vertical-component airborne magnetometers are also used occasionally. See also variometer and squid magnetometer .

* magnetosphere: The space pervaded by the Earth's magnetic field, usually extending to more than 10 Earth radii on the sunlit side and to 40 Earth radii on the shadow side. Charged particles particularly concentrate around 1600 and 3000 km.

* map convolution: A two-dimensional convolution often applied to potential field maps, whereby each point on the map grid is replaced by a weighted sum of the values at other grid points.

••Equation••

y_x,y are the output values, f_x,y the input values, and f_a,b is the weighting scheme, called the template. Simple residual maps are made by subtracting an average of values around the point from the value at the point. The values for different distances may be weighted and sometimes a bias is included ••(i.e., S S fa, b ≠ 0), so that the residual does not change sign very often. By weighting the points to give horizontal derivatives and using Laplace's equation, second-vertical-derivative maps may be made. Other weighting schemes can be used for field continuation, wavelength filtering, etc. See grid residual .

matched filter method: A method to separate the effects of sources at different depths where a log-power spectrum shows distinctive linear slopes. See Cowan and Cowan (1993).

microgravimetry: Measuring gravity to tens of microgals.

* micropulsations: Small amplitude fluctuations in the Earth's magnetic field, usually in the frequency range from 0.01 to 3 Hz and usually with amplitudes less than 10 nT. Micropulsations having amplitudes up to tens of nanotesla result from interactions between plasma emitted from the sun (solar wind) and the Earth's field. Micropulsations are classified as continuous (pc), irregular (pi), pearl (pp), etc. See also magnetic storm .

Nabighian's algorithm: A procedure for calculating the vertical derivative from horizontal derivatives.

* nanotesla (nT): A unit of magnetic flux density. A nanotesla = 10^-9 tesla = 1 gamma.

* natural remanent magnetism (NRM): See remanent magnetism .

Naudy filter: A space-domain filter which replaces very small anomalies (such as spikes) by interpolated values.

* Naudy's method: An automated profile-based depth-estimation method (see also inflection-tangent-intersection method) involving cross-correlation of a magnetic profile with theoretical anomalies, usually dikes or plates. See Shi, 1991.

* Neel point: See Curie point .

negative pole: A south-seeking magnetic pole (q.v.).:

* normal gravity: The value of gravity at sea level according to a formula which assumes the earth to have a simple, regular ellipsoidal shape. See latitude correction .

* normal magnetic field: 1. A smooth component of the Earth's magnetic field which is free of anomalies of exploration interest. Ordinarily computed from a low-order spherical harmonic expansion constrained by satellite measurements. The normal field of the Earth varies slowly with time. Often identified with the IGRF (q.v.). 2. The magnetic field of the Earth (q.v.) during an epoch when it is roughly aligned with the present-day field. Antonym: reversed magnetic field.

* north-seeking pole: See magnetic pole .

nose stinger: A mounting for an instrument (often a magnetometer) that protrudes from the nose of a survey aircraft.

offleveling error: Gravity measurement errors because of the effect of high-amplitude horizontal accelerations on a gyrostabilized platform.

* optically-pumped magnetometer: A magnetometer such as the cesium magnetometer (q.v.) or rubidium-vapor magnetometer which involves nuclear magnetic resonance as a transfer mechanism between light and an RF field at the Larmor frequency. See Figure O-3. Such magnetometers can be made extremely sensitive (≈ 0.001 nT). They measure absolutely the total magnetic field.

* Overhauser-effect magnetometer: (o' v∂r how, z∂r) Instead of using an impressed polarizing field to align proton nuclei with the external magnetic field, as in the conventional proton magnetometer, the proton nuclear spins are polarized by interaction with free electrons. Resonance of paramagnetic free electrons results from excitation by a VHF field.

* paleomagnetism: Study of natural remanent magnetization of rocks and other materials in order to determine the intensity and direction of the Earth's field at the time the materials were magnetized. It has as adjuncts archeomagnetism (study of the Earth's magnetism during historical times) and rock magnetism (basic study of the magnetic properties of rocks and minerals). See remanent magnetism.

parallax correction: Compensation for the separation of a measuring instrument from a determined location, as of a magnetometer bird from the towing plane.

* paramagnetic: (par, ∂ mag net' ik) Weakly magnetic with small positive susceptibility. The magnetic moments of individual atoms are uncoupled so that each atom behaves independently. Paramagnetism usually contributes only a few nanoteslas to the magnetic field at the Earth's surface. Compare diamagnetic and ferromagnetic .

* parasitic ferromagnetism: A weak ferromagnetism associated with imperfect antiferromagnetism (q.v.) in such substances as hematite.

* permeability: (pur me ∂ bil' i te) 1. The ratio of the magnetic field B to the magnetizing force H. 2. A measure of the ease with which a fluid can pass through the pore spaces of a formation. Measured in millidarcy (1/1000 darcy) units. The permeability constant k is expressed by Darcy's law as k = m q /(dp /dx ), where m is fluid viscosity, q is linear rate of flow, and dp /dx is the hydraulic pressure gradient. The presence of more than one fluid can change the effective permeability, so that in multiphase flow the effective permeabilities of the component fluids may not add to the total permeability. See relative permeability.

* permeability of free space: See magnetic field .

* Peters' length: A measurement made on potential-field profiles (especially magnetic), with the objective of determining the depth of an anomalous mass (magnetized body). Peters' rule gives the depth as the Peters' length (horizontal distance between the points on the side of an anomaly where the slope is half of the maximum slope) divided by the Peters' index (0.8-1.0 for vertical thin sheet, 1.0 for horizontal thin sheet, 1.6 for thick sheet, 1.8-2.0 for wide body or contact, default often 1.6). See Peters (1949) and Figure D-7.

Phillips method: An automated depth-estimation method that compares a running autocorrelation of a magnetic anomaly profile with the model autocorrelation of a thin dike or magnetic contact. See Phillips, 1979.

* piezoremanent magnetism (PRM): (pi e, zo rem' ∂ n∂nt) See remanent magnetism .

plate: 1. One of the lithosphere units in plate tectonics (q.v.). 2. A sheet-like magnetic body with a vertical thickness of 0.1 to 1.0 times the depth to its top.

*Poisson's Relation: For bodies having uniform susceptibility and density contrast, the magnetic potential is directly proportional to the derivative of the gravity potential in the direction of magnetization.

* polarization: (po, l∂r i za' sh∂n) 1. Dipole moment per unit volume. In induced polarization, current dipole moment per unit volume. 2. The polarity or potential near an electrode. 3. A preferential direction of wave motion, as the component of S -waves whose motion is confined to a horizontal plane (SH). 4. Preferential direction of motion involved in seismic wave passage, as determined with a three-component geophone or triphone. See polarization filtering . 5. Magnetic orientation concerning only the vector direction and not the magnitude.

* pole: 1. A singular point, where the value of a function becomes infinite. If a function has the factor (x - a )^m in its denominator, a is a pole of order m . If m = 1, a is a simple pole. Also called a singularity. 2. A magnetic pole (q.v.). 3. One electrode of a pair whose companion electrode (infinite electrode) is so far away that its location does not affect the measurements.

pole strength: See magnetic pole.

positive pole: A north-seeking magnetic pole (q.v.).:

* potential field: A field which obeys Laplace's equation, such as gravity, magnetic, or electrical fields.

potential field tilt: tan^-1(vertical derivative/horizontal derivative).

* Pratt hypothesis: (prat) A model of compensation for isostasy (q.v.). See also Figure I-6. Named for John Henry Pratt (1809-1871), British mathematician and geodesist.

preferential continuation: Continuation that selectively enhances a certain range of spatial frequencies.

prism: A semi-infinite, vertical parallelepiped source body. See Figure M-10.

proof mass: The suspended weight in a gravimeter.

* proton-resonance magnetometer: The proton (hydrogen nucleus) has a magnetic moment because of its spin. The nuclei precess about the Earth's magnetic field H at a frequency nL (Larmor frequency),

nL = gH /2π,

where g = gyromagnetic ratio (2π/23.4868 Hz/nanotesla for protons). Precession of polarized nuclear-spins induces a voltage at the precession frequency in a measuring coil. The induced frequency is measured by a counting arrangement (Figure P-13) to determine the value of the Earth's magnetic field. For the normal Earth field of about 50 000 nanotesla, nL = 2100 Hz. As the protons gradually relax into random orientation, the induced-field strength drops to zero. The rate of drop depends on interatomic forces and hence on molecular structure. Achievable accuracy: 0.1 nT. Compare optically-pumped magnetometer .

pseudodepth slice: The result of spectral-domain filtering that emphasizes sources around a specified depth.

* pseudogravity: The gravity field calculated from magnetic-field measurements by means of Poisson' s relation (q.v.). Calculation involves conversion of susceptability to density and vertical integration of reduced-to-the-pole magnetic data.

quick and dirty method: The method of Peters' length (q.v.).

radar altimeter: An instrument for measuring elevation above the ground by timing reflected radar waves. Accuracy about 0.15 m. See also satellite altimetry.

radial power spectrum: An average of power spectra (amplitude squared) calculated in different azimuth directions. Usually plotted as log of the radial power spectrum vs. wavenumber. Generally values decline steeply for small but increasing wavenumbers (representing deep and/or broad sources) and then decline more gently for larger wavenumbers (representing shallow localized sources). Source depth is given by slope of the log power spectrum divided by 4π.

radius of regionality: A specification of the size of the region over which isostatic compensation is distributed in the Vening Meinesz concept of isostasy (q.v.); it is of the order of 200 km.

* raw gravity: Gravity measurements before applying latitude, terrain, and elevation corrections.

reduction to the equator: Converting magnetic data recorded at various magnetic field inclinations to what they would be with zero inclination (horizontal).

* reduction to the pole (RTP): Removing the dependence of magnetic data on the magnetic inclination, i.e., converting data which were recorded in the inclined Earth's magnetic field to what they would have been if the magnetic field had been vertical. Reduction to the pole removes anomaly asymmetry caused by inclination and locates anomalies above the causitive bodies, assuming that the remanent magnetism is small compared to the induced magnetism.

* regional: The general field if features smaller than a given size are eliminated. Regional dip is the general dip attitude ignoring local structure. Regional gravity is the gravity field produced by large-scale variations ignoring small anomalies, often showing the field produced by density variations within or below basement. See residualize .

regional-residual separation: See residualize .

regular noise: Coherent noise.

* remanence: See remanent magnetism .

* remanent magnetism: Remanence; the magnetization remaining in the absence of an applied magnetic field. (a). Natural remanent magnetization (NRM) is the residual magnetization possessed by rocks and other materials in situ; unless otherwise qualified, this is the meaning implied. (b). Thermoremanent magnetization (TRM) remains after a sample has been cooled from a temperature above the Curie point in a magnetic field. (c). Chemical remanent magnetization (CRM) is acquired when a magnetic substance is chemically formed or crystallized in a magnetic field at temperature below the Curie point. (d). Depositional (or detrital) remanent magnetization (DRM) is acquired in sediments when magnetic mineral particles are preferentially aligned during deposition (usually by settling through water) in response to the effect of the ambient magnetic field. (e). Isothermal remanent magnetization (IRM) is remanent magnetization in the ordinary sense, i.e., the magnetization after application and subsequent removal of a magnetic field; it is not involved in paleomagnetism. (f). Pressure (or piezo) remanent magnetization (PRM) is remanence acquired as a result of the application of stress; the effects generally become more pronounced as the strain proceeds from elastic to plastic deformation. See also viscous magnetization and alternating-field demagnetization..

replacement density: The difference in density between that assumed for rock and that of sea water, used for making a Bouguer correction of marine gravity.

* residual: (r∂ zij' ∂ w∂l) 1. The difference between observed data and the regional, as in gravity and magnetics. What is left after the regional has been removed. See residualize . 2. An anomaly, the difference between a measurement of a quantity and the expected value; what is not otherwise accounted for. 3. Salt residual (q.v.).

* residual disturbance: Disturbances that persist during relatively quiet days following magnetic storms.

* residualize: (r∂ zij' ∂ w∂l iz,) 1. To separate a curve or a surface into its long wavelength(or low-frequency) parts, called the regional, and its short-wavelength (or high-frequency) parts, called the residual. Residualizing attempts to predict regional effects and find local anomalies by subtracting the regional effects. This separation is not unique. The regional may be drawn graphically (Figure R-9a,b), by gridding methods (Figure R-9c,d), by surface fitting, by Fourier analysis and filtering, and by other methods, most of which can be thought of as two-dimensional convolution operations (map convolution). Some of these methods produce halo effects (q.v.) about local anomalies. Residualizing sometimes is done in steps. Residualizing methods include (a) graphical methods, in which a smooth regional is drawn on a profile or con tours are smoothed and spaced more uniformly; (b) polynomial method, in which the regional is represented by a polynomial fit to the observed data; (c) spectral-domain filtering, in which certain wanenumbers are attenuated by filtering; (d) stripping method, in which the field of a model that represents certain parts of the geology is calculated and subtracted from the observed field; (e) upward continuation, which attenuates the effects of shallow sources. See Cowan and Cowan (1993). 2. The process of determining what is not accounted for by a particular model. The effects of the model are calculated and subtracted from the observed field, the residual being those effects still unaccounted for. See salt residual .

reversed magnetic field: See normal magnetic field .

rock magnetism: Study of the magnetic properties of rocks and minerals.

RTP: Reduction to the pole (q.v.).

running window: An aperture whose position moves a sample value at a time. Also called a sliding window.

satellite altimetry: Measuring surface relief by radar from a satellite, where the elevation of the satellite is nearly constant. Measurements of the sea surface reveal undulations of the geoid, which permit mapping gravity anomalies. Capable of measuring the sea surface to an accuracy of 1-6 m depending on sea-surface roughness.

satellite gravity: Determining the gravity field over the oceans from satellite altimetry (q.v.) with an accuracy of 3-7 mGal and 20-30 km resolution.

satellite magnetics: Measuring the magnetic field in satellites at about 400 km to a resolution of 1-2 nT.

* second-derivative map: A map of the second vertical derivative of a potential field, such as gravity. Such maps tend to emphasize local anomalies and isolate them from a regional background. Often made using Laplace's equation relating the second vertical derivative to second horizontal derivatives, which can be approximated from differences in the values near the point. See also grid residual.

* secular variation: A change that does not repeat within a long period of time. From the Latin for "long period of time". The "secular variation of the Earth's magnetic field" often means periods greater than 30 to 300 years. Geomagnetic poles precess about the geographic poles with a period of about 7000 years.

sensel: (Sensor elevation) A graph of aircraft height above ground level.

separation filtering: Separating regional and residuals (residualizing, q.v.), generally by upward continuation. See also Jacobsen filter.

* shipboard gravimeter: An instrument or system for measuring the acceleration of gravity from a ship in motion. Complex arrangements are used to insulate the meter from the many accelerations to which the ship is subject and to correct the data for the effects of measuring while moving (see Eötvös effect ).

sill: A tabular igneous interlayer which is longer in horizontal dimension than vertical. See plate.

slab correction: See Bouguer correction.

sliding window: An aperture whose position moves a sample at a time. Also called a running window.

Smith rule: See Bott-Smith method.

* soft magnetism: That portion of magnetization which has relatively low coercive force. In paleomagnetism studies, soft magnetization is removed by alternating-field demagnetization in order to isolate harder remanent magnetism.

* solar wind: Ionized particles flowing radially outward from the sun. Transient magnetic disturbances (see K-index ) are correlated with solar wind: The effect is to produce a time-variable external magnetic field.

source parameter imaging method (SPI): Source parameter imaging that assumes either a dipping contact or a dipping thin sheet. iSPI, standing for" Improved SPI," relates local wavenumbers to a structural index to discriminate between depths determined by basic models.

Spector-Grant method: Magnetic depth-estimation based on linear slopes of log power spectra. Source depth is the gradient divided by 4π. See Spector and Grant (1971).

spectral analysis: Examination of the spectra of potential-field data to locate changes in graphs of the slope of logarithm of the power spectra (log of amplitude squared) versus wavenumber. See also radial power spectrum .

* spinner magnetometer: A device which spins a sample and measures the induced ac-voltage to determine the strength and direction of the sample's magnetic field.

* SQUID magnetometer: (skwid) A sensitive magnetometer which detects magnetic field changes by means of a superconducting loop containing one or two Josephson junctions. Acronym for "superconducting quantum interference device". A SQUID carries supercurrent up to a certain critical value, beyond which a finite resistance appears in the loop. The value of this critical current depends upon the external flux as well as the geometry. In the rf-SQUID magnetometer, a loop with one Josephson junction is driven inductively by a high-frequency (typically 30 MHz) alternating current which periodically exceeds the critical current. The voltage appearing depends upon the value of the critical current which in turn depends upon the external flux. In the dc-SQUID magnetometer a dc-current slightly greater than the critical current is fed into a loop containing two Josephson junctions. This produces high-frequency oscillations in the loop due to the ac-Josephson effect. Thus the current periodically exceeds the critical current and a voltage apppears which depends upon the external flux. Both the rf- and the dc-SQUIDS are usually incorporated in negative feedback circuits which detect and null the flux. The output of the negative feedback circuit is proportional to the output of the SQUID. SQUID magnetometers are capable of detecting fields on the order of 10-5 nanotesla, and are used in magnetotelluric and controlled-source electromagnetic field techniques. See Clarke (1974) and Weinstock and Overton (1981).

stabilized downward continuation: Downward continuation (q.v.) after removing high frequencies.

* stabilized platform: A platform on which instruments (such as gravimeters) can be mounted where they will remain nearly level despite tilt of the platform support. The platform, mounted on gimbals, is controlled by a gyroscope coupled to an accelerometer-controlled servo system on each gimbal axis. Used in measuring gravity on a ship in motion and in mounting inertial navigation sensors.

* Steenland-Vaquier rule: (sten' land vak' ∂ a) See straight slope measurement . Named for Nelson C. Steenland and Victor Vacquier (1907- ), American geophysicists.

* straight slope measurement: The source depth is given by the horizontal distance over which a magnetic anomaly is nearly linear at the maximum slope, divided by an index value. Indices are 1.9 for vertical thin sheet, 1.9 for horizontal thin sheet, 1.7 for thick sheet, 1.4 for plug-like body, 1.3 for wide body, 1.2 for a contact, and ofter 1.5 as a default value. Also called maximum slope distance, Vaquier rule,.Steenland-Vaquier rule. See Figure D-7 and depth rule .

Strakhov filter: A linear filter that smooths a spectrum in a least-squares manner.

strike filter: A band-pass filter designed to pass or attenuate Fourier components along a specified azimuth.

superconducting magnetometers: See SQUID magnetomneter .

swarm: 1. A series of minor earthquakes, none of which may be identified as the main shock, occurring in a limited area and time. 2. A group of roughly parallel igneous intrusives.

* T: Tesla (q.v.).

tail stinger: A mounting for an instrument (often a magnetometer) that protrudes from the tail of a survey aircraft.

Talwani inversion: Interpretation of gravity data to determine the depth to the top of a homogeneous layer composed of vertical prisms assuming only one contrast. Differences between thr gravity calculated from the model and observed gravity is used to change the depths to the prisms iteratively.

* Talwani modeling: (tal wa' ne) The gravity field of a body is represented by horizontal polygonic thin layers and the field of each is calculated. Can accommodate density variation with depth. Named for Manik Talwani (1933- ), American geophysicist.

* tare: A discontinuity in data indicating an error in measurement or computation rather than a real jump in the quantity being measured. Sometimes spelled tear.

* terrain correction: 1. A correction to gravity data required because the surroundings are not all at the same elevation as the meter. Relief in the immediate vicinity of the station may require special surveying (terrain surveying), whereas corrections for more remote relief often are made from a topographic map using a terrain-correction template or a zone chart. 2. A correction to seismic data because of the effect of topographic loading on velocity. 3. A correction to magnetic or electrical data because of terrain effects.

* terrestial magnetism: See magnetic field of the Earth .

* tesla (T): A unit of magnetic induction B. 1 tesla = 1 weber/m2 = 1 newton/amp.m = 10₄ gauss = 10⁹ gamma. 1 nanotesla = 1 gamma. Named for Nikola Tesla (1851-1943), American inventor.

Thalen method: The depth of a magnetic source is 0.7 times the horizontal distance between selected maxima and minima. See also depth rules.

theoretical gravity: Values given by ther International Gravity Formula (q.v.).

thermal remanent magnetism (TRM): See remanent magnetism.

* thermoremanence: See remanent magnetism .

thick/thin dike: A thick dike is a vertical body whose width is about the same as the depth to its top. The width of a thin dike is much less than the depth of its top; also called thin sheet.

* Tiburg rule: A depth rule (q.v.) used in magnetic-data interpretation: the depth to a pole is 2/3 of the horizontal distance at half the maximum amplitude.

* tidal correction: See tidal effect .

* tidal effect: Variations in gravity observations resulting from the attraction of the moon and sun and the distortion of the Earth so produced. Tidal corrections to gravity observations are made by means of tables or are included with drift corrections.

* torsion balance: 1. An instrument for measuring second derivatives of the gravitational potential. In a non-uniform field, the forces on equal masses at opposite ends of a horizontal beam suspended by a very fine torsion wire differ, producing a torque which can be measured by counter balancing it with a known torque. The measured gradients can be integrated to make a gravity map. 2. A device for measuring the derivatives of force fields, such as magnetic or electrical.

* total intensity: Usually refers to the total magnetic intensity as opposed to the components in the vertical or horizontal directions.

towed deep ocean gravimeter (Towdog): An automated gravimeter towed just above the seafloor.

* triplets: A method of determining the elevation correction factor (ecf) for gravity data from sets of three readings each. It is assumed that elevation does not correlate with geologic structure. If the difference between the height at a station and the weighted mean of the heights of stations on either side of it is hi and the difference between the observed gravity reading at the station and the weighted mean at the neighboring stations is gi (where the weighting is usually taken as inversely proportional to the distance), then the elevation correction factor k is given by:

••k = -(S h_ig_i )/S h_i²,

and the probable error e in k is

••e = 0.67[(S g_i²/S h_i² - k ²)/n ]^1/2.

See Siegert (1942).

two-and-a-half dimensional (2.5-D) body: A body that is limited in extent perpendicular to the profile line.

2 1/2-D modeling: Modeling of profile data where bodies perpendicular to the line have limited predetermined extent.

* upward continuation: Calculation of the potential field at an elevation higher than that at which the field is known. The continuation involves the application of Green's theorem and is unique if the field is completely known over the lower surface (which could be true for gravity and magnetic fields) and where all sources above the lower surface are known (usually all are zero). Upward continuation is used to smooth out near-surface effects and to tie aeromagnetic surveys flown at different heights.

Vaquier rule: (vak' ∂ a) See straight slope measurement . Named for Victor Vacquier (1907- ), American geophysicist.

* variometer: (var, e om' i t∂r) An instrument for measuring small magnetic variations. Consists essentially of a magnet suspended on a torsion fiber. Slight rotations of the magnet deflect a light beam reflected by a small mirror attached to the magnet, and the position of the beam is recorded on photographic paper. See also magnetometer.

* Vening Meinesz hypothesis: (ven' ing mi' nez) See isostacy . Named for Felix Andries Vening Meinesz (1887-1966), Dutch geophysicist.

* vertical intensity: The component of the total-intensity field in the vertical direction.

* viscous magnetization (VRM): Remanent magnetization produced by a weak magnetic field over a long period of time. It is generally proportional to the logarithm of the time and parallel to the weak applied field. Viscous magnetization has its origin in thermal energy which is large enough to realign the magnetization direction of domains with rather high energy barriers. The weak field of the Earth acts to bias the direction of these jumps.

* volume magnetization: Magnetic moment per unit volume.

* VRM: Viscous magnetization (q.v.).

* wavenumber: 1. The number of waves per unit distance perpendicular to a wavefront, that is, the reciprocal of the wavelength. It is thus equal to k/2π, that is, wavenumber is to k as frequency n is to angular frequency w. Some authors define k as the wavenumber. 2. Spatial frequency, the number of wave cycles per unit of distance in a given direction (direction of the spread); apparent wavenumber. Specifically, the reciprocal of the apparent wavelength lapp along the spread direction:

1/l_app = f/V_app = k_app /2π,

where f = frequency and Vapp is apparent velocity. If a wavefront makes the angle q with the given direction,

k = 2pn (sin q)/V .

where V is the actual velocity of the wavefront. A wavenumber of zero indicates a wavefront striking a line of detectors simultaneously. See f-k plot. 3. See propagation constant ..

* weber: The unit of magnetic flux in the SI system, being one joule/ampere. The analogous unit in the cgs system is the maxwell = one erg/abampere. 1 weber = 10⁸ maxwells. Named for Wilhelm Edward Weber (1804-1891), German physicist.

* Weiss's theory of magnetism: (visz ∂z or wisz ∂z) A ferromagnetic material is made up of small regions or domains magnetized to saturation (i.e., spins aligned cooperatively) despite the tendency of thermal agitation to disorient the spins (as in the case in paramagnetism). A weak external field can orient the domains with the field direction, and if strong enough, can align the domains irreversibly, making a permanent magnet. Named for Pierre Weiss (1865-1940), French physicist.

Werner deconvolution: (wur' n∂r) A method of inverting regularly spaced magnetic data such as obtained from aeromagnetic surveys. The method assumes that anomalies are produced by thin sheets or planar interfaces with infinite strike and depth extent which are perpendicular to the line of measurement. The anomaly produced by a thin sheet can be expressed in terms of four unknowns so that, in a noise-free environment, values at four successive points suffice for a solution. Similarly, the vertical or horizontal derivative of the anomaly produced by a planar interface between rocks of differing magnetization can be expressed in terms of four unknowns. Usually two (sometimes three) additional unknowns are added to allow for interferences and a solution is found for each successive 6 (or 7) points on an overlapping basis. The results (which consist of position, depth, dip, and susceptibility contrast or thickness) are sometimes analyzed to remove erratic solutions. The relation between an anomaly and its magnetic source is expressed as a convolution, hence calling the operation deconvolution (or sometimes filtering). See Hartman et al. (1971: 891-918) and Ku and Sharp (1983).

* Werner filtering entry delete

* window carpentry: Abrupt changes, such as at the edges of a boxcar window, produce undesirable ringing and overshoot effects. Window carpentry concerns designing the boundaries of windows to minimize undesirable effects by weighting the values within a window according to some scheme. Window weightings in common use are shown in Figure W-11. Note the tradeoff between narrowness of the major lobe and low sidelobe energy.

* Worden: A type of gravimeter. Light weight and insulated by a thermos bottle, the meter is very portable. See Figure G-5.

* wrap around: 1. Aliasing in the f-k domain (q.v.). Wrap-around can be prevented by padding (q.v.) with zeroes. See also Figure F-8b. 2. The effect produced when a digital memory element (usually a register) is incremented (decremented) past its maximum (minimum) value. For example, a 4-bit register can contain any value from 0 to 15. When it contains 15, incrementing it results in a value of zero.

* zero-length spring: A spring whose effective length, as measured from its fixed point of support, is zero when the external forces acting upon it are zero. The stress-strain relationship between its points of attachment projected back to zero length has zero strain. Gravimeters using a zero-length spring are linear and have extreme sensitivity combined with stability and reduced sensitivity to leveling error.

* Zietz-Andreasen method: A magnetic interpretation method; see Zietz and Andreasen (1967).

* zone chart: A template for making terrain corrections or isostatic corrections to gravity data. The zone chart (Figure Z-2) is laid over a topographic map with its center at the station being corrected. The difference in mean absolute elevation between each zone and the station's elevation is tabulated without regard for sign (because the correction is always positive regardless of whether zones are higher or lower than the station elevation) to determine the terrain correction. With a zone chart for isostatic correction, the mean elevation above sea level in each zone is used in calculating the correction.

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