C

Calculated Terrain  – an airborne survey term to define the calculated Earth’s surface topography.  C.T.  represents the difference between values recorded by the GPSZ channel (i.e. flight height above mean sea level) and those recorded by Radar Altimeter channel (i.e. flight height above the Earth’s surface) .  See also Digital Terrain Model.

Calculated Vertical Gradient  – a vertical gradient of the magnetic or gravity not measured during the survey, but calculated by applying various algorithms. One of the most common methods is a three-step procedure: 1) space domain calculation of horizontal gradients in two orthogonal directions (“x” and “y”) from the observed field; 2) transformation of calculated horizontal gradients into the spectral domain using Fourier Transform; 3) spectral domain calculation of the vertical gradient using Hilbert Transform. ^{[2, 12, 94, 127, 154, 164, 165, 166, 177, 189].} See also Vertical Gradient, Measured Vertical Gradient and Analytic Signal.

Calibration  – a gravity data reconstruction procedure used to convert the gravity field readings from counter (dial) units to milligals by applying the respective Interval Factor or Milligal Constant. See Milligal.

Calibration Factor  – see Interval Factor and Milligal Constant.

Cartesian Coordinates  – coordinates in which the position of a point in space is defined by its distances from an origin along three mutually orthogonal axes (“X”, “Y” and “Z”).

Cascaded Filtering  – a sequential application of several filtering procedures, one after another, to a given dataset in order to ensure a consecutive enhancement of a pre-selected range of wavelength components of the potential field. In C.F., the output of each preceding step is the input for the next step. When filters are linear, the order in which they are cascaded does not affect the final result. Non-linear filters such as Horizontal Gradient must be cascaded in the same sequence to obtain the same result. ^{[81, 124].}

Causal Function  – a function defined only for positive values of its argument, being zero otherwise. For such functions, their Fourier Transform has the property that the real and imaginary parts of the corresponding Analytic Signal are Hilbert Transform of each other. ^{[83, 164, 165, 166].}

Causal Spectrum  – an amplitude spectrum obtained after Fourier Transform of the observed space-domain data and modified to meet requirements for the causal function: negative frequencies are changed to zero and amplitudes of positive frequencies are doubled. ^{[164, 165, 166].}

Causative Body  – a theoretical approximation of a source which generates the potential field anomaly. Causative magnetic or gravity bodies are assumed to represent geological discontinuities within the sedimentary section and the basement and they are defined geometrically or geologically as thin sheets, dikes (faults), prisms, contacts (interfaces and faults), cylinders, etc. ^{[83, 178].} See Gravity Modeling Shapes and Magnetic Modeling Shapes.

Cell  – see Grid Cell.

Cell Size  – a size of the regular spaced square cells that constitute Grid of the observed potential field data. C.S. is the same for all cells and commonly is about one-third of the traverse line spacing. See also Gridding, Control Lines and Traverse Lines.

Central Frequency  – see Central Wavenumber.

Central Wavenumber  – a user-selected parameter of the pass filter (high-pass or low-pass) which defines a wavenumber value where filter function is half its maximum value. C.W. is the equivalent of a cutoff wavenumber or frequency value for bandpass filters.

Cesium Magnetometer  – an optically pumped magnetometer. Its sensor outputs Larmor Frequency which is proportional to the total magnetic field. This frequency signal is then measured by a magnetometer processor board. The achievable sensitivity is 0.001 nT. The total field intensity range is about 20,000-100,000 nT. For Cesium-133 isotope, Gyromagnetic Ratio is about 82 times higher than that of the common Proton Precession Magnetometer and it is the reason that C.M. has a higher sensitivity. ^[223]. See Optically Pumped Magnetometer.

Channel Filters  – a group of the line-base filters designed for applying to the gravity and magnetic data, assigned to a separate Channel in the project Database, before Gridding. Standard set of C.F. includes High-Pass Filter, Band-Pass Filter, Low-Pass Filter, Median Filter, RTP Filter and some others. High-pass and low-pass filtering is usually performed by Butterworth Filter. Its low-pass option can be used as Alias Filter. Often, C.F. are referred to as Line Filters as they are applied to the data originating from measurements along survey lines.

Chemical Remanent Magnetization  – one of five main types of the remanent (residual) magnetization. C.R.M. originates from the rocks’ exposure to the external magnetic field during chemical reactions which result in the changes in the shape and/or composition of magnetic grains. C.R.M. makes significant contribution to magnetization of sedimentary and metamorphic rocks. ^{[33, 54, 238].} See also Detrital R.M., Isothermal R.M., Thermal R.M. and Viscous Remanent Magnetization.

Chessboard Method  – a potential field continuation method. In this method, the potential field measured on the horizontal surface of the survey flight height (AGL) is continued to several horizontal surfaces spanning the elevation range of a desired “drape” surface. This 3-D volume of data resembles multiple tiers in 3-D chessboard. To evaluate the potential field on this “drape” surface, the vertical interpolation is used between the fields on the nearest bounding horizontal surfaces. C.M. is applied for level-to-drape, drape-to-level and drape-to-drape continuations. When C.M. is used for the parallel-surface continuation, it becomes identical to Simple Fourier Method. ^[196]. See Continuation Filtering and Equivalent Source Continuation.

Chimney  – a vertical column of sediments over a hydrocarbon reservoir with a different mineralogy, magnetization and diagenetic alterations as compared to adjacent host rocks. C. origin is assumed to be related to Hydrocarbon Seepage. ^{[6, 61, 62, 151].}

Chopping Filter  – a term that refers either to High-Pass (Low-Cut) Filter or High-Cut (Low-Pass) Filter.

Circular Convolution  – a property of a convolving process in computation of the filtered data values in the Fourier (frequency) domain. As Fourier Transform assumes the discretely sampled data and filter operator to be periodic (even if they are not), the applying filter, like RTP Filter, at one edge of the gridded data convolves data not only at the side of this edge, but also data from the other side of the opposite edge, causing Wraparound Effect. ^[148]. See FIR RTP Filter and Linear Convolution.

Clarke Ellipsoid  – the reference geodetic datum (Reference Ellipsoid) used in the most of the Western Hemisphere prior to the use of a satellite datum (such as WGS 1984).  Often referred to as the Clarke 1866 ellipsoid.  There is also a Clarke 1880 ellipsoid which is used in Africa. ^{[223 ].}

Clip Filter  – a space-domain profile-based processing operator that nulls out any data points whose value lie outside the specified upper and lower bounds of C.F.

Coherence  – a space measure of similarity (i.e., systematic phase relationship) between wavelengths at adjacent grid cells over extended distance on a map of the gridded potential field data. ^[8].

Coherence Map  – a map of similarities and discontinuities in the gridded potential field data. High-resolution coherence algorithms are able to identify both low-intensity anomaly axes and subtle discontinuities associated with magnetized faults. ^[8].

Coherent Filtering  – a procedure which is applied to the gridded potential field data in order to enhance the similarity among such map events as peaks, troughs and other coherent events. C.F. operators are based on computation of cross-correlation function maxima in windows of a user-specified length. As compared to conventional anomaly maxima computations, C.F. is less sensitive to local data oscillations caused by variations in Terrain Clearance of the survey aircraft and side effects of gridding algorithms providing, therefore, more stable (i.e., less noisy) mapping of coherent events. C.F. can also be used to map non-magnetic fault zones as zones of the least similarity (i.e., discontinuities in similarity). ^{[8, 94].} See Coherence.

Coherent Noise  – noise events which exhibit systematic (regular) phase and amplitude relations between adjacent observation lines or grid cells. C.N. includes Cultural Noise, Corrugations, gridding errors and others. C.N. is also referred to as Regular Noise. ^[219].

Color Bar  – a display of the map or Grid values represented by user-defined range of different colors. ^{[223 ].}

Color Wheel  – a full-circle (360º) distribution of colors in the “sun” illumination technique where each C.W. segment represents the direction of correlated map events like contact dip or fault strike. There is a “coned” C.W. where colors have a varying saturation from dark to light, and a “flat” C.W. where colors have a constant saturation. Sometimes, the use of a “coned” C.W. (also called Full Vector Sun Image) shows faults and other subtle map events that are not imaged with a “flat” C.W. See Artificial Sun Illumination.

Color-Coded Map  – see Pseudocolor.

Color-Scaled Map  – see Pseudocolor and Contour Map.

Combined Elevation Correction  – see Elevation Correction.

Compensation Flight  – see Figure-Of-Merit (FOM).

Compensation Test  – one of On-Site Magnetometer Calibrations made by test measurements along at least four flight lines oriented in the direction of the survey lines with the following aircraft maneuvers: Pitch, Roll and Yaw with oscillating ± 5(10) degrees about the normal survey vector and flown at much higher altitude as compared to the planned survey flying. The purpose of C.T. is to derive a set of compensation coefficients to correct for the effects the aircraft has on magnetometer sensors. See also Figure-Of-Merit, Heading Test and Lag Test.

Compensator  – an electronic device which is installed in aircraft to compensate magnetometer readings for the magnetic effects of the aircraft itself and its flight maneuvers, and different orientations with respect to the Earth’s magnetic field vector. See also Real Time Magnetic Compensation System.

Complementary Filter  – a spectral domain pass filter which is complementary to the previously applied pass filter. For example, C.F. of 2400 m low-pass filter is 2400 m high-pass filter. C.F. shows the components of data removed by the previous high-pass or low-pass filtering operation. Butterworth Filter is often used as C.F.

Complete Bouguer Correction  – see Bouguer Correction.

Complete Bouguer Field  – the gravity field obtained after applying Bouguer Correction and Terrain Correction to the observed gravity data. See also Simple Bouguer Field.

Complex Analytic Signal  – see Analytic Signal.

Complex Attributes  – three attributes of the analytic signal: 1) Instantaneous Amplitude (more often called Analytic Signal Absolute Value, Analytic Signal Amplitude or Energy Envelope); 2) Instantaneous Frequency; 3) Instantaneous Phase. The term “instantaneous” makes clear that these attributes are different from their spectral namesakes. As potential field data are spatial rather than temporal, the term “local” is often used instead of “instantaneous.” ^{[94,  226,  236,  242].} See Analytic Signal.

Complex Gradient  – a 2-D vector quantity corresponding to the resultant of the vertical and horizontal gradients. C.G. is computed to interpret anomalies produced by dikes using characteristic points of their anomalies as well as phase plots. ^[203].

Composite Forms  – a number of generalized geometric forms (horizontal cylinders, thin and/or thick dikes, prisms, etc.) with different dimensions and different density/susceptibility values that simulate a presumed subsurface structure. C.F. are the basic ones for Inversion By Forward Modeling where the user adjusts dimensions and values of various component parts of a particular model until theoretical and observed gravity/magnetic curves fit. ^[54].  See also Gravity Model and Magnetic Model.

Composite Image  – a grid data image which is obtained by overlaying one image, original or processed, with another dataset (line, point, polygon or grid) display. For example, the total magnetic field image overlaid with the point dataset of the 3-D Euler depth solutions or the total magnetic field contour lines as an overlay for the image of the filtered total magnetic field grid. See also Drape Image.

Compu-Drape™  – a processing technique that recalculates (“drapes”) the magnetic and gravity data to any reference surface (Digital Elevation Model, sea floor, estimated Basement, etc.) as well as drapes a loose  Drape Survey to a tight drape and applies height corrections to minimize mis-ties.  Trademark of Geosoft Inc.  See Mis-Tie.

Constrained Regional Gravity Field  – a quantitative estimate of the regional component of Bouguer Gravity calculated from control points where depth to the major Density Contrast is known from independent sources such as wells, seismic interpretation and Geologic Map of the area under study. ^[84]. See also Constrained Residual Gravity Field and Gravity Basement.

Constrained Residual Gravity Field  – a quantitative estimate of the residual component of Bouguer Gravity calculated by subtracting Constrained Regional Gravity Field from the Bouguer gravity field. C.R.G.F. is assumed to represent the gravity effect caused by the major Density Contrast in the gravity survey area, referred to as Gravity Basement. ^[84]. See also Talwani Inverse Solution.

Contact  – a boundary (often, a fault) between two blocks of differing susceptibility/density values or rock types. High-offsetting fault blocks can generate anomalies similar to those of C. See Analytic Signal and Analytic Signal Amplitude.

Continental Crust  – See Crust.

Continental Margin  – a part of the ocean (or sea) floor between the shoreline and a depth of about 4000 m below sea level. The Gulf of Mexico is an example of one of the world’s largest C.M. petroleum provinces. The combined effects of a large sedimentary thickness, salt tectonics, and oceanic-continental Crust relationships give rise to high-amplitude regional magnetic and gravity anomalies here. ^{[13 ].} See also Continental Shelf.

Continental Shelf  – a part of the ocean (or sea) floor between the shoreline and a depth of 200 m below sea level. C.S. is characterized by its very gentle slope of about 0.1°. By present, the largest discovered oil and gas reserves are concentrated within C.S. areas. ^{[13 ].} See also Continental Margin.

Continuatio n – a data processing concept which is based on the potential field continuity, i.e. the observed gravity or magnetic field can be recomputed at an elevation higher (Upward Continuation) or lower (Downward Continuation) than that at which the potential field was measured. ^{[223 ].}   See also Continuation Filtering.

Continuation Concept  – see Frequency–Depth Rule.

Continuation Filtering  – a procedure to recompute the observed potential field at an elevation other than that at which the measurements were made. Upward or downward, this procedure is straightforward and stable as long as no sources exist between a selected level and the level of measurements. In the spectral domain, C.F. behaves like a low-pass filtering (Upward Continuation) or high-pass filtering (Downward Continuation). When used in the separation filtering, C.F. can accentuate a particular range of anomaly wavelengths representative of a given depth range, yielding a new picture of magnetic or gravity trends not readily apparent on the original unfiltered map. ^{[42, 48, 59, 118, 184].} See Separation Filtering.

Continuation Filters  – a group of the spectral domain grid or line dataset operators which process the data in such a way that, when reverse transformed from the spectral domain back to the original space domain, the processed data appear to have been collected at another level (upward or downward) as compared to the level of actual measurements. Depending on the quality of data and survey targets, C.F. can be used for either random noise suppression and separation applications (upward option) or short-wavelength components enhancement (downward option). ^{[39, 42, 48, 118, 184, 196, 250].} See also Continuation Filtering and Separation Filtering.

Contour Map  – a map of continuous lines (contours), connecting the same values of the observed gravity or magnetic field. Instead of contours, the map is often represented in the color spectrum shades where each shade corresponds to a particular range of the gravity or magnetic field values, from low to high. Such maps are called color-scaled or color-coded maps. See Pseudocolor.

Contrast Normalization Filter  – a grid-based averaging operator whose resulting effect is similar to that of Automatic Gain Control. ^[230]. See also Histogram Equalization.

Control Lines  – survey lines which are usually orthogonal or sometimes oblique to Traverse Lines and commonly flown with a larger spacing (three times and more) as compared to the traverse line spacing. C.L. are often referred to as Tie Lines and are intended to control line-to-line instrument variations in the process of measurements.

Convolution  – a data filtering operation which changes the amplitude and wavelength content of the original sampled data. In the space domain, each input sample amplitude will be replaced by another amplitude scaled proportionally to Impulse Response of the convolution (filter) operator and the output will be the superposition of all scaled sample amplitudes that occur at the same space points within a length of the operator’s sliding window. In the spectral domain (after Fourier Transform), the output will be presented by multiplying the amplitude spectra and adding the phase spectra of original sampled data and convolution operator. ^[223]. See also Deconvolution, Circular Convolution and Linear Convolution.

Convolution Grid Filter  – a space domain filter which modifies a given grid through the processing each grid cell using a combination of values of its neighbors.

Coordinate Rotation Method  – a method which re-projects, by coordinate rotation and re-gridding, the subparallel or fanning elongated short-wavelength anomalies caused, for example, by mafic dikes (“dike swarms”) that lie on a single azimuth trend along the new coordinate axis. Re-projected anomalies along this trend can then be easily removed by Directional Filtering and data are re-gridded and projected back to their original condition. C.R.M. provides more selective and less disturbing removal of the various unwanted directional trends as compared to spatially invariant spectral domain directional filtering. ^[198]. C.R.M. is also referred to as Coordinate Transformation Method.

Coriolis Acceleration – The acceleration of a moving body (for example, a shipborne gravimeter platform) with respect to the Earth resulting from the rotation of the Earth.  If body moves on the Earth’s surface with the velocity “V”, then C.A. formula can be represented as

C.A. = 2TVsinN ,

where “T” is angular rotation of the Earth. “N” is the latitude.  C.A. of a moving gravimeter is involved in Eötvös Effect.  ^{[223 ].}

Coriolis Effect  – the horizontal component of the resultant vector in a vector addition of the gravimeter’s platform velocity and the Earth’s rotational velocity. The corresponding vertical component is Eötvös Effect. ^{[13, 223, 238].}

Correction of Magnetic Data  – a compensation of the observed (recorded) magnetic data for a) irregular solar micropulsations and magnetic storms; b) regular diurnal and secular variations; c) instrument drift; d) flight elevation above ground surface (AGL); e) location ties (mis-ties) between traverse and control lines; f) the Earth’s gradient field (based on the International Geomagnetic Reference Field – IGRF); g) local Inclination and Declination of the magnetic field (Reduction-to-the-Pole, i.e., RTP, or Reduction-to-Equator, i.e., RTE); h) Cultural Editing. Not all of these corrections are commonly applied and not necessarily in this order.

Corrugation Anomaly  – an artificial anomaly arisen from residual errors in Leveling and Gridding of the survey line datasets. C.A. can be effectively removed by Directional Filtering if it meets the following criteria: a) relatively small dynamic range; b) quasi-symmetrical waveform; c) the shortest possible wavelength is orthogonal to Traverse Lines, and it is not longer than twice the traverse line spacing; d) the longest possible wavelength is along the traverse lines, and it is not shorter than twice the control line spacing. See Decorrugation.

Corrugations  – small amplitude artificial anomalies (i.e., Artifacts) elongated along both traverse and control (tie) lines. C. represent the residual errors remaining after conventional Leveling and Gridding of the observed potential field data. C. are attenuated or removed in the process of Microleveling. Sometimes, C. are referred to as Acquisition Footprint or Striping. See also Corrugation Anomaly and Decorrugation.

Cosine Bell Filter  – an edge smoothing spectral domain grid filter which converts the original grid edge data values into a “bell-shaped” cosine curves to ensure a smooth transition of these data to zero at the edges of a grid. ^[176]. See Edge Smoothing Filters.

Cosine Correction  – a correction which is applied if a long axis of magnetic anomaly is not orthogonal to the orientation of magnetic profile. Magnetic depth estimates will be artificially deeper due to this skew and C.C. will compensate for this discrepancy by shallowing depth estimates.

Cosine Rolloff Filter  – a spectral domain pass filter which retains long- or short-wavelength components of observed data using Taper with a smooth cosine curve in Rolloff Range. User specifies high and low frequency (short- and long-wavelength) cutoffs for the rolloff range and a degree of the cosine function: the higher degree – the steeper transition between passed and rejected portions of the data spectrum. Differing from the conventional pass filters, C.R.F. has strongly reduced or no Ringing effects. ^[230].

Cosine Taper Filter  – see Cosine Rolloff Filter.

Crab  – a steady Heading of the survey aircraft or ship at an angle to the selected course to compensate for a crosswind. ^{[223 ].}  See also Pitch, Roll and Yaw.

Creep – a gradually increasing deformation of a spring in the gravimeter sensing system as a result of a thermal expansion, elastic aging or excessive movement. ^{[238 , 255 ].}

Critical Surface Concept  – a concept that postulates a particular surface above which physical property contrasts (such as Density Contrast or Susceptibility Contrast) are either horizontally stratified or absent, or relative small, and below which these contrasts are large and reliably identified. C.S.C. considers physical property contrasts as invariants with depth and, therefore, effects of sources near and below the critical surface will predominate in the observed field. In magnetic explorations, the top of Crystalline Basement is the example of a critical surface. ^[45].

Crossing-Point Method  – a method of calculating magnetic parameters of Dike and Contact (such as depth to top, effective dip angle, Susceptibility or Susceptibility Contrast) using the crossing points of Horizontal Derivative (“G_x”) and Vertical Derivative (“G_z”) profiles. Over dikes, profiles of “G_x” and “G_z” cross at two points. Over contacts, they cross at only one point. All sources (thin or thick dikes, contact) are assumed to have Induced Magnetization. Real data depth errors are estimated to be about 5-10 percent. ^[171]. See also Thick Dike, Thin Dike and Profile.

Crossovers  – points of data measurements where the traverse and control (tie) lines cross each other. Crossover point values of the measured magnetic or gravity field are used in the process of Leveling. Most of the differences in airborne crossover values are due to problems with acquisition height.

Crust  – the outermost layer of the Earth above Mantle. Mean density of C. is about 2.8 – 2.9 g/cu.cm. C. represents less than 0.1% of the Earth’s total volume. Continental C. is predominantly granitic and ranges in thickness from about 35 km up to 60 km. Oceanic C. is basaltic and about 5-10 km thick. ^{[13, 223, 238].}

Crustal Magnetic Field  – the remaining magnetic field after removal of the external field effects (diurnal variations and other solar radiation activity) and the Earth’s main magnetic field (International Geomagnetic Reference Field – IGRF) from the observed data.

Cryogenic Magnetic Levitation  – Magnetic Levitation under temperatures near absolute zero. C.M.L. is used in the design of high-sensitivity gravimeters. ^[36]. See Virtual Spring.

Cryogenic Magnetometer  – a high-sensitive magnetometer which operates at the temperature of a liquid nitrogen. ^{[223 ].}  See Squid Magnometer.

Crystalline Basement  – see Basement.

Cultural Magnetic Anomalies  – see Cultural Noise.

Cultural Editing  – the removal of artificial non-geologic magnetic effects generated by man-made objects (pipelines, wellheads, power lines, etc.) from the observed magnetic data. There are two basic approaches to C.E. : 1) automated Filtering , including a wavelet transform filter technique, and 2) manual peak selection controlled by the flight video records. C.E. is also referred to as Deculturing. ^{[57,109, 139 ].} See also Cultural Noise, Cultural Suppression and Video Vewing.

Cultural Noise  – non-geologic, usually short-wavelength (high-frequency), high-intensity anomalous components of the observed magnetic field generated by man-made objects: pipelines, wellheads/casings, large metal buildings and others. C.N. should be edited out of the original line dataset prior to Leveling. ^{[57, 73, 109].} See Cultural Editing.

Cultural Suppression  – a technique where a space variant filter such as a Naudy Filter is used to reduce sharp anomalies of cultural origin to an amplitude below a threshold value. ^[109].

Curie Point  – the temperature at which magnetized rocks lose their ability to retain magnetic properties. C.P. of the most rocks is about 550º C which is usually reached at depths of 30-40 km. C.P. is also referred to as Demagnetization Temperature. ^{[223, 238].}

Curvature  – a reciprocal of the radius of a circular arc that can be best fitted to the portion of a line in the point’s immediate vicinity. C. defines the rate of change of the slope of a curve or surface. The second derivative of a function is a measure of the function’s curvature. See also Differential Curvature.

Curvature Correction  – a correction which is applied to the observed gravity data to compensate (“bend”) Bouguer Slab in order to conform it to the shape of the Earth in a more reasonable way. Since this correction changes the Bouguer slab at considerable distances from the point of measurements, the corresponding C.C. values are generally small. ^{[34, 135].} See Bullard B Correction.

Curvature of Gravity  – a vector calculated from the gravity gradient data (such as the torsion-balance) indicating the shape of an equipotential surface. It points in the direction of the longer radius of curvature. ^{[36 , 223 ].}

Cutoff  – a spatial frequency (wavenumber) or wavelength value which designates the effective operational range of a given filter. For example, 1200 m–4800 m Band-Pass Filter has a short-wavelength C. at 1200 m and a long-wavelength C. at 4800 m. See also Cutoff Wavelength and Cutoff Frequency.

Cutoff Frequency  – a spectral domain filter parameter which controls the half-power or 30% amplitude point of the filter response curve in terms of Spatial Frequency (i.e., in cycles per grid or distance unit). See also Filter Cutoff.

Cutoff Wavelength  – a wavelength filter parameter corresponding to Cutoff Frequency which controls the half-power or 30% amplitude point of the filter response curve in terms of Wavelength, i.e., it defines a wavelength value at which Wavelength Filter reaches 50% of its maximum response. See also Filter Cutoff.

Cutoff Wavelength Width  – a wavelength interval within which the filter characteristic changes from its minimum response to its maximum response. The optimum C.W.W. to reduce Ringing and other side effects is recommended to be about one Octave. ^[257]. See also Cutoff Wavelength and Filter Order.