R

Radar Altimeter  – an instrument which is installed on board the aircraft to measure and record the flight height above the Earth’s surface (AGL) with the common accuracy of about 0.15 m (0.5 ft). ^[57]. See also Barometric Altimeter.

Radar Altimetry  – see Satellite Altimetry.

Radar Imagery – a method and instrumentation to measure and map the Earth’s surface relief by the radar installed on board the aircraft or orbiting satellite. ^{[223 ].} See Radar Altimeter.

Radial Frequency  – unit of reference on the Radial Power Spectrum curve or the filter amplitude response curve. R.F. is presented in cycles per meter or in cycles per km or, sometimes, in cycles per grid unit.

Radial Power Spectrum  – a logarithmic plot of the Fourier transformed gridded magnetic data representing a logarithm of a power (i.e., square of an amplitude) versus Wavenumber relationship. R.P.S. is derived from the normalized Map Power Spectrum by integrating each Radial Frequency component over all 360º azimuths, i.e. R.P.S. represents the average spectral content in Grid over all directions. Instead of wavenumbers in cycles per km or meter, the horizontal axis can represent values of Nyquist Fraction. It is common for the lower wavenumbers to have a higher energy. This phenomenon gives R.P.S. curves the characteristic descending shape. Generally, R.P.S. curve can be divided into two main portions: 1) steeply declining energy (amplitude) portion at low wavenumbers which represents sources that are deep and/or very broad; 2) more gently declining portion at the higher wavenumbers which represents sources that are comparatively shallow and more localized. Based on this relation, linear segments on R.P.S. (usually, not more than three or four) are interpreted for depths of the dominant ensembles of source bodies in the survey area. R.P.S. is also referred to as Radially Averaged Power Spectrum or Fourier Spectrum. ^{[25, 48, 228].} See also Spectrum, Spector-Grant Method and Power Spectrum.

Radially Averaged Power Spectrum  – see Radial Power Spectrum.

Random Gridding  – a process of converting the observed magnetic or gravity data, recorded at randomly distributed observation stations, into Grid (map) by creating the smoothest possible (Minimum Curvature) surface composed of a continuous set of regularly spaced cells, each representing the interpolated or original data value assigned to the center of a cell. See also Line Gridding, Grid Cell, and Station.

Random Noise  – unwanted high-frequency (short-wavelength) components of the potential field data which does not exhibit correlation between the survey lines or distant cells of the gridded data. R.N. is generated by occasionally (i.e., randomly) distributed near-surface sources. R.N. is also referred to as White Noise. ^[219]. See also Coherent Noise.

Range  – an instrument characteristic which defines the extent of actually measured values within their lowest and largest limits established for measurements, like Operating Range and Temperature Range. See also Accuracy and Resolution.

RAPS  – see Radially Averaged Power Spectrum.

Raster Grid  – an image grid in which data is arranged as a set of horizontal rows (“lines”) and vertical columns (“samples”). Individual cells that constitute R.G. are called pixels. Digital Image Processing concept is based on the use of R.G. See Pixel.

Raw Gravity  – the gravity field measurements obtained at the gravity stations. R.G. represents the gravity field values before applying the Bouguer, free-air, latitude and other corrections. R.G. is also called as “measured gravity” or “observed gravity”.

Raw Gravity & Magnetics  – measured gravity or magnetic values at any point on or above the Earth’s surface after applying instrumentation corrections. See also Drift, Diurnal Variations, On-Site Magnetometer Calibrations.

Reading Resolution  – an analogue instrument (gravimeter or magnetometer) accuracy characteristic which defines the smallest change of a measured value detectable by the human eye. See also Resolution.

Real-Time  – a term that is applied to data processing systems to describe their capability to process and/or record data instantly, i.e., at the same time and at the same rate as those at which these data are detected.

Real-Time DGPS  – a survey positioning system which computes the real-time location of the survey platform as instant as Differential GPS data is collected. See also Global Positioning System (GPS).

Real-Time Gravity  – measurements of the Earth’s gravity field using digital recording systems and computer-aided Real-Time processing of the measured gravity values. For land surveys, R.-T.G. includes the following sequential steps: 1) entering gravity observations; 2) entering local terrain data (from parallel measurements); 3) entering GPS coordinates; 4) merging with the regional terrain data; 5) applying Gravity Corrections to the observed data; 6) calculating Bouguer Gravity; 7) mapping.

Real-Time Magnetic Compensation System  – a computerized system which allows to compensate the magnetometer sensors for the effects of the aircraft maneuvers (Pitch, Roll, Yaw) as well as for residual airframe magnetism on board the aircraft in real time using the fluxgate sensors. Magnetometer compensation can also be post-processed based on the information recorded during the survey flight. See also Post-Flight Quality Control.

Real-Time Shaded Relief  – an interactive imaging technique that allows creation of Shaded Relief images of gridded data using a light source (“sun”), controlled by the cursor position. The zenith angle (i.e., “sun” height above surface) and the azimuth (i.e., direction of “sun” illumination) are changed by movements of a cursor and, hence, map shading effects can be observed in Real-Time. See also Gridding.

Real-Time Video  – a time-synchronous color video recording of the ground surface below the aircraft in the progress of survey measurements. R.-T.V. is required to identify non-geologic cultural anomalies which must be edited out of the dataset prior to Microleveling and subsequent processing of the magnetic data. In older airborne surveys, R.-T.V. was used as a positioning aid in lieu of DGPS. See also Cultural Editing and Video Viewing.

Reduction Density  – an average rock Density above sea level, which is used in calculation of Bouguer Correction. See also Replacement Density.

Reduction Filters  – a general definition of the data processing operators which perform Reduction-to-Pole (RTP) or Reduction-to-Equator (RTE). In the RTP case, R.F. are applied to the observed magnetic data to correct for Inclination (I) of the Earth’s magnetic field as well as for Declination (D). Magnetic anomalies within an inclined source field show phase distortions which are removed by R.F. After RTP the survey data will be the same as it was measured at the Pole (i.e., I = 90º, D = 0°). RTE is a complementary filtering to RTP procedure which transforms the observed Earth’s magnetic field to the inclination of 0º (instead of 90º as in the RTP case). Sometimes, R.F. are referred to as Magnetics Filters.

Reduction-To-Equator (RTE)  – a data processing method of recalculating the Earth’s magnetic field from its observed Inclination (“I”) and Declination (“D”) to that of the magnetic Equator where “I” = 0º while “D” varies from 0º to ±25º. As a rule, RTE is not used in magnetic exploration data processing. In the same manner as RTP, this procedure tends to center the anomalies over respective sources, but the shapes of the anomalies may become artificially stretched in the east-west direction relative to the horizontal dimensions of sources. ^{[25, 121].} See also Reduction-To-Pole (RTP).

Reduction-To-Pole (RTP)  – a data processing method of recalculating the Earth’s magnetic field from its observed Inclination (“I”) and Declination (“D”) to that of the North or South magnetic Pole (i.e., I = ±90º, D = 0º). RTP transforms originally dipolar magnetic anomalies to the monopolar anomalies centered exactly over their source bodies, i.e., it is a phase shift procedure which changes both the position and the amplitude of the anomaly peaks, making them sharper and, hence, better resolved laterally. Physically, RTP removes the assymetry of magnetic anomalies due to a non-vertical direction of the Earth’s magnetic field and locates anomalies above their source bodies. No significant Remanent Magnetization is assumed here. In areas where this assumption is not satisfied, the anomalies after RTP may become smeared with a slight loss in resolution. Below the latitudes of about 15-20º, it is recommended to adjust only the phase, not the amplitudes of the observed magnetic data, as the RTP calculation can be unstable at these latitudes. Sometimes, such RTP errors may appear as narrow anomalies elongated in parallel to the local Declination of the Earth’s magnetic field. ^{[25, 91, 102, 121, 223].} See also Reduction-to-Equator (RTE).

Reference Body  – a source body (i.e., Causative Body) imported into the gravity or magnetic Model as the initial approximation of the anomaly source. R.B. parameters are obtained from available geological and geophysical information.

Reference Elevation  – see Datum.

Reference Ellipsoid  – a) 3-D mathematical surface of Survey Positioning which the best represents the Earth’s shape for that specific project survey area. b) Reference Spheroid. See also Positioning and Reference Spheroid.

Reference Spheroid  – a mathematical model of the Earth’s shape adopted for the gravity data corrections.  R.S. is related to Mean Sea Level with excess land masses removed and ocean deeps filled, i.e. there are no undulations in the Earth’s surface.  R.S. is the equipotential surface: the gravity force is everywhere normal to this surface.  The theoretical value of the total gravitational attraction of R.S. (Theoretical Gravity) at any point on R.S. is given by International Gravity Formula.  One of the latest approximations of R.S., established by satellite measurements, is WGS84. ^{[ 25 , 54 , 238 ].}  See also Geoid.

Reference Upward Continued Distance  – a distance at which Bouguer Gravity is upward continued in the process of Variable Datum Gravity Inversion. ^[84].

Regional  – see Regional Component.

Regional Component  – a term which is used to describe the wavelength components of the observed gravity or magnetic field data which are greater in length than the dominant wavelength of an average observed anomaly or on the order of and greater than the survey area extent, i.e. R.C. is generated by large-scale variations of Susceptibility or Density in deep subsurface. R.C. can be estimated graphically, by surface fitting, by Gridding methods, by filtering in Fourier Domain and by other methods. ^{[223, 255].} See also Local Regional Component.

Regional Gravity Field  – a long wavelength component of the gravity field usually attributed to the density variations which are located deeper than the general exploration interest, e.g., the gravity field component due to the crustal density variations or undulations of the crust/mantle interface. Subjective R.G.F. can be designed and subtracted from the original field to enhance the residual gravity anomalies of a primary interest. ^{[25, 157, 223].} See Crust, Mantle and Residual Gravity Field.

Regional Magnetic Field  – a long wavelength component of the total magnetic field representing major tectonic features such as basins, regional uplifts, troughs and fault zones. R.M.F. is attributed to Susceptibility variations at depth levels which are usually considered to be associated with intermediate and deep parts of Crystalline Basement. A subjective R.M.F. can be designed and subtracted from the original total field to enhance the residual anomalies of shallow basement levels and intra-sedimentary section. ^{[47, 115, 157, 238].} See also Residual Magnetic Field.

Regional Map  – a map where residual (i.e., short-wavelength) components of the observed potential field are removed by Filtering or other methods of Residual-Regional Anomaly Separation. See Residual Map.

Regional Potential Field  – the most generalized definition of a portion of the observed gravity or magnetic field caused by deep subsurface source distributions, i.e. Susceptibility or Density variations within or below Basement. ^{[25, 157].} See Regional Gravity Field and Regional Magnetic Field.

Regional Wavelength Filter  – a filter that retains (passes) long wavelength components of the observed potential field, and rejects all wavelengths smaller than the user-specified Cutoff Wavelength. Conceptually, R.W.F. is the equivalent of Low-Pass Filter. ^[257]. See Residual Wavelength Filter.

Regional–Residual Anomaly Separation  – a separation of the long-wavelength large amplitude smoothly varying regional anomalies, typically caused by deep-seated sources in Magnetic Basement, from the short-wavelength low amplitude sharply varying anomalies associated with shallower sources in the upper portion of the magnetic basement and within the sedimentary section. There are six basic methods of R.-R.A.S. applied correspondingly in the gravity and magnetic exploration: 1) graphical method, in which the regional component (regional trend) is drawn manually on the plotted magnetic or gravity anomaly profile along the survey line and then the difference between the observed and regional curves is calculated ; 2) polynomial method, where the regional magnetic or gravity field is estimated by the N-order polynomial and then subtracted from the observed data; 3) spectral domain filtering method, which is based on a filter-assisted separation between wavenumbers as reciprocals of the long (regional) and short (residual) wavelength components of the observed magnetic or gravity field and it is performed by Bandpass Filtering, Highpass Filtering, Lowpass Filtering, Matched Filtering, Separation Filtering and others; 4) stripping method, in which the field of an approximated regional geological model (i.e., an ensemble of magnetic or gravity sources) is calculated and subtracted from the observed data; 5) upward continuation method, where the regional magnetic or gravity field is approximated by Upward Continuation and then subtracted from the observed data; and 6) Wavelet Analysis, based on decomposition of the potential field into constituent Wavelet components with subsequent separation into portions of a frequency spectrum over selected space domain windows. ^{[42, 48, 82, 97, 118, 184, 186].} See also Data Enhancement and Filtering.

Regolith  – an assemblage of the fragmental and unconsolidated rock material, whether residual or transported, that forms the surface of the land and overlies the unweathered bedrock. R. contains both detrital magnetic minerals accumulated from the weathered bedrock and secondary magnetic minerals originating from the chemical changes during the weathering processes. Magnetic effects of these shallow magnetic minerals are often observed as random magnetic spikes having vague areal concentration. Such spikes are usually regarded as Noise, which obscures short-wavelength, low-amplitude, intra-sedimentary magnetic anomalies. ^{[50, 94].} See also Regolith Enhancement.

Regolith Enhancement  – a processing technique which extracts the magnetic effects of Regolith from the observed HRAM data and processes the resulting anomalies in such a way that coherent mappings of the magnetic regolith units are obtained. In some cases, R.E. can significantly contribute to the improved resolution of the HRAM data by eliminating the calculated magnetic effects of Regolith. ^{[50, 94].}

Regular Noise  – see Coherent Noise.

Remanence  – see Remanent Magnetism.

Remanent Magnetism  – a phenomenon of the rock magnetization remaining after removal of the magnetic field which caused this magnetization. ^{[223 ].}

Remanent Magnetization  – the permanent magnetization that remains regardless of an external magnetic field. Magnetic dipoles in rocks are able to maintain this orientation even in the presence of a new inducing magnetic field. There are several types of R.M.: Chemical R.M., Detrital R.M., Isothermal R.M., Thermal R.M., Viscous R.M. and others. R.M. can often be ignored in exploration problems except in cases where Extrusive Rocks are present. R.M. is also referred to as Residual Magnetization. ^{[25, 33, 61, 213].} See Induced Magnetization.

Repeats  – see Gravity Repeats.

Replacement Density  – a density used in calculating Bouguer Correction to the gravity data obtained during the marine gravity survey with on-board gravimeters. R.D. is the difference in Replacement Rock density and that of sea water. ^[223].

Replacement Rock  – a hypothetic rock used to replace sea water in calculating Bouguer Correction to the gravity data obtained during the marine gravity survey. R.R. density is assumed as Bouguer Density. ^[223].

Resampling  – see Grid Resampling.

Residual – a difference between the observed data and its Regional Component, i.e. the remaining part of the observed data after the effects of large-scale (long-wavelength) variations have been removed.^{[223 ].}

Residual Gravity Field  – a short wavelength component of Bouguer Gravity attributed to density contrasts within the high density Basement and/or the lower density overburden (i.e., sedimentary section). Anomalies in the residual gravity field are usually of the exploration interest. R.G.F. is obtained as a result of the variously performed attenuation and/or removal of the long wavelength regional components from the Bouguer gravity field. See First Residual Gravity and Regional Gravity Field.

Residual Magnetic Field  – a short and mid-wavelength components of the total magnetic field. R.M.F. is usually attributed to Susceptibility contrasts within the shallower portion of Magnetic Basement and lower value susceptibility distributions of the sedimentary section. R.M.F. anomalies are usually of exploration interest. Generally, residual magnetic fields are obtained through calculation of a difference between the total magnetic field (as a rule, after RTE or RTP applied) and either polynomial approximation of the regional magnetic field or upward continuation(s) of the total magnetic field. See also Regional Magnetic Field and Residual-Regional Anomaly Separation.

Residual Magnetization  – see Remanent Magnetization.

Residual Map  – a map where regional (i.e., long-wavelength) components of the observed potential field are removed by Filtering or other methods of Residual-Regional Anomaly Separation. Generally, it is assumed that R.M. contains predominantly shallow source effects which represent local anomalies. It should be taken into consideration that the remaining short-wavelength components of a bigger and deeper regional anomalies (that are expected to be filtered out) may be of significant amplitudes and mistakenly identified as shallow local anomalies. See Regional Map and Energy Leakage.

Residual Potential Field  – the most generalized definition of a portion of the observed magnetic or gravity field caused by relatively shallow subsurface source distributions, which are usually the main target of magnetic and gravity exploration. See Residual Gravity Field and Residual Magnetic Field.

Residual Wavelength Filter   – a filter which retains (passes) short wavelength components of the observed potential field and rejects all wavelengths longer than Cutoff Wavelength. R.W.F. is the equivalent of High-Pass Filter. ^[257]. See also Regional Wavelength Filter and Residual Map.

Residualizing – 1) methodology that attempts to estimate the regional (i.e. large-scale) effects and isolate local (i.e. residual) anomalies of exploration interest by subtracting these regional effects.  R. is not unique.  The regional variations can be estimated graphically, by gridding methods, by surface fitting , by filtering in Fourier Domain and by other methods; 2) a process of determining what is not accounted for a particular model: the effect of a model is calculated and subtracted from the observed data and the remaining portion is assumed to be a residual component. ^{[223 ].}  See Observed Gravity, Gravity Corrections, Residual Gravity Field and Residual Magnetic Field.

Residual-Regional Analysis  – a methodology that separates anomaly patterns of the kind one is looking for from the remaining portion of the observed potential field based on the use of Filtering, upward or downward continuation, calculation of derivatives and other data processing methods. See Regional-Residual Anomaly Separation.

Resolution  – a) the ability to separate laterally and vertically interfering potential field anomalies produced by closely spaced sources; b) an instrument (gravimeter or magnetometer) characteristic which defines the smallest detectable change of the measured potential field value. ^[223]. See also Lateral Resolution and Reading Resolution.

Resultant Gradient  – a vector sum of the first-order derivatives in three orthogonal directions calculated for the magnetic or gravity anomaly modified by a filter which is designed on the basis of an assumed source geometry. The shape of the obtained R.G. function is used for estimating location and depth of 3-D Causative Body. ^[222].

Reverse Spectral Transform  – a processing procedure which converts the data from the spectral domain back to their original space domain using Inverse Fourier Transform. See also Spectral Domain and Space Domain.

Rift  – a) long relatively narrow regional trough bounded by normal faults; b) graben of regional extent associated with the wrench tectonics of a pull-apart zone and, often, with volcanism and igneous rock intrusions. ^[13]. See also Intrusion.

Ringing  – see Gibbs’ Phenomenon.

Roll  – a side-to-side rotational motion of the survey aircraft or ship about the horizontal axis of the selected course. See also Crab, Pitch and Yaw.

Rolloff Ramp  – see Rolloff Range.

Rolloff Range  – a tapering range of a filter over which the values of the passed (or rejected) space or spectral domain data gradually decrease to their zero values. See also Taper.

Rolloff Region  – see Rolloff Window.

Rolloff Window  – an extended region at each end of the line or a grid where the values of the first or last original data points are rolled-off to zero value. R.W. is created in order to improve the performance of Line Filtering before Fourier Transform to prevent loss of data as well as the creation of artifacts (“edge effects”) at the line or grid ends. R.W. is also called Rolloff Region or Taper.

RTE  – see Reduction-To-Equator.

RTP  – see Reduction-To-Pole.

RTP Analytic Signal  – Analytic Signal of the magnetic anomalous field calculated after applying Reduction-To-Pole (RTP). Usually, RTP A.S. is calculated by taking the square root of the sum of squared derivatives in all three directions (“X”, “Y”, “Z”). See also Analytic Signal Method.

RTP Anomaly  – a general term for maps (grids) showing the anomalous magnetic field in the survey area after all pertinent corrections and Reduction-To-Pole (RTP). Usually, such maps are presented in several versions: regional, residual, band-pass filtered, depth sliced, vertical or horizontal derivatives, etc. See also Grid, Total Magnetic Field, RTP Regional Anomaly, and RTP Residual Anomaly.

RTP Filter  – a convolution filter that performs Reduction-to-Pole for the gridded magnetic data. This filter ensures phase shifts of magnetic anomalies to remove their skew caused by a non-vertical direction of the Earth’s magnetic field. The maxima of magnetic anomalies on the RTP-filtered maps are located directly above causative bodies. Phase shifts increase with decrease in latitude. ^[148]. See also Causative Body, Convolution and FIR RTP Filter.

RTP Regional Anomaly  – a regional component of Total Magnetic Field after applying Reduction-To-Pole (RTP) to the gridded magnetic data. RTP R.A. field is dominated by deep-seated magnetic source bodies and structures. See Regional-Residual Anomaly Separation, RTP Anomaly and RTP Residual Anomaly.

RTP Residual Anomaly  – a residual component of Total Magnetic Field after applying Reduction-To-Pole (RTP) to the gridded magnetic data. RTP R.A. field is dominated by magnetic effects caused by relatively shallow and local subsurface features, such as Magnetic Basement structures and intra-sedimentary magnetized Faults. See RTP Anomaly and RTP Regional Anomaly.

Rubidium-Vapor Magnetometer  – see Optically Pumped Magnetometer.

Running Window – a line-based or grid-based operator of a specified length (i.e. “window”) whose position moves one sample value or grid value at a time. ^{[223 ].}   See Smoothing.