T

Tabular Body  – a model approximation in the gravity and magnetic field calculations. T.B. is a body of finite thickness with one edge nearly horizontal but other edges “infinitely” remote from the point of measurements.  T.B. width (i.e. orthogonal lateral extent) is assumed to be more than 50 times its thickness. Also called Infinite Dike  ^{[223 ].}  See Thick Dike and Thin Dike.

Tail-Buoy Magnetometer – see Overhauser-Effect Magnetometer.

Talwani Inverse Solution  – a result of the gravity Inversion that determines a subsurface mass distribution causing the residual gravity field. In 3-D case, a grid of rectangular prisms of the same lateral extent and various depths is used to approximate the shapes and depths of causative bodies. Such inversion of the residual gravity assumes: a) a model of two homogeneous layers without large scale lateral Density Contrast; and b) an interface formed by these two layers is the primary source of a density contrast generating the residual gravity field. T.I.S. is obtained through an iterative process that includes the calculation and summation of the gravity effects of all prisms. The difference between the iteratively calculated and actual residual gravity values is used to adjust the depths of prisms. As an option, the prisms can have their tops fixed at the pre-selected Datum, while their bases are adjusted. The iterative process is continued until Standard Deviation of the difference is less than a specified value. The inversion algorithm can incorporate a density contrast function that defines the decrease of a density contrast with depth. ^[84]. See also Causative Body, Prism and Talwani Method.

Talwani Method  – a method of calculating the gravity anomaly caused by 2-D or 3-D source body of an arbitrary shape. In 3-D, the source body at first is represented by contours. Then each contour is replaced by a horizontal irregular N-sided polygonal lamina (i.e., very thin layer). The gravity anomaly caused by each lamina can be determined at any external point. By interpolation between contours combined with a numerical integration, the gravity anomaly of a given 3-D source body can be calculated to a high degree of precision. The possibility that density varies with depth can be easily incorporated into the calculation of anomaly by assigning a separate density value to each contour. ^[235]. See also Gravity Model, Forward Modeling and Inverse Modeling.

Taper  – a space-domain or frequency-domain interval (window) assigned to the filter cutoff value or specified at the end of a line or grid, where the data gradually decrease to their zero values. T. is used to prevent Ringing and the loss of data at the line and/or grid ends. See also Gibbs’ Phenomenon and Data Extension.

Target  – a geological object of exploration interest (ore body, Faults, Basement and sedimentary structures, salt domes, etc.) at which the gravity or magnetic survey is aimed. ^[223].

Tare  – a sudden jump in the gravity meter readings, i.e. an instrumental error.  The jump may be a) temporaty, when readings go up or down but eventually come back to the baseline; b) permanent, when readings show a permanent baseline shift.  Large tares (about 50 microGal and larger) are assumed to be caused by movement (slippage) at the measuring spring hooks.  Most tares are less than 10 microGal and they are caused by temporal variations of Proof Mass resulting from contamination and migration of dust, lubricating oil and other volatiles inside the sensor compartment. ^{[4 ].}

Tectonic Province  – a large region characterized by its tectonic style and development, i.e., major structural or deformational features (basins, uplifts, troughs and fault zones), their relations, origin and historical evolution. ^[13].

Temperature Coefficient  – a gravity instrument characteristic that defines a change in the measurement values caused by temperature changes. T.C. unit of measure is microGal per ºC. See Gal.

Temperature Range  – an instrument characteristic that defines the lowest and the highest temperatures acceptable for making measurements. See also Temperature Coefficient.

Template  – a transparent overlay for calculating the gravity effects such as Terrain Correction, Isostatic Correction or, sometimes, residual components of the measured field. ^{[223 ].}  See Residualizing and Zone Chart.

Temporary Base  – a local Base Station that is set up temporarily in the area of the gravity survey to provide reference measurements of the gravity field. T.B. is tied to Absolute Base.

Tensor  – a mathematical entity (commonly, vector) represented by components that vary in a special way depending on the choice of a coordinate system. ^[223]. See Full Tensor Gradient, Magnetic Gradient Tensor, Gravity Gradient Tensor and FTG Technology.

Terracing  – a line-based iterative method that transforms smoothly varying continuous gravity or magnetic field profiles into a stepped (terraced) function composed of steeply dipping or flat segments. The obtained terraced function simulates Density or Magnetizations distributions, which have discontinuous first vertical derivatives (i.e., abrupt boundaries), and can be transformed into a geologic-map-like image. T. detects local segments (domains) of relatively homogeneous physical properties and various lateral extent. These domains are compared to independently identified geological features within Crystalline Basement or other critical surface, and a basement bulk susceptibility map or other physical property map can be constructed. ^[45]. See also Critical Surface Concept.

Terracing Inversion  – see Terracing.

Terrain Chart  – a template used for the calculation of Terrain Correction. T.C. is a set of concentric circles and radial lines that form sectors whose areas increase with the distance from the center. T.C. is placed over the digital topographic map with the center of circles at the gravity station. The average elevation in a single compartment is estimated from the map contours within it and, then, it is subtracted from the station elevation value. T.C. is also referred to as Hammer Chart or Zone Chart. ^[238].

Terrain Clearance  – see AGL.

Terrain Correction  – a correction applied to the gravity data to compensate for the effects of local topographic features when the whole area (terrain) cannot be approximated by Bouguer Slab, as not all the surroundings are at the same elevation as an observation point. Generally, T.C. is applied when Bouguer Correction did not account for: a) the absence of mass below an observation point (i.e., Station); b) the absence of mass below and the presence of mass above an observation point; c) the presence of mass above an observation point. Since these effects are close to the point of measurements,  T.C. can be important in high relief areas. For land and underwater stations, T.C. is always added whether the feature is a hill or valley. For sea surface stations over relatively deep water, it may be negative. T.C. is made by dividing the topography into compartments or radial segment zones and totaling the individual effects at each station. ^{[25, 34, 134, 137, 179, 180, 215, 223, 234].} See also Terrain Chart, Inner Zone Terrain Correction and Outer Zone Terrain Correction.

Terrain Elevation  – see Surface Elevation.

Terrane  – a fault-bounded area of the regional extent whose geologic and tectonic history differs from that of the surrounding areas. ^[223].  Magnetic terranes can be delineated using the calculated maps of Horizontal Gradient (often, low-pass filtered) as it reaches its maximum value above the boundaries (i.e. contacts) between large rock masses of differing magnetic properties.  See Magnetic Contact.

Tesla  – a unit of measure for Magnetic Induction (Magnetic Flux Density) or simply magnetic field in the International System of Units (SI). 1 tesla = 10⁴ gauss (in cgs units) = 10⁹ gamma = 10⁹ nanotesla (nT). The magnetic field maps are contoured, mostly, in nanoteslas and, sometimes, in gammas (1 gamma = 1 nT). ^[223].

Thalen Method  – a graphic method which is used for the isolated magnetic anomaly source depth estimation. “Depth” = “horizontal distance between maximum amplitude of selected anomaly and its minimum amplitude H 0.7”. The minimum amplitude here is the maximum negative value in the trough adjacent to the positive peak on the profile of this anomaly. ^[53]. See also Depth Rules.

Theoretical Gravity  – a mathematical model of the Earth’s gravity field. T.G. is also referred to as Gravity Reference Field. The formula, which specifies the computation of T.G., is known as International Gravity Formula (IGF). ^[34].

Theoretical Gravity Correction  – a correction applied to the observed gravity data to compensate for the theoretical value of the Earth’s gravity field at the latitude of the gravity Station.  This theoretical value is defined by International Gravity Formula. ^{[25, 34, 134, 215].} See also Reference Spheroid.

Theoretical Latitude Correction  – same as Theoretical Gravity Correction.

Thermal Remanent Magnetization (TRM)  – one of five main types of the remanent (residual) magnetization. T.R.M. originates from the cooling of rock material below its Curie Point in the presence of the external magnetic field. The remanence of this type is particularly stable and makes the largest contribution to magnetization of the igneous and metamorphic rocks. ^{[33, 238].} See also Chemical Remanent Magnetization, Detrital Remanent Magnetization, Isothermal Remanent Magnetization, and Viscous Remanent Magnetization.

Thick Dike  – a model approximation for the magnetic sources of an igneous rock body whose width is about the same as the depth to its top. ^{[203, 215].} See also Thin Dike and Two-Contact Block.

Thin Dike  – a model approximation for the magnetic sources of an igneous rock body or magnetized fault or fracture zone, whose width is much less than the depth to its top. ^{[54, 203, 215, 238].} See also Thick Dike and Magnetized Intra-Sedimentary Fault.

Thin Sheet  – see Thin Dike.

Three-Dimensional (3-D) Analytic Signal  – a 3-D generalization of the 2-D analytic signal. Defining “x”, “y” and “z” as unit vectors in “x”, “y” and “z” directions allows the 3-D analytic signal of the potential field anomaly “M” to be presented as

A(x,y) = xdM/dx + ydM/dy – zdM/dz

            Here, its real part “xdM/dx + ydM/dy” (i.e., Horizontal Derivative) and imaginary part “zdM/dz” (i.e., Vertical Derivative) constitute Hilbert Transform Pair. Definitions of Energy Envelope, Instantaneous Phase and Instantaneous Frequency follow the similar definitions for the profile 2-D case. ^{[103, 147, 152, 161, 166, 214].} See also Analytic Signal.

Three-Dimensional (3-D) Bouguer Correction  – a multi-step correction procedure that results in the construction of a 3-D Gravity Model of the area topography. This process effectively combines Simple Bouguer Correction and Terrain Correction into one precise model-based correction. ^[34].

Three-Dimensional (3-D) Euler Deconvolution  – a grid-based automated method of the magnetic data interpretation for the source depths and locations using Euler’s Homogeneity Equation. The method employs horizontal and vertical gradients, either measured or calculated (typically, using the Fourier methods). The obtained grid is sampled using a moving square window the size of which is selected big enough to contain the gradient and field values from sources of interest, but small enough to minimize the effects from adjacent sources. For each point in the selected window, one Euler’s equation may be written, so the window provides an overdetermined equation set which may be solved for a source position (“x_o”, “y_o”, “z_o”) and the regional value “B” in accordance with the Euler’s homogeneity equation. Here, it is also necessary to assume Euler’s Structural Index value. For each structural index, a map of depth solutions can be plotted. The method is quite effective in the delineation of structural trends such as basement faults (often, despite a poor choice of a structural index) and estimates of their depths. The method cannot yield any dip information. Observed data need not be reduced to the Pole and Remanent Magnetization seems to be a non-interfering factor. The gravity anomalies of some geologic features also obey the Euler’s homogeneity equation and, hence, this method can also provide useful information on faults and near-vertical contacts where the density contrasts exist. ^{[206, 207].} See also Euler Deconvolution (2-D).

Three-Dimensional (3-D) Gravity  – see Gravity Gradiometry.

Three-Dimensional (3-D) Hilbert Transform Operator  – a frequency domain operator applied to calculate Vertical Derivative, when horizontal derivatives in two orthogonal directions “x” and “y” are available. ^[214]. See also Hilbert Transform and Hilbert Transform Pair.

Three-Dimensional (3-D) Inversion  – a methodology that produces a geophysically interpretable 3-D model of the subsurface structure based on the observed potential field data. ^{[144, 145].} See Inversion.

Three-Dimensional (3-D) Model  – a network or grid of values which model subsurface geological boundaries or blocks and bodies represented as 3-D surfaces and bodies of Density contrast in Gravity Model or 3-D blocks and bodies of Susceptibility contrast in Magnetic Model.

Three-Dimensional (3-D) Susceptibility Inversion  – method of inverting the observed magnetic data to recover 3-D susceptibility model. Model solutions are obtained based on minimizing a general Objective Function and pre-selected misfit between Model Response and the observed data. ^[144]. See Minimizing Inversion.

Tiburg Method  – a graphic method used for the isolated magnetic anomaly source depth estimation. “Depth to magnetic pole” = “2/3 the horizontal distance between points at the level of half maximum anomaly amplitude”. T.M. is also referred to as Half-Maximum Method or Tiburg Rule. ^{[53, 223].} See also Depth Rules.

Tiburg Rule  – see Tiburg Method.

Tidal Correction  – see Earth Tide Correction.

Tidal Effect  – a distortion of the Earth’s surface (up to about 10 cm) due to attraction of the sun and moon. T.E. results in the gravity measurement variations which should be corrected. Correction for T. E.  are made by means of tables or included in Drift Correction. ^[223]. See Earth Tide Correction.

Tie  – an observation repeated at one of previously observed points in order to check for Drift, error, etc. or to establish relationship of two datasets. ^{[223 ].}  See also Gravity Repeats.

Tie Lines  – see Control Lines.

Tilt  – see Potential Field Tilt and Potential Field Tilt Angle.

Time Variation Correction  – a correction that is applied to the observed gravity data to compensate for the Earth’s tides and instrument drift. T.V.C. is determined by the repeated measurements at the gravity base station, assuming that the gravity values at all stations within the survey area vary in the same manner as at Base Station. See Drift, Earth’s Tides, Earth Tide Correction and Drift Correction.

Time-Lapse (4-D) Gravity Survey  – a gravity survey repeatedly performed at the same stations in the area of the oil field under development: at first, prior to the fluid injection (to obtain baseline data) and, then, over a period of years later with the purpose of the waterflood surveillance. Differences in the gravity anomaly, associated with the change in a fluid volume and fluid distribution, can be obtained. T.-L.G.S. requires the use of Global Positioning System (GPS) and a microGal-precision gravimeter. The gravity signal of interest is derived from the observed gravity data corrected, along with standard corrections, for instrument Drift, Earth’s Tides and elevation. ^[105]. See also Microgravity Modeling.

TMI  – see Total Magnetic Intensity.

Topographic Correction  – see Terrain Correction.

Torsion Balance  – a) an instrument for measuring gradients of the observed gravity field using the arrangement where two equal “proof” masses at opposite ends of a horizontal beam are suspended by a very fine torsion wire.  The attracting (i.e. gravity) forces on these masses differ and, hence, produce a torque which can be measured by counter balancing with a known torque (such as balancing or null screw); b) a physical principle of operation of some gravimeters. The T-shaped moving system is horizontally supported by fine torsion fibers (wires) attached to the cross-bar with a weight on the end of a cross-arm. The torque due to the gravity field acting on the weight is balanced by the torsion of these elastic supports. The balancing or null screw, operating on the moving system through a spring and mechanical linkage, is adjusted at each reading. Differences in the gravity field values are proportional to differences in the position (dial reading) of the null screw when the system is balanced. The Atlas, Worden, World-Wide, Sharpe, and some other gravimeters are of this type.  Sometimes, T.B. is referred to as Torsion Fiber. ^{[174, 223 ].} See also Zero-Length Spring and Weight-On-Spring.

Torsion Fiber  – see Torsion Balance.

Total Bouguer Correction  – see Complete Bouguer Correction.

Total Geomagnetic Intensity  – a magnitude of the Geomagnetic Field Vector at the point of measurement. T.G.I., measured at fixed points over the survey area and corrected for IGRF, solar pulsations, diurnal variations and several other effects, is called Total Magnetic Intensity (TMI) or Total Magnetic Field. ^[25]. See also Horizontal Geomagnetic Intensity and Vertical Geomagnetic Intensity.

Total Gradient  – a vector sum of three potential field gradients: two horizontal gradients in “x” and “y” directions and Vertical Gradient. In the general form, T.G. magnitude (Modulus) can be presented as

T.G. = [(dM/dx)² + (dM/dy)² + (dM/dz)² ]^1/2

            where M = M(x,y,z) is the potential field anomaly. T.G. is always positive over Causative Body. T.G. maxima are centered directly above vertical thin dikes and contacts between two blocks of contrasting susceptibilities or densities. Over thick dikes, T.G. has two maxima equidistant from a local minimum, which is directly above the center of a thick dike. ^[171]. In the case of a dipping dike or contact, T.G. maxima are usually shifted updip. Based on this phenomena, the spatial relationship between the total and horizontal gradient maxima can be used to infer the location and dip of the magnetic or gravity Contact as well as location of a magnetized fault (see Gradient Dip Estimation and Goussev Filter). Modulus of T.G. equals to Analytic Signal Absolute Value (which is often called Energy Envelope) and for this reason Total Gradient Method is also referred to as Analytic Signal Method. See Thick Dike and Thin Dike.

Total Gradient Method  – see Total Gradient and Analytic Signal Method.

Total Intensity  – a term which is usually refers to Total Magnetic Intensity as opposed to the Earth’s magnetic field components in the vertical (Vertical Gradient) and horizontal (Horizontal Gradient) directions.^{[223 ].}

Total Magnetic Field  – the resulting magnetic field after applying the following some or all corrections to the observed magnetic data (not necessarily in this order): a) removal of the Earth’s main (core) magnetic field based on International Geomagnetic Reference Field – IGRF model appropriate for the date of the survey; b) compensation for the solar radiation energy, i.e., irregular solar pulsations; c) compensation for the regular diurnal variations; d) instrument drift compensation; e) flight elevation compensation; f) Leveling, i.e., Mis-Tie elimination; g) Cultural Editing. As a rule, T.M.F. is assumed to represent the gridded magnetic data after basic corrections, but before Reduction-To-Pole (RTP) or Reduction-To-Equator (RTE). Often, T.M.F. is referred to as Total Magnetic Intensity. ^{[25, 53, 238].} See Diurnals, RTP Anomaly, and Total Magnetic Field WRTP.

Total Magnetic Field Anomaly  – an anomaly of the observed magnetic field after Magnetic Corrections and before applying filters or other processing operations. See Anomaly.

Total Magnetic Field Measurements  – measurements of the magnitude of the Earth’s magnetic field without regard to its vector direction, using standard total-field magnetometer (as compared to measurements of components of the total field in the vertical or horizontal directions using Gradiometer). ^[25].

Total Magnetic Field WRTP  – Total Magnetic Field after applying Wiener Noise Filter and Reduction-To-Pole (RTP).

Total Magnetic Intensity (TMI)  – see Total Magnetic Field.

Total Magnetization  – see Total Polarization.

Total Polarization  – a vector sum of Remanent Magnetization and Induced Magnetization. In general, T.P. may be different from the direction of the Earth’s magnetic field. T.P. is used with the same meaning as Magnetization. T.P. vector is defined by three parameters: 1) Pseudosusceptibility; 2) magnetic azimuth (often, the same as the present Earth’s magnetic field); and 3) magnetic Inclination or dip (for ore body anomalies, it is usually significantly different from the inclination of the present Earth’s magnetic field). ^[17].

TOWDOG  – a towed deep ocean gravity meter. The instrument consists of a marine gravimeter modified to fit inside a pressure case that is mounted on a platform designed for towing stability. The gravity sensor unit (sensor package) is tethered to a ship and towed just above the sea floor, providing much higher resolution of anomalous masses as compared to conventional sea surface measurements. ^[256].

Towed Bird System  – an airborne magnetic survey system wherein the Magnetometer is mounted in a streamlined cylindrical housing, which is towed by cable below and behind the aircraft. See Bird.

Towed Deep Ocean Gravimeter  – see TOWDOG.

Transform  – a mathematical operation that provides the same information content in different domains. For example, Fourier Transform maps space domain potential field data to their equivalent frequency (wavenumber) Domain. ^[223].

Transverse Mercator  – see Universal Transverse Mercator (UTM).

Traverse  – see Gravity Traverse.

Traverse Lines  – survey lines along which magnetic or gravity data are recorded. In HRAM survey, T.L. are flown at close spacing (100-800 m depending on the depth to exploration targets), preferably, orthogonal to the regional geologic strike with the mean ground clearance of 90-120 m. ^{[78, 205]}  See also Control Lines.

Trend  – a general term for direction of dominant alignments on structural and tectonic maps and on images of the anomalous gravity or magnetic fields. ^{[223 ].} See also Grain, Fabric, and Signature.

Trend Analysis  – see Trend Surface Analysis.

Trend Replacing  – a restoration of the overall data trend (overall slope) removed from the observed potential field data by Detrending.

Trend Surface Analysis  – a grid-based methodology for Residual-Regional Anomaly Separation and identifying trends and dominant wavelengths in the residual and regional components of the observed field. Generally, T.S.A. is based on the fitting Bouguer Gravity or magnetic field (often, after RTP applied) with a polynomial surface of the pre-determined order, from the 1^st through N-th. The resulting polynomial fit is assumed to be an N-th order polynomial approximation of the regional component of the potential field. By subtracting the N-th order polynomial surface from the original potential field, the user obtains the residual component of this field.  Also called Surface Fitting. ^{[223 ].}

Triangular Filter  – see Bartlett Filter.

Tri-Axial Fluxgate Magnetometer  – a three-directional Fluxgate Magnetometer which is installed on board the aircraft to monitor magnetic effects caused by the aircraft’s maneuvers (Pitch, Roll, Yaw) during the flight along survey lines. T.-A.F.M. data are used as input to Real-Time Magnetic Compensation System. See also Aeromagnetic Survey Equipment.

Trimming  – a grid-based procedure generally used to cut away Edge Effects at the grid ends to provide a better image of the processed data. T. can also be used to select the specified region within the original grid and cut away the rest of the grid keeping this region for the subsequent detailed processing.

Tripod Correction  – a correction applied to Observed Gravity values to compensate for the height of the instrument tripod. T.C. can be presented as

T.C. = h ´ dg/dz,

            where “dg/dz” is the vertical gradient of gravity (0.30861 mgal/m) and “h” is the height of a tripod.

Two-and-Half (2.5) Dimensional Body  – a magnetic or gravity source body which is limited in the strike direction, but its strike length is significantly larger than a length in any other direction. See also Two-Dimensional (2-D) Body.

Two-Contact Block  – a model approximation of the potential field source with two separate susceptibility or density vertical contacts (interfaces) and “infinite” depth extent. The width of T.-C.B. is much larger than the depth to its top. See also Contact.

Two-Dimensional (2-D)  – a term of general approximations and Modeling meaning that under given assumptions there is no variation in one of three dimensions or directions: “X”, “Y” and “Z”. ^{[223 ].}

Two-Dimensional (2-D) Body  – a magnetic or gravity source body which is unlimited in the strike direction, i.e. it has an “infinite” length meaning that it is so long that the effects of the ends are negligible. In practice of Modeling, this length should be at least 15 or, preferably, 20 times larger than a length in any other direction. See Two-and-Half (2.5) Dimensional Body and Strike.

Two-Dimensional (2-D) Euler Deconvolution  – see Euler Deconvolution.

Two-Dimensional (2-D) Directional Filtering  – a frequency domain Microleveling technique based on use of 2-D directional filters and Fast Fourier Transform (FFT) applied to the standard leveled magnetic grids. Before filtering, the removal of the first order trends, as well as expansion to square grid dimensions, is required. The modified grid is filtered in two directions to construct the leveling error pass notch using: 1) high-pass Butterworth Filter in the direction of the control lines and a cutoff set 2-4 times the traverse line spacing to pass the unchanged spatial frequencies of an order of these line spacing; 2) Directional Cosine Filter along the traverse lines to pass only the wavelengths of an order of the control line spacing in this direction. Finally, the resulting error grid containing elongated anomalies (line corrugations) is subtracted from the original grid to obtain a new grid filtered in two directions. ^[67]. See also One-Dimensional (1-D) Directional Filtering.

Two-Dimensional Fast Fourier Transform (2-D FFT) Filters  – a group of Fourier Domain filters that are applied to the gridded (i.e., two-dimensional) magnetic and gravity data. See also One-Dimensional Fast Fourier Transform (1-D FFT) Filters, Grid, and Gridding

Two-Dimensional (2-D) Fourier Transform  – see Fourier Transform.