E

Earth Tide Correction  – a time-varying correction applied to the gravity survey data to compensate for Earth Tides. Often, E.T.C. is included as a part of Drift Correction and referred to as Tidal Correction. ^{[223, 255].}

Earth Tides  – a time-varying response of the solid Earth’s surface to the tidal influences of the moon and sun. E.T. can produce displacements up to about 10 cm and generate the anomaly of about 0.2 – 0.3 mGal. The magnitude of E.T. effects depends on a latitude and time; it is the greatest at low latitudes and has a strong periodic component with a period of about 12 hours. Over a short period of time (about 60 minutes), the tidal gravity variation is considered to be linear with time. ^{[25, 223].} See Earth Tide Correction and Time Variant Correction.

Earth’s Core  – a central portion of the Earth, beginning at the depth of about 2900 km and probably consisting of metal (iron-nickel) substance. E.C. radius is about 3500 km. E.C. is divided into the outer core (depth interval from about 2900 km to 5000 km) that may be in the liquid state, and the inner core of about 1300 km in radius that may be in the solid state. ^{[13, 223].} See also Core.

Earth’s Gravity Field  – a vector field of the gravitational acceleration (attraction) “g” of the mass “m” due to the presence of the Earth’s mass “M”:

g = F/m = – GM / R ² ,

            where “F” is Gravity Force; “G” is Universal Gravity Constant; “R” is the Earth’s radius at the point of measurement. In gravity exploration, E.G.F. is often referred to as Gravity Acceleration. ^{[25, 34, 54, 182, 238].}

Earth’s Magnetic Field  – a vector field approximated as that of Magnetic Dipole originating at the Earth’s center and defined by three parameters: 1) magnitude or Magnetic Field Strength expressed in nanoteslas (nT); 2) Inclination or dip expressed in degrees; 3) Declination or angle east of the geographic North direction expressed in degrees. E.M.F. varies over the Earth’s surface and with time. For the airborne magnetic measurements, E.M.F. intensity (magnetic field strength) is inversely proportional to the square of distances above the sources. Measured differences in the magnetic field strength are related to the differences in subsurface distribution of magnetic sources. Since such variations reflect changes in geological structures, they can be used to interpret the geology of the subsurface. ^{[25, 54, 223, 238].} See Earth’s Magnetic Field Components.

Earth’s Magnetic Field Components  – three basic components that explain the origin and constitute the observed magnetic field of the Earth: 1) main field which is of the internal (core) origin and varies slowly over hundreds and thousands of years. The main field contributes the largest part to the magnitude of the Earth’s magnetic field and varies in its values from 70,000 nT at the magnetic Poles to 25,000 nT at the magnetic Equator. Inclination of the main field is vertical at the magnetic Poles and horizontal at the magnetic Equator; 2) external field which originates outside the Earth and is characterized by rapid changes in time, partly cyclic and partly random. The external field is the cause of Diurnal Variations and Magnetic Storms which can strongly affect magnetic survey measurements. The variation of the external field can be about 1-2 nT for small diurnal variations up to 1000 nT and more for severe magnetic storms; 3) local field is the magnetic field which represents the result of interaction between the above two components and the local distribution of magnetic materials in the upper part of the Earth’s crust. The local field is much smaller than the main field and considered as constant in time and location. The local field magnitude may vary from 0.1 to 100 nT over magnetically quiet deep sedimentary basins up to several thousand nT over highly magnetized crystalline basement rock outcrops, like some of the basic igneous rocks. ^{[25, 54, 238].} See also Earth’s Magnetic Field, Ionosphere, and Magnetosphere.

Earth’s Magnetic Poles  – see Geomagnetic Poles.

Easting  – a component of a survey leg in the east direction.  On maps and grids in Cartesian Coordinates, it may be expressed as an “X” value. ^{[223 ].}  See also Northing, False Easting and False Northing.

Economic Basement  – see Basement.

ECF  – see Elevation Correction Factor.

Edge Effect Anomaly  – the region-scale free-air gravity anomaly comprised in its simplest form of a gravity “high” (which correlates with the outer shelf area and usually centers above the present-day shelf break) and a gravity “low” (which correlates with the continental slope sink and the oceanic crust rise areas). E.E.A. is the distinct geophysical feature of rifted continental margins and it is traditionally interpreted as the result of Juxtaposition of thick continental crust and thin oceanic crust, with contributing density contrasts of sea water, prograded sediments, continental and oceanic crusts, and Mantle. ^[245]. See also Crust, Density Contrast, Replacement Density and Free-Air Gravity.

Edge Effect Correction  – a grid-based Spectral Domain procedure that eliminates high-intensity artificial anomalies near Grid edges and removes “waves” or “halo” around anomalies within the grid by: a) limiting anomalies that exceed a specified threshold value; and b) tapering grid data to zero at a specified distance near grid edges and, thus eliminating “stripes.” See also Maximum Entropy Prediction.

Edge Effects  – distortions of data which appear at the edges of grid images after applying filter operators or other grid or line data transformations. Assigning Taper or applying Data Extension and Edge Smoothing Filters allows to minimize E.E. ^{[223,  251].}

Edge Smoothing Filters  – a group of the space domain and spectral domain filters which can be applied to line and grid datasets before their purpose-oriented processing in order to smooth the edges of data curves (line dataset) or surface (grid dataset) and ensure a smooth transition of data values to zero at the ends of lines and grid edges. E.S.F. minimize Edge Effects. ^[230].

Elevation  – a vertical distance (height) from Mean Sea Level to a given point on the Earth’s surface. Airborne survey area E. is calculated based on GPS, Barometric Altimeter and Radar Altimeter data. See also Altitude.

Elevation Correction  – a correction applied to the observed gravity data to compensate for the difference between the elevation of the point of measurements and the reference elevation. E.C. is sometimes called Combined Elevation Correction as it represents the integrated result (i.e. the sum) of Free-Air Correction and Bouguer Correction:

E.C. = (0.3086 – 0.04192 D) h₁ = (0.09406 – 0.01278 D) h₂ ;

          where “D” is the assumed density in g/cm³; “h₁” is the elevation of the point of measurement above survey Datum in meters, “h₂” is of the same meaning as “h₁” but in feet. ^{[54,  223].}

Elevation Correction Factor  – a calculation parameter which is used to obtain Elevation Correction as the difference between elevation of the point of measurement and Reference Elevation multiplied by E.C.F.  The E.C.F. formula is presented as  

E.C.F.=  (0.3086 – 0.04192D) mGal/m   or

E.C.F. = (0.09406 – 0.01278D) mGal/ft,

            Where  “D ” is the assumed average density of Replacement Rock in g/cm³. ^{[223 ].}

Ellipsoid  – a 3-D shape for which every plane cross-section is an ellipse. Geoid is usually approximated as E. that rotates about one of its axes. ^[223].

Energy Envelope  – the absolute value of Analytic Signal which is also called Amplitude Envelope or 3-D Analytic Signal Amplitude. E.E. is defined as a square root of the sum of squared vertical and two horizontal derivatives (in “x” and “y” directions) of the magnetic or gravity field. With certain assumptions, the depth to the magnetic source bodies can be estimated from the E.E. shape. Using E.E. images, the interpreter should take into consideration the following: a) E.E. magnitude and shape are dependent on the Earth’s magnetic field parameters and E.E. maximum values are always offset from locations directly above magnetic contacts; b) over closely spaced or dipping magnetic contacts, E.E. calculations become non-linear and the result cannot be deconvolved into elementary bell-shaped functions assumed for a single contact; c) E.E. calculations are based on derivatives of the potential field anomalies and, hence, all kinds of noise events (gridding artifacts, line corrugations, random noise, etc.) will be significantly enhanced. ^{[147, 214].} See also Analytic Signal Amplitude and Analytic Signal Absolute Value.

Energy Leakage  – one of the inherent properties of the potential fields which reflects their fundamental ambiguity in respect to quantitative source depth interpretation. In data filtering, E.L. is represented by the spectral overlap of predominantly low frequency deep source anomalies with predominantly high frequency shallow source anomalies. By this reason, the filtered images of data (obtained after processing in Spectral Domain according to the energy of particular frequencies but irrespective to the depth of their origin) can be used only for approximate qualitative estimate of the source ensemble’s depth, i.e., “relatively deeper” or “relatively shallower.” ^{[81, 82, 197].} E.L. is also referred to as Spectral Overlap.

Energy Rosette  – see Map Power Spectrum.

Enhanced Analytic Signal  – the analytic signal derived from the Nth-order Vertical Derivative values of two horizontal gradients (in “x” and “y” directions) and one Vertical Gradient of the potential field anomaly. E.A.S. is defined as:

A_n(x,y) = {d(d ⁿM/dz ⁿ)/dx}x + {d(d ⁿM/dz ⁿ)/dy}y + i{d(d ⁿM/dz ⁿ)/dz}z,

            where “M” is the potential field anomaly; “x”, “y”, “z” are unit vectors. The E.A.S. concept is the basis for interpretation of 3-D potential field anomalies with the purpose of high-resolution imaging of the geological boundaries such as Contact and Fault as well as for estimating the corresponding depth to each interpreted geological boundary. ^[116]. See Enhanced Analytic Signal Amplitude and Analytic Signal.

Enhanced Analytic Signal Amplitude  – an amplitude of the enhanced analytic signal defined as:

| A_n(x,y)| = {[d ⁿ(M_x ) / dz ⁿ] ² + [d ⁿ(M_y ) / dz ⁿ] ² + [d ⁿ(M_z ) / dz ⁿ] ²} ^1/2 ,

            where “M” is the potential field anomaly; M_x = dM/dx; M_y = dM/dy; M_z = dM/dz.

For n =2, this equation corresponds to Enhanced Analytic Signal derived from Second Vertical Derivative, and, hence, the amplitude of this second-order enhanced analytic signal is defined as

|A₂(x,y)| = {[d²(M_x) / dx²]² + [d ²(M_y) / dy²]² + [d ²(M_z) / dz²]} ^½

The outlines of geological boundaries can be determined by tracing the maxima of the calculated E.A.S.A. This technique provides significantly improved lateral resolution of anomalies and better visualization of geological boundaries when interference effects of closely spaced sources are considerable and other methods cannot provide reliable results. Under several simplifying assumptions, the corresponding depth to each detected geological boundary can be estimated from the amplitude ratio of the enhanced analytic signal and the simple (conventional) analytic signal:

“depth” = [2 |A₀(x,y)| _max / |A₂(x,y)| _max ] ^½ ,

where “|A₀(x,y)| _max” is the maximum value of the simple (conventional) Analytic Signal Amplitude (n = 0); “|A₂(x,y)| _max” is the maximum value of the second-order enhanced analytic signal amplitude (n = 2). ^[116].

Enhancement Operators  – a general term for various Data Enhancement procedures. E.O. include Reduction-To-Pole, Filtering, Shadow Manipulation, calculation of First Vertical Derivative (1VD), Second Vertical Derivative (2VD), Horizontal Gradient, and others. ^[115]. See also FTG Technique and Magnetic Gradient Tensor.

Ensemble  – a group of source bodies in a certain qualitatively estimated depth range. See Matched Filtering and Source Body.

Envelope  – a long-wavelength curve which bounds a range of the specified quantities like amplitude (“amplitude envelope”) or squared amplitude (“energy envelope”).

Eötvös Correction  – a correction which is applied to the observed gravity data to compensate for the velocity of the gravimeter movement during non-stop observations in shipborne and airborne surveys. E.C. can be presented as

E.C. = 7.503 V CosN Sin2+ V ²/R,

            where “V” is the velocity of the observation platform (ship or aircraft) in knots; “N” is the latitude in degrees; “2” is the platform heading in degrees from the North; “R” is the radius of the Earth at this latitude in meters. The largest E.C. values will be obtained if the observation platform has a velocity component in the east-west direction. ^{[25, 106, 223].} See Eötvös Effect.

Eötvös Effect  – a motion-related effect defined as the vertical component of the resultant vector in a vector addition of the gravimeter’s platform velocity and the Earth’s rotational velocity. The corresponding horizontal component is Coriolis Effect. E.E. affects the centrifugal accelerational and, hence, the apparent gravitational attraction value. E.E. is one of the most important factors that limit the accuracy of the gravity data acquired on a moving platform in a shipborne or airborne survey with the use of conventional gravimeters. ^{[25, 106, 223, 238].} See Eötvös Correction and Gravimeter.

Eötvös Unit (EU)   – a standard unit which is used in the gravity gradient  measurements. 1E4 = 10^-6 mGal/cm = 0.1 mGal/km ^[223].

Equipotential Surface  – an imaginary continuous surface which is everywhere perpendicular to the vector of the potential field. For example, mean sea level is E.S. for the gravity field. Any departures from a uniform density distribution below the Earth’s surface (which generate gravity anomalies on this surface) will warp E.S. above. ^[223].

Equivalent Layer  – a concept which is based on assumption that any observed gravity or magnetic field can be approximated by a single layer of many sources where distribution of density or magnetization produces the same gravity or magnetic field as the observed field. In magnetic exploration, once E.L. has been calculated, it can be used to recompute a field corresponding to this E.L. at other magnetic inclinations, on other observation surfaces or with arbitrary space grid intervals. E.L. concept can be used as a basis for more stable and accurate Reduction-to-Pole (RTP), elevation corrections and gridding algorithms as compared to traditional methods. For example, RTP with the use of E.L.-based algorithm does not suffer from the instability encountered with Fourier transform methods at low magnetic latitudes and, hence, RTP can be accurately achieved using the magnetic field originating near or at the magnetic Equator. Sometimes, E.L. is referred to as Equivalent Source. ^{[25,  43,  49,  92,  183,  190,  196,  251].} See Equivalent Source Continuation.

Equivalent Source  – see Equivalent Layer.

Equivalent Source Continuation  – a three-dimensional method of the airborne data Gridding. Differing from the traditional gridding methods, E.S.I. requires the knowledge of the flight level (i.e., elevation above surface – AGL) at each data point in addition to its lateral location. E.S.I. enables data acquired at different flight levels to be brought to a common datum and eliminates gridding artifacts associated with these elevation differences. (Alternatively, data acquired on any flight surface can be calculated on any other flight surface). As a conceptual analog of Equivalent Layer, E.S.C. method can be used for applying Reduction-To-Pole to the magnetic data observed at low latitudes. E.S.C. is also referred to as Equivalent Source Interpolation. ^{[100,  250].}

Euler Deconvolution  – a mathematical procedure (algorithm) which is applied to the line or gridded magnetic data to solve Euler’s Homogeneity Equation for the source depths and locations. For 2-D (line data) case, E.D. uses the total field profile values to create a depth section along each survey line containing solutions for sources of a particular structural type (i.e., source geometry) defined by Euler’s Structural Index. Each calculation is run for a wide variety of window lengths to obtain solutions for different depths. A valid depth pick is made once a certain minimum number of depth solutions falls within a pre-selected radius of a point. Vertical or near-vertical alignments of depth solutions may be interpreted as geologically meaningful features such as faults, filled-in with magnetic materials, or contacts across basement blocks of differing susceptibilities. Sometimes, E.D. is referred to as Euler Modeling because the process is based on the model approximation of a source geometry and is not, strictly speaking, a mathematical deconvolution. ^{[10, 11, 14, 64, 107, 206, 207, 239].} See also 3-D Euler Deconvolution and Euler Method.

Euler Method  – an automated inverse method applied to either profile (line) or gridded potential field data to obtain estimates of locations and depths for causative bodies of a particular structural type. E.M. based on the concept that anomalous magnetic or gravity fields of localized structures are homogeneous functions of the source coordinates and, therefore, satisfy Euler’s Homogeneity Equation. This equation can be solved parametrically for the source locations and depths. Generally, E.M. results proved to be more effective in mapping structural boundaries such as faults and contacts (as trends of the Euler depth marks) rather than estimating the basement depth. ^{[25, 206, 207, 215, 239].} See also Euler Deconvolution, 3-D Euler Deconvolution, and Euler’s Structural Index.

Euler Modeling  – see Euler Deconvolution.

Euler’s Equation  – see Euler’s Homogeneity Equation.

Euler’s Homogeneity Equation  – a partial differential equation that constitutes the theoretical basis for the application of Euler Method. It can be presented as

(x – x_o) dT/dx + (y – y_o) dT/dy + (z – z_o) dT/dz = N(B – T ),

            where (x_o, y_o, z_o) is the position of a source whose magnetic or gravity total field “T” is detected at coordinates (x, y, z); “B” is the regional value of the total field; “N” is Euler’s Structural Index. ^{[25, 64, 107, 206, 207, 239].}

Euler’s Structural Index (SI)  – a degree of homogeneity “N” interpreted physically as a measure of the rate of the potential field change with a distance (i.e., fall-off rate) for the particular model geometry. For example, magnetic field of a sphere (point dipole) falls off as the inverse cube (SI = 3); intrusive pipe (vertical line source) has an inverse square fall-off (SI = 2). Extended bodies are approximated as assemblages of dipoles with the following SI values: thin dike – 1.0 (sometimes, 2.0); contact – 0 (sometimes, 0.5); irregular sill – 1.0. Real data contain anomalies from sources with various SI values and therefore require solutions for a range of indices to make a proper selection of estimates. Generally, the Euler depth estimate for a given body will increase with increased SI. Results of modeling suggest that dominant structural trends can still be outlined despite a poor choice of SI. ^{[11, 64, 107, 206, 207, 239].} See also Euler Deconvolution, Euler’s Homogeneity Equation, and Euler Method.

Evaporites  – sediments deposited from aqueous solutions as a result of extensive or total evaporation. Rock Salt and anhydrite are examples of E. Both are strongly non-magnetic (susceptibility is about – 0.01 in units of 10³ SI), but significantly differ in their densities: 2.1 – 2.6 g/cm³ (average 2.22 g/cm³) for salt and 2.9 – 3.0 g/cm³ (average 2.93 g/cm³) for anhydrite. ^[13].

Exponential Taper Filtering  – a pass filter method that retains a pre-selected part of the data wavelengths using a specifically designed exponential Taper in order to enhance the suppression of the ringing effects and increase the resolving power. There are high-pass and low-pass options available. E.T.F. can also be used as Stripping Filter. ^[42].

External Magnetic Field  – the magnetic field produced as a result of interaction between the Earth’s internal magnetic field and Solar Wind coupled with the Earth’s rotation, tidal forces and thermal effects. ^[25]. See also Earth’s Magnetic Field Components.

Extrusion  – a flowout of molten Lava onto the Earth’s surface. Highly magnetized Volcanic Rocks are formed after E. ^[13]. See also Intrusion and Magma.

Extrusive Rocks  – igneous rocks that have been erupted onto the Earth’s surface. E.R. include highly magnetized Lava flows, which can cover relatively large areas, and hence, form local Magnetic Basement. ^[13]. See also Extrusion.