L

Lag Correction  – a correction applied to the airborne data to compensate for physical time delays due to the distance between sensors and GPS antenna and electronic delays due to the time taken to record the observed value in the data acquisition system. L.C. is determined during Lag Test and, as a rule, its typical value are about 0.3–0.6 sec. See also Instrumentation Lag.

Lag Test  – one of On-Site Magnetometer Calibrations made by test measurements along two lines flown in opposite directions over the known surface magnetic feature. After data reduction and plotting, the lag value is determined as one-half the time shift required to match the corresponding anomalous responses. See also Compensation Test, Lag Correction and Parallax Correction.

Laplace Convolution  – a heavy smoothing procedure which is sometimes applied after Initial Gridding in order to improve the condition of the gridded data for subsequent applying the minimum curvature smoothing operator. See Gridding.

Laplace Filter  – a triangular-shaped line-based or grid-based convolution filter that calculates the curvatures in the observed data: high values indicate high curvatures, and zero values indicate inflection points. See also Second Vertical Derivative.

Laplace’s Equation  – a second-order differential equation which defines Potential Field at space points not occupied by its sources:

d²U/d²x² + d²U/dy² + d²U/dz²  = 0,

            where, “U” is the potential function and “x”, “y”, “z” are the rectangular coordinates. ^[25]. See also Potential.

Larmor Frequency  – a frequency with which magnetic moments of atoms and nuclei precess about the direction of the externally applied steady magnetic field such as the Earth’s magnetic field. L.M. is defined as

L.M. = (H/2B,

            where “(” is Gyromagnetic Ratio, “H” is the Earth’s magnetic field. For the value of the Earth’s magnetic field 50000 nT, L.F. is 2100 Hz. ^[223]. See Cesium Magnetometer, Optically Pumped Magnetometer, and Proton Precession Magnetometer.

Larmor Signal  – a signal generated by the proton-resonance or optically pumped magnetometer sensors, which is proportional to the intensity of an external magnetic field. Electronic console converts L.S. into values of the total magnetic intensity in nanoteslas (nT) using Gyromagnetic Ratio. See Cesium Magnetometer, Optically Pumped Magnetometer and Proton Precession Magnetometer.

Lateral Resolution  – a resolution of the potential field data (observed or processed) in the horizontal direction, i.e., along “x” and “y” coordinates. Increased L.R. separates interfering anomalies generated by closely spaced sources. See also Lateral Separation.

Lateral Separation  – a distinction between the potential field anomalies caused by closely spaced source bodies. Without L.S., determination of geological boundaries usually suffers from nearby sources interference that yields mislocations. Commonly, L.S. is performed by Filtering. Quite often, L.S. is used with the same conceptual meaning as Lateral Resolution. See also Enhanced Analytic Signal, Goussev Filter and Vertical Separation.

Latitude Correction  – a correction applied to the observed gravity data to compensate for the increase of the gravitational acceleration (attraction) from the value of about 978000 mGal on the Equator to about 983000 mGal at the Poles due to a) variation of the Earth’s radius because of Polar Flattening; b) variation of the centrifugal force (which opposes the gravitational acceleration) resulting from the Earth’s rotation, as the distance to the Earth’s axis varies with latitude. L.C. obtained by differentiating International Gravity Formula (often, based on GRS67) and can be defined as:

L.C. = 0.8108 Sin 2N,  (in mGal/km)

or

L.C. = 1.3049 Sin 2N,  (in mGal/mile)

            where “N” is the reference latitude.  L.C. value is multiplied by the N-S horizontal distance from the reference latitude and added, as we move towards the Equator, to the observed value at the point of measurement.  At present, for the most exploration surveys, L.C. is not commomly calculated as separate value because it is assumed to be incorporated into the latest versions of International Gravity Formula.  For Microgravity Survey applications, L.C. is defined as:

)g_L = "0.8108 )S Sin2N,

            where )g_L is given in “microGals”, “)S” is the north-south distance in meters between the observation point and Base Station, and “N” is the reference latitude of the base station. Here, L.C. is added to the measured value if the observation point is positioned south of the base station, and subtracted from the measured value if the observation point is positioned north of the base station. ^{[34, 223, 238, 255].}  Sometimes, L.C. is mentioned with the same conceptual meaning as Theoretical Gravity Correction.

Lava  – a fluid igneous rock that flows out of a volcano and may cover large areas. This term is also applied to the same rock material solidified by cooling. ^[13]. See Extrusive Rocks, Igneous Rocks and Magnetic Basement.

Layer Filtering  – see Separation Filtering.

Leveling  – a procedure of adjusting the survey data so that they tie at line intersections.  In aeromagnetic surveys, L. is a general term for a variety of procedures applied to the recorded magnetic data in order to correct for the following main distorting effects of the acquisition process: a) diurnal variations; b) positioning errors (primarily, the height of a flight along adjacent lines); c) mis-ties between traverse and control lines. In the ground gravity surveys, L. is usually applied to correct for mis-ties between survey lines. ^{[85, 149, 172, 187, 223 ].}  See also Decorrugation, Line Leveling and Microleveling.

Line-to-Line Noise  – see Line Corrugations.

Line Corrugations  – artificial anomalies elongated in the direction of the traverse and/or control (tie) lines. L.C. represent residual errors remaining after standard leveling of the observed potential field data. L.C. are removed by applying Microleveling techniques. See also Decorrugation.

Line Data  – the potential field data measured along the survey lines and arranged in the form of the line point datasets. Consecutive line samples are assigned with consecutive Fiducials.

Line Direction  – the orientation of the survey lines in respect to the geographic coordinates. See also Line Length and Line Spacing.

Line Filter Window  – a line interval which includes a specified number of data points on either side of a target data point for which a new value is calculated by the process of Line Filtering.

Line Filtering  – convolution procedure applied to the profiles of line datasets (i.e., to the data measured along acquisition lines) before Gridding to suppress narrow-band noise events such as Cultural Noise, leveling errors, or external magnetic field outbursts. See also Line Filter Window.

Line Filters  – see Channel Filters.

Line Gridding  – a method that makes a Grid (i.e., map) of the gravity of magnetic data obtained during measurements along pre-planned survey lines by creating the smoothest possible (i.e., Minimum Curvature) surface that fits all data values. See also Random Gridding and Bi-Directional Gridding.

Line Length  – a survey parameter derived from the extent of the area planned for the mineral or petroleum exploration. For Fixed Wing Survey, the minimum L.L. is usually in the order of 8-10 km. See also Line Direction and Line Spacing.

Line Leveling  – a multi-step procedure applied to the observed data to remove leveling errors between survey lines. At first, all intersection points between control and traverse lines are found and the mis-ties are determined. Then, the control lines are leveled to the traverse lines using a statistical approach. The mis-ties are calculated once more, this time using the statistically leveled tie lines as reference values. Finally, the traverse lines are leveled to the statistically leveled tie lines using the linear interpolation. See Leveling and Microleveling.

Line Power Spectrum  – a power spectrum graph for the specified gate or segment of the survey line. L.P.S. is usually displayed before and after application of the spectral domain line filters. L.P.S. vertical axis represents energy (i.e., spectral power, which is equal to the square of amplitude); the horizontal axis represents wavenumber in cycles per km (sometimes, in cycles per meter) or in cycles per grid unit. See Power Spectrum.

Line Resampling  – a data conditioning procedure that replaces the original line dataset with a new dataset where data are evenly distributed along the line without internal data gaps. Data gaps (null samples) are replaced in the process of L.R. by interpolated values. L.R. is applied in order to prepare the data for Line Filtering.

Line Spacing  – a distance in meters between traverse or control lines of the survey. Distance between traverse lines is the most important parameter of the airborne survey. For mineral exploration, the traverse L.S. is derived mainly from the target size, such as an ore body or Kimberlite Pipe, and can be about 100-150 m or less. For petroleum exploration, the traverse L.S. is estimated as a function of the depth of a target interval which anomalies are expected to be resolved. Often, the basement depth is taken as the reference level for L.S. value estimates: the shallower Basement – the closer L.S. and vice versa. Generally, L.S. for traverse lines vary from 400-800 m up to 1600-2400 m; L.S. for control (tie) lines can vary from 1 to 20 times the traverse L.S., but 3-5 times value is the most common. ^{[78, 205].} See also High Resolution Aeromagnetic (HRAM) Survey, Line Direction and Line Length.

Lineaments  – linear topographic features of regional extent detected on airborne or satellite images as alignments of vegetation and soil color anomalies, topographic scarps, straight stream courses, and others. The vast majority of L. are considered to be true fractures or fracture zones (i.e., faults without relative vertical displacement of adjacent rock masses) that extend near vertically to great depths, including Basement. Often, L. act as conduits for migrating fluids (and, hence, can be magnetized enough for reliable detection by HRAM surveys), increase the permeability and porosity of penetrated lithological units, as well as create fractured reservoirs in structural and stratigraphic traps. ^[218]. See also Faults.

Linear Convolution  – a mathematical operation that performs computation of filtered data values in Space Domain. In a single dimension, when the set of sampled non-periodic data “F(s)” is filtered by the operator “R(s)”, the result of filtering “P(s)” is obtained through (a) shifting a filter operator by one sample interval at a time; (b) multiplying the corresponding data and filter (Impulse Response) values; and (c) summing the product terms, i.e.,

            where “sN” is the number of data samples over the filter operator length. For periodic data, L.C. is accomplished by Padding both data and filter operator with zero values. L.C. eliminates Wraparound Effect. ^[148]. See also Circular Convolution and FIR RTP Filter.

Linear Filter  – a) a space domain convolution filter, which action is pre-determined by its response to a spike or unit impulse. If continuous input function is considered as a succession of spikes, the L.F. response to this function could be obtained by integration using the principle of superposition. The order of applying two linear filters can be reversed without changing the outcome. Amplitudes of either the filter or the data can be scaled with the same results; b) an optimum-type filter designed from Power Spectrum of the observed data to remove anomalies caused by a pre-determined set of sources in a way similar to the older smoothing methods. ^{[82, 167, 223].} See also Convolution and Wavelength Filter.

Lithosphere  – the Earth’s outermost layer of relative strength as compared to the underlying weak Asthenosphere. L. includes Crust and a part of the upper Mantle, and it is about 100 km in thickness. ^[13]. See Plate Tectonics.

Local Gravity  – a residual component of the gravity field.  Often, L.G. is Bouguer Gravity from which the estimated regional component has been subtracted ^{[223 ].}

Local Frequency  – the same as Instantaneous Frequency. The term “local” is used to make clear that it is related to the potential field data, which are spatial rather than temporal. ^{[226, 242].} See also Complex Attributes, Local Phase and Local Wavenumber.

Local Magnetic Anomalies  – magnetic anomalies of Residual Magnetic Field generated by source  (i.e. causative) bodies in the uppermost part of Crust. ^{[223 ].}  See Causative Body

Local Median Filter  – a space domain filter applied to the gridded or line data to reduce the effects of irregular high-frequency noise components (spikes). L.M.F. moves a window of the specified length over the data and replaces the data at the middle (center) point with the median value of the data within the window. For line data, this window consists of a number of data points surrounding the “target” point. For gridded data this window represents a square configuration of several cells with the “target” cell in its center. L.M.F. is often referred to as Median Filter. ^[230].

Local Phase  – the same as Instantaneous Phase. The term “local” is used to make clear that it is related to the potential field data, which are spatial rather than temporal. ^{[226, 242].} See also Local Frequency and Local Wavenumber.

Local Regional Component  – a spatial wavelength component of the observed potential field data which is larger than that of the dominant wavelengths of the target anomalies, but smaller than the spatial wavelengths on the order of the survey area extent. ^[255]. See also Regional Component.

Local Wavenumber  – the space domain quantity “k” used instead of Local Frequency in the analysis of the magnetic field data in SPI Method:

k = d {tan^–1[(dM/dz)/(dM/dx)]}/dx,

            where “M” is the magnitude of the anomalous magnetic field. L.W. is also referred to as the first-order local wavenumber. ^[242]. See also Improved Source Parameter Imaging (iSPI) Method.

Local Wavenumber Method  – see Source Parameter Imaging (SPI) Method and Improved Source Parameter (iSPI) Method.

Log-Energy Spectrum  – see Power Spectrum.

Loop-Closure Correction  – one of the data leveling corrections applied to the observed location data using an iterative procedure for repeated adjustments of “Z” values for each crossover and all acquisition lines to minimize overall misclosure for the crossovers’ dataset and distribute the residual errors. Ground gravity data are often acquired in loops, so that stations measured at the beginning of the acquisition period are revisited at the end of the period. Among other things, this facilitates estimation of a temporal instrument drift. The technique also helps to locate survey “busts” in the data. ^{[ 85 , 149 ].} See Crossovers and Drift.

Low-Cut Filter  – see High-Pass Filter.

Low-Pass Filter  – see High-Cut Filter.

Low-Pass Rolloff Filters  – a group of the spectral domain grid or line filters that retain (pass) the low-frequency range of Power Spectrum using a smooth curve in Rolloff Range to prevent Ringing after applying Reverse Spectral Transform. ^[230].