P

Padding  – an extension of discretely sampled data with zero values in order to accomplish Linear Convolution in computation of filtered data values and eliminate Wraparound Effect. [148]. See FIR RTP Filter.

Paleomagnetism  – the history of the Earth’s magnetic field as recorded in the magnetic properties of rocks. Paleomagnetic studies indicate that the Earth’s magnetic field has varied in its magnitude and has reversed its polarity several times in the geological past. [223, 238]. See Remanent Magnetization.

Parallax Correction  – one of the leveling corrections which is applied to airborne data to compensate for relatively small errors in the recorded geographical location of the readings due to a horizontal distance separating aircraft and a cable-towed sensor unit called a Bird. P.C. is also used to describe the time delay that may exist between the time a navigation position is recorded and the time the corresponding geophysical measurement is recorded. [85]. See Lag Test.

Paramagnetics  – weakly magnetized rock materials. Paramagnetism is due to the electron spin of unpaired electrons that creates magnetic moments. Susceptibility in P. is positive and small. Magnetic effect is weak, only a few nanoteslas added to the magnetic field observed at the Earth’s surface. [33, 223]. See also Ferrimagnetics, Ferromagnetics, and Diamagnetics.

Parametric Inversion  – a methodology where parameters of a few geometrically simple bodies are sought and corresponding values are found by solving overdetermined problems (i.e., number of applied equations is more than number of unknowns). P.I. requires the initial estimate of input geometrical parameters and limits of Susceptibility or Density allowed. The problem of non-uniqueness is addressed by the restrictive nature of the inversion algorithm, which considers only a small set of pre-specified models and their solutions. [144]. See also Inversion and Minimizing Inversion.

Parzen Filter  – an edge smoothing space-domain filter which is used to smooth edges of line datasets (line curves) by superimposing a weighted polynomial function on original point values to ensure their smooth transition to zero at the ends of lines. P.F. is also referred to as Parzen Window. [124, 223]. See Edge Smoothing Filters.

Parzen Window  – see Parzen Filter.

Pass Filters  – a group of the spectral domain grid-based or line-based filters which retain (i.e., pass) a pre-selected range of frequencies (wavenumbers). See High-Pass Filter and Low-Pass Filter.

Permeability  – a magnetic medium proportionality constant. Its value depends on the properties of a medium where magnetic poles are situated. P. is defined as the ratio of Magnetic Induction (“B”) to the inducing Magnetic Field Strength (“H”):

µ = B /µoH,

            where “µo is the permeability of free space. P. has the value of “1” in vacuum, and practically “1” in the air. [33, 238]. See also Permeability-Susceptibility Relation.

Permeability-Susceptibility Relation  – a relation between the magnetic permeability “µ” and magnetic susceptibility “k” defined as

µ = 1 + 4B k (cgm system)  or  µ = 1 + k (SI system)

            [54, 223]. See also Permeability and Susceptibility.

Peters Half-Slope Method  – a graphic method used for the isolated magnetic anomaly source depth estimation. It requires the determination of several curve parameters on the profile of a magnetic anomaly: maximum slope, half-maximum slope, tangent points, and a distance between them. Estimation of depth also requires the knowledge of a structural index, i.e., Peters Index:

“depth” = “Peters Length / Peters Index”

            The horizontal location of the obtained depth pick is the south tangent point in the northern hemisphere and the north tangent point in the southern hemisphere. [53, 193]. See also Depth Rules and “Quick-And-Dirty” Peters Method.

Peters Index  – a structural index used in Peters Half-Slope Method of the magnetic anomaly source depth estimates. P.I. value is based on a given assumption about the source geometry. The following indices are commonly applied: vertical thin sheet = 0.8–1.0; horizontal thin sheet = 1.0; thick sheet = 1.6; wide body (block) = 1.8–2.0; single interface (contact) = 1.8–2.0; plug-like body = 1.8; default option (dike model) = 1.6. [193, 215]. See also Peters Length.

Peters Length  – an isolated magnetic anomaly profile parameter used in Peters Half-Slope Method. P.L. can be determined using the following steps: 1) determine the maximum slope of the anomaly profile; 2) calculate ˝ the maximum slope and draw a corresponding line (“half-slope line”); 3) with two triangles to keep the line parallel, project the obtained “half-slope line” onto the anomaly profile to find two tangent points in the lower and upper parts of the anomaly profile; the horizontal distance between these two tangent points is P.L. [215]. See also Peters Index.

Phase  – a spatial waveform parameter that represents an angular measure of difference between a reference point on the observation surface and a specific point on a wave. See Instantaneous Phase and Wavelength. [223].

Phillips Method  – an automated method of the magnetic source depth estimation using the autocorrelation function of the magnetic anomaly profile and the basic model approximation as vertical Thin Dike (thin sheet) or Magnetic Contact. P.M. employs the maximum-entropy algorithm to calculate the first few lags of the autocorrelation function in a short window. The depth to a dipping sheet source can be computed from these lags and their differences. Two-dimensional (2-D) Magnetic Basement surface is constructed by laminating together a large number of very thin vertical or near vertical dikes of infinite extent in “y” and “z” directions. The magnetic anomaly profile (observed at the surface z = 0) is assumed to be a superposition of anomalies produced by each thin dike. [194, 195]. See also Euler Method and Werner Method.

Pill Box Effect  – see Bull’s Eye Effect.

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

Pixel  – a picture element in the form of an individual cell in the two-dimensional grid that represents a digital image. Spatially, each P. corresponds to a certain area on the potential field map. See Raster Grid. [223].

Plate  – a) sheet-like magnetic source body approximation with a limited vertical dimension. P. thickness may range from 0.1 to 1.0 times its depth-to-top. Magnetic anomaly of P. is similar to that of a set of dipoles; b) large, torsionally rigid segment of the Earth’s Lithosphere, which may be assumed to move horizontally, being carried by slow convection currents in the underlying Asthenosphere. [13, 121,  215,  223,  238]  See Plate Tectonics and Magnetic Modeling Shapes.

Plate Tectonics  – a concept of global tectonics that describes the Earth’s Lithosphere as divided into variously shaped, torsionally rigid, slowly moving plates of a regional extent which are carried along by slow convection currents in Asthenosphere. At present, plates interact with one another at their boundaries, causing structural-tectonic deformations and seismic activity. Along mid-oceanic ridges plates are moving away from each other, and a new Crust is being created by the convective uprising of Magma. [13, 33, 223]. See also Plate and Sea Floor Spreading.

Pluton  – a big intra-basement or, sometimes, intra-sedimentary igneous rock body.  Magnetic anomalies generated by large uniformly magnetized masses of plutons represent one of the main regional components of the observed magnetic field and often transect regional Magnetic Grain patterns .[13, [140 ].   See Igneous Rocks and Magma.

Plutonic Rocks  – igneous rocks formed at considerable depths by crystallization of Magma. Generally, P.R. are strongly magnetic, unless they are granites with little or no mafic minerals. [13]. See Igneous Rocks and Pluton.

Plutonic Water  – water derived from the crystallization of Magma. P.W. may significantly contribute to magnetization of the intra-basement faults and, probably, intra-sedimentary faults. [13]. See Pluton and Plutonic Rocks.

Point-Like Anomalies – short-wavelength single maxima magnetic anomalies generated mostly by cultural effects such as wellhead casings, grain elevators, dams, etc.  Sometines, P.-L.A. may represent localized sources of geological significance like magnetite-bearing minettes and similar intrusions. [140 ].  See also Intrusion and Kimberlite Pipe.

Poisson’s Relation  – a relation between the magnetic and gravity potentials of the same Causative Body when both density and magnetic dipole moment are constant; the magnetic potential is directly proportional to the derivative of the gravity potential in the direction of assumed magnetization. When magnetization is vertical, P.R. can be presented as:

dM / dz = k dgz / dz,

            where “dM/dz” is the vertical component of the magnetic field; “dgz / dz” is the vertical component of the gravity field (i.e., Vertical Gravity); “k” is the combined constant: “k = n/GD where n is the magnetic moment per unit volume (i.e., Intensity of Magnetization), “G” is Universal Gravitational Constant, D is the assumed rock density. P.R. is used to make the pseudogravity maps from the observed magnetic data. [9, 223]. See Pseudogravity.

Polar Flattening  – the Earth’s shape parameter, which is the difference between the equatorial and polar radii divided by the equatorial radius. P.F. value is about 1/298.257. P.F. is also referred to as Flattening Coefficient. [25, 238].

Polarization  – see Magnetic Polarization.

Pole Reduced Magnetics  – a total magnetic field of the Earth (i.e., Total Magnetic Intensity – TMI) in the survey area after applying Reduction-To-Pole (RTP), usually, to the leveled and gridded magnetic data. See Grid, Gridding and Leveling.

Polynomial Fitting  – an analytical method to separate a long wavelength regional component from an observed shorter wavelength anomaly. The regional component of the potential field is fitted by a polynomial surface of low orders, which is then subtracted from the observed potential field to obtain an estimate of the residual component. See Residual-Regional Anomaly Separation.

Positioning  – determining the actual location of a measurement platform, survey ship or aircraft in the process of measurements with respect to the geodetic coordinates. See Global Positioning System (GPS) and Differential GPS. [223]. See also Survey Positioning and Positioning Accuracy.

Positioning Accuracy  – the accuracy of determining the location of a measurement platform, survey ship or aircraft in the process of measurements with respect to the geodetic coordinates. Depending on the positioning system applied, P.A. may vary from 50-100m to 2-5m or less. See also Positioning.

Post-Flight Quality Control  – a set of QC checks to verify the accuracy of the parameters of airborne survey flown and their agreement with the planned survey specifications. Usually, P.-F.Q.C. for aeromagnetic surveys comprises four main steps: 1) flight path reconstruction to ensure the lines were flown within allowable tolerances; 2) videotape flight path checking to confirm the cultural noise sources’ locations; 3) visual examination of the diurnal profiles obtained at Base Station; 4) noise level checking to confirm acceptance values. [58]. See also Diurnals, Cultural Noise and On-Site Magnetometer Calibrations.

Potential  – a mathematical function that describes Potential Field at any given space point. P. at a point in Gravity Field is the amount of energy (work) required to move a unit mass from a point at an “infinite” distance to the given point. Similarly, P. at a point in Magnetic Field is the amount of energy required to move a fictitious unit pole from “infinity” to the given point. [25, 54, 223, 238].

Potential Field  – a space varying field that obeys a differential equation known as Laplace’s Equation, which describes P.F. at any given space point through derivatives of Potential. Gravity and magnetic fields are vector potential fields. Most exploration gravity surveys utilize the vertical component of the gravity field, while the most exploration magnetic surveys utilize the scalar total intensity of the magnetic field. The observed gravity or magnetic P.F. may be described as the additive combination of deep and shallow subsurface source distributions. In the most general approximation, P.F. can be presented as the sum of the regional and residual gravity or magnetic fields. [25, 54, 238]. See Regional Potential Field and Residual Potential Field.

Potential Field Anomaly  – a composite magnetic or gravity anomaly which represents the sum of effects from all source bodies in subsurface: the interference of anomalies caused by closely spaced source bodies and superposition of anomalies caused by source bodies at significantly different depth levels. Generally, each anomaly on the gravity or magnetic map contains a whole spectrum of wavelengths (spatial frequencies or wavenumbers) instead of just one. [25, 173, 178, 238]. See also Gravity Anomaly, Magnetic Anomaly and Energy Leakage.

Potential Field Map  – a map of composite magnetic or gravity anomalies representing the additive combination of the gravity or magnetic effects of deep and shallow subsurface source distributions.

Potential Field Tilt  – a concept for determining a location of the potential field sources based on the ratio of Vertical Derivative to Horizontal Gradient (the latter should be calculated in both “x” and “y” directions). The vertical gradient is positive over a source and has zero value over its edges, while the horizontal gradient peaks over edges and is zero over the center of a source. This concept can be effectively used for identifying the presence of subtle magnetic and gravity anomalies as well as for deducing the location of the magnetic or gravity source body edges and anomaly peak values through calculating the potential field parameter called Potential Field Tilt Angle. [159].

Potential Field Tilt Angle  – a parameter defined in terms of the ratio of Vertical Derivative to Horizontal Gradient (the latter should be calculated in both “x” and “y” directions):

P.F.T.A. = tan–1(vertical derivative / horizontal gradient)

            P.F.T.A. values are always in the range from –90ş to +90ş. P.F.T.A. has large positive values over a source, passes through zero at or near the edge of a vertical sided source body, and it is negative outside the source region. P.F.T.A. has the property of being relatively insensitive to the depth of a source body and resolves anomalies from both shallow and deep sources equally well, therefore, allowing identification of the presence of subtle sources, which are often swamped in the stronger responses of larger and more intensive sources. In practice, a grid of tilt angles, calculated at each point on the potential field grid, can be obtained. This P.F.T.A. grid is then color-coded to define positive and negative tilt angle values. The result of this process is a map that delineates horizontal locations of both shallow and deep sources. [159]. See Potential Field Tilt.

Power Spectral Density – see Radial Power Spectrum.

Power Spectrum  – the square of Amplitude Spectrum of the gravity and magnetic data, i.e., squared amplitude-versus-wavenumber relation. The energy (power) of the observed data components is presented in the logarithmic scale, wavenumbers - in cycles per km (meter) or, sometimes, in the decimal fractions of Nyquist Frequency. P.S. provides the slope and intercept parameters for the design of Matched Filtering operator. It is assumed that the decay of the P.S. curve can be approximated by three or four linear slopes (gradients) corresponding to the clearly separated depth ensembles of magnetic sources. Power spectra, which do not exhibit distinct linear slopes (i.e., non-linear power spectra), cannot be interpreted in this way. P.S. of the area is a statistical estimate representing the area averages. It means that the analysis of the calculated spectra covering, for example, more than one tectono-magnetic Terrane may produce averages not present in either terrane. P.S. is also referred to as the Log-Power Spectrum, Log-Energy Spectrum, Radial Power Spectrum (in case of gridded magnetic data) or Power-Density Spectrum. [25, 228]. See also Map Power Spectrum and  Spector-Grant Method..

Pratt Hypothesis  – an hypothesis of gravitational (isostatic) equilibrium between Crust and Mantle. It assumes a uniform crust thickness below sea level (i.e., no mountain “roots” as in Airy Hypothesis), but laterally variable crust Density so that areas of a lower density rise above sea level higher than areas of a higher density. In the most general approximation, the relationship among densities of regional crust blocks can be presented as

 F 1 <  F 2 <  F 3

            where “F 1” is the crust density of a mountainous region; “F 2” is the crust density of a flat Earth’s region; and “ F 3” is the crust density below ocean basins. Heiskanen Modification of P.H. combines lateral variations of the crust density with variable crust thickness (about 2/3 of the topographic high is compensated by mountain “roots”) and also assumes a gradual increase of density with depth. [25, 54, 223, 238]. See also Isostasy.

Precision  – an instrument characteristic that defines the repeatability of readings and estimated as the mean deviation of a set of readings from their average value. See also Accuracy and Sensitivity. [223].

Predictive Filter  – a processing operator (algorithm) which fills gaps in the gridded data remaining after applying standard Gridding and interpolation procedures.

Preferential Continuation  – a spectral domain anomaly enhancement procedure designed on the basis of Optimum Filtering and Equivalent Layer concepts for the downward and upward continuation of the potential field data. Differing from the standard upward and downward continuation operators, P.C. operator selectively (or preferentially) enhances a certain range of spatial frequencies in Amplitude Spectrum. Downward P.C. can enhance deep-source (long wavelength) components of the potential field without overamplifying shallow-source (short wavelength) components. Upward P.C. effectively attenuates shallow-source and very shallow-source (i.e., short wavelength) components while minimally attenuating deep-source (long wavelength) components, as it often happens after applying the standard upward continuation. [184]. See also Downward Continuation and Upward Continuation.

Pre-Filter Transformation  – a set of supplementary procedures applied to the line or grid datasets in order to improve the performance of filter operations both in space and spectral domains. P.-F.T. includes Detrending, Despiking, Data Extension, edge smoothing, filling data gaps, etc. [230 ].

Pre-Survey Magnetometer Calibrations  – see On-Site Magnetometer Calibrations.

Prism  – a model source body approximation defined as a parallelepiped of semi-infinite length in the vertical dimension, i.e., its depth-to-bottom distance is at least four times its depth-to-top distance. Magnetic anomaly caused by P. is similar to that of a magnetic Monopole or line of poles. Two-dimensional P. (semi-infinite vertically and normal to the plane of view) is sometimes referred to as Dike model. [215]. See Magnetic Modeling Shapes.

Profile  – see Profile Graph.

Profile Graph  – a) cross-section of the gridded data defined by a segmented path or straight-line direction that the user traces over Grid; b) cross-section of the potential field anomaly along the survey line.

Proof Mass  – a suspended weight in the gravimeter sensing system. Position of the P.M. is altered by a change in the gravitational attraction (acceleration). See Gravity Acceleration, Torsion Balance, Weight-On-Spring and Zero-Length Spring.

Proton Precession Magnetometer  – a magnetometer which determines the value of the Earth’s magnetic field by, first, polarizing water with a high proton (hydrogen nuclei) content and, then, measuring the precession of hydrogen nuclei (protons) when the polarizing field is removed. The frequency of the precession is proportional to the intensity of the Earth’s magnetic field and called Larmor Frequency. The achievable accuracy is up to 0.1 gamma. No orientation is necessary, i.e., P.P.M. sensor arrangement is omni-directional. However, Sampling Rate is limited by how often the polarization cycle can be applied. P.P.M. is also called Proton-Resonance Magnetometer. [57, 223]. See Cesium Magnetometer, Fluxgate Magnetometer and Optically Pumped Magnetometer.

Proton Resonance Magnetometer  – see Proton Precession Magnetometer.

Pseudo-Anomaly  – see Artifact.

Pseudocolor  – a method of mapping the observed and/or filtered data as a color-coded (color-scaled) grid where each color spectrum shade corresponds to a particular range of the cell values in the obtained grid, from low to high. P. is often referred to as Color-Coded Map, Color-Scaled Map or Pseudocolor Map. See also Color Wheel and Grey-Scale Map.

Pseudocolor Map  – see Pseudocolor.

Pseudo-Depth Slice  – a grid image of the magnetic field data obtained after applying Matched Filtering to the observed or reduced-to-pole data. Each P.-D.S. highlights a particular range of spatial frequencies (wavelengths) corresponding to a quantitatively estimated depth in the subsurface. Fundamental ambiguity of the relationship between a potential field and its sources precludes reliable qualitative estimates of this kind. Sometimes, P.-D.S. image is referred to as MagSlice Image. [18, 48, 175]. See also Spatial Frequency and Pseudo-Depth Slicing (PDS).

Pseudo-Depth Slicing (PDS)  – a spectral domain filtering method applied to the observed total magnetic intensity grids or reduced-to-pole (RTP) magnetic field grids. PDS produces a set of grid images (slices) highlighting the particular ranges of the spatial frequency (wavelength) content generated by the magnetic source bodies at different depths in the subsurface. PDS is based on the theory of Matched Filtering and designed from the analysis of the radial power spectra. It is assumed that magnetic sources are ensembles of semi-infinite vertical prisms occurring at the same or close depths. This assumption allows to approximate Radial Power Spectrum curve by straight-line segments (slopes) each representing magnetic sources at a particular depth and this depth corresponds to a particular slope of the curve. The final space domain pseudo-depth slices are obtained by Inverse Fourier Transform of the filtered spectral domain data. [18, 48, 79, 175, 215]. See also Prism, Pseudo-Depth Slice and Spector-Grant Method.

Pseudogravity  – a concept that is based on approximation of the gravity field by observed magnetic field. P. requires the conversion of Susceptibility values to Density values and can be defined mathematically as the vertical integral of the reduced-to-pole total magnetic field data. P. calculations are based on Poisson’s Relation. [9, 25]. See also Pseudogravity Transform and Pseudomagnetics.

Pseudogravity Filter  – see Pseudogravity Transform.

Pseudogravity Transform  – a procedure to calculate an approximation of the gravity field from the observed magnetic field.  P.T. is a linear filtering procedure, usually applied in Fourier Domain, that transforms the magnetic anomaly over magnetization distribution “M(x,y,z)” into the corresponding gravity anomaly that would be observed if the density D satisfies the requirement defined as:

D (x,y,z) = kM(x,y,z),

            where “k” is a constant. It should be remembered that anomalies produced by P.T. are not real gravity anomalies, but transformed magnetic anomalies, and the obtained map is measured in units of “nT/km”. P.T. enhances relatively lower Spatial Frequency components and attenuates high-frequency effects of the surface cultural features. In some cases, P.T. – based map can accentuate the areal extent of magnetically anomalous relatively shallow zones. Detrending with the use of a higher order (third or fourth) polynomials is recommended before P.T. [25]. See also Pseudogravity and Pseudomagnetics.

Pseudomagnetics  – an approximation of the magnetic field derived from the observed gravity field. P. is based on Poisson’s Relation: the magnetic potential is directly proportional to the derivative of the gravity potential in the direction of assumed magnetization. Because the magnetization variability of rocks is usually much more complex than the density variability, in practice it is far more common to calculate Pseudogravity rather than P. [25].

Pseudosusceptibility  – a ratio between Total Magnetization and the Earth’s magnetic field. This term is often used in mining exploration. [17].