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].