Wavelength
– a
distance between successive repetitions of the waveform, from one peak to the
next peak, measured perpendicular to the wavefront. In gravity and magnetic
exploration, depth to the source of observed anomaly is related to the
horizontal distance of the slope (i.e., about half-wavelength) of this anomaly.
Generally, long W. is related to a deep source, and short W. is related
to a relatively shallow source. [23,
223].
See Magnetic
Anomaly Wavelength and Gravity Anomaly Wavelength.
Wavelength Analysis
– a
methodology which is based on transformation of the observed potential field
data from the original Space Domain
to the equivalent Frequency Domain using Fourier
Transform. After
transformation, low-pass or band-pass or high-pass filters can be constructed to
analyze a wavelength (or equivalent frequency) content of the gravity or
magnetic anomalies. The wavelength-filtered maps are usually compared with the
input (unfiltered) data for combined examination in order to get a better
spatial understanding of the relationship between relatively deep/broad/thick
sources and relatively shallow/narrow/thin sources. [257].
See Wavenumber.
Wavelength Filter
– a space
domain or spectral domain filter that separates anomalies of different
horizontal extent by passing or rejecting a certain wavelength range from the
mapped potential field data. Originally, W.F.
was developed as Linear Filter for application in the space domain. Modern software
packages offer conceptually equivalent and more effective anomaly separation
option based on filtering in the spectral (frequency) domain where the user
makes a choice of filter parameters either in wavenumber or grid units (grid
intervals) or wavelength values. [257].
See also Anomaly Wavelength.
Wavelength Resolution
– a
quantitative estimate of the smallest Wavelength
where the noise and target signal levels are equal. W.R.
is limited by Sampling Interval and by wavelength filtering applied to suppress Noise and enhance target signal. In the case of Station data, W.R.
is twice Station Spacing. In the case of data obtained with the use of a moving
platform (marine, airborne and satellite surveys), it is the noise-suppressing
filter parameters that determine W.R.
[253]. See also Anomaly
Resolution.
Wavelet
– a waveform
component consisting of only a few wave cycles and having a short length.
According to the Fourier synthesis concept, each W. is the
result of superposition of many harmonic waves of different frequencies and
amplitudes. In its turn, the superposition of short-length wavelets constitutes
the longer wavelength components of the observed potential field. [223].
See Wavelet Transform
and Fourier Analysis.
Wavelet Analysis
– see Wavelet
Transform.
Wavelet Decomposition
– see Wavelet
Transform.
Wavelet Transform (WT)
– a space
and spectral analysis technique that complements traditional Fourier methods. W.T.
views any potential
field signal as a combination of finite length wavelets. W.T.
decomposes input signals into constituent wavelet components with the subsequent
analysis of a portion of their frequency spectrum over a selected space domain
window. Based on results of the multi-window test, lateral resolution of the
potential field data can be significantly improved. W.T. can also be used for Regional-Residual
Anomaly Separation. Aliasing
in the transform domain is a problem that should be properly
addressed when using this technique. W.T.
is also referred to as Wavelet Analysis, Space-Frequency
Localization or Wavelet
Decomposition. [35,
65,
69].
See Wavelet.
Wavelet Transform Filtering
–
a two-step procedure which is based on high-resolution decomposition by Wavelet
Transform: 1) data
decomposition into different resolution levels; 2) signal reconstruction by
Inverse Wavelet Transform
while discarding unwanted noise components of the transform.
Wavenumber
– a
spatial frequency (i.e., space domain analog of the time domain frequency) or
the number of wave cycles per unit of distance or per grid unit in a given
direction “x” or “y”. W.
is a reciprocal of Wavelength:
“wavenumber”
= “1 / wavelength”
See Spatial Frequency and Local
Wavenumber.
Wavenumber Filter
– a general
term of a filter from a group of Spectral
Domain Filters which
have their Cutoff
values defined in wavenumber units and operate based on the concept of
discrimination against certain wavenumbers relative to others. W.F.
is the equivalent of Wavelength Filter. See Wavenumber.
Weighted Euler Deconvolution
–
a technique that weights the Euler’s homogeneity equations (which are solved
for the source body depth estimates using 3-D
Euler Deconvolution of
gridded gravity data) by an error function proportional to a) Accuracy
of the gravity station measurements, i.e., the larger errors, the smaller
weight; b) distance between a grid point and the nearest Station,
i.e., the larger distance, the smaller weight. Erroneous depth estimates
resulting from low accuracy measurements and the gridded field’s Aliasing
due to irregular station distribution or large spacing between regular survey
lines can be rejected. [
128
].
See Euler Deconvolution and Euler’s
Homogeneity Equation.
Weight-On-Spring
– a basic
physical principle of operation of some gravimeters. The change of a length of
the spring with a weight attached to its end is proportional to the change of
the gravity field. High-accuracy optical systems, with multiple reflections or
others, are required to make changes of the order of one part in a million or
less apparent and measurable. The Gulf and Hartley gravimeters are of this type.
[174].
See also Zero-Length Spring
and Torsion Balance.
Werner Deconvolution
– an
automated magnetic source parameter estimation procedure (algorithm) based on
the analysis of 2-D profiles of the magnetic anomalies from source bodies
approximated by Thin Dike
or Magnetic Contact
model geometries. The Werner’s equation expresses the total magnetic intensity
anomaly of a thin dike and the first horizontal derivative anomaly of a contact
in terms of six parameters to fit Window with at least seven points from the anomalous profile. The
window is moved along the profile to generate solutions (coordinates “x” and
“z” of the top of a dike, or contact as well as Susceptibility and
dip values) for each anomaly. The process is usually run for 15‑20
different window sizes to look for progressively deeper solutions. The final
result is the depth section of solutions along each survey line. Using line data
sampled every 7‑10 meters, W.D.
provides high-resolution information which is superior to that of the
gridded data because: a) grid represents the potential field data sampled
according to Cell Size,
i.e., each 50-250 meters; and b) field curvature data crucial to resolution and
depth analysis is often distorted in the process of Gridding. [25,
66,
120,
129,
131,
153,
215].
Sometimes, W.
D. is referred to as Werner
Filtering. See also Werner
Method, 2-D Euler
Deconvolution, and 3-D
Euler Deconvolution.
Werner Depth Estimation
– see Werner
Deconvolution.
Werner Filtering
–
see Werner Deconvolution.
Werner Method
– a 2-D
(i.e., profile-based) potential data interpretation method that was originally
developed for magnetic data and based on two assumptions: 1) distribution
of magnetic sources in subsurface can be described by ensembles of variously
dipping, differently magnetized dikes occurring at different depths and striking
orthogonally to the line of measurements; 2) interference from a neighboring
anomaly or regional anomaly can be expressed as a simple polynomial added to the
residual anomaly of interest. Basically, W.M.
separates the magnetic field contributed by a particular Dike
(or thin sheet) under study from the interference of both
neighboring and distant dikes (thin sheets). W.M. can be
extended to models other than dikes (or thin sheets) as well as applied to the
gravity data. For example, Magnetic
Contact model and Horizontal
Cylinder model apply W.M.
for Horizontal Derivative of the magnetic field and the vertical component of
the gravity field respectively to obtain estimates of the source depth and other
parameters. [129,
215].
See Werner Deconvolution.
Werner Profile Analysis
– see Werner
Deconvolution.
WGS84 – one
of the latest versions of Reference Spheroid.
White Noise
– see Random
Noise.
Wiener Filter
– see Wiener
Noise Filter.
Wiener Noise Filter
– an
optimum-type low-pass data stabilizing filter. Generally W.N.F. is used to suppress any geophysically meaningless
high-frequency noise (Random Noise)
before applying Reduction-To-Pole or Reduction-To-Equator.
Basic principles of a more general Wiener
filter, as an optimum-type filter, are used in developing anomaly
separation methods, reduction-to-the-pole techniques and Equivalent
Layer concept. [91,
92,
102,
118,
183,
186].
Window
–
a portion of the line dataset or grid dataset chosen as a basis for designing
the data processing or inversion operators or other considerations.
Also called Gate
[223
]. See
also Running
Window and Werner Deconvolution.
Windowing
– a grid
edge smoothing procedure which is applied before Fourier Transform and calculation of Power
Spectrum to prevent
the loss of data at grid edges and minimize Edge Effects.
[240].
See also Rolloff Window.
Worden Gravimeter
– see Torsion
Balance.
Wraparound Effect
– an
undesirable edge effect caused by Circular
Convolution, which
occurs when conventional RTP Filter
is applied in the Fourier (frequency) domain. W.E.
enhances artificial edge anomalies that could be misinterpreted as real
structural trends. To eliminate W.E. and minimize noise and other edge effects, the applying FIR
RTP Filter is recommended. [148].
See Fourier Domain,
Linear Convolution and Padding.