Geoscience Reference
In-Depth Information
2.5.3
Anomaly definition
spatial series. These series constitute a set of samples of
what is a continuous variation in the parameter being
measured. In order for the samples to accurately represent
the true variation, these series must be appropriately
sampled, i.e. readings must be taken at an appropriate
spacing or interval.
The rate at which the sampling occurs is known as the
sampling frequency, which for time series is measured in
units of 1/time (frequency, in units of hertz (Hz)); for
frequency series, 1/frequency (period, in units of seconds
(s)); and for spatial series, 1/distance (units of reciprocal
metres (m
-1
)). The time, frequency or distance between
samples is the sampling interval. A little confusingly,
spatial sampling for a moving sensor is usually defined in
terms of temporal sampling. For example, detectors used in
aeromagnetic surveys measure (or sample) the Earth
Surveys designed to improve the definition of an anomal-
ous response are aimed at obtaining more information
about the source of the anomaly, and are often used for
designing drilling programmes. The surveys are conducted
at prospect scale and during exploration in the mine
environment. It may be a detailed ground survey to follow
up an anomaly detected by an airborne survey or possibly a
wider-ranging lower resolution ground survey. Informa-
tion about the source such as its extent, shape, dip and
depth can be obtained, usually by modelling the anomaly
(see
Section 2.11
). Accurately characterising a response
requires careful consideration of the survey con
guration
and the distribution of the measurements within the area
of interest (see
Section 2.6
)
.
'
s
magnetic
field typically every 0.1 s, i.e. 10 times per second,
referred to as 10 Hz sampling. A
fixed-wing aircraft acquir-
2.6
Data acquisition
ing magnetic data
flies at about 70 m/s, so at
'
10 Hz
We describe the acquisition of geophysical survey data in
terms of survey design based on the fundamental concepts
of data sampling and feature detection. Throughout this
section we encourage the use of computer modelling as an
aid to survey design.
Modern geophysical survey equipment stores the digital
measurements for later download. Airborne survey
systems, and some ground systems, acquire high-precision
positional data directly from satellite-based positioning
systems, simultaneously with the geophysical measure-
ments. Survey systems often measure
sampling
the spatial sampling interval is 7 m.
If the measurements are not spaced closely enough (in
time, frequency or distance) to properly sample the par-
ameter being measured, a phenomenon known as aliasing
occurs. It is respectively called temporal, spectral or spatial
aliasing. Consider the situation where a time-varying signal
being measured varies sinusoidally. The effect of sampling
at different sampling frequencies to produce a time series is
demonstrated in
Fig. 2.8a
. The true variations in the signal
are properly represented only when the sampling fre-
quency is high enough to represent those variations; if
not, the signal is under-sampled or aliased. When under-
sampling occurs, the frequency of the sine wave is incor-
rectly represented by being transformed to spurious longer
wavelength (lower frequency) variations. Clearly then, the
very act of sampling a signal can produce artefacts in the
sampled data series that are indistinguishable from legit-
imate responses. Strategies can be adopted to combat the
problem of aliasing, but if data are aliased it is impossible
to reconstruct the original waveform from them.
'
data
acquired for the purpose of post-survey compensation of
survey-induced errors, removal of external sources of noise
appearing in the
'
secondary
'
data, and use in enhancing the
data (see
Section 2.7
)
. Examples include: time of each
measurement; the orientations of sensors and transmitters;
relative positions between sensors on the survey platform;
sensor height; air temperature and pressure; and,
'
primary
'
for
moving platforms, velocity.
2.6.1
Sampling and aliasing
2.6.1.1
Sampling interval
It is shown in
Appendix 2
that a complex waveform can be
represented as a series of superimposed sine waves each
with a different frequency. To avoid aliasing a waveform
containing a range of frequencies, it is necessary to sample
the waveform at a sampling frequency greater than
twice the highest frequency component of the waveform.
This is the Nyquist criterion of sampling (
Fig. 2.8b
). In
As described in
Section 2.2
, a geophysical measurement
may consist of one reading or a series of readings made at
the same location. Measurements made over a period of
time or range of frequencies form time and spectral series,
respectively, for that location. Whether a single reading or
a series of readings is made at each location, a survey will
consist of measurements at a number of stations to form a
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