Geology Reference
In-Depth Information
2
Geophysical data processing
methods of data analysis are based are brought together
in this chapter.These are accompanied by a discussion of
the techniques of digital data processing by computer
that are routinely used by geophysicists.Throughout this
chapter, waveforms are referred to as functions of time,
but all the principles discussed are equally applicable to
functions of distance. In the latter case, frequency (num-
ber of waveform cycles per unit time) is replaced by
spatial frequency or
wavenumber
(number of waveform
cycles per unit distance).
2.1 Introduction
Geophysical surveys measure the variation of some
physical quantity, with respect either to position or to
time. The quantity may, for example, be the strength of
the Earth's magnetic field along a profile across an
igneous intrusion. It may be the motion of the ground
surface as a function of time associated with the passage
of seismic waves. In either case, the simplest way to pre-
sent the data is to plot a graph (Fig. 2.1) showing the vari-
ation of the measured quantity with respect to distance
or time as appropriate. The graph will show some more
or less complex waveform shape, which will reflect
physical variations in the underlying geology, superim-
posed on unwanted variations from non-geological fea-
tures (such as the effect of electrical power cables in the
magnetic example, or vibration from passing traffic for
the seismic case), instrumental inaccuracy and data col-
lection errors. The detailed shape of the waveform may
be uncertain due to the difficulty in interpolating the
curve between widely spaced stations.The geophysicist's
task is to separate the 'signal'from the 'noise'and interpret
the signal in terms of ground structure.
Analysis of waveforms such as these represents an es-
sential aspect of geophysical data processing and inter-
pretation. The fundamental physics and mathematics of
such analysis is not novel, most having been discovered
in the 19
th
or early 20
th
centuries.The use of these ideas
is also widespread in other technological areas such as
radio, television, sound and video recording, radio-
astronomy, meteorology and medical imaging, as well
as military applications such as radar, sonar and satellite
imaging. Before the general availability of digital com-
puting, the quantity of data and the complexity of the
processing severely restricted the use of the known tech-
niques. This no longer applies and nearly all the tech-
niques described in this chapter may be implemented in
standard computer spreadsheet programs.
The fundamental principles on which the various
2.2 Digitization of geophysical data
Waveforms of geophysical interest are generally contin-
uous (analogue) functions of time or distance. To apply
the power of digital computers to the task of analysis, the
data need to be expressed in digital form, whatever the
form in which they were originally recorded.
A continuous, smooth function of time or distance
can be expressed digitally by sampling the function at a
fixed interval and recording the instantaneous value of
the function at each sampling point.Thus, the analogue
function of time
f
(
t
) shown in Fig. 2.2(a) can be repre-
sented as the digital function
g
(
t
) shown in Fig. 2.2(b) in
which the continuous function has been replaced by a
series of discrete values at fixed, equal, intervals of time.
This process is inherent in many geophysical surveys,
where readings are taken of the value of some parameter
(e.g. magnetic field strength) at points along survey lines.
The extent to which the digital values faithfully repre-
sent the original waveform will depend on the accuracy
of the amplitude measurement and the intervals between
measured samples. Stated more formally, these two para-
meters of a digitizing system are the sampling precision
(dynamic range) and the sampling frequency.
Dynamic range
is an expression of the ratio of the largest
measurable amplitude
A
max
to the smallest measurable
amplitude
A
min
in a sampled function. The higher the
