Geology Reference
In-Depth Information
Time domain
Frequency domain
(a)
(b)
(c)
(d)
Fig. 2.8
Fourier transform pairs for
various waveforms. (a) A spike function.
(b) A 'DC bias'. (c) and (d) Transient
waveforms approximating seismic pulses.
Time
Frequency
t
= 0
In this case, the time variable is replaced by horizontal
distance and the frequency variable by wavenumber
(number of waveform cycles per unit distance). The
application of two-dimensional Fourier techniques to
the interpretation of potential field data is discussed in
Chapters 6 and 7.
frequency 'hiss', or to emphasize the low-frequency
'bass'. Filtering is an inherent characteristic of any system
through which a signal is transmitted.
2.4.1 Convolution
Convolution (Kanasewich 1981) is a mathematical
operation defining the change of shape of a waveform
resulting from its passage through a filter. Thus, for ex-
ample, a seismic pulse generated by an explosion is
altered in shape by filtering effects, both in the ground
and in the recording system, so that the seismogram (the
filtered output) differs significantly from the initial
seismic pulse (the input).
As a simple example of filtering, consider a weight
suspended from the end of a vertical spring. If the top of
the spring is perturbed by a sharp up-and-down move-
ment (the input), the motion of the weight (the filtered
output) is a series of damped oscillations out of phase
with the initial perturbation (Fig. 2.9).
The effect of a filter may be categorized by its
impulse
2.4 Waveform processing
The principles of convolution, deconvolution and cor-
relation form the common basis for many methods of
geophysical data processing, especially in the field of seis-
mic reflection surveying. They are introduced here in
general terms and are referred to extensively in later
chapters.Their importance is that they quantitatively de-
scribe how a waveform is affected by a filter. Filtering
modifies a waveform by discriminating between its con-
stituent sine wave components to alter their relative am-
plitudes or phase relations, or both. Most audio systems
are provided with simple filters to cut down on high-
