Geophysical data processing - An Introduction to Geophysical Exploration

Geology Reference

In-Depth Information

forms themselves are presented in a form in which they

simulate an image of the subsurface structure. The

most obvious examples of this are in seismic reflection

(Chapter 4) and ground-penetrating radar (Chapter 9)

sections, where the waveform of the variation of reflect-

ed energy with time is used to derive an image related to

the occurrence of geological boundaries at depth. Often

magnetic surveys for shallow engineering or archaeo-

logical investigations are processed to produce shaded,

coloured, or contoured maps where the shading or

colour correlates with variations of magnetic field which

are expected to correlate with the structures being

sought. Imaging is a very powerful tool, as it provides a

way of summarizing huge volumes of data in a format

which can be readily comprehended, that is, the visual

image. A disadvantage of imaging is that often it can be

difficult or impossible to extract quantitative informa-

tion from the image.

In modelling, the geophysicist chooses a particular

type of structural model of the subsurface, and uses this

to predict the form of the actual waveforms recorded.

The model is then adjusted to give the closest match be-

tween the predicted (modelled) and observed wave-

forms.The goodness of the match obtained depends on

both the signal-to-noise ratio of the waveforms and the

initial choice of the model used.The results of modelling

are usually displayed as cross-sections through the struc-

ture under investigation. Modelling is an essential part of

most geophysical methods and is well exemplified

in gravity and magnetic interpretation (see Chapters 6

and 7).

Problems

1. Over the distance between two seismic

recording sites at different ranges from a seismic

source, seismic waves have been attenuated by

5 dB. What is the ratio of the wave amplitudes ob-

served at the two sites?

2. In a geophysical survey, time-series data are

sampled at 4 ms intervals for digital recording.

(a) What is the Nyquist frequency? (b) In the

absence of antialias filtering, at what frequency

would noise at 200 Hz be aliased back into the

Nyquist interval?

3. If a digital recording of a geophysical time

series is required to have a dynamic range of

120 dB, what number of bits is required in each

binary word?

4. If the digital signal ( - 1, 3, - 2, - 1) is convolved

with the filter operator (2, 3, 1), what is the con-

volved output?

5. Cross-correlate the signal function ( - 1, 3, - 1)

with the waveform ( - 2, - 4, - 4, - 3, 3, 1, 2, 2) con-

taining signal and noise, and indicate the likely

position of the signal in the waveform on the

basis of the cross-correlation function.

6. A waveform is composed of two in-phase

components of equal amplitude at frequencies f

and 3 f . Draw graphs to represent the waveform in

the time domain and the frequency domain.

Kulhanek, O. (1976) Introduction to Digital Filtering in Geophysics .

Elsevier, Amsterdam.

Menke,W. (1989) Geophysical Data Analysis: Discrete Inverse Theory .

Academic Press, London.

Rayner, J.N. (1971) An Introduction to Spectral Analysis . Pion,

England.

Robinson, E.A. & Trietel, S. (2000) Geophysical Signal Analysis .

Prentice-Hall, New Jersey.

Sheriff, R.E. & Geldart, L.P. (1983) Exploration Seismology Vol 2:

Data-Processing and Interpretation . Cambridge University Press,

Cambridge.