Geology

The FFT and Nuclear Explosions

Seismic research has always been a common user for the Discrete Fourier Transform (and the FFT). If you look at the history of the FFT you will find that one of the original uses for the FFT was to distinguish between natural seismic events and nuclear test explosions because they generate different frequency spectra.

Seismic Reflection Method

The major exploration tool used by the oil and gas industry for locating new hydrocarbon reserves is the SEISMIC REFLECTION METHOD. This technique enables sub-surface sedimentary rock layers to be mapped, from measurements of the amplitude and reflection times of events obtained by the reflection of seismic (sound) waves from the layers.

The basic features of the technique are:

  1. A source of seismic energy which is activated at the Earth's surface.
  2. The downward propagation of seismic wavges into the earth.
  3. The reflection of seismic waves from the interfaces seperating geological media having dissimilar acoustic properties.
  4. The upward propagation of reflected seismic waves.
  5. Detection of the reflected seismic waves at the Earth's surface using receivers located at various distances from the source.
  6. Recording of the signals at each receiver.
The data recorded at the receivers under goes extensive DSP to produce a seismic section which is a representation of a cross section of the Earth. This is then interpreted in terms of what the survey was looking for.

One of the many problems in extracting the information from the data is that the receivers that record the reflected seismic waves also pick up the signature of the source. (The signature of a source is the wave-form that it emits upon activation.) The signature can be removed from the seismic data by deconvolution as long as you also have a recording of the signature, as well as information about the ghost reflections, absorption, and instrument response. These can all be recorded at the time of the survey or can be deduced later from the data.

The (fast) Fourier transform is used to convert the signal into the frequency domain, where convolution between two signals is obtained simply multiplying them together. Once again the Fourier Transform is used as a tool in Digital Signal Processing to perform other operations, rather than producing an end result itself.

An example seismic section. This is a very interesting peice of data as it shows various geological features such as the continous layers at the top. More importantly, at the top of the picture, to the right of the middle, there are sedimentary layers that have cut off by more recent layers. This could possible be an area of trapped hydrocarbons. The data is composed of 1000 traces each of 400 samples, and is of an area in the North Sea mapped by Shell.
In another  seismic section the data contains two salt domes. The one on the left is unusual in that its size is far greater then normally encountered. The data is of an area in the North Sea mapped by BP.

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