Maximum array length for given apparent velocity
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| Series | Geophysical References Series |
|---|---|
| Title | Problems in Exploration Seismology and their Solutions |
| Author | Lloyd P. Geldart and Robert E. Sheriff |
| Chapter | 8 |
| Pages | 253 - 294 |
| DOI | http://dx.doi.org/10.1190/1.9781560801733 |
| ISBN | ISBN 9781560801153 |
| Store | SEG Online Store |
Problem
Reflections in the zone of interest have apparent velocities around 6300 m/s, whereas the velocity just below a uniform LVL is 2100 m/s. If we wish to avoid severe attenuation below 80 Hz when using an array, what is the maximum inline array length?
Background
The LVL is discussed in problem 4.16. Apparent velocity is defined in problem 4.2d. See problem 8.6 for a discussion of array response. Note that the array length, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): n\Delta x , is larger than the distance between the first and last geophones, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): (n-1)\Delta x .
Solution
To avoid deterioration, the response curve for the array length Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): n\Delta x , where n is the number of geophones and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): \Delta x the geophone interval, must not extend beyond the first null (see Figure 8.6b). Equation (8.6b) shows that the first null occurs when Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): n\gamma /2=\pi or Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): n=2\pi /\gamma , where $ \gamma $ is the phase difference between adjacent geophones. Problem 8.6a gives Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): \gamma =2\pi \left(\Delta x/\lambda \right)\sin \alpha , so
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): \begin{align} n&=2\pi /2\pi \left(\Delta x/\lambda \right)\sin\alpha ,\\ \mbox{and }\qquad\qquad n\Delta x&=\lambda /\sin \alpha =\lambda _{a} =V_{a} /f, \end{align} ()
where $ V_{a}= $ apparent velocity and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): \lambda _{a} = apparent wavelength. Thus.
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): \begin{align} n\Delta x=2100/80\mbox{ m}=26\mbox{ m}. \end{align}
The geophone interval must not exceed Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): \Delta x=26/n .
Continue reading
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|---|---|
| Attenuation of air waves | Response of a linear array |
| Previous chapter | Next chapter |
| Seismic equipment | Data processing |
Also in this chapter
- Effect of too many groups connected to the cable
- Reflection-point smear for dipping reflectors
- Stacking charts
- Attenuation of air waves
- Maximum array length for given apparent velocity
- Response of a linear array
- Directivities of linear arrays and linear sources
- Tapered arrays
- Directivity of marine arrays
- Response of a triangular array
- Noise tests
- Selecting optimum field methods
- Optimizing field layouts
- Determining vibroseis parameters
- Selecting survey parameters
- Effect of signal/noise ratio on event picking
- Interpreting uphole surveys
- Weathering and elevation (near-surface) corrections
- Determining static corrections from first breaks
- Determining reflector location
- Blondeau weathering corrections
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