https://wiki.seg.org/index.php?title=Determining_vibroseis_parameters&feed=atom&action=historyDetermining vibroseis parameters - Revision history2021-12-02T16:24:09ZRevision history for this page on the wikiMediaWiki 1.31.12https://wiki.seg.org/index.php?title=Determining_vibroseis_parameters&diff=132642&oldid=prevAgeary: added page2019-06-25T18:44:46Z<p>added page</p>
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| name = Problems in Exploration Seismology and their Solutions<br />
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| width = 120px<br />
| series = Geophysical References Series<br />
| title = [[Problems in Exploration Seismology and their Solutions]]<br />
| part = <br />
| chapter = 8<br />
| pages = 253 - 294<br />
| author = [[Lloyd P. Geldart]] and [[Robert E. Sheriff]]<br />
| doi = 10.1190/1.9781560801733<br />
| pdf = <br />
| store = https://shop.seg.org/shop/products/detail/897<br />
| isbn = ISBN 9781560801153<br />
}}<br />
== Problem 8.14a ==<br />
8.14a Signal and noise characteristics determined from a previous dynamite survey are shown in Figure 8.14a. The principal objective is at 3000 m with a stacking velocity of 3000 m/s. What frequencies should be covered by a linear sweep?<br />
<br />
[[file:Ch08_fig8-14a.png|thumb|{{figure number|8.14a.}} Signal and noise spectra (from Evans, 1997).]]<br />
<br />
=== Background ===<br />
The vibroseis method employs a vibrator to impart to the ground a long train of harmonic signals of varying frequency. The vibrator consists of a piston pressing against a steel plate which is held against the ground by the weight of the vehicle. For the usual linear sweep, the vibrator, which is actuated hydraulically, exerts a pressure <math>{\mathcal{P}}(t)</math> against the plate of the form<br />
<br />
{{NumBlk|:|<math><br />
\begin{align}<br />
{\mathcal{P}}(t)=A(t)\sin \{2\pi t[f_{0} +({\rm d}f/{\rm d}t)t]\},<br />
\end{align}<br />
</math>|{{EquationRef|8.14a}}}}<br />
<br />
where <math>f_{0}</math> is the starting frequency and <math>({\rm d}f/{\rm d}t)</math> is either positive (for an ''upsweep'') or negative (''downsweep''). The amplitude <math>A(t)</math> is constant (except for about 0.2 s at the beginning and end of the sweep, when it increases from or decreases to zero. The frequency varies between about 12 and 60 Hz and the duration of the sweep is usually 7 to 35 s.<br />
<br />
Each sweep generates a signal train which is reflected at each of the reflectors; since reflections are much more closely spaced than the length of the sweep, the recorded signal is a complex superposition of many reflected wave trains. To interpret a vibroseis record, the input sweep is recorded and crosscorrelated (see problem 9.8) with the record; this compresses the reflected wavetrains into short wavelets, thereby removing much of the overlap of the lengthy reflected wavetrains to produce a more-or-less normal seismic record.<br />
<br />
The response of the ground is not an exact reproduction of the motion of the piston and distortion introduces harmonics into the ground, principally the second harmonic. The second harmonic produces reflected wavetrains like the primary reflected wavetrains, but these correlate with the sweep signal to indicate different arrival times. This effect, called ''correlation ghosts'', adds a spurious set of reflection events to the record (Sheriff and Geldart, 1995, 208). The arrival time of this ghost <math>t_{g}</math> is<br />
<br />
{{NumBlk|:|<math><br />
\begin{align}<br />
t_{g} =f_{L} T/(f_{i} -f_{f} ),<br />
\end{align}<br />
</math>|{{EquationRef|8.14a}}}}<br />
<br />
where <math>f_{L}</math> is the lowest sweep frequency, <math>T</math> the sweep time, <math>f_{i}</math> the initial sweep frequency, and <math>f_{f}</math> the final sweep frequency. For an upsweep, the ghosts arrive before <math>t=0</math>, so the ghost is no problem; to avoid this problem with downsweeps, we can use long sweeps so that the ghost is delayed until after the zone of interest is recorded.<br />
<br />
If we have <math>n</math> records on which the signal shape is essentially constant and the noise is random, stacking builds up the signal strength whereas random noise tends to cancel and the signal-to-noise ratio (S/N) varies as <math>n^{1/2}</math> (Sheriff and Geldart, 1995, 184).<br />
<br />
When multiple source units are used, the vibrators are actuated synchronously at locations a few meters apart. Generally, several sweeps at closely spaced locations constitute a single vibrator point.<br />
<br />
=== Solution ===<br />
The signal and noise spectra in Figure 8.14a show that the signal spectrum is strong between 15 to 55 Hz while the noise spectrum is confined largely to the narrow peak centered around 15 Hz. A passband of 20–60 Hz would include most of the signal and exclude much of the noise. This is a bandwidth of roughly 1.5 octaves.<br />
<br />
== Problem 8.14b ==<br />
If a downsweep of 8 s is used, at what time will the correlation ghost appear for a 9-s 60–15 Hz linear sweep? Will it interfere with the objective?<br />
<br />
=== Solution ===<br />
Assume a downsweep that lasts 8 s and goes from 60 Hz to 15 Hz, that is, 5.6 Hz/s. Fundamental frequencies may generate second harmonic correlation ghosts which fall within the passband. The ghosts of 30–15 Hz may interfere with desired reflections arriving after<br />
<br />
<math><br />
\begin{align}<br />
t=15\times 8/\left(60-15\right)=2.667\mbox{ s},<br />
\end{align}<br />
</math><br />
<br />
according to equation (8.14b).<br />
<br />
== Problem 8.14c ==<br />
If a single vibrator sweep of 8 s yields an S/N of 0.2 at the objective depth for a 15 to 60 Hz sweep, how many sweeps will have to be stacked to give <math>\mbox{S/N}=2.0</math>?<br />
<br />
=== Solution ===<br />
Assuming the noise is random, the S/N varies as <math>n^{1/2}</math>. If we need to increase S/N by a factor of 10, we require <math>10^{2} =100</math> sweeps. Note that the improvement of S/N by the factor <math>n^{1/2}</math> does not apply to coherent noise.<br />
<br />
== Problem 8.14d ==<br />
Assume that recording continues for an additional time of 6 s (listen time) beyond the sweep time and that it takes 10 s to move the vibrators between sweep points; how long will be required for four vibrators to record one vibrator point?<br />
<br />
=== Solution ===<br />
The sweep time plus the listening time is 14 s; adding the time to move the vibrators, we get a total of 24 s per sweep. To obtain 100 sweeps as required by part (c), we must move the four vibrators 25 times, taking <math>25\times 24=600\mbox{ s}=10</math> minutes. However, the vibrators probably build up the signal more than they build up the noise and much of the noise is probably not random, so the number of required sweeps should be cut at least in half.<br />
<br />
== Continue reading ==<br />
{| border="1" cellpadding="5" cellspacing="0" align="center"<br />
|-<br />
! style="background: #426580; color: white;" | Previous section<br />
! style="background: #E5D75F;" | Next section<br />
|-<br />
| align="center" | [[Optimizing field layouts]]<br />
| align="center" | [[Selecting survey parameters]]<br />
|-<br />
! style="background: #426580; color: white;" | Previous chapter<br />
! style="background: #E5D75F;" | Next chapter<br />
|-<br />
| align="center" | [[:Category: Seismic equipment|Seismic equipment]]<br />
| align="center" | [[:Category: Data processing|Data processing]]<br />
|-<br />
| align="center" colspan="2" |<br />
[[Problems_in_Exploration_Seismology_and_their_Solutions|Table of Contents (book)]]<br />
|}<br />
<br />
== Also in this chapter ==<br />
* [[Effect of too many groups connected to the cable]]<br />
* [[Reflection-point smear for dipping reflectors]]<br />
* [[Stacking charts]]<br />
* [[Attenuation of air waves]]<br />
* [[Maximum array length for given apparent velocity]]<br />
* [[Response of a linear array]]<br />
* [[Directivities of linear arrays and linear sources]]<br />
* [[Tapered arrays]]<br />
* [[Directivity of marine arrays]]<br />
* [[Response of a triangular array]]<br />
* [[Noise tests]]<br />
* [[Selecting optimum field methods]]<br />
* [[Optimizing field layouts]]<br />
* [[Determining vibroseis parameters]]<br />
* [[Selecting survey parameters]]<br />
* [[Effect of signal/noise ratio on event picking]]<br />
* [[Interpreting uphole surveys]]<br />
* [[Weathering and elevation (near-surface) corrections]]<br />
* [[Determining static corrections from first breaks]]<br />
* [[Determining reflector location]]<br />
* [[Blondeau weathering corrections]]<br />
<br />
== External links ==<br />
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