Dominant frequencies of marine sources

Problems in Exploration Seismology and their Solutions

Series	Geophysical References Series
Title	Problems in Exploration Seismology and their Solutions
Author	Lloyd P. Geldart and Robert E. Sheriff
Chapter	7
Pages	221 - 252
DOI	http://dx.doi.org/10.1190/1.9781560801733
ISBN	ISBN 9781560801153
Store	SEG Online Store

Problem 7.8

The dominant period of a marine seismic source is often determined by the source depth; this is the case when the second half-cycle of the downgoing wave is reinforced

Figure 7.7a  An air-gun array.

by the ghost reflection at the surface. Assuming that this is true for the source signatures in Figure 7.8a, determine their depths.

Background

For discussion of reinforcement depth in marine recording, see problem 3.5. The ghost is the wave reflected at the surface (or at the base of the LVL) with a reversal of phase (see problem 3.8).

When a gas at high pressure is suddenly generated by an underwater explosion or injected into the water by an air gun at sufficient depth that the gas does not quickly escape into the air, oscillation occurs as the gas expands until stopped by the water pressure, then contracts until the gas pressure becomes very high,

Figure 7.8a  Far-field waveshapes of marine sources. (a) Single 120 in3 air gun; (b) array of air guns of different sizes selected to attenuate bubble effects by destructive interference; (c) sleeve exploder; (d) Vaporchoc; (e) Maxipulse; (f) Flexichoc; (g) water gun; (h) 5 kJ sparker. Curves are intended to show features of waveshape, not amplitude relationships. $ {\textit {B}} $ indicates bubble effects; the interval between successive bubbles decreases with time; I indicates implosion (after Sheriff and Geldart, 1995)

Table 7.8a. Source depth from frequency.

	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/":): T (ms)	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/":): d (m)
a) air gun	22	8
b) air-gun array	24	9
c) sleeve exploder	26	10
d) Vaporchoc	18	7
e) Maxipulse	24	9
f) Flexichoc	28	11
g) water gun	22	8
h) sparker	4	2

after which it expands again and the cycle is repeated. Each expansion is effectively a new activation of the source and so a new reflection sequence is generated. This phenomenon is called the bubble effect.

Air guns are described in problem 7.7, imploders, water guns, and sparkers in problem 7.4. FlexichocFailed 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/":): ^{\rm TM} , sleeve gun, VaporchocFailed 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/":): ^{\rm TM} , and MaxipulseFailed 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/":): ^{\rm TM} are devices (now obsolete) designed to diminish the bubble oscillation. Flexichoc used the explosion of a small charge at the center of a steel cage that attenuated the bubble, the sleeve gun utilized the explosion of a propane-oxygen mixture inside a flexible chamber with the gases vented to the surface, Vaporchoc injected superheated steam into the water, and Maxipulse recorded the bubble oscillation for later processing to remove the bubble effects.

Solution

The phase of a ghost is reversed by reflection at the surface, hence to reinforce the downgoing wavelet the ghost must return to the source at time 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/":): T/2 , where 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/":): \textit{T} is the period measured in Figure 7.8a. Therefore the depth of the source 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/":): d=V_{w} T/4=380 T m, taking 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/":): V_{w} ={} velocity in water 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/":): {}=1500 m/s. The results are shown in Table 7.8a.

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Table of Contents (book)

Also in this chapter

• Radiolocation errors because of velocity variations
• Effect of station angle on location errors
• Transit satellite navigation
• Effective penetration of profiler sources
• Directivity of linear sources
• Sosie method
• Energy from an air-gun array
• Dominant frequencies of marine sources
• Effect of coil inductance on geophone equation
• Streamer feathering due to cross-currents
• Filtering effect of geophones and amplifiers
• Filter effects on waveshape
• Effect of filtering on event picking
• Binary numbers

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