smith 1975 airgun waveforms

8/2/2019 Smith 1975 Airgun Waveforms

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Geophys. J . R . astr. SOC. 1975) 42, 273-280.

Research NoteMeasurement of Airgun WaveformsS. G. Smith

(Received 1975 January 23)

SummaryAirgun waveforms in the deep sea were measured from 160in3 and300in3 guns with known firing pressure and depth, known geometry ofsource and receiver, and a recording system with known impulse response.The waveforms were compared with waveforms predicted from bubbleoscillation theory and were found to be similar.

IntroductionIt is important to know the shape of airgun waveforms in order to design reflec-tion profiling systems and for synthetic seismic modelling. The use of a waveform insynthetic seismic reflection profiling modelling will be presented in a future paper.

Attempts have been made to measure airgun waveforms (Giles 1968; Ziolkowski1970; Mayne & Quay 1971; Schulze-Gatterman 1972; Giles & Johnston 1973) butthese are not considered to satisfy adequately all the requirements: known impulseresponse of the recording system, adequate depth of water so that bottom reflectionsdo not interfere with primary arrivals, known geometry of gun and receiver, andmeasurement at a sufficient depth to measure the downgoing wave into the sea bed.These effects are considered separately.

1. Impulse response of recording systemAirgun waveforms contain significant energy in the band 2-200 Hz. To record awaveform without distortion a recording system with a flat amplitude and phaseresponse over this band would be needed. This is usually impossible, but if thefrequency response or the impulse response of the system is known accurately theeffect of the recording system on the waveform can be computed.

2. Adequate depth of waterIf an airgun waveform has significant energy up to a time of n s after the initialpulse, then no reflected energy must be received until after n s . For a waveform

duration of 1s the sea bed must be at least 0.75 km below the recording hydrophone.273


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274 S . G . Smith

FIG.1 . The d irect wave, Pd, and the reflected wave, Pr.

3. Known geometry of gun and receiverAn airgun radiates energy in all directions (Ziolkowski 1970) so a receiver recordsa direct wave from the gun and also a wave reflected from the sea surface (Fig. 1).The shape of the waveform recorded depends on the distance travelled by the directwave, Dd , and the distance travelled by the reflected wave, Dr. Fig. 2 is afterZiolkowski (1971) and shows the direct waveform, P d , the reflected waveform, Pr,and P t , the received waveform, which is the sum of Pd and Pr. The relative ampli-tudes of Pd and P r in Pr is given approximately by the ratio:

P d : P r = D r : Ddassuming symmetrical spreading and amplitude inversely proportional to distancetravelled, for small amplitude oscillations. As Dd becomes larger the amplitudes ofPd and P r in P t tend to be equal.4. Measurement at sdiicient depth

I wished to measure airgun waveforms produced by a gun when it is being usedfor deep-sea profiling, in water depths of usually greater than 2km. As the recorded

Pd

Pr

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FIG.2. The measured wave, P t , formed from Pd and Pr.


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Research note 215waveform varies with the geometry of source and receiver it is necessary to have areceiver a t this depth to measure the waveform going into the sea bed. Unfortunatelythe waveform reflected from the sea bed would interfere with the downgoing wavefor a reflector near the sea bed, so this is impossible. In practice it is necessary to usea receiver with at least 0.75 km of water below it (Section 2) and record an approxi-mation t o the deep sea waveform . W hen the receiver is vertically below the gun:

Dr = Dd +2 hwhere h is the g un dep th, a nd when the receiver is sufficiently deep so that Dd B 212

DrDd_ A- - I

so that the amplitude ratio of Pd : Pr 1 in P t and the waveform is a sufficientapproximation to that measured a t depth. Fo r less tha n 5 per cent erro r in Dr/Dd = 1this demands a Dr > 400 m with h = 10m.This waveform cannot be computed by measuring Pd independently from Prand computing P t , by m easuring the waveform near th e gun, where Pd is mu ch greaterthan Pr , because non-linear wave propa gation can occur in the near-field of the gun.

Experimental measurementThe experimental arrangemen t is shown in Fig. 3. A hydrophone (a cylindricallead titanate-zirconate pressure transducer potted in epoxy resin) and a pre-amplifierwere suspended 40 0m below a sonoradio buoy. The hydrophone was weighted tokeep it vertically below the buoy, an d vertical motions of the cable due t o u p an d downmovement of the buoy were damped out by spherical floats attached to the top ofthe cable. This kept the 400 m of cable approximately stationary in the water while

the buoy moved u p and down with the waves. The ship steamed slowly past thebuoy firing a Bolt airgun, passing within 10m of the buoy. G un chamber sizes of

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Hydrophone kIG .3 . The experimental arrangement used for measuring airgun w aveforms.


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278 S. G. Smith


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Research note 279160 in3 and 300 in3 were used. A calibrated pressure transd ucer w as used to con-tinuously monitor the g un depth. Airgun signals were transmitted from the buoy tothe ship, monitored on a jet-pen recorder and recorded on m agnetic tape. This wasrepeated with th e gun a t different depths.The impulse response of the whole recording system from hydrophone to taperecorder was mea sured: a fixed frequency voltage was input in series with the hy dro-phone, passed through the recording system, compared with the input signal, andamplitude and phase shift measured. It was no t possible to define the low amp litudeparts of the frequency response accurately by measurement, so these were calculatedfrom electrical circuit theory (Girling & G oo d 1969). A t higher amplitudes thecalculated response was in agreement with the measured response. The am plitudeand phase spectra for the recording system and the impulse response of the system(the Fourier transform of the frequency spectrum) are shown in Fig. 4. The passband of the system is 4-160 Hz a t - dB level.Results

The results for the 160 in 3 an d 300 in3 guns ar e show n in F igs 5(a) and 6(a).Attempts have been made to predict airgun waveforms from bubble oscillationtheory by Ziolkow ski (1 970) an d Schu lze-Gattermann (1972). Schulze-Gattermanstheory a pplies to small am plitude oscillations, whereas Ziolkowskis allows for finiteamplitude oscillations, so is mo re useful. Ziolkowskis theory was used to comp uteairgun waveforms for the same conditions of cham ber volume, firing pressure, de pthand geometry of gun a nd receiver as the measured waveforms. Dam ping constantsof 2.5 and 1.8 s- l were chosen for the 160 and 300 in3 guns, as this provided th e bestmatch to the measured waveforms. This is in agreement with the damp ing constantof 31*6/JV where V = gun chamber volume in in3 suggested by Ziolkowski (1972,private comm unication). Th e theoretical waveforms ar e shown in Figs 5(b) an d 6(b).These were also convolved with th e impulse response of the recording system an d a reshown in Figs 5(c) an d 6(c), for com parison with the measured waveforms.The general form of the convolved waveforms approximates to the measuredwaveforms, indicating tha t bubble oscillation theory provides an approx imate descrip-tion of airgun waveforms. Th e main difference is tha t the bubble oscillation perioddecreases slightly faster than pre dicted. Ziolkowks i (1970) note d this, an d suggestedthat this was due t o the proximity of the air-water free surface.Acknowledgment

I thank Dr Anton Ziolkowski for his airgun waveform prediction program.Department of Geodesy and Geophysics,University of Cambridge,

Cambridge.Madingley Rise, Madingley Road,

ReferencesGiles, B. F., 1968. Pneu matic acou stic energy source, Geophys. Prospe ct., 16,21-53.Giles, B. F. & Johnston, R. C . , 1973. System approa ch to air-gun array design,Geophys. Prospect., 21 , 77-101.Girling, F. E. J. & Good, E. F., 1969. Ac tive filters, Wireless W orld, 75, 403-408.Mayne, W. H. & Quay, R. G.,1971. Seismic signatures of large air guns, Geophysics,36, 1162-1173.


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280 S. G. SmithSchulze-Gattermann, R., 1972. Physical aspec ts of the Airpulser, Geophys.Prospect.Ziolkowski, An ton , 1970. A method for calculating the o utp ut pressure waveformZiolkowski, An ton , 1971. Design of a m arine seismic reflection profiling system

20, 155-192.from an air gun, Geophys. J . R . astr. SOC.,1, 137-161.using air guns as a sound source, Geophys. J . R. astr. SOC.,3, 499-530.

smith 1975 airgun waveforms

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