SCALING OF SOUND SOURCE SIGNATURES IN UNDERWATER SEISMIC EXPLORATION

Abstract: Method of determining the location in the earth of sub-surface boundaries and/or the acoustic properties of sub-surface features substantially in the absence of the far field source wavelet and noise and with errors due to reflections of sound waves from the water being substantially compensated for. The invention uses point sound sources or arrays thereof at a first depth and then scales the energy, pressure and spacing of a similar source at a second depth to provide data which is used to obtain a seismic record.

Description: SCALING OF SOUND SOURCE SIGNATURES IN UNDERWATER SEISMIC EXPLORATION This Invention relates to the scaling of sound source sig¬ natures in underwater (e.g. marine) seismic exploration. The present Invention extends and mproves the Inventions described and claimed n British Patent Appl cations 8013438 (Serial No 2048481) and 8013437 (Serial No. 2048480) In the name of Antonl Marj ' an Z1olkowsk1. The present Application relates 1n particular to sound sources having the special feature of controllable Initial firing pressure, e.g. air guns, which 1s necessary for the utilization of this Invention. In copendlng Application Serial no. GB 2048481, the contents of which are ncorporated herein by reference, It 1s proposed that the seismic method be applied twice 1n each place, with both the shot and receiver positions unchanged, but with the second shot a scaled version of the first shot. In the two received selsmograms x,(t) and x 2 (t), the earth Impulse response g(t) Is the same, because the positions of shot and receiver are unchanged. However, the two source signatures s,(t) and s«(t) are different and are shown to be related to each other by a source scaling law. Thus there are three unknown quantities S j (t), S ( ) and g(t) which are related by the three equations: OMPI WIPO SU 1 1 1 '-J> » > ■ £ x χ (t) = s 1 (t) * g(t) (1) x 2 (t) = s 2 (t) τ*g(t) (2) x 2 (tϊ - As^t/ct) (3) where the asterisk denotes convolution and the scale factor iX 1s defined as the relation r_ Energy In source 2 1/3 = (4) Energy In source ij Equations (1) and (2) neglect noise. These equations may be solved to obtain s^ft), s t) and g(t) from the measurements x.(t) and x 2 (t), by a robust method described In the above Appli¬ cation, which method Is stable In the presence of noise. 2 -3J-3 a i i I* i ----- OMPΓ The point of the Invention of that ADoHcatlon 1s that previous technology was able to provide only one equation, l rfce equatFoπ (lj contaFning two unknowns. There has always been a chronic problem of determining g(t) precisely in the absence of accurate FnformatFon a tout Sj (t). Repeating the experi¬ ment, as the Application GB 2048481 proposes, would not mafe sense without the additional information provided by the seal ng law, equatFon (3l- For thfs scaling lav/ to apply, the only parameter which can 5~e changed Fs- the m 's-Fze of the point source. For example, Ff explosFves are used at sea, the chemical composition must be the same for source 1 and source 2; the depths below the sea surface mus ~ t also 5e the same; only the sizes are different and a re. related 5y Q (thus the mass of the second explosive ^ o tFmes the mass of the first) . If s t r guns a re used, their volumes must differ by a factor σ(. 3 , but the depths and firing pressures must be the same. [π the second application, GB 2048480, the idea was extended to two-dimen ional arrays of point sources, with a t r gun arrays as an example. It was proposed that each point source element Fπ one scaled a r ray be simply a scaled version of the corresponding element in the other array. That is, the ratio of the energies of the corresponding elements of a r ray 2 to array 1 is o (obeying equation 4). The dimensions of the two arrays correspondingly scale by a factor o< " > thus the horizontal dimensions of array 2 are £>. times those of array 1. No other parameters are changed. The depths are the same; and the pres-sures- (of aFr gunsj or cfie-πFcal composFtions (of explo- s-tves-I are the -rame. Fn thes-e condftFons equatFon (3) relates the w aves s,(tl and s, (tl whFch would Be generated at a given distance and Fn a gFven dFrectFon from the two scaled arrays. ThFs- Fs- fully explained Fn applfcatFon No. GB 2048480,. the conten+s of which are Incorporated herein " by reference. Ϋτo5 } ems''"cvF ' f fi~ the Two ' P rev Tous App 1 i ca t i ons There are two problems with the solutions of previous applications which both concern the "ghost reflection" from the sea surface. ^P^oblB .The ' "ofKϊSt reflectFon" Fs the reflectFon of the sound wave by the surface. fn the case of a marine seismic source the s-ea acts 1 FKe a Frror with a reflectFon coefficient of almost exactly -1. (t has- the effect of creating a virtual seismic source whose sound wave Fs of opposite polarFty to the real source, as shown in FFgure 1. The sound wave which reaches the point Q. ts the sum of Eoth waves: the direct wave from the source and the reflected wave or "ghost" which appears to originate from the virtual source. It is convenient to think of the wave generated by any source as the sum of its own direct wave and its ghost reflection. In our conception of the seis ogram described by equations (l) and (2) we have treated this ghost reflection as separate from the source wavelet s . ( or s 2 (t) . We have treated Ft as belongFng to g( j- Thus, when we take out s-(t) from equation (lj we fFnd g(tj whFch Fncludes this ghost. Similarly when we take out s 2 (tj from equation (2) we find another estimate of g(tL which includes this ghost. Thus we have .created a situation fn wh . Fch g(t), as we have defined Ft, Fs riot the Fmpulse response of the earth, But the response to- two impulses in two different places. The first Fmpulse occurs at the position of the source at time t = 0. The second one occurs a t the same time but appears to come from the 'virtual source and has opposite polarity. In order to find the true Fmpulse response we must remove this second "ghost response" which Is very inconvenient- It would be much more convenient if the s, (t) in equation (l) and the s-ft) Fn equation (2) represented the ful 1 wave, including the ghost- This cannot be the case, with the existing applications, because the ghost does not scale. We may see this with reference to Figures 1 and 2. Figure 2 shows the direct wave s(t) and its "ghost" -s(t - t,) arriving at the point Q. The sum of these two waves is P (t) = s(t) - s(t - t,) , (5) where the time delay t, = 2D cos θ , (6) SUBSTITUTE and the minus- sign occurs because the sea surface has a reflection coefficient of almost exactly -1- When we have two different sources at the same depth, the direct waves s-|(t) and s^(t) scale, as in equation (3), but the ghost delay t, does not change and therefore the sum of the direct wave plus the ghost does not scale- This is illustrated in Figure 3- Prohlem 2 We have been discussing the source and its virtual image, or ghost, as Ff they were almost independent- Of course the ghost is totally dependent on the source and the surface, as we know. However, the source Fs not enti rely independent of i s own ghost: there Fs a kFnd of feed-back effect which is not completely negligFBle. In the case of an air gun, for example, the sound wave Is generated by the oscFllatFons of e bubble produced by the guπ- eferrFng to Figure k , we see that there is a pressure difference 6-etween the Fnside of the bubble and the pressure outside, that is-, hydrostatic pressure. Initially the internal pressure is typical ly about 135 atmospheres, whereas hydrostatic pressure is about 2 atmospheres- The bubble therefore rapFdfy expands against the water, overshoots the equilibrium position at which the inter¬ nal and external pressure are equal, slows down and then stops - The bubble has now reached its maximum size and the internal pressure fs less than hydrostatic pressure- The pressure dif¬ ference now acts inwards. The bubble collapses, and the collapse is halted only by the rapid build-up of pressure inside the bubble. OMPI .-=--~-** ** -» ' At this point the oscillation is ready to begin again. It is these bubble oscillations, pushing the water around, which are the source of the sound waves (in much the same way as loudspeakers are effective sound sources by their ability to push air around). Now the ghost reflectionis a pressure wave which travels past the oscillating bubble. It is a pressure disturbance superimposed on ambient pressure. That is, it adds a dynamic .term P α (t) to the static pressure in the water P„. The water pressure at the bubble is thus not constant, it varies with time as: where Pw,(t) is the total pressure in the water at time t, P„ is the hydrostatic pressure and P (t) is the dynamic term due to the ghost reflection. In normal operation P (t) is small compared with P-,, so ? w (t) is fairly constant. Nevertheless the effect does exist and is not negligible. In the case where we have scaled air guns - either point sources or arrays - P., will be the same for both. However, since P (t) is the reflection of the wave generated by the source, it will be different for scaled sound sources and therefore Pw(t) is different for scaled- sound sources. It follows that the dynamics of the bubble oscillations will be different for the scaled sources, and the scaling law, equation (3) will not be obeyed exactly. The present invention has as its object the partial or complete solution to both these problems. SUBS I UTE 3 "* H '■ ' E ■"" & l■ f oMPi /., WIPO Present Invention The essence of the present Invention 1s to scale the depth of source 2 such that 1t 1s equal o<Λ. times the depth of source 1, where o ( 1s the time scale factor desired for signature scaling (see equation(3)), whilst maintaining essentially the same dynamical properties of the scaled source at the scaled depth. According to the present Invention there Is provided a method of determining the location In the earth of sub-surface boundaries and/or the acoustic properties of sub-surface features 1n the earth, which method Includes a) employing at a selected location and at a predetermined depth 1n water a first sound source to generate a first sound wave having elastic radiation of predetermined energy and at a predetermined Initial pressure, and, subsequently, employing a second sound source of the same type as- sad first sound source at the same location but at a second and different predetermined depth In water to generate a second sound wave having elastic radiation of a second and different predetermined energy and at a second and different predetermined initial pressure, the depths, energies and initial pressures being selected such that the energy of the elastic radiation emitted by the second source is greater by a factor o 3. / i 2 than that emitted by the first source and that the frequency spectra of the respective sound waves overlap, that the depth D p of the second source is greater by a factor °^ than the depth D^ of the first source, and that the initial pressure P« of the sound wave emitted by the second source is rel ated to that P-- of the sound wave emi tted by the first source by the equation : P 2 - fl /Z CP j + P H i β 1/Z - D ] . wherein P-, represents the hydrostatic pressure at the "l first source, P„ represents hydrostatic pressure at the second H 2 source, and b) detecting by means of one or more receivers, reflections from within the earth of the sound waves to generate respective first and second seismic signals and c) subjecting these signals to analysis and comparison to derive the impulse response of the earth substantially 1n the absence of the far field source wavelet and noise and with errors due to reflections of the sound wave from the water surface being substantially compensated for. The first and the second sound sources can each be point sound sources or can each be an array of mutually interacting point sound sources. In the latter case the array forming the second source should contain the same number and type of point sound sources as that of the first source, and in the same spatial relationship although the spacing between individual point sound sources of the array of the second source should be scaled by the factor oC with respect to the corresponding spacing of the array of the first source. The point sound sources of an array should all lie at a common depth. Suitable values for 0< and β are from 1.1 to 3, preferably from 1.5 to 3. OMPI u sUW It is generally necessary that the initial firing pressure of the guns be adjustable in order that the pressure rel tionships defined hereinbefore are satisfied; the use of air guns as the point sound sources is accordingly preferred although other sources the initial pressure of which is adjustable may be used. In the case of an air gun source, there are two par rr-etsrs which car. be varied once the depth has been fixed: the initial internal pressure, or firing pressure, and the gun vcl πe. No , the cur. olume does not affect the dynamics tc any large extent. In fact, as we have described, whenever the vol -r-e is varied and the depth and pressure are -r.air-tair.ed constant, the- sound wave maintains the sa-e shape apart from the scaling described by equation 3, in which e is equal to the c- jr>a root of the vol τe ratio. This scaling is a si-pie expression cf the constant dynamics of the oscillating bubble, with the scale factor relaring only to the size cf the bubble and not to the dynamics. There is a small voiu.τ.e- -: pendenr feedback effect due to the ghost, as described above (under Prc-rlem 2), which affects the dynamics slightly. 3ut it is otherwise true that the volume has no effect on the bubble dynamics. Apari from the feedback effect, the bubble dynaτιics depend only cn the depth and internal pressure. Once the depth has been fixed, he internal pressure is the only para m eter which can be varied to cc-pensate for the varying conditions. As described above, it is the pressure difference acr ss th= ~ • >->..-: OMPT WIPO ■ ■ *»> ' ^ oscillations and consequent radiated sound wave. Thus the internal pressure of the bubble must be scaled appropriately to the change in hydrostatic pressure if the dynamics are to be maintained. It can be shown by a rigorous analysis of the dynamics of the oscillating bubbles, that scaling can be achieved for arrays of air guns including the interaction between guns, and between guns and their ghosts, provided the following assumptions are made : (1) Each bubble produced by an air gun must be small compared with the wavelength of sound generated. This is an experimental fact for airguns operating under normal conditions. (2) The fraction of the total available energy which is converted into seismic waves is the same for any two scaled sources. This is exactly the same assumption as that required by application no. GB 2048481. The condition which must be satisfied in order to achieve source scaling is that the ghost interaction must scale. Under these con¬ ditions we can achieve exact scaling for point sources and arrays of point sources. We explain first the point source scaling, and then the array scaling. Point source scaling (Air Guns) Consider an air gun of volume V initial firing pressure P., and depth D_. • Ke wish to fire a gun of certain volume V_ at the depth D-, with initial pressure P_ such that the sound wave generated by the second gun and its ghost is a scaled version of the sound wave generated by the first gun and its ghost. The time scale factor α must be the same as the depth ratio. Thus =- α (8) The hydrostatic pressures at the two guns are 'H, + p g D, (9) ' H-. = P n + P g D, (10) where P is atmospheric pressure, p is the density of water and g is the acceleration due to gravity. We let the ratio of hydrostatic pressures be β : and note that, since D_ and D, are related by equation (8), β is not independent of a . Exact scaling occurs if both the volume and initial firing pressure rations are chosen properly. Assume that the scaled sources can each be thought of as a notional spherical oscillating bubble, at depths D-, and σ ϋ- respectively, with hydrostatic pressures P H and $?■■ (Equ 11) respectively and with internal and external pressures P,(t), P-(c t) and Pw.(t), P 2 ( < *-t) respectively. When these two notional bubbles obey the same dimensionless equation of motion their radii are related as: H 2 (c-t) = a s^ R ( t ) (12) 2-~refcre. when t = 0, we know R 2 (0; = fe 5* " j ,( ). (13) i Ci- * -.-ce- the b ;;*bl--- v"-—- v •*;.- , • - ■ - V = ^ 3 r. .? , (14) : i fol-vs t hat t he ra t io of the initial vrl re of , e two P , t ,-.. al -•=•=> _s : 2 . 1.11 — = a' &~ fc . (15) BAD ORIGINAL . S<2*vi ' .*«- ,'-' - . * i * * , *_> J * 14 T.--3 pressure differences across z ' walls cf z ' r.s scaled ab ies are relate bv ecuaticn (16) : ?2 ( t; - S 2 ' - ( ■ 5. Crj] (16) :-sn = 0, ?- Q) - P s τ r= (0) - ?. (17) or: 5 2 [? -.L(0 -.. t u (18] We can simply transfer the relations obtained from the linear notional bubble to the nonlinear real bubble. That is, the ratio of depths and hydrostatic pressures remain as for the linear bubble, but so do the ratios of initial bubbl e volumes, equation (15) and pressures, equation (17). y-l CMP ϊ Under the relationships of equations (15) and (17,' the wavefield generated by the second gun is scaled version of the wavefield cenerate-d by the first gun. -sexer: ≤igr-al ? (t) received at a point Q j at coorcir. Lon (r, 9; φ relative to gun, is related to the signal ? Λ (t 1 received :ns corresooncinα point Q. at coordinate position (cr, θ , G' ) relative to the second gun. The. relationship between ? (t) and ? Λ (t) B P α (t) (19) z If the distance r is large compared with the dimensions of the source and its ghost - that is, if r is laroe compared with 2D. » 2D (20) ϊhace of the sound wave dees not Λi n increasing distar. e . 3 t , because the v.-avef ent ar tne wave --rcpacates fu r.er r rom :ne :urcε , .1 . ** = c -—. ■ .- - • _ ■ J 1- r -.''.-:----- e cecreases in¬ versely crccort cr-al to the distance r . Tne re-io in which thiϊ ■ iterion is sat sriec is where "the source " in this case consists cf the air gun and its BAD ORIGINAL O PΓ . 7-. »..ή£ET ghost considered as a unit. When this far field condition is satisfied we may write P Q (t) - s l (θ< *• *-§> (21) and Po (a ) . ) (22) 3r s 2 (θ< * > βt c where c is the speed of sound and the θ and φ specify the direction of the signal as shown in Figure (5). Putting delayed time τ _= (23) * - c we find the scaling law for the far field radiation of our depth- scaled point sources as: s 2 (θ, φ, ax) oβs 1 (θ, φ, τ) (24) Or, more simply, in a given direction from our sources, defined by the angles θ and φ, the far field signatures at a given distance are related by the equation s 2 (ατ ) αSs j ^τ ) or ( 25) This scaling law is very similar to the one used for the point source scaling. The only difference is the factor β which arises from the need to maintain the dynamics of the oscillations of the bubbles the same at different hydrostatic pressures. The factor β is the ratio of the hydrostatic pressures. Array scaling Consider an array of n air guns such that the ith gun in the array has volume V.. initial firing pressure P. and coordinates (x. , y. , 2. ). as shown in Figure 6. The depth coordinate is referred to the water surface and, for scaling to be possible, must be the same for all guns in the array. Thus 2-_ = z 2 = z 3 = . . . = z n = Z (26) The guns in the array may fire at different preselected times t i » t 2 ' ( 27) Of course, when the guns have been designated to fire simultaneously the firing times are equal : = t- = t but this is not a necessary condition for scaling). S We now wisfv to create a scaled air gun array such that the wavefield generated by this array and its ghost is a scaled version of the wavefield generated by the first array and its ghost. There are interactions between the guns in an array in exactly the same way as there is interaction, or feedback, between a single air gun and its own ghost. Tb ensure scaling of the interactions we must scale the dimensions of the array. If we use a subscript s to denote the scaled array and choose α as our time stretch factor, as before, we find the coordinates of the ith gun of the scaled array are (x s ' y s ' z s } ' where i i i αx i = <*! (28) CtZ. = αz 1 The hydrostatic pressure at each gun in the scaled array is: = P + ct p g z = β P, (29) " H P p g z (30) Scaling of the elements in the array follows from the rules for scaling of single air guns: The volumes of the n guns in the scaled array are: O..ΪPI - R t 2 a" ,3/2 V i = i. 2, ( 31 ) The initial firing pzsss' sss are: βf [P, + P H (B 2 - 1)] i = 1 (32) and the firing times of the guns are Figure 7 shows how the arrays might look in practice. As in application no. G3204S4S0 the arrays could be towed one behind the other and separated by a distance D equal to a multiple of the receiver group interval, such that receiver positions for the second, scaled array are the same as for the first array. It is also possible to use more than one first array and mere than one second scaled array, providing the arrays are not so close as to interact with each other. If interaction occurs between any two such first arrays, they should be treated as a single array, and the seconc scaled array designed according to the-criteria described above. OMPI /., WIIFFOO If more than one non-i nteracting arrays is empl oyed, then the same number of arrays should be empl oyed for both the second and fi rst sound source, with each of those of the second source being scal ed as described hereinbefore, rel ative to the corresponding arrays of the first sound source. The arrays may be fired simul tane¬ ously to produce the desired sound waves or they may be fired one after the other and the seismic signal s which are generated then summed to produce the desired seismic signal . A combination of consecutive and simul taneous firings may al so be empl oyed . Once the arrays are built, usage is exactly as described in the two previous applications, G3 2043431 and GS 2048430, except that the scaling law contains the extra dept -dependent scale factor 3 : s 2 (τ ) , a. s s 1 (f/β) " (35) The-importance of this whole scaling law method lies in two factors. First, it is not: necessary to mae any about the phase spectrum of s^t ) cr _= 2 (t) cr to assume anything about the statistical properties of the earth impulse response g(t) Secondly, it is not necessary even to measure s. (t) or s,Ct) provided the sources are scaled correctlv. Ihe earth i-r-cuis-** * response may be calculated in any ■-<.:-_..■ * /-.*ITdirectly from the data collected from the two independent shot records and the scaling law. As in the copending Applications, it is to be understood that the elastic energy will normally be detected and measured as particle v el ocites or sound pressures using respectively any suitable geophone or a hydrophone. - ' i > U i l ζsri

Claims: CLAIMS 1. A method of determining the l ocation in the earth of sub-surface boundaries and/or the acoustic properties of sub-surface features 1n the earth, which method incl udes a) empl oying at a sel ected l ocation and at a predetermined depth in water a first sound source to generate a first sound wave hav ing el astic radiation of predetermined energy and at a pre¬ determined initial pressure, and, subsequently, empl oying a second sound source of the same type as said first sound source at the same l ocation but at a second and different predetermined depth in water to generate a second sound wave having el astic radiation of a second and di fferent predetermined energy and at a second and different predetermined initial pressure, the depths, energies and initial pressures being sel ected such that the energy of the el astic radiation emitted by the second source is greater by a factor c . 3 . β V 1 than that emitted by the first source and that the frequency spectra of the respective sound waves overl ap, that the depth D~ of the second source is greater by a factor < than the depth D, of the first source, and that the initial pressure P« of the sound wave emi tted by the second source is rel ated to that P, of the sound wave emitted by the first source by the equation : P 2 = fi [P 1 + P H β UZ " 1 )] ' wherein P H represents the hydrostatic pressure at the first source, P u represents hydrostatic pressure at the second M 2 source, and D fi - b) detecting by means of one or more receivers, reflections from within the earth of the sound waves to generate respective first and second seismic signals and c) subjecting these signals to analysis and comparison to derive the impulse response of the earth substantially in the absence of the far field source wavelet and noise and with errors due to reflections of the sound wave from the water surface being substantially compensated for. 2. A method according to claim 1, wherein said first and second sound sources each constitutes a point sound source. 3. A method according to claim 1 wherein said first and second sources each comprises an array of mutually interacting point sound sources, said array of the second source containing the same number and type of point sound sources as the array of the first source and in the same spatial relationship, the spacing between individual point sound sources of the array of the second source being scaled by a factored with respect to the corresponding point sound sources of the array of the-first source, and the firing times for the point sound sources of the first source being scaled by the factoro with respect to the corresponding SUBSTITUTE Sl-JώST point sound sources of the second source, all of the point sound sources in a said array being at a common depth. 4. A method according to cl aim 3, wherein a first pl ural ity of non-interacting arrays i s empl oyed as the first source, the seismic signal s derived from each array being summed to generate said first seismic signal and wherein the same number of non- interacting arrays, each scal ed rel ative to the corresponding arrays of said first pl ural ity of arrays, i s empl oyed as the second source, the seismic signal s derived from each array being summed to generate said second seismic signal . 5. A method according to cl aim 3, wherein a first pl ural ity of non-interacting arrays is empl oyed as the first source and is fired simul taneously to produce said first sound wave, and wherein the same number of non-interacting arrays, each scal ed rel ative to the corresponding arrays of said first pl ural ity of arrays, is employed as the second source and the said second arrays are fired simul taneously to produce said second sound wave. 6. A method according to cl aim 1, wherein each point sound source comprises an air gun. 7. A method according to cl aim 3, wherein each point sound source comprises an air gun. OMPI W WIIPPOO 8. A method according to claim 3, wherein a plurality of spaced receivers is employed and wherein said arrays are towed through the water one behind the other, at a separation which is equal to a multiple of the receiver group interval, such that receiver positions for the second scaled array are the same as for the first array. 9. A method according to claim 1, wherein c. has a value of from 1.1 to 3. 10. A method according to claim 9, wherein σ has a value of from 1.5 to 3. 11. A method according to claim 1, wherein β has a value of from 1.1 to 3. 12. A method according to claim 11, wherein β has a value of from 1.5 to 3. 13. A method according to claim 1, which produces a seismogram of the Impulse response of the earth. 14. A seismogram of the impulse response of the earth when obtained by the method of claim 13. SUBSTITUTE SHEET

Inventors: ZIOLKOWSKI ANTONI MARJAN, ZIOLKOWSKI, ANTONI, MARJAN
Applicants: BRITOIL PLC
Application year: 1983
Main classification: G01V1
IPC codes: G01V1, G06F13