WO2020097844A1

WO2020097844A1 - Combined virtual and real depths-based marine wideband air gun seismic sources

Info

Publication number: WO2020097844A1
Application number: PCT/CN2018/115606
Authority: WO
Inventors: 沈洪垒; 陶春辉; 王汉闯; 周建平; 丘磊; 柳云龙
Original assignee: 国家海洋局第二海洋研究所
Priority date: 2018-11-15
Filing date: 2018-11-15
Publication date: 2020-05-22

Abstract

Combined virtual and real depths-based marine wideband air gun seismic sources, comprising a primary seismic source and N-level secondary seismic sources, wherein a first wave of a first-level secondary seismic source in the N-level secondary seismic sources and a ghost wave of the primary seismic source are completely canceled at a far field end; a first wave of a lower-level secondary seismic source and a ghost wave of an upper-level secondary seismic source are completely canceled at the far field end; the secondary seismic sources are equivalent to air gun seismic sources set at a specific virtual depth; at the same time, the primary seismic source and the N-level secondary seismic sources are designed as an air gun array that has a combination of real depths; and the in-phase superposition of the first waves of air guns at different depths in the primary seismic source may be achieved by using a delayed excitation manner. The present invention may effectively improve a low-frequency response while simultaneously compensating frequency-domain notches introduced by the ghost waves of the virtual and real depths, and the design of wideband seismic source wavelets is achieved.

Description

Vibration source of offshore wide-band air gun based on combination of virtual and real depth

Technical field

The invention belongs to the field of air gun seismic source design, in particular to a marine broadband air gun seismic source based on a combination of virtual and real depth.

Background technique

At present, the air source seismic source commonly used at sea is composed of multiple air guns with different capacities at the same depth. The multi-gun simultaneous excitation method is used to achieve the first wave in-phase superposition, and at the same time, due to the difference in capacity, the bubble oscillation period is different to offset the residual bubbles. When the first wave propagates to the surface of the sea, a polarity reversal occurs to form a ghost wave. The existence of ghost waves in the source causes the loss of some specific frequencies in the frequency domain and reduces the resolution of the seismic data, which is called the notch effect. In order to eliminate the notch effect, it is proposed to place the air gun sub-array or single gun at different depths, and use delayed excitation to ensure that the first wave is superimposed in phase, and the delay of the excitation time causes the ghost waves to no longer superimpose in phase, thereby realizing the compensation of the notch. . However, both theoretical and practical observations show that this stereo combination does not improve the response at the ultra-low frequency end (mainly below 7 Hz), which is mainly due to the "neutralization effect" (Hopperstad, dominated by ghost wave trapping and bubble oscillation main frequency). et.al., 2012). The cited literature information is as follows: Hopperstad, J.F., Laws, R., and Kragh, E. 2012. Hypercluster of airguns–more airfrequencies for the same quantity of air. 74th Annual International Meeting, EAGE, Expanded Abstracts, Z011.

The "neutralization effect" that causes the lack of low frequency can be understood from two aspects: 1) After the high-pressure gas is released into the water, it will generate periodic oscillations. The main frequency of oscillation increases with the increase of the depth of the air gun excitation, and the suppression of low-frequency energy changes Strong, as shown in Figure 1; 2) The notch effect introduced by the ghost wave in the frequency domain weakens with increasing depth, and the suppression of low-frequency energy is weakened, as shown in Figure 2. The two effects interact in the far field, and even a change in depth will not cause a change in low-frequency energy, as shown in Figure 3. It can also be seen from Fig. 3 that ghost wave trapping causes the loss of certain frequencies in the middle and high frequencies, which affects the integrity of the spectrum. At the same time, the notch frequency changes with depth, showing a variety of characteristics.

Ni. Et al. (2017) proposed to use auxiliary sources with a smaller capacity than the main source (such as 1/3 of the main source energy) to offset part of the main source ghost wave, which enhanced the low frequency energy to a certain extent. However, due to partial cancellation, the low frequency improvement is very limited, and at the same time, there is no compensation for the low frequency notch introduced thereby and the original mid and high frequency notch. The cited literature information is as follows: Ni, Y., Shen, H., and Elboth, T. 2017. Method and device for boosting low-frequencies for marine seismicity. US2017 / 0276774A1. The present invention realizes complete cancellation of ghost waves based on auxiliary seismic sources Greatly enhance the low-frequency response, combined with the combination of the true depth of the notch diversity, to achieve the design purpose of the broadband air gun source.

Summary of the invention

The purpose of the present invention is to overcome the shortcomings of the prior art. Based on the multi-depth stereo combination, the present invention intends to offset the main source ghost wave by introducing an auxiliary source to break the neutralization effect, improve the low frequency response, and compensate for the mid and high frequency depression Wave, realizing the design of a wideband air gun source in a true sense.

The technical solution of the present invention is as follows:

The marine broadband air gun source based on the combination of virtual and real depth includes: main source and N-level auxiliary source, N≥1; the main source is used to obtain the main excitation signal;

Among the N-level auxiliary source, the first-level auxiliary source is used to excite the first auxiliary excitation signal; the first auxiliary excitation signal and the main excitation signal form the same ghost wave, but the polarity is opposite, the first-level auxiliary source When the excitation time of the main source reaches the first-stage auxiliary source, the first-stage auxiliary source's first wave and the main source's ghost wave completely cancel out in the far field;

The excitation signal of the next-level auxiliary source is the same as the ghost wave formed by the excitation signal of the previous-level auxiliary source, but the polarity is opposite. When the source is in focus, the first wave of the secondary auxiliary source and the ghost wave of the secondary auxiliary source completely cancel out in the far field.

Preferably, the main source and the N-level auxiliary source are multi-depth stereo sources.

Preferably, the main source and the N-level auxiliary source are composed of multi-level air gun units at different depths; each air-level unit includes one or more air guns, and the main source and the N-level auxiliary source have the same number of air gun units .

Preferably, the main source and the N-level auxiliary source have the same air gun type, capacity combination, arrangement depth and depth interval.

The invention also discloses a deep combined excitation method of the offshore broadband air gun seismic source, including the following steps:

1) According to the exploration needs, design and arrange the main source, which is a multi-depth stereo source, and design and arrange the N-level auxiliary source according to the main source, so that the first auxiliary excitation signal and the main excitation signal form the same ghost wave, but The polarities are opposite, the excitation signal of the auxiliary source of the next level and the excitation signal of the auxiliary source of the previous level form the same ghost wave, but the polarities are opposite;

2) According to the depth interval of the three-dimensional source, the delayed excitation method is used to excite the main source, so that the first wave of each air source composed of the main source is superimposed in phase;

3) When the ghost wave of the main source reaches the first-stage auxiliary source, the first-stage auxiliary source is also excited by the delayed excitation method, so that the first wave of the first-stage auxiliary source and the ghost wave of the main source completely cancel out in the far field ; When the ghost wave of the secondary auxiliary source reaches the secondary auxiliary source, excite the secondary auxiliary source in the same way, so that the first wave of the secondary auxiliary source is far from the ghost wave of the secondary auxiliary source The field is completely cancelled until the N-level auxiliary sources are all excited.

In the above method, the auxiliary source is not necessarily the same as the main source (combination mode and placement depth, etc.), when the depth of the two is different, the auxiliary source can be changed, and the main source can be adjusted by adjusting the volume, pressure and multi-gun combination mode. The wave field approximated by the ghost wave of the source can also cancel the ghost wave of the main source. As a preferred embodiment, the N-level auxiliary source is a multi-depth stereo source.

Furthermore, the N-level auxiliary source and the main source are composed of multi-level air gun units at different depths; each air-gun unit includes one or more air guns, the main source and the N-level auxiliary source air gun unit series the same. At this time, the step 3) the delayed excitation mode of the auxiliary source is specifically:

The ghost wave of the main source is composed of ghost waves excited by the airgun units at all levels of the main source. The ghost waves of the airgun units at all levels arrive at the first-stage auxiliary source at different times; In order to completely eliminate the ghost wave generated by the corresponding number of air gun units in the main source; the excitation time of the air gun units of each stage in the first-stage auxiliary source reaches the level of the air gun unit. Moment of

The airgun units at all levels in the next-level auxiliary source are used to completely eliminate ghost waves generated by the corresponding series of airgun units in the previous-level auxiliary source; their excitation time is generated by the corresponding series of airgun units in the previous-level auxiliary source. The moment the ghost wave reaches the airsoft unit of that level.

Further, the main source and the N-level auxiliary source have the same arrangement depth, the same type of air gun, the same volume combination and the same depth interval. In this case, the main source or the N-level auxiliary source have different depths The air gun uses a delayed excitation method, and sets different excitation times t _i according to the depth:

Wherein, t _0, h _s respectively disposed shallowest airgun depth of the main source and in firing time, h _{_i,} t _i is the depth at which the i-th airgun the same source and the corresponding excitation time, c is the sound wave in water Velocity, N is the secondary source level, Sp and Sa represent the main source and auxiliary source respectively.

Compared with the prior art, the beneficial effects of the present invention are:

The present invention introduces the auxiliary source Sa on the basis of the design of the conventional source Sp (main source). When the ghost wave of Sp reaches the depth of Sa, Sa is excited. At this time, the first wave caused by Sa and the ghost pole of Sp On the contrary, when the far field is reached, the two cancel each other, so that the final wavelet of the far field is the superposition of the first wave of the main source and the ghost wave of the auxiliary source. At this time, the first wave corresponds to the depth h when the main source is excited, and the arrival time of the ghost wave relative to the first wave is further delayed, which is similar to the result of the air gun placed at a virtual depth of 2h, thus breaking the same The neutralization effect dominated by depth.

The present invention proposes to introduce a multi-depth stereo source into a virtual depth source design, place different air guns or sub-arrays at different depths, and use the delayed excitation method to realize the in-phase superposition of the first wave of different air guns, while using the trap wave Diversity of frequency changes with depth, so notch compensation can be performed effectively.

The combination of virtual and real depth seismic source of the present invention effectively improves the low frequency response, and at the same time compensates the trap of the horizontal seismic source; it achieves the design purpose of the broadband seismic source wavelet.

BRIEF DESCRIPTION

Figure 1 shows the simulation results of the near-field wavelet when the 250cu.in single gun is excited at different depths. Figure 1 (a) is the time-domain wavelet morphology; Figure 1 (b) is the corresponding spectrum curve.

Fig. 2 is the comparison result of the impulse response of the ghost wave trapping effect under different depth excitation conditions. Fig. 2 (a) is the pulse source wavelet shape; Fig. 2 (b) is the corresponding frequency spectrum, in which the sea surface reflection coefficient is assumed to be -1.

Fig. 3 is the simulation results of the far-field wavelet excited by the 250cu.in single gun at different depths. Fig. 3 (a) is the time-domain wavelet shape; Fig. 3 (b) is the corresponding spectrum curve.

Figure 4 shows the process of virtual depth construction. Fig. 4 (a) is a schematic diagram of the observation system; Fig. 4 (b) is the schematic diagram of the relationship between the excitation time of the main source and auxiliary source and the corresponding ghost wave time.

Figure 5 is a schematic diagram of the working principle of the virtual depth source. Figure 5 (a) is the time-domain pulse wavelet, assuming that the depth of the main source and auxiliary source is 6m; Figure 5 (b) is the corresponding amplitude spectrum.

Figure 6 Amplitude adjustment factor Scalar varies with the number of auxiliary sources and frequency. The calculation results are based on a depth of 6m and a water speed of 1500m / s. n = 0 corresponds to the case where there is only the main source, and there is a suppression effect on the selected frequency signal.

FIG. 7 is a schematic diagram of a virtual depth source based on an inclined air gun mode. In the picture, the main source and auxiliary source are all combined with multiple air guns arranged at an angle.

Figure 8 Schematic diagram of the arrival time of the far-field wavelet of the virtual depth source based on the combination of two layers of depth.

Fig. 9 is a comparison result of virtual depth source amplitude adjustment factors based on the combined mode of horizontal (Fig. 8 (a)) and tilt (Fig. 8 (b)). The depth of the horizontal source is 6m, and the depth of the inclined source is 6-7-8-9-10-11m. Both sources use a combination of 6 shots, and the amplitude adjustment factor Scalar = 1 corresponds to the fidelity signal.

Figure 10 is a comparison of a conventional horizontally tuned gun array and a tilted combination simulated virtual depth source containing an auxiliary source. Figure 9 (a) is the wavelet shape in the time domain, and Figure 9 (b) is the corresponding spectrum curve.

detailed description

The invention will be further described below with reference to the drawings.

In order to break the neutralization effect, the offshore wide-band air gun source based on the combination of virtual and real depth of the present invention includes: a main source and an N-level auxiliary source, N≥1; of the N-level auxiliary sources, the first-level auxiliary source is used for The first auxiliary excitation signal is obtained by excitation; the first auxiliary excitation signal is the same as the main excitation signal. When the ghost wave of the first-stage auxiliary source reaches the first-stage auxiliary source, the excitation time of the first-stage auxiliary source is The first wave completely cancels the ghost wave of the main source; the excitation signal of the next-level auxiliary source is the same as the excitation signal of the previous-level auxiliary source. The excitation time of the next-level auxiliary source is the ghost wave of the previous-level auxiliary source. When the secondary source is of the first level, the first wave of the secondary source of the next level completely cancels the ghost wave of the secondary source of the previous level.

The explanation is as follows with reference to the drawings: the auxiliary source Sa is introduced on the basis of the design of the conventional source Sp (main source), as shown in FIG. 4 (a). When the ghost wave of Sp reaches the depth of Sa, Sa is excited. At this time, the first wave excited by Sa is opposite to the polarity of the Sp ghost wave. When the far field is reached, the two cancel each other, so that the final far field The wave is the superposition of the first wave of the main source and the ghost wave of the auxiliary source, as shown in Figure 4 (b). At this time, the first wave corresponds to the depth h when the main source is excited, and the arrival time of the ghost wave relative to the first wave is further delayed, which is similar to the result of the air gun placed at a virtual depth of 2h, thus breaking the same The neutralization effect dominated by depth. In order to achieve the complete cancellation of Sp ghost waves, the simplest method is to design the auxiliary source to have the same composition and placement depth as the main source.

Figure 5 shows the virtual depth source with pulse wavelet as an example. At this time, the main source and auxiliary source are placed at a depth of 6m. As can be seen from Figure 5 (a), the final ghost wave has twice the time delay , Corresponding to a virtual depth of 12m. Correspondingly in the frequency domain, low-frequency energy will be compensated, as shown in Figure 5 (b). But correspondingly, a notch will be introduced at about 60 Hz.

For only one auxiliary source as shown in Figures 4 and 5, the final far-field wavelet P (t) can be expressed as:

P (t) = P _p (t) -P _p (t + 4h / c) (1)

Where P _p (t) is the first wave of the main pulse, h is the depth of the main source and auxiliary source, and c is the speed of the acoustic wave in the water.

In order to further improve the low-frequency response, more auxiliary sources can be introduced to offset the ghost waves of the auxiliary source of the previous level, so that the final far-field wavelet P (t) is the ghost wave of the main source first wave and the last auxiliary source Overlay result:

P (t) = P _p (t) -P _p (t + 2 (n + 1) h / c) (2)

Where n is the number of auxiliary sources. It can be seen from formula (2) that compared with the first wave, the ghost wave can be regarded as the excitation result corresponding to the depth of (n + 1) * h.

Formula (2) is Fourier transformed into the frequency domain, and the amplitude spectrum is obtained:

P (f) | = Scalar | P _p (f) | (3)

Where P (f) and P _p (f) are the amplitude spectra of P (t) and P _p (t), respectively. The introduction of the auxiliary source to the change of the first wave can be described by the product term amplitude adjustment factor Scalar.

Figure 6 shows how Scalar changes with the number of auxiliary sources n and frequency f. When Scalar> 1, it means that the first wave energy is enhanced, but on the contrary, it is compressed. The ideal situation is that the adjustment factor value of all frequencies is 1, which means that the signal fidelity is high. It can be seen from Fig. 6 that for the low frequency part below 7 Hz, when Sa is less than 5, its energy increases approximately linearly as Sa increases, especially for ultra-low frequency signals, such as the 2 Hz signal in the figure, a sufficient amount of Sa ( Such as 10 in this example) can completely cancel the suppression effect of ghost waves. For frequencies above 7Hz, too much Sa causes the notch frequency to become lower due to the excessive virtual depth, so it shows the characteristics of increasing first and then decreasing. For example, the 15Hz frequency signal is strongly suppressed when n = 7, and the frequency response is even lower than only the main In the case of the source, the phenomenon that the introduction of virtual depth leads to the decrease of the notch frequency is consistent with Fig. 5. For full-waveform inversion, the low-frequency signal is the dominant method, and the mid- and high-frequency notch introduced by this auxiliary source will not cause much impact. However, for high-resolution seismic exploration, since the broadband source is needed to ensure the spectral integrity, Therefore, it is necessary to compensate for the high-frequency notch.

In order to overcome this problem, the present invention proposes to introduce multi-depth stereoscopic sources into the design of virtual depth sources. The notch frequency f _n caused by ghost waves is related to depth and can be expressed as:

Where θ is the incident angle of the wavelet, and θ = 90 ° when it is below the vertical air gun.

By placing different air guns or sub-arrays at different depths, the first wave of different air guns can be in-phase superimposed by using the delayed excitation method, and at the same time, the diversity of the notch frequency with depth is used, so effective notch compensation can be performed. Figure 7 shows a schematic diagram of the virtual depth source based on the tilted air gun combination mode. The left part of Fig. 7 is the conventional inclined air gun source, and the right part of the figure is the auxiliary source. The firing time t _{i of the} air gun can be expressed as:

Among them, h _s and t ₀ are the depth and excitation time of the shallowest main source air gun, respectively, and h _i is the placement depth of the air gun i. The excitation time of each single shot in the auxiliary source is delayed by 2h _s / c than the single shot of the main source placed at the same depth.

Fig. 8 shows the schematic diagram of the excitation time of each air gun in the virtual depth source combined by two layers of depth. It can be seen that the use of real depth combination can destroy the in-phase superposition of ghost waves, and the differentiated ghost wave arrival time breaks the neutralization effect dominated by the same depth.

Similarly, for the case where there are n-level auxiliary sources (with tilted array as the unit), the final far-field wavelet P (t) can be expressed as:

Among them, P _i (t) is the wavelet of the air gun i, and m is the number of main source air guns. It is assumed here that the main source and auxiliary source wavelet shapes are the same, but there is a delay in time. This can be achieved by arranging them in the manner of coherent guns at the same depth (one main source and one auxiliary source air gun, in this case, d ~ = 1m in Figure 7).

Using the same ideas as equations (3) and (4), applying Fourier transform to equation (7) and obtaining its amplitude spectrum at the same time, the amplitude adjustment factor Scalar in the combined mode of tilted air gun can be obtained:

Based on formula (8), the influence of the number of auxiliary sources is simulated, and the results shown in Fig. 9 are obtained. It is assumed here that the main source of the tilt combination is composed of 6 guns and the depth combination is 6-7-8-9-10-11m. The picture on the left is the virtual depth source results based on the horizontal air gun combination mode (depth 6m). It can be clearly seen that as the number of auxiliary sources increases, the low frequency energy is enhanced and the degree of sag is eased, but at the same time, in the same Within the frequency band, the increase in the number of auxiliary sources increases the frequency of notches. For the virtual depth source with tilted air gun combination, the low-frequency improvement effect is equivalent to the horizontal mode. At the same time, thanks to the multi-depth notch diversity, the number of mid- and high-frequency notch waves is significantly lower than that of the conventional horizontal mode. In the dominant frequency band excited by the air gun (such as 10-150 Hz), the second notch will not appear until 4 sets of auxiliary sources are introduced.

Figure 10 compares the horizontal source of the 6-gun combination (250-150-100-80-60-40cu.in tuned gun array), the horizontal source of the 12-gun combination (2 groups of 6-gun tuned gun arrays), and the tilt based on 6-11m The model includes a layer of Sa virtual depth source (250-150-100-80-60-40cu.in sequence combination, depth interval 1m) far-field wavelet morphology and spectrum curve. Compared with the combined source of 6 guns, it can be clearly seen that the virtual depth source effectively improves the low frequency response, and at the same time compensates the notch of the horizontal source at 125 Hz. The design purpose of the broadband source wavelet is realized. Compared with the combination of 12 guns (the total capacity of the air guns used by the two is the same), the virtual source has a slight advantage for low-frequency enhancement capabilities, and can avoid the high pulses caused by the direct accumulation of conventional volumes (the long and dashed lines in Figure 10 (a)). Damage to the environment.

It should be pointed out that the auxiliary source is not necessarily the same as the main source (combination mode and placement depth, etc.). When the two depths are different, the auxiliary source needs to be changed, and the main source can be obtained by adjusting the volume, pressure and multi-gun combination mode. The wave field approximated by the ghost wave of the source can also cancel the ghost wave of the main source.

Claims

A marine broadband air gun seismic source based on a combination of virtual and real depths, characterized by including:

Main source, used to obtain the main excitation signal;

N-level auxiliary source, N≥1;

Among the N-level auxiliary source, the first-level auxiliary source is used to excite the first auxiliary excitation signal; the first auxiliary excitation signal and the main excitation signal form the same ghost wave, but the polarity is opposite, the first-level auxiliary source When the excitation time of the main source reaches the first-stage auxiliary source, the first-stage auxiliary source's first wave and the main source's ghost wave completely cancel out in the far field;

The excitation signal of the next-level auxiliary source is the same as the ghost wave formed by the excitation signal of the previous-level auxiliary source, but the polarity is reversed. The excitation time of the next-level auxiliary source is the ghost wave of the previous-level auxiliary source reaching this level of auxiliary When the source is in focus, the first wave of the secondary auxiliary source and the ghost wave of the secondary auxiliary source completely cancel out in the far field.
The offshore broad-band air gun source based on the combination of virtual and real depth according to claim 1, wherein the main source and the N-level auxiliary source are multi-depth stereo sources.
The offshore broad-band air gun source based on the combination of virtual and real depth according to claim 1 or 2, characterized in that the main source and N-stage auxiliary source are composed of multi-stage air gun units at different depths; The unit includes one or more air guns, and the main source and the N-level auxiliary source have the same series of air gun units.
The offshore broad-band air gun source based on the combination of virtual and real depths according to claim 1 or 2, characterized in that the main source and the N-level auxiliary source have the same air gun type, capacity combination, arrangement depth and depth interval.
A deep combined excitation method based on the offshore broadband air gun seismic source according to claim 1, characterized in that it includes the following steps:

1) According to the exploration needs, design and arrange the main source, which is a multi-depth stereo source, and design and arrange the N-level auxiliary source according to the main source, so that the first auxiliary excitation signal and the main excitation signal form the same ghost wave, but The polarities are opposite, the excitation signal of the auxiliary source of the next level and the excitation signal of the auxiliary source of the previous level form the same ghost wave, but the polarities are opposite;

2) According to the depth interval of the three-dimensional source, the delayed excitation method is used to excite the main source, so that the first wave of each air source composed of the main source is superimposed in phase;

3) When the ghost wave of the main source reaches the first-stage auxiliary source, the first-stage auxiliary source is also excited by the delayed excitation method, so that the first wave of the first-stage auxiliary source and the ghost wave of the main source completely cancel out in the far field ; When the ghost wave of the secondary auxiliary source reaches the secondary auxiliary source, excite the secondary auxiliary source in the same way, so that the first wave of the secondary auxiliary source is far from the ghost wave of the secondary auxiliary source The field is completely cancelled until the N-level auxiliary sources are all excited.
The method according to claim 5, wherein the N-level auxiliary source is a multi-depth stereo source.
The method according to claim 6, characterized in that the N-stage auxiliary source and the main source are composed of multi-stage air gun units at different depths; each air-gun unit includes one or more air guns, the main source and N The number of airgun units in the secondary source is the same.
The method according to claim 7, wherein the step 3) the delayed excitation mode of the auxiliary source is:

The ghost wave of the main source is composed of ghost waves excited by the airgun units at all levels of the main source. The ghost waves of the airgun units at all levels arrive at the first-stage auxiliary source at different times; In order to completely eliminate the ghost wave generated by the corresponding number of air gun units in the main source; the excitation time of the air gun units of each stage in the first-stage auxiliary source reaches the level of the air gun unit. Moment of

The airgun units at all levels in the next-level auxiliary source are used to completely eliminate ghost waves generated by the corresponding series of airgun units in the previous-level auxiliary source; their excitation time is generated by the corresponding series of airgun units in the previous-level auxiliary source. The moment the ghost wave reaches the airsoft unit of that level.
The method according to claim 5, characterized in that the arrangement depth of the main source and the N-stage auxiliary source are the same, the type of the air gun is the same, the capacity combination and the depth interval are the same.
The method according to claim 9, characterized in that the air guns at different depths in the main source or the N-level auxiliary source use a delayed excitation mode and set different excitation times t i according to the depth:

Wherein, t 0, h s respectively disposed shallowest airgun depth of the main source and in firing time, h i, t i is the depth at which the i-th airgun the same source and the corresponding excitation time, c is the sound wave in water Velocity, N is the secondary source level, Sp and Sa are the main source and auxiliary source, respectively.