Unified bubble theory-based non-ideal gas gun wavelet simulation method

Abstract

The invention belongs to the field of marine seismic exploration, and particularly relates to a non-ideal gas gun wavelet simulation method based on a unified bubble theory, which comprises the following steps: acquiring sea environment parameters; designing air gun working parameters and an air gun array; calculating the bubble radius, the bubble volume, the bubble pressure, the bubble heat loss rate, the gas release rate, the bubble volume change rate and the bubble temperature change rate at each moment according to the sea area environment parameters, the air gun working parameters and the air gun array; and calculating a pressure signal generated at any point in the seawater by bubble oscillation at each moment. According to the method, a non-ideal gas thermodynamic state equation is introduced on the basis of a traditional bubble dynamic model, and an evolution mechanism of the whole process of generation, expansion, contraction and the like of bubbles is considered in a unified manner on the basis of a unified bubble theory, so that sound wave wavelet signals generated by an air gun in an actual working environment are simulated more accurately; and the accuracy and adaptability of neutron wave modeling and inversion in seismic exploration are improved.

Description

Technical Field

[0001] The invention belongs to the field of marine seismic exploration, and in particular relates to a non-ideal gas airgun wavelet simulation method based on unified bubble theory. Background Art

[0002] Airguns, the most commonly used artificial seismic sources in marine seismic exploration, operate by rapidly releasing compressed gas under high pressure, forming expanding bubbles in the water, which in turn stimulate low-frequency acoustic signals. Airgun signals are widely used in two-dimensional, three-dimensional, and even four-dimensional seismic exploration due to their wide spectrum, high energy, and good repeatability. Traditional airgun wavelet simulation methods are mostly based on the ideal gas assumption and classical bubble oscillation theory (such as the Gilmore equation and the Keller-Miksis equation). These methods predict the acoustic pressure signal by solving bubble dynamics equations. While these models have a certain degree of accuracy in describing basic bubble behavior, they suffer from shortcomings such as neglecting non-ideal gas effects, failing to uniformly consider the multi-stage expansion process, and limited wavelet simulation accuracy.

[0003] To overcome the above shortcomings, technicians in this field have tried to introduce more complex state equations or multi-bubble interaction mechanisms in recent years to improve the accuracy of bubble oscillation simulation. However, there is still a lack of a systematic modeling method that can uniformly consider the thermodynamic behavior of non-ideal gases, multi-stage bubble evolution mechanisms and multi-force coupling.

[0004] Therefore, it is urgent to develop a new airgun wavelet simulation method based on unified bubble theory that can take into account non-ideal gas behavior and is oriented towards practical application needs, so as to describe the bubble dynamic characteristics more realistically and accurately and improve the fidelity and engineering applicability of wavelet simulation. Summary of the Invention

[0005] Based on this, the present invention proposes a non-ideal gas airgun wavelet simulation method based on the unified bubble theory. The non-ideal gas thermodynamic state equation is introduced on the basis of the traditional bubble dynamics model, and the evolution mechanism of the entire process of bubble generation, expansion, and contraction is uniformly considered based on the unified bubble theory, so as to more accurately simulate the acoustic wavelet signal generated by the airgun in the actual working environment, and improve the accuracy and adaptability of wavelet modeling and inversion in seismic exploration.

[0006] In a first aspect, the embodiments of the present application provide a non-ideal gas airgun wavelet simulation method based on unified bubble theory, including: Obtain sea area environmental parameters; Design airgun operating parameters and airgun arrays; According to the sea environment parameters, airgun operating parameters and airgun array, the bubble radius, bubble volume, bubble pressure, bubble heat loss rate, gas release rate, bubble volume change rate and bubble temperature change rate at each moment are calculated; Calculate the pressure signal generated by the bubble oscillation at any point in the seawater at each moment.

[0007] In one possible implementation, the bubble radius, bubble volume, bubble pressure, bubble heat loss rate, gas release rate, bubble volume change rate, and bubble temperature change rate at each moment are calculated as follows: According to the airgun operating parameters and airgun array, the van der Waals non-ideal gas equation is used to calculate The amount of non-ideal gas in the airgun chamber at time and The amount of gas in the bubble at the time ; Set the total simulation time and simulation time step , and get the time series , , , ; calculate The amount of non-ideal gas in the airgun chamber at time , the calculation formula is: , in, express The amount of non-ideal gas in the airgun chamber at time , express Gas release rate at the time; calculate The amount of gas in the bubble at the time , the calculation formula is: , express The amount of gas in the bubble at that moment; calculate The bubble wall change speed at the moment , the calculation formula is: , in, express The velocity of the bubble wall change at each moment; express The first time derivative of the velocity of the bubble wall at time ; Based on the airgun working parameters, 、 and ,calculate Bubble radius at the moment , bubble volume , bubble pressure , bubble heat loss rate , gas release rate , bubble volume change rate and bubble temperature change rate ; Based on the marine environmental parameters, the unified bubble theory is used to calculate The first time derivative of the bubble wall velocity at time ,Will As the next moment , substitute the bubble wall velocity The calculation formula is repeated for the next moment; Repeat the above steps to calculate the time series The bubble radius, bubble volume, bubble pressure, bubble heat loss rate, gas release rate, bubble volume change rate and bubble temperature change rate at each moment.

[0008] In one possible implementation, The amount of non-ideal gas in the airgun chamber at time and The amount of gas in the bubble at the time The calculation formula is: , , in, Indicates chamber working pressure; Indicates the volume of the airgun chamber; 、 represents the van der Waals constant; represents the universal gas constant; represents the chamber temperature; express Bubble pressure at the moment; express The volume of the bubble at the moment; express The bubble temperature at the moment.

[0009] In one possible implementation, Bubble radius at the moment The calculation formula is: , express The bubble radius at the moment; Bubble pressure at the moment The calculation formula is: , in, express Bubble temperature at the moment; Bubble volume at the moment The calculation formula is: .

[0010] In one possible implementation, Bubble temperature change rate at time The calculation formula is: , in, represents the specific heat capacity at constant pressure; Bubble volume change rate at time The calculation formula is: .

[0011] In one possible implementation, Bubble temperature at the moment The calculation formula is: , express The bubble temperature at the moment, express The rate of change of bubble temperature at time t.

[0012] In one possible implementation, Bubble heat loss rate at time The calculation formula is: , in, represents the heat transfer coefficient, Indicates chamber temperature and Bubble temperature at the moment difference.

[0013] In one possible implementation, Gas release rate at time The calculation formula is: , in, represents the throttling constant, represents the volume of the airgun chamber, represents the throttling power exponent, Indicates the chamber working pressure, Indicates the airgun release rate.

[0014] In one possible implementation, The first time derivative of the bubble wall velocity at time The calculation formula is: , in, represents the speed of sound in seawater, represents the bubble wall enthalpy difference, represents the time differential of the bubble wall enthalpy difference; Bubble wall enthalpy difference The calculation formula is: , Indicates the pressure on the bubble wall; Indicates environmental pressure; Indicates the density of seawater; Pressure on the bubble wall The calculation formula is: , in, represents the vapor pressure, represents the surface tension of seawater, Indicates the viscosity of seawater.

[0015] In one possible implementation, at each moment The bubble oscillation at any point in the sea water The pressure signal generated at The calculation formula is: , in, Indicates the density of seawater; Indicates the serial number of the air gun; Indicates the total number of airguns; Indicates the An air gun Any point in the sea water caused by constant agitation The time derivative of the velocity potential; Indicates the An air gun Any point in the seawater caused by interface reflection at any moment The time derivative of the velocity potential, represents the interface reflection path; Indicates the An air gun Any point in the sea water caused by constant agitation speed; Indicates the An air gun Any point in the seawater caused by interface reflection at any moment speed; The calculation formula is: , in, Represents the position coordinates of any point in the sea water, Indicates the The center position of the bubble of the air gun, express Moment The bubble radius of the airgun, represents the speed of sound in seawater; represents the bubble wall enthalpy difference; express Moment The bubble wall change speed of each air gun; The calculation formula is: .

[0016] The present invention proposes a non-ideal gas airgun wavelet simulation method based on the unified bubble theory, aiming to improve the accuracy and applicability of airgun wavelet simulation. This method fully considers the thermodynamic behavior and interaction of bubbles in a non-ideal gas environment, and constructs a mathematical model based on the unified bubble theory that includes the non-ideal gas state equation, heat conduction effect, interaction between bubbles and boundary effects. By numerically solving the model, the bubble oscillation process and the radiation sound pressure field can be accurately simulated to obtain a more realistic and reliable airgun wavelet waveform. The present invention can effectively reflect the collective behavior of the bubble group generated by the airgun array under non-ideal gas conditions, and is suitable for providing airgun source wavelet simulation for marine geophysical exploration under different pressure, temperature and gas composition environments, which is beneficial to improving the quality of seismic data and imaging resolution.

[0017] Compared with the prior art, the present invention has the following beneficial effects: (1) The present invention fully considers the limitation that the gas in the airgun chamber and the gas in the bubble do not conform to the ideal gas state under the high pressure condition of the airgun, and accurately describes the gas state under high pressure conditions through the van der Waals non-ideal gas equation.

[0018] (2) The present invention fully considers the effects of factors such as surface tension, viscosity and the speed of bubble oscillation in the bubble oscillation process, so that the airgun sub-wave simulation is more consistent with the actual excitation situation of the airgun.

[0019] (3) In the calculation of the airgun sub-wave signal, the present invention makes up for the limitation of the existing technology that only considers the velocity potential caused by bubble agitation. The change in seawater velocity caused by bubble oscillation is quantitatively added to the calculation formula of the airgun sub-wave signal, so that the low-frequency signal energy of the airgun sub-wave signal is stronger under the actual excitation condition of the airgun. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0021] Figure 1 A flow chart of a non-ideal gas airgun wavelet simulation method based on unified bubble theory provided in an embodiment of the present invention; Figure 2 A schematic diagram of an air gun array provided in an embodiment of the present invention; Figure 3 An airgun wavelet simulation diagram provided by an embodiment of the present invention; Figure 4 This is a sub-wave spectrum diagram of an air gun provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0022] In order to better understand the technical solution of the present application, the embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0023] It should be understood that the embodiments described are only a portion of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0024] The terms used in the embodiments of the present application are for the purpose of describing specific embodiments only and are not intended to limit the present application. The singular forms "a", "an", "the" and "the" used in the embodiments of the present application and the appended claims are also intended to include plural forms unless the context clearly indicates otherwise.

[0025] It should be understood that the term "and / or" as used herein simply describes a relationship between associated objects, indicating that three possible relationships exist. For example, "A and / or B" can represent: A alone, A and B together, or B alone. Furthermore, the character " / " in this document generally indicates an "or" relationship between the associated objects.

[0026] See also Figure 1 , which is a flow chart of the non-ideal gas airgun wavelet simulation method based on the unified bubble theory provided by the embodiment of the present invention. Figure 1 As shown, the method includes: Step S1, obtaining sea area environmental parameters.

[0027] Specifically, the environmental parameters of the sea area are obtained through marine seismic exploration and related sea area data.

[0028] Furthermore, the sea environment parameters include water temperature , seawater density , seawater sound speed , seawater depth , surface tension of seawater , seawater viscosity , vapor pressure .

[0029] Step S2, designing airgun operating parameters and airgun array.

[0030] Furthermore, the air gun operating parameters include the throttling constant , throttling power index , airgun release rate , heat transfer coefficient .

[0031] Furthermore, the airgun array includes airgun type, airgun quantity, airgun position relationship, airgun chamber volume, , chamber working pressure , chamber temperature .

[0032] See also Figure 2 , is a schematic diagram of an air gun array provided by an embodiment of the present invention. Figure 2 As shown, the horizontal and vertical axes represent the horizontal position of the air guns. There are a total of 36 air guns, which are numbered 1-36, with two air guns in a group. The capacity of the air gun is marked after the number. Taking 1-40cu.in as an example, it means that the volume of air gun No. 1 is 40cu.in. In the air gun array provided by the embodiment of the present invention, the working pressure of each air gun chamber is set to 2000psi, and all are located 5m underwater. Throttle constant , throttling power index , airgun release rate , heat transfer coefficient .

[0033] Step S3, based on the sea environment parameters, airgun operating parameters and airgun array, calculate the bubble radius, bubble volume, bubble pressure, bubble heat loss rate, gas release rate, bubble volume change rate and bubble temperature change rate at each moment. Specifically: According to the air gun array, the van der Waals non-ideal gas equation is used to calculate The amount of non-ideal gas in the airgun chamber at time and The amount of gas in the bubble at the time .

[0034] and The calculation formula is: ,

[0035] in, Indicates chamber working pressure; Indicates the volume of the airgun chamber; 、 represents the van der Waals constant. In this application, , ; represents the universal gas constant; represents the chamber temperature; express The bubble pressure at the moment is equal to the sum of atmospheric pressure and hydrostatic pressure, that is, , represents atmospheric pressure, represents the density of seawater, Indicates the depth of seawater. represents the gravity coefficient; express The volume of the bubble at the moment is equal to the volume of the airgun chamber, ; express The bubble temperature at the moment, .

[0036] Set the total simulation time and simulation time step , and get the time series , , , Based on the air gun working parameters, The amount of non-ideal gas in the airgun chamber at time and The amount of gas in the bubble at the time , loop calculation time series Each Bubble radius at the moment , bubble volume , bubble pressure , bubble heat loss rate , gas release rate , bubble volume change rate and bubble temperature change rate .

[0037] The bubble wall change speed at the moment The calculation formula is: , It is worth noting that The bubble wall change speed and The first-order time derivative of the bubble wall velocity at the moment is 0, that is, , For the second cycle and beyond, The acceleration of the bubble wall is given by the following steps: The calculation formula is calculated to complete the entire time cycle. calculate.

[0038] Bubble radius at the moment The calculation formula is: , in, express The bubble radius at the moment, express The bubble wall change speed at each moment.

[0039] It is worth noting that Bubble radius at the moment Depend on Bubble volume at the moment Calculation, that is: .

[0040] Bubble volume at the moment The calculation formula is: , in, express The bubble radius at that moment.

[0041] Will update Bubble volume at the moment Substituting into the following formula, we can get Bubble pressure at the moment .

[0042] Bubble pressure at the moment The calculation formula is: , in, express The amount of gas in the bubble at the time, express The bubble temperature at the moment.

[0043] The amount of gas in the bubble at the time The calculation formula is: , in, express The amount of gas in the bubble at that moment; express Gas release rate at time.

[0044] It is worth noting that The amount of gas in the bubble at the time It has been calculated in the previous step. Gas release rate The calculation formula is obtained.

[0045] Gas release rate at time The calculation formula is: , in, represents the throttling constant, represents the volume of the airgun chamber, represents the throttling power exponent, Indicates the chamber working pressure, express Bubble pressure at the moment, express The amount of non-ideal gas in the airgun chamber at time , express The amount of gas in the bubble at the time, Indicates the airgun release rate.

[0046] The amount of non-ideal gas in the airgun chamber at time The calculation formula is: , in, express The amount of non-ideal gas in the airgun chamber at time , express Gas release rate at time.

[0047] It is worth noting that The amount of non-ideal gas in the airgun chamber at time It has been calculated in the previous step.

[0048] Bubble temperature at the moment The calculation formula is: , in, express The bubble temperature at the moment, express The rate of change of bubble temperature at time t.

[0049] It is worth noting that Bubble temperature at the moment , The bubble temperature change rate The calculation formula is obtained.

[0050] Bubble heat loss rate at time The calculation formula is: , in, express The bubble radius at the moment, represents the heat transfer coefficient, Indicates chamber temperature and Bubble temperature at the moment The difference, that is, .

[0051] Bubble volume change rate at time The calculation formula is: , in, express The bubble radius at the moment, express The bubble wall change speed at each moment.

[0052] Bubble temperature change rate at time The calculation formula is: , in, express The bubble radius at the moment; express Bubble temperature at the moment; express Gas release rate at the time; represents the van der Waals constant, ; express The volume of the bubble at the moment; express The amount of gas in the bubble at any moment; express Bubble pressure at the moment; express The rate of change of bubble volume at the moment; express Bubble heat loss rate at the moment; It represents the specific heat capacity at constant pressure.

[0053] Based on the sea environment parameters, the unified bubble theory is used to calculate The first time derivative of the bubble wall velocity at time ,Will As the next moment , substitute the bubble wall velocity in the previous step The calculation formula is used to cycle for the next moment.

[0054] The first time derivative of the bubble wall velocity at time The calculation formula is: , in, express The bubble wall change speed at the moment, represents the speed of sound in seawater, represents the bubble wall enthalpy difference, express The bubble radius at the moment, represents the time derivative of the bubble wall enthalpy difference.

[0055] Bubble wall enthalpy difference The calculation formula is: , in, represents the speed of sound in seawater, The pressure on the bubble wall is Indicates the ambient pressure, which is equal to the sum of atmospheric pressure and hydrostatic pressure; Represents the density of seawater.

[0056] Pressure on the bubble wall The calculation formula is: , in, express Bubble pressure at the moment, represents the vapor pressure, represents the surface tension of seawater, Indicates the viscosity of seawater.

[0057] Step S4, calculating the pressure signal generated by the bubble oscillation at any point in the seawater at each moment.

[0058] Every moment The bubble oscillation at any point in the sea water The pressure signal generated at The calculation formula is: , in, Indicates the density of seawater; Indicates the serial number of the air gun; Indicates the total number of airguns; Indicates the An air gun Any point in the sea water caused by constant agitation The time derivative of the velocity potential; Indicates the An air gun Any point in the seawater caused by interface reflection at any moment The time derivative of the velocity potential, represents the interface reflection path; Indicates the An air gun Any point in the sea water caused by constant agitation speed; Indicates the An air gun Any point in the seawater caused by interface reflection at any moment speed.

[0059] The calculation formula is: , in, Represents the position coordinates of any point in the sea water, Indicates the The center position of the bubble of the air gun, express Moment The bubble radius of the airgun, represents the speed of sound in seawater; represents the bubble wall enthalpy difference; express Moment The bubble wall change speed of each air gun; The calculation formula is: .

[0060] See also Figure 3 , is a simulation diagram of the airgun wavelet provided by an embodiment of the present invention. Figure 3 As shown, according to Figure 2The airgun array shown in the figure uses the non-ideal gas airgun wavelet simulation method based on the unified bubble theory provided by the embodiment of the present invention to calculate the Any point in the seawater caused by bubble oscillation The pressure signal generated at the point is recorded and plotted to obtain the simulated airgun wavelet diagram. Figure 4 , the airgun wavelet spectrum provided by the embodiment of the present invention is Figure 3 The obtained airgun wavelet simulation diagram is Fourier transformed to obtain the airgun wavelet spectrum.

[0061] The above description is merely a specific embodiment of the present invention. Any modifications or substitutions that may be readily conceived by a person skilled in the art within the technical scope disclosed herein are intended to be encompassed within the scope of protection of the present invention. The scope of protection of the present invention shall be determined by the scope of protection of the claims.

Claims

1. A non-ideal gas airgun wavelet simulation method based on unified bubble theory, characterized in that: include: Obtain sea area environmental parameters; Design airgun operating parameters and airgun arrays; According to the sea environment parameters, airgun operating parameters and airgun array, the bubble radius, bubble volume, bubble pressure, bubble heat loss rate, gas release rate, bubble volume change rate and bubble temperature change rate at each moment are calculated; Calculate the pressure signal generated by the bubble oscillation at any point in the seawater at each moment.

2. The non-ideal gas airgun wavelet simulation method based on unified bubble theory according to claim 1 is characterized in that: Calculate the bubble radius, bubble volume, bubble pressure, bubble heat loss rate, gas release rate, bubble volume change rate, and bubble temperature change rate at each moment, specifically: According to the airgun operating parameters and airgun array, the van der Waals non-ideal gas equation is used to calculate The amount of non-ideal gas in the airgun chamber at time and The amount of gas in the bubble at the time ; Set the total simulation time and simulation time step , and get the time series , , , ; calculate The amount of non-ideal gas in the airgun chamber at time , the calculation formula is: ， in, express The amount of non-ideal gas in the airgun chamber at time , express Gas release rate at the time; calculate The amount of gas in the bubble at the time , the calculation formula is: ， express The amount of gas in the bubble at that moment; calculate The bubble wall change speed at the moment , the calculation formula is: ， in, express The velocity of the bubble wall change at each moment; express The first time derivative of the velocity of the bubble wall at time ; Based on the airgun working parameters, 、 and ,calculate Bubble radius at the moment , bubble volume , bubble pressure , bubble heat loss rate , gas release rate , bubble volume change rate and bubble temperature change rate ; Based on the marine environmental parameters, the unified bubble theory is used to calculate The first time derivative of the bubble wall velocity at time ,Will As the next moment , substitute the bubble wall velocity The calculation formula is repeated for the next moment; Repeat the above steps to calculate the time series The bubble radius, bubble volume, bubble pressure, bubble heat loss rate, gas release rate, bubble volume change rate and bubble temperature change rate at each moment.

3. The non-ideal gas airgun wavelet simulation method based on unified bubble theory according to claim 2 is characterized in that: The amount of non-ideal gas in the airgun chamber at time and The amount of gas in the bubble at the time The calculation formula is: ， ， in, Indicates chamber working pressure; Indicates the volume of the airgun chamber; 、 represents the van der Waals constant; represents the universal gas constant; represents the chamber temperature; express Bubble pressure at the moment; express The volume of the bubble at the moment; express The bubble temperature at the moment.

4. The non-ideal gas airgun wavelet simulation method based on unified bubble theory according to claim 3 is characterized in that: Bubble radius at the moment The calculation formula is: ， express The bubble radius at the moment; Bubble pressure at the moment The calculation formula is: ， in, express Bubble temperature at the moment; Bubble volume at the moment The calculation formula is: 。 5. The non-ideal gas airgun wavelet simulation method based on unified bubble theory according to claim 4 is characterized in that: Bubble temperature change rate at time The calculation formula is: ， in, represents the specific heat capacity at constant pressure; Bubble volume change rate at time The calculation formula is: 。 6. The non-ideal gas airgun wavelet simulation method based on unified bubble theory according to claim 5 is characterized in that: Bubble temperature at the moment The calculation formula is: ， express The bubble temperature at the moment, express The rate of change of bubble temperature at time t.

7. The non-ideal gas airgun wavelet simulation method based on unified bubble theory according to claim 2 is characterized in that: Bubble heat loss rate at time The calculation formula is: ， in, represents the heat transfer coefficient, Indicates chamber temperature and Bubble temperature at the moment difference.

8. The non-ideal gas airgun wavelet simulation method based on unified bubble theory according to claim 2 is characterized in that: Gas release rate at time The calculation formula is: ， in, represents the throttling constant, Indicates the volume of the airgun chamber, represents the throttling power exponent, Indicates the chamber working pressure, Indicates the airgun release rate.

9. The non-ideal gas airgun wavelet simulation method based on unified bubble theory according to claim 2, characterized in that: The first time derivative of the bubble wall velocity at time The calculation formula is: ， in, represents the speed of sound in seawater, represents the bubble wall enthalpy difference, represents the time differential of the bubble wall enthalpy difference; Bubble wall enthalpy difference The calculation formula is: ， Indicates the pressure on the bubble wall; Indicates environmental pressure; Indicates the density of seawater; Pressure on the bubble wall The calculation formula is: ， in, represents the vapor pressure, represents the surface tension of seawater, Indicates the viscosity of seawater.

10. The non-ideal gas airgun wavelet simulation method based on unified bubble theory according to claim 1, characterized in that: Every moment The bubble oscillation at any point in the sea water The pressure signal generated at The calculation formula is: ， in, Indicates the density of seawater; Indicates the serial number of the air gun; Indicates the total number of airguns; Indicates the An air gun Any point in the sea water caused by constant agitation The time derivative of the velocity potential; Indicates the An air gun Any point in the seawater caused by interface reflection at any moment The time derivative of the velocity potential, represents the interface reflection path; Indicates the An air gun Any point in the sea water caused by constant agitation speed; Indicates the An air gun Any point in the seawater caused by interface reflection at any moment speed; The calculation formula is: ， in, Represents the position coordinates of any point in the sea water, Indicates the The center position of the bubble of the air gun, express Moment The bubble radius of the airgun, represents the speed of sound in seawater; represents the bubble wall enthalpy difference; express Moment The bubble wall change speed of each air gun; The calculation formula is: 。

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