Non-ideal gas airgun wavelet modeling method based on uniform bubble theory

Abstract

The application belongs to the field of marine seismic exploration, and particularly relates to a non-ideal gas air gun wavelet simulation method based on a unified bubble theory, comprising: obtaining sea area environment parameters; designing air gun working parameters and an air gun array; according to the sea area environment parameters, the air gun working parameters and the air gun array, calculating 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; and calculating the pressure signal generated by bubble oscillation at any point in seawater at each moment. The application introduces a non-ideal gas thermodynamic state equation on the basis of a traditional bubble dynamics model, and considers the evolution mechanism of the whole process of bubble generation, expansion, contraction and the like based on the unified bubble theory, so that the sound wave wavelet signal generated by the air gun under the actual working environment is more accurately simulated, and the accuracy and adaptability of wavelet modeling and inversion in seismic exploration are improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of marine seismic exploration, and particularly relates to a non-ideal gas air gun wavelet simulation method based on a unified bubble theory. BACKGROUND

[0002] Air guns are the most commonly used artificial seismic sources in marine seismic exploration, and their working principle is to rapidly release compressed gas under high pressure to form an expanding bubble in water, which in turn excites a low-frequency acoustic signal. Due to the advantages of air gun signals such as wide frequency spectrum, large energy, and good repeatability, air guns are widely used in 2D, 3D, and even 4D seismic exploration. Traditional air gun wavelet simulation methods are mostly based on the ideal gas assumption and classical bubble oscillation theory (such as Gilmore equation, Keller-Miksis equation, etc.), and the acoustic pressure signal is predicted by solving the bubble dynamics equation. Although such models have certain accuracy in describing the basic bubble behavior, they have defects such as ignoring the non-ideal gas effect, not considering the multi-stage expansion process, and limited wavelet simulation precision.

[0003] In order to overcome the above-mentioned deficiencies, in recent years, those skilled in the art have attempted to introduce more complex state equations or multi-bubble interaction mechanisms to improve the precision of bubble oscillation simulation, but there is still a lack of a systematic modeling method that can consider the non-ideal gas thermodynamic behavior, multi-stage bubble evolution mechanism, and multi-force coupling.

[0004] Therefore, it is urgent to develop a new air gun wavelet simulation method based on the unified bubble theory and considering the non-ideal gas behavior to more realistically and accurately describe the bubble dynamics characteristics and improve the fidelity and engineering applicability of wavelet simulation. SUMMARY

[0005] Based on this, the application provides a non-ideal gas air gun wavelet simulation method based on the unified bubble theory, which introduces a non-ideal gas thermodynamic state equation based on the traditional bubble dynamics model, and considers the evolution mechanism of the whole process of bubble generation, expansion, and contraction based on the unified bubble theory, thereby more accurately simulating the acoustic wavelet signal generated by the air gun in the actual working environment and improving the accuracy and adaptability of wavelet modeling and inversion in seismic exploration.

[0006] In a first aspect, the embodiments of the application provide a non-ideal gas air gun wavelet simulation method based on the unified bubble theory, which includes:

[0007] Obtaining sea environment parameters;

[0008] Designing air gun working parameters and air gun array;

[0009] According to the sea environment parameters, the air gun working parameters and the air gun array, 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 are calculated.

[0010] The pressure signal generated by the bubble oscillation at each moment at any point in the seawater is calculated.

[0011] In a possible implementation, 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 are calculated, specifically as follows.

[0012] According to the air gun working parameters and the air gun array, the amount of non-ideal gas in the air gun chamber at each moment is calculated by using the Van der Waals non-ideal gas equation. The amount of non-ideal gas in the air gun chamber at each moment is calculated by using the Van der Waals non-ideal gas equation. The amount of gas in the bubble at each moment is calculated by using the Van der Waals non-ideal gas equation.

[0013] The total simulation time and the simulation time step are set to obtain a time sequence.

[0014] The amount of non-ideal gas in the air gun chamber at each moment is calculated. The calculation formula is as follows.

[0015]

[0016] Wherein, Q represents the amount of non-ideal gas in the air gun chamber at each moment, and R represents the gas release rate at each moment. The amount of gas in the bubble at each moment is calculated. The calculation formula is as follows.

[0017]

[0018]

[0019] The calculation formula is as follows. The change speed of the bubble wall at each moment is calculated.

[0020] The calculation formula is as follows.

[0021] ​​​​​​​​​​​​​​​​​​​

[0022] in, express The rate of change of the bubble wall at any given moment; express The first time derivative of the rate of change of the bubble wall at any given moment;

[0023] Based on air gun operating parameters, , and ,calculate Bubble radius at time Bubble volume Bubble pressure Bubble heat loss rate Gas release rate Bubble volume change rate and bubble temperature change rate ;

[0024] Based on marine environmental parameters, calculations were performed using the unified bubble theory. First time derivative of the rate of change of the bubble wall at any given moment ,Will As the next moment Substitute the rate of change of the bubble wall The calculation formula is used to cycle through the next time step;

[0025] 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 are recorded.

[0026] In one possible implementation, Non-ideal gas volume in the air gun chamber at any given time and The amount of gas inside the bubble at time 1 The calculation formula is:

[0027] ,

[0028] ,

[0029] in, Indicates the working pressure of the chamber; Indicates the volume of the air gun chamber; , Denotes the van der Waals constant; Represents the universal gas constant; Indicates the temperature of the chamber; express Bubble pressure at any given moment; express the bubble volume at the time instant; denotes the bubble temperature at the time instant.

[0030] In one possible implementation, the bubble radius at the time instant The calculation formula is:

[0031] ,

[0032] denotes the bubble radius at the time instant;

[0033] the bubble pressure at the time instant The calculation formula is:

[0034] ,

[0035] wherein, denotes the bubble temperature at the time instant; the bubble volume at the time instant The calculation formula is:

[0036] .

[0037] In one possible implementation, the bubble temperature change rate at the time instant The calculation formula is:

[0038] ,

[0039] wherein, denotes the specific heat capacity at constant pressure; the bubble volume change rate at the time instant The calculation formula is:

[0040] .

[0041] In one possible implementation, the bubble temperature at the time instant The calculation formula is:

[0042] ,

[0043] denotes the bubble temperature at the time instant, denotes the bubble temperature change rate at the time instant.

[0044] In one possible implementation, Bubble heat loss rate at time The calculation formula is:

[0045] ,

[0046] in, Indicates the heat transfer coefficient. Indicates chamber temperature and Bubble temperature at time difference.

[0047] In one possible implementation, Gas release rate at time The calculation formula is:

[0048] ,

[0049] in, Represents the throttling constant. Indicates the volume of the air gun chamber. Indicates the power exponent of throttling. Indicates the working pressure of the chamber. This indicates the air gun's release rate.

[0050] In one possible implementation, First time derivative of the rate of change of the bubble wall at any given moment The calculation formula is:

[0051] ,

[0052] in, Indicates the speed of sound in ocean water. This represents the enthalpy difference of the bubble wall. This represents the derivative of the enthalpy difference of the bubble wall with respect to time.

[0053] enthalpy difference of bubble wall The calculation formula is:

[0054] ,

[0055] This indicates the pressure exerted on the bubble wall; Indicates environmental pressure; Indicates the density of seawater;

[0056] Pressure on the bubble wall The calculation formula is:

[0057] ,

[0058] in, Indicates vapor pressure. denotes the surface tension of seawater, denotes the viscosity of seawater.

[0059] In one possible implementation, at each moment the pressure signal generated by the bubble oscillation at any point in seawater is calculated by the formula:

[0060] ,

[0061] wherein, denotes the density of seawater; denotes the serial number of the air gun; denotes the total number of air guns; denotes the time derivative of the velocity potential at any point in seawater caused by the oscillation of the th air gun at the th moment; denotes the time derivative of the velocity potential at any point in seawater caused by the reflection of the interface by the th air gun at the th moment, denotes the interface reflection path; denotes the velocity of seawater at any point in seawater caused by the oscillation of the th air gun at the th moment; denotes the velocity of seawater at any point in seawater caused by the reflection of the interface by the th air gun at the th moment;

[0062] the calculation formula is:

[0063] ,

[0064] wherein, denotes the position coordinate at any point in seawater, denotes the bubble center position of the th air gun, denotes the bubble radius of the th air gun at the th moment, denotes the sound speed in seawater; denotes the enthalpy difference of the bubble wall; denotes the bubble wall change speed of the th air gun at the th moment;

[0065] the calculation formula is:

[0066] .

[0067] The application proposes a non-ideal gas air gun wavelet simulation method based on a unified bubble theory, aiming to improve the accuracy and applicability of air gun wavelet simulation. The method fully considers the thermodynamic behavior and interaction of bubbles in a non-ideal gas environment, and based on the unified bubble theory, a mathematical model is constructed including the non-ideal gas state equation, heat conduction effect, interaction between bubbles and boundary effect. By numerically solving the model, the bubble oscillation process and the radiation sound pressure field can be accurately simulated, and more realistic and reliable air gun wavelet waveform can be obtained. The application can effectively reflect the collective behavior of the bubble group generated by the air gun array under the condition of non-ideal gas, and is suitable for providing air gun source wavelet simulation for marine geophysical exploration under different pressure, temperature and gas composition environments, which is beneficial to improve the quality and imaging resolution of seismic data.

[0068] Compared with the prior art, the application has the following advantages:

[0069] (1) The application fully considers the limitations of the gas in the air gun chamber and the gas in the bubble under high pressure conditions, which do not conform to the ideal gas state, and accurately describes the state of the gas under high pressure conditions through the Van der Waals non-ideal gas equation.

[0070] (2) The application fully considers the effects of surface tension, viscosity and velocity generated by bubble oscillation in the bubble oscillation process, so that the air gun wavelet simulation is more consistent with the actual excitation of the air gun.

[0071] (3) The application compensates for the limitation of only considering the velocity potential caused by bubble oscillation in the prior art, and quantitatively adds the change of seawater velocity caused by bubble oscillation to the calculation formula of air gun wavelet signal, so that the air gun wavelet signal is consistent with the actual excitation of the air gun, and the low-frequency signal energy is stronger. BRIEF DESCRIPTION OF DRAWINGS

[0072] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiments.

[0073] Figure 1 The flow chart of the non-ideal gas air gun wavelet simulation method based on the unified bubble theory provided by the embodiments of the application is shown in the figure.

[0074] Figure 2 The schematic diagram of the air gun array provided by the embodiments of the application is shown in the figure.

[0075] Figure 3 A gas gun subwave simulation diagram provided by the embodiment of the present application;

[0076] Figure 4 A gas gun subwave spectrum diagram provided by the embodiment of the present application. DETAILED DESCRIPTION

[0077] In order to better understand the technical solutions of the present application, the embodiments of the present application are described in detail below with reference to the drawings.

[0078] It should be clear that the described embodiments are only some of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative labor are within the scope of protection of the present application.

[0079] The terms used in the embodiments of the present application are only for the purpose of describing the specific embodiments, and are not intended to limit the present application. The singular forms "a", "an" and "the" used in the embodiments of the present application and the appended claims are also intended to include the plural forms, unless the context clearly indicates otherwise.

[0080] It should be understood that the term "and / or" used herein is only to describe the association relationship of the associated objects, which means that there can be three relationships, for example, A and / or B, which can represent the three cases of A alone, A and B together, and B alone. In addition, the character " / " in this paper generally represents that the front and rear associated objects are a "or" relationship.

[0081] Reference Figure 1 A flowchart of a non-ideal gas air gun subwave simulation method based on a unified bubble theory provided by the embodiment of the present application. As Figure 1 shown, the method comprises:

[0082] Step S1, obtaining sea area environment parameters.

[0083] Specifically, the environment parameters of the sea area are obtained through marine seismic exploration and related sea area data.

[0084] Further, the sea area environment parameters include water temperature , seawater density , seawater sound speed , seawater depth , seawater surface tension , seawater viscosity , vapor pressure .

[0085] Step S2, designing air gun working parameters and air gun array.

[0086] Further, the air gun working parameters include throttle constant , throttle power index , air gun release rate , heat transfer coefficient .

[0087] Further, the air gun array includes air gun type, air gun number, air gun position relationship, air gun chamber volume , chamber working pressure , chamber temperature .

[0088] Referring to Figure 2 , the air gun array schematic diagram provided by the embodiment of the present application is shown. As Figure 2 shown, the horizontal and vertical coordinates represent the horizontal position of the air gun, a total of thirty-six air guns, respectively using 1-36 serial numbers to identify, every two air guns a group, the serial number is marked with the capacity of the air gun, for example, 1-40 cu. in, indicating that the volume of the No. 1 air gun is 40 cu. in. The air gun array provided by the embodiment of the present application, the working pressure of each air gun chamber is set to 2000 psi, and is located at 5m underwater. Throttle constant , throttle power index , air gun release rate , heat transfer coefficient .

[0089] Step S3, according to the sea environment parameters, air gun working parameters and air gun 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. Specifically:

[0090] 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 air gun chamber at the moment and the amount of gas in the bubble at the moment .

[0091] and The calculation formula is:

[0092] ,

[0093]

[0094] Among them, represents the chamber working pressure; represents the air gun chamber volume; , represents the Van der Waals constant, in this application, , ; represents the universal gas constant; represents the chamber temperature; represents the bubble pressure at time t, which is equal to the sum of the atmospheric pressure and the hydrostatic pressure, i.e. , represents the atmospheric pressure, represents the seawater density, represents the seawater depth, represents the gravitational coefficient; represents the bubble volume at time t, which is equal to the chamber volume, ; represents the bubble temperature at time t, .

[0095] The total simulation time and the simulation time step are set, and the time sequence , , , is obtained. Based on the air gun working parameters, the amount of non-ideal gas in the air gun chamber at time t and the amount of gas in the bubble at time t , the bubble radius at each time t in the time sequence , 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 are calculated in a loop. The calculation formula of the bubble wall change speed at time t

[0096] is:

[0097] ,

[0098] It is worth noting that the bubble wall change speed at time t and the first time derivative of the bubble wall change speed at time t are both 0, i.e. , For the second loop and later, the bubble wall acceleration at time t is calculated from the calculation formula of the bubble wall acceleration at time t , and the calculation of the bubble wall change speed at each time t in the entire time loop is completed.​​ The calculation.

[0099] The bubble radius at time t is The calculation formula of the bubble radius at time t is

[0100] ,

[0101] Wherein, The bubble radius at time t is The bubble wall change speed at time t is The bubble radius at time t is

[0102] It is worth noting that, The bubble radius at time t is The bubble volume at time t is The bubble volume at time t is calculated, that is,

[0103] .

[0104] The bubble volume at time t is The calculation formula of the bubble volume at time t is

[0105] ,

[0106] Wherein, The bubble radius at time t is The bubble volume at time t is

[0107] The updated bubble volume at time t is substituted into the following formula, and the bubble pressure at time t is calculated The calculation formula of the bubble pressure at time t is .

[0108] The calculation formula of the bubble pressure at time t is

[0109] ,

[0110] Wherein, The amount of gas in the bubble at time t is The bubble temperature at time t is The calculation formula of the amount of gas in the bubble at time t is

[0111] The calculation formula of the amount of gas in the bubble at time t is

[0112] ,

[0113] Wherein,​​​​​​​ represents the amount of gas in the bubble at the time t, represents the gas release rate at the time t.

[0114] Notably, the amount of gas in the bubble at the time t has been given in the previous step, is obtained from the calculation formula of the gas release rate .

[0115] the gas release rate at the time t is obtained from the calculation formula:

[0116] ,

[0117] wherein, represents the orifice constant, represents the volume of the airgun chamber, represents the orifice power exponent, represents the chamber working pressure, represents the bubble pressure at the time t, represents the amount of non-ideal gas in the airgun chamber at the time t, represents the amount of gas in the bubble at the time t, represents the airgun release rate.

[0118] the amount of non-ideal gas in the airgun chamber at the time t is obtained from the calculation formula:

[0119] ,

[0120] wherein, represents the amount of non-ideal gas in the airgun chamber at the time t, represents the gas release rate at the time t.

[0121] Notably, the amount of non-ideal gas in the airgun chamber at the time t has been given in the previous step.

[0122] the bubble temperature at the time t is obtained from the calculation formula:

[0123] ,

[0124] wherein, express Bubble temperature at any given time express The rate of change of bubble temperature at time t.

[0125] It is worth noting that, Bubble temperature at time , From the rate of change of bubble temperature The calculation formula is obtained.

[0126] Bubble heat loss rate at time The calculation formula is:

[0127] ,

[0128] in, express Bubble radius at time [time] Indicates the heat transfer coefficient. Indicates chamber temperature and Bubble temperature at time The difference, that is, .

[0129] rate of change of bubble volume at time 1 The calculation formula is:

[0130] ,

[0131] in, express Bubble radius at time [time] express The rate of change of the bubble wall at any given time.

[0132] rate of change of bubble temperature at time The calculation formula is:

[0133] ,

[0134] in, express Bubble radius at time; express The temperature of the bubble at any given moment; express The gas release rate at any given time; Denotes the van der Waals constant. ; express The volume of the bubble at any given time; express The amount of gas inside the bubble at any given time; express Bubble pressure at any given moment; express The rate of change of bubble volume at time t; express The heat loss rate of bubbles at time t; This indicates the specific heat capacity at constant pressure.

[0135] Based on marine environmental parameters, calculations were performed using the unified bubble theory. First time derivative of the rate of change of the bubble wall at any given moment ,Will As the next moment Substitute the rate of change of the bubble wall from the previous steps. The calculation formula is used to cycle through to the next time step.

[0136] First time derivative of the rate of change of the bubble wall at any given moment The calculation formula is:

[0137] ,

[0138] in, express The rate of change of the bubble wall at time t, Indicates the speed of sound in ocean water. This represents the enthalpy difference of the bubble wall. express Bubble radius at time [time] This represents the derivative of the enthalpy difference of the bubble wall with respect to time.

[0139] enthalpy difference of bubble wall The calculation formula is:

[0140] ,

[0141] in, Indicates the speed of sound in ocean water. This indicates the pressure exerted on the bubble wall. It represents environmental pressure, and its value is equal to the sum of atmospheric pressure and hydrostatic pressure; This indicates the density of seawater.

[0142] Pressure on the bubble wall The calculation formula is:

[0143] ,

[0144] in, express Bubble pressure at any given moment Indicates vapor pressure. Indicates the surface tension of seawater. This indicates the viscosity of seawater.

[0145] Step S4: Calculate the pressure signal generated by bubble oscillation at any point in the seawater at each moment.

[0146] Every moment Bubbles oscillate at any point in the seawater Pressure signal generated at the location The calculation formula is:

[0147] ,

[0148] in, Indicates the density of seawater; Indicates the serial number of the air gun; Indicates the total number of air guns; Indicates the first An air gun Any point in the seawater caused by constant turbulence The time derivative of the velocity potential; Indicates the first An air gun Any point in the seawater affected by interface reflection at any moment The time derivative of the velocity potential Indicates the interface reflection path; Indicates the first An air gun Any point in the seawater caused by constant turbulence speed; Indicates the first An air gun Any point in the seawater affected by interface reflection at any moment The speed.

[0149] The calculation formula is:

[0150] ,

[0151] in, Represents the position coordinates of any point in the seawater. Indicates the first The center position of the air bubble in the air gun. express Time of the first The radius of the bubble in an air gun. Indicates the speed of sound in ocean water; This represents the enthalpy difference of the bubble wall; express Time of the first bubble wall velocity of each air gun;

[0152] The calculation formula is:

[0153] .

[0154] Referring to Figure 3 , the air gun subwave simulation diagram provided by the embodiment of the present application. As shown in Figure 3 , according to the air gun array shown in Figure 2 , the pressure signal generated at any point in the seawater caused by the bubble oscillation at each time is calculated by using the non-ideal gas air gun subwave simulation method based on the unified bubble theory provided by the embodiment of the present application, and the air gun subwave simulation diagram is obtained by recording and drawing. Referring to Figure 4 , the air gun subwave spectrum provided by the embodiment of the present application is the air gun subwave spectrum obtained by performing Fourier transform on the air gun subwave simulation diagram obtained in Figure 3 .

[0155] The above is only a specific embodiment of the present application, and any person skilled in the art can easily think of changes or replacements within the technical range disclosed by the present application, which should be covered within the protection range of the present application. The protection range of the present application should be subject to the protection range of the claims.​

Claims

1. A method for simulating a non-ideal gas airgun wavelet based on a unified bubble theory, characterized in that, The method comprises the following steps: acquiring sea area environment parameters; designing air gun working parameters and air gun arrays; calculating, according to the sea area environment parameters, the air gun working parameters and the air gun arrays, a bubble radius, a bubble volume, a bubble pressure, a bubble heat loss rate, a gas release rate, a bubble volume change rate and a bubble temperature change rate at each moment; calculating a pressure signal generated by bubble oscillation at each moment at any point in seawater; the calculation of 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 is specifically as follows: According to the air gun working parameters and the air gun array, the initial amount of the non-ideal gas in the air gun chamber is calculated through the Van der Waals non-ideal gas equation and the initial amount of the gas in the bubble ; Setting the total simulation time and the simulation time step , resulting in a time series , , , ; Computing The amount of non-ideal gas in the airgun chamber at a time instant The formula is: ， wherein represents the amount of non-ideal gas in the airgun chamber at time t, represents the gas release rate at time t; Computing The amount of gas in the bubble at the time The formula is: ， indicates the amount of gas in the bubble at the time instant; Computing The bubble wall velocity at the moment The formula is: ， wherein represents the speed of change of the bubble wall at the time instant; represents the first time derivative of the speed of change of the bubble wall at the time instant; based on the air gun operating parameters, , and , the bubble radius , bubble volume , bubble pressure , bubble heat loss rate , gas release rate , bubble volume change rate , and bubble temperature change rate at the moment are calculated; Based on the sea environment parameters, through the unified bubble theory calculation The first order time derivative of the bubble wall change speed at the moment , the The next moment , the bubble wall change speed The calculation formula is substituted into the next moment cycle; The time series is calculated iteratively bubble radius, bubble volume, bubble pressure, bubble heat loss rate, gas release rate, bubble volume change rate, and bubble temperature change rate at each time point; At each instant The pressure signal generated by the bubble oscillation at any point in the sea water The calculation formula is: ​ ， wherein, denotes the density of the sea water; denotes the number of the air gun; denotes the total number of air guns; denotes the time derivative of the velocity potential at a point in the sea water caused by the excitation of the nth air gun at the time instant t; denotes the time derivative of the velocity potential at a point in the sea water caused by the reflection of the interface for the nth air gun at the time instant t; denotes the path of the reflection of the interface; denotes the velocity at a point in the sea water caused by the excitation of the nth air gun at the time instant t; denotes the velocity at a point in the sea water caused by the reflection of the interface for the nth air gun at the time instant t; ​​​​​​​​​​​​ The calculation formula is: ， wherein, represents the position coordinates of any point in seawater, represents the bubble center position of the thair gun, represents the bubble radius of the thair gun at time t; represents the seawater sound speed; represents the bubble wall enthalpy difference; represents the bubble wall change speed of the thair gun at time t; The calculation formula is: 。 2. The non-ideal gas airgun wavelet modeling method based on the unified bubble theory according to claim 1, characterized in that, Initial amount of non-ideal gas in a gas gun chamber and initial amount of gas in a bubble The formula is: ， ， wherein, represents the chamber working pressure; represents the airgun chamber volume; , represents the van der Waals constant; represents the universal gas constant; represents the chamber temperature; represents the bubble initial pressure; represents the bubble initial volume; represents the bubble initial temperature.

3. The non-ideal gas airgun wavelet modeling method based on the unified bubble theory according to claim 2, characterized in that, Bubble radius at time t The formula is: ， representing the bubble radius at the time instant; Bubble pressure at time The formula is: ， wherein, represents the bubble temperature at the time instant; the bubble volume at the time instant The calculation formula is: 。 4. The non-ideal gas airgun wavelet modeling method based on the unified bubble theory of claim 3, wherein, the rate of change of the bubble temperature over time, The calculation formula is: ， wherein, represents the specific heat capacity at constant pressure; the rate of change of the bubble volume at the time instant The calculation formula is: 。 5. The non-ideal gas airgun wavelet modeling method based on the unified bubble theory of claim 4, wherein, Bubble temperature at time The calculation formula is: ， indicates the bubble temperature at the time, indicates the bubble temperature change rate at the time.

6. The non-ideal gas airgun wavelet modeling method based on the unified bubble theory of claim 1, wherein, Bubble heat loss rate at the moment The calculation formula is: ， wherein, represents the heat transfer coefficient, represents the chamber temperature with the bubble temperature at the moment of the difference.

7. The non-ideal gas airgun wavelet modeling method based on the unified bubble theory of claim 1, wherein, Gas release rate at time The calculation formula is: ， wherein, represents the orifice constant, represents the airgun chamber volume, represents the orifice power exponent, represents the chamber operating pressure, represents the airgun release rate.

8. The non-ideal gas airgun wavelet modeling method based on the unified bubble theory of claim 1, wherein, the first time derivative of the speed of the bubble wall at the moment in time The calculation formula is: ， wherein, denotes the sound speed of seawater, denotes the bubble wall enthalpy difference, denotes the derivative of the bubble wall enthalpy difference with respect to time; Bubble wall enthalpy difference The calculation formula is: ， Pb represents the pressure on the bubble wall; P0 represents the ambient pressure; Pw represents the seawater density; The pressure to which the bubble wall is subjected The calculation formula is: ， wherein, represents the vapor pressure, represents the surface tension of seawater, represents the viscosity of seawater.

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