Fluid-porous solid interface seismic source excitation sound wave reflection coefficient analysis method

Abstract

The invention discloses a fluid-porous solid interface seismic source excitation sound wave reflection coefficient analysis method. The method comprises the steps of 1, deducing general forms of potential functions of point seismic source excitation fast and slow longitudinal waves and transverse waves in a porous solid medium; step 2, deducing an equation relationship among potential functions of incident sound waves, reflected sound waves, transmission fast and slow longitudinal waves and transmission transverse waves excited by the point seismic source by utilizing fluid-porous solid boundary conditions and a relationship between displacement and displacement potential and a relationship between stress and strain; 3, solving incident and reflected sound wave displacement fields of a fluid medium at the fluid-porous solid seabed interface excited by the point seismic source; and step 4, deriving an analytic equation of the point seismic source excitation sound wave reflection coefficient at the fluid-porous solid seabed interface. The method can accurately describe the fluid-porous solid seabed interface point seismic source excitation sound wave reflection characteristics, and is of great significance to seabed sound field simulation, underwater target detection and seabed resource exploration.

Description

Technical Field

[0001] The invention relates to the field of marine geophysical technology, and in particular to a method for analyzing the reflection coefficient of acoustic waves excited by a seismic source at a fluid-porous solid interface. Background Art

[0002] About 71% of the earth's surface is covered by the ocean, so it is particularly important to study the reflection characteristics of the seabed acoustic field. The point source hypothesis in the ocean is relatively common. For example, surface ships and underwater ships are relatively large-scale, and air guns used in the exploration of seabed oil, gas, combustible ice, minerals and other resources can all be considered point sources. Studying the acoustic wave reflection coefficient and acoustic wave reflection characteristics of the fluid-porous solid seabed interface excitation point source is of great significance to improving the accuracy of seabed acoustic field simulation, geoacoustic inversion, and underwater target detection. In the field of marine geophysics, the plane wave reflection coefficient of the fluid-porous solid seabed interface has been deeply studied (Stolland Kan, 1981; Santos et al., 1992; Denneman et al., 2002; Madeo and Gavrilyuk, 2010; Lyu et al., 2014; Yang et al., 2023), and has been widely used in geoacoustic inversion to improve the accuracy of seabed acoustic field simulation and underwater target detection. However, under very low frequency and short distance conditions, the plane wave reflection coefficient encounters some fundamental difficulties, making it difficult to accurately characterize the acoustic field and acoustic wave reflection characteristics of the fluid-porous solid seabed interface, limiting the accuracy of geoacoustic inversion, seabed acoustic field simulation and underwater target detection.

[0003] At present, there is no technical solution in the existing technology to realize the analysis of the acoustic wave reflection coefficient of the fluid-porous solid seabed interface excited by a point seismic source. It is urgent to propose a method for analyzing the acoustic wave reflection coefficient of the fluid-porous solid seabed interface excited by a point seismic source, so as to realize the simulation of the acoustic wave reflection characteristics and acoustic field modeling of the fluid-porous solid seabed interface. Summary of the invention

[0004] In view of the problems existing in the prior art, the purpose of the present invention is to provide a method for analyzing the reflection coefficient of sound waves excited by point seismic sources at the interface between fluid and porous solid seabed, which can characterize the reflection characteristics of sound waves excited by point seismic sources at the interface between fluid and porous solid seabed, and help improve the accuracy of seabed wave field modeling, geoacoustic parameter inversion and underwater target detection.

[0005] To achieve the above object, the technical solution adopted by the present invention is: a method for analyzing the reflection coefficient of acoustic waves excited by a source at a fluid-porous solid interface, comprising the following steps: Step 1: Establish the relationship between displacement and body force vector and potential function through Helmholtz decomposition theory, substitute the displacement and body force vector represented by the potential function into the displacement equation of porous solid medium, perform spatial Fourier transform on it, and obtain the integral equation of spherical acoustic wave displacement potential in the wave number domain. Apply the residue theorem to derive the general form of the potential function of fast and slow longitudinal and transverse waves excited by a midpoint source in porous solid medium; Step 2: Using the fluid-porous solid boundary conditions and the relationship between displacement and displacement potential, stress and strain, derive the equation relationship between the potential functions of the incident sound wave, reflected sound wave, transmitted fast and slow longitudinal wave, and transmitted shear wave excited by the point source; Step 3: Solve the incident and reflected acoustic wave displacement fields of the fluid medium at the fluid-porous solid seafloor interface excited by the point source; Step 4: Derive the analytical equation for the acoustic wave reflection coefficient excited by a point source at the fluid-porous solid seafloor interface.

[0006] In the above-mentioned method for analyzing the reflection coefficient of acoustic waves excited by a seismic source at the interface of fluid-porous solid, step 1 includes the solid displacement potential function and the pore fluid relative to the solid displacement potential function.

[0007] The above-mentioned method for analyzing the reflection coefficient of acoustic waves excited by a source at a fluid-porous solid interface, step 1 comprises: Step 1-1: Apply the Helmholtz decomposition theory to obtain the displacement vector of the solid skeleton , the displacement of the pore fluid relative to the solid skeleton , the body force acting on the volume material , the body force acting on the fluid term ,in, represents the gradient, represents the curl, represents the solid displacement longitudinal wave potential function, represents the solid displacement shear wave potential function, represents the longitudinal wave potential function of the fluid relative to the solid displacement, represents the shear wave potential function of the fluid relative to the solid displacement, The longitudinal wave potential function representing the body force acting on the volume material, is the shear wave potential function representing the body force acting on the volume material, represents the longitudinal wave potential function of the body force acting on the fluid term, The shear wave potential function representing the body force acting on the fluid term; Step 1-2: Construct the displacement equation of porous solid media, expressed as: , in represents partial differential, represents the second-order differential, t Indicates time, , represents the porosity, represents the density of the bulk material, represents the density of the pore fluid, represents the density of solid particles, , represents the fluid viscosity coefficient, represents the rock permeability coefficient, , S represents the structure factor, , , represents the second Lamé parameter, represents the first Lamé parameter of the dry rock skeleton, The first Lamé parameter representing the fluid rock, α is the biot coefficient, , , K S represents the bulk modulus of solid particles, K fl represents the bulk modulus of the fluid, K dry represents the bulk modulus of the dry rock skeleton, represents the divergence, represents the Laplace operator; Step 1-3: Substitute the potential function in step 1-1 into the displacement equation of the porous solid medium to obtain, Longitudinal wave potential function: , Shear wave potential function: , in F p , f p , F s and f s is a constant, i represents the imaginary unit, represents the angular frequency, yes , , and The spatial Dirac's delta function, x represents the position vector; Step 1-4: f p and f sSet it to 0, perform Fourier transform on the longitudinal wave potential function and the transverse wave potential function, and get a transformation function: , in , , v p1 Indicates the fast longitudinal wave velocity of porous solid media, v p2 represents the slow longitudinal wave velocity of porous solid media, v s represents the shear wave velocity of porous solid media; Step 1-5: Perform inverse Fourier transform on the formula in step 1-4 and use the residue theorem to obtain The displacement potential of a spherical transmission fast longitudinal wave of a solid skeleton is expressed as ,in, , represents the 0th order Bessel function, r Indicates the horizontal distance between the source and the receiver point. z represents the ordinate of the detection point, and represents the horizontal and vertical slowness in porous media, represents the zero-order Bessel function; The displacement potential of the spherical transmission slow longitudinal wave of the solid skeleton is expressed as, ,in, ; The displacement potential of the spherical transmission shear wave of the solid skeleton is expressed as ,in, , ; The spherical transmission fast longitudinal wave displacement potential of the pore fluid relative to the solid phase is expressed as ,in, , ; The spherical transmission slow longitudinal wave displacement potential of the pore fluid relative to the solid phase is expressed as ,in, , ; The spherical transmission shear wave displacement potential of the pore fluid relative to the solid phase is expressed as ,in, , ; The displacement potential of a spherical incident longitudinal wave in a fluid medium is expressed as ,in, , , represents the plane wave incident angle, v p represents the speed of sound waves, hIndicates the vertical distance between the earthquake source and the reflection interface; The displacement potential of a spherical reflected longitudinal wave in a fluid medium is expressed as ,in Indicates the intensity of longitudinal waves reflected from the spherical surface.

[0008] In the above-mentioned method for analyzing the reflection coefficient of acoustic waves excited by a source at a fluid-porous solid interface, step 2 comprises: Step 2-1: Use the continuity boundary condition of the fluid entering and exiting the solid skeleton in the z direction ,in, , and represent the displacements of seawater, solid and pore fluid in the z direction, respectively; Step 2-2: Using the continuity boundary condition for normal stress ,in, represents the fluid pressure, represents the fluid density, , , ; Step 2-3: Using the Continuity Boundary Condition for Fluid Pressure ,in, ; Step 2-4: Using the boundary condition of zero shear stress ,in, represents the shear stress on the solid skeleton, ; Step 2-5: Combine the above four boundary conditions to establish: ,in , It represents the plane acoustic wave reflection coefficient of the fluid-porous solid seafloor interface without considering the point source.

[0009] In the above-mentioned method for analyzing the reflection coefficient of acoustic waves excited by a source at the interface of fluid-porous solid, step 3 comprises: The displacement field of the incident acoustic wave of the fluid medium at the fluid-porous solid seafloor interface excited by a point source is: ,in is the incident angle of the acoustic wave excited by the point source; The displacement field of the reflected acoustic wave of the fluid medium at the interface between the fluid and porous solid seabed excited by a point source is: .

[0010] In the above-mentioned method for analyzing the reflection coefficient of acoustic waves excited by a source at the interface of fluid-porous solid, step 4 comprises: Step 4-1: Define the acoustic wave reflection coefficient equation of the fluid-porous solid seafloor interface excited by a point source as the ratio of the reflected acoustic wave excited by the point source to the incident acoustic wave; Step 4-2: The analytical equation for the acoustic wave reflection coefficient excited by a point source at the fluid-porous solid seafloor interface can be expressed as: , in, represents the first-order Bessel function, .

[0011] The beneficial effect of the analytical method of the reflection coefficient of sound waves excited by a source at a fluid-porous solid interface of the present invention is that: compared with the prior art, the present invention takes into account the wavefront propagation and reflection theory of spherical waves at the fluid-porous solid seafloor interface, and can accurately characterize the reflection characteristics of sound waves excited by a point source at the fluid-porous solid seafloor interface. Under low-frequency point source excitation conditions, near shallow seas, and environments where the bottom buoy / hydrophone is close to the seafloor, there are certain errors in the plane wave theory, and it is impossible to accurately describe and characterize the underwater reflected sound field. The reflection coefficient of sound waves excited by a source at a fluid-porous solid interface of the present invention can accurately describe the underwater reflected sound field under the above environment, which is of great significance to improving the accuracy of seafloor sound field simulation, underwater target detection, and seafloor resource exploration. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 This is a schematic diagram of the overall process in an embodiment of the present invention; Figure 2 It is a first schematic diagram of the spherical wave reflection coefficient of the seabed fluid-porous solid interface calculated in the embodiment; Figure 3 It is a second schematic diagram of the spherical wave reflection coefficient of the seabed fluid-porous solid interface calculated in the embodiment. DETAILED DESCRIPTION

[0013] In order to facilitate the understanding of the present invention, the present invention is described in more detail below in conjunction with the accompanying drawings and specific embodiments. However, the present invention can be implemented in many different forms and is not limited to the embodiments described in this specification. On the contrary, the purpose of providing these embodiments is to make the understanding of the disclosure of the present invention more thorough and comprehensive.

[0014] Example 1 like Figure 1 As shown, a method for analyzing the acoustic wave reflection coefficient of a fluid-porous solid interface excited by a seismic source includes the following steps.

[0015] Step 1: derive the general form of the potential function of fast and slow longitudinal waves and shear waves excited by a point earthquake source in a porous solid medium, including the solid displacement potential function and the pore fluid relative to the solid displacement potential function.

[0016] Specifically, the Helmholtz decomposition theory is applied to establish the relationship between the displacement and body force vector and the potential function; the displacement and body force vector represented by the potential function are substituted into the displacement equation of the porous solid medium, and a spatial Fourier transform is performed on it to obtain the integral equation of the spherical acoustic wave displacement potential in the wavenumber domain; the residue theorem is used to derive the general form of the potential function of fast and slow longitudinal and transverse waves excited by a midpoint seismic source in the porous solid medium, including the solid displacement potential function and the pore fluid relative to the solid displacement potential function.

[0017] Step 2, using the fluid-porous solid boundary conditions and the relationship between displacement and displacement potential, stress and strain, derive the equation relationship between the potential functions of the incident sound wave, reflected sound wave, transmitted fast and slow longitudinal wave, and transmitted shear wave excited by the point source.

[0018] Step 3, solve the incident and reflected acoustic wave displacement fields of the fluid medium at the fluid-porous solid seabed interface excited by the point source.

[0019] Specifically, the displacement potential function of the incident and reflected sound waves excited by the point source is used to solve the displacement field of the incident and reflected sound waves of the fluid medium at the interface of the fluid-porous solid seabed excited by the point source. Finally, the analytical equation of the reflection coefficient of the sound wave excited by the point source at the interface of the fluid-porous solid seabed is derived.

[0020] Step 4, derive the analytical equation for the acoustic wave reflection coefficient excited by a point source at the fluid-porous solid seafloor interface.

[0021] Example 2 This embodiment describes Embodiment 1 in detail.

[0022] like Figure 1 As shown, a method for analyzing the acoustic wave reflection coefficient of a fluid-porous solid interface excited by a seismic source includes the following steps.

[0023] Step 1: derive the general form of the potential function of fast and slow longitudinal waves and shear waves excited by a point earthquake source in a porous solid medium, including the solid displacement potential function and the pore fluid relative to the solid displacement potential function.

[0024] The displacement motion equation in porous solid media can be expressed as: (1), in, represents partial differential, represents the second-order differential, t Indicates time; , represents the porosity, , and denote the density of bulk material, pore fluid and solid particles respectively; , u represents the displacement vector of the solid skeleton; and w represent the displacement of pore fluid and pore fluid relative to the solid skeleton, respectively; , and represents the fluid viscosity and rock permeability coefficient; , S represents the structure factor, which can be expressed by Find; F and f represent the body forces acting on the volume material and fluid terms; , , represents the second Lamé parameter (shear modulus), and denote the first Lamé parameters of dry rock skeleton and fluid-saturated rock, respectively, , ; K S , K fl and K dry represents the bulk modulus of solid particles, fluids, and dry rock skeletons; , and Represents divergence, gradient, and curl; Represents the Laplace operator.

[0025] Applying the Helmholtz decomposition theory, we can get: , and denote the solid displacement longitudinal and transverse wave potential functions respectively; , and They represent the longitudinal and transverse wave potential functions of the fluid relative to the solid displacement, respectively; , and They represent the longitudinal and transverse wave potential functions of the body force acting on the volume material respectively; ,in and represent the longitudinal and transverse wave potential functions of the body force acting on the fluid term, respectively. , , and is a time steady-state oscillation. , , and is the spatial Dirac's delta function, expressed as , x represents the position vector.

[0026] Substituting the potential function into equation (1) we can obtain the longitudinal wave potential function: (2), And the shear wave potential function: (3), in, F p , f p , F s and f s is a constant, i represents the imaginary unit, Represents the angular frequency.

[0027] we will f p and f s Set to 0 to study the disturbance caused when the body force acts only on the volume material. Performing Fourier transform on equations (2) and (3), we can finally obtain: (4), in, ; ; v p1 , v p2 and v s Represents the velocities of fast longitudinal waves, slow longitudinal waves and shear waves in porous solid media.

[0028] By performing inverse Fourier transform on equation (4) and using the residue theorem, the displacement potential of the spherical transmission fast longitudinal wave of the solid skeleton can be obtained, which is expressed as: (5), in, ; represents the 0th order Bessel function; r Indicates the horizontal distance between the earthquake source and the receiver point; z Indicates the ordinate of the detection point; and Represents horizontal and vertical slowness in porous media; represents the zero-order Bessel function.

[0029] The displacement potential of the solid skeleton for spherical transmission of slow longitudinal waves is: (6), in, ; .

[0030] The displacement potential of the spherical transmission shear wave of the solid skeleton is: (7), in, ; .

[0031] The spherical transmission fast longitudinal wave displacement potential of the pore fluid relative to the solid phase is: (8), in, ; .

[0032] The spherical transmission slow longitudinal wave displacement potential of the pore fluid relative to the solid phase is: (9), in, ; .

[0033] The spherical transmission shear wave displacement potential of the pore fluid relative to the solid phase is: (10), in, and .

[0034] The displacement potential of a spherical incident longitudinal wave in a fluid medium is: (11) in, ; ; represents the plane wave incident angle; v p represents the speed of sound waves; h Indicates the vertical distance between the earthquake source and the reflection interface.

[0035] The displacement potential of a spherical reflected longitudinal wave in a fluid medium is: (12) in, It represents the intensity of longitudinal wave reflected from the spherical surface (displacement potential amplitude).

[0036] Step 2, using the fluid-porous solid boundary conditions and the relationship between displacement and displacement potential, stress and strain, derive the equation relationship between the potential functions of the incident sound wave, reflected sound wave, transmitted fast and slow longitudinal wave, and transmitted shear wave excited by the point source.

[0037] Using the continuity of the fluid in and out of the solid skeleton in the z direction, the continuity of the normal stress, the continuity of the fluid pressure, the boundary condition of zero shear stress, and the relationship between displacement and displacement potential, and stress and strain, it is possible to establish: (13) in, ; It represents the plane acoustic wave reflection coefficient of the fluid-porous solid seafloor interface without considering the point source.

[0038] Formula (13) is used to establish the relationship between the displacement potential amplitude of the incident sound wave excited by the source on the fluid-porous solid interface and the displacement potential amplitude of the reflected sound wave, and then the reflection coefficient of the sound wave excited by the source on the fluid-porous solid interface is obtained.

[0039] Step 3, solving the incident and reflected acoustic wave displacement fields of the fluid medium at the fluid-porous solid seafloor interface excited by the point source; The displacement field of the incident acoustic wave of the fluid medium at the fluid-porous solid seafloor interface excited by a point source is: ,in is the incident angle of the sound wave excited by the point source.

[0040] The displacement field of the reflected acoustic wave of the fluid medium at the interface between the fluid and porous solid seabed excited by a point source is: . The displacement fields of the incident sound wave and the reflected sound wave can be obtained through these two formulas.

[0041] Step 4, derive the analytical equation for the acoustic wave reflection coefficient excited by a point source at the fluid-porous solid seafloor interface.

[0042] The equation for the acoustic wave reflection coefficient of the fluid-porous solid seabed interface excited by a point seismic source is defined as the ratio of the reflected sound wave excited by the point seismic source to the incident sound wave.

[0043] Therefore, the analytical equation for the acoustic wave reflection coefficient excited by a point source at the fluid-porous solid seafloor interface can be expressed as: (14) in, represents the first-order Bessel function; .

[0044] Example 3 This embodiment adopts the method provided in the above embodiment and uses the fluid-porous solid seafloor interface model parameters to calculate the point source excited acoustic wave reflection coefficient of the fluid-porous solid seafloor interface. The point source excited acoustic wave frequency and seafloor depth are set to 10 Hz and 500 m respectively.

[0045] The first case: a porous solid medium with seawater on the upper layer and pore-filling water on the lower layer. Parameters of the upper-layer seawater fluid medium: velocity 1414 (m / s), density 1000 (kg / m3); parameters of the lower-layer porous solid medium: bulk modulus of solid particles 3.6*1010 (pa), bulk modulus of pore fluid 22.5*109 (pa), bulk modulus of dry rock skeleton 4.36*107 (pa), shear modulus 2.61*107 (pa), porosity 0.47, density of pore fluid 1000 (kg / m3), density of solid particles 2650 (kg / m3), permeability 10-10 (cm2), fluid viscosity 10-3 (Pa*s). Figure 2 It is a schematic diagram of the acoustic wave reflection coefficient excited by a point source at the fluid-porous solid seabed interface calculated in the first case at a frequency of 10 Hz and a seabed depth of 500 m. Figure 2 On the left side (a) in it is the amplitude of the reflection coefficient, and on the right side (b) is the phase of the reflection coefficient. It can be seen that the real and imaginary parts of the reflection coefficient (dashed line) of the acoustic wave (spherical wave) excited by a point source at the fluid-porous solid seabed interface are significantly different from the real and imaginary parts of the corresponding plane wave reflection coefficient (solid line), indicating that the spherical acoustic wave excited by a point source at the fluid-porous solid seabed interface has different reflection characteristics from the approximately plane acoustic wave under the conditions of far distance and high frequency.

[0046] The second case: a porous solid medium with seawater on the upper layer and pores filled with gases such as natural gas and carbon dioxide on the lower layer. Different from the parameters in Example 1: the density of the pore fluid in the lower-layer porous solid medium is 139.8 (kg / m3), and the bulk modulus of the pore fluid is 0.5543*109 (pa), and other parameters are the same as those set in Example 1. Figure 3 It is a schematic diagram of the acoustic wave reflection coefficient excited by a point source at the fluid-porous solid seabed interface calculated in the second case at a frequency of 10 Hz and a seabed depth of 500 m. Figure 3 On the left side (c) in it is the amplitude of the reflection coefficient, and on the right side (d) is the phase of the reflection coefficient. It can be seen that, similar to Example 1, there are obvious differences in the reflection characteristics of the spherical acoustic wave excited by a point source at the fluid-porous solid seabed interface and the plane acoustic wave.

[0047] Compared with the plane wave reflection coefficient at the fluid-porous solid seabed interface in the prior art ( Figure 2 and Figure 3 shown by the black solid line in), the present technology proposes an analytical method for the reflection coefficient of acoustic waves excited by a point source at the fluid-porous solid seabed interface. As shown in Figure 2 and Figure 3As shown, compared with the prior art, the present invention takes into account the wavefront propagation and reflection theory of spherical waves at the interface between fluid and porous solid seabed, and can accurately characterize the reflection characteristics of sound waves excited by point seismic sources at the interface between fluid and porous solid seabed, which is of great significance to improving the accuracy of seabed acoustic field simulation, underwater target detection and seabed resource exploration. The above embodiments are only for illustrating the inventive concept and features of the present invention, and their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly, and they cannot be used to limit the protection scope of the present invention. Any equivalent changes or modifications made based on the essence of the content of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for analyzing the reflection coefficient of acoustic waves excited by a source at a fluid-porous solid interface, characterized in that: The following steps are involved: Step 1: Establish the relationship between displacement and body force vector and potential function through Helmholtz decomposition theory, substitute the displacement and body force vector represented by the potential function into the displacement equation of porous solid medium, perform spatial Fourier transform on it, and obtain the integral equation of spherical acoustic wave displacement potential in the wave number domain. Apply the residue theorem to derive the general form of the potential function of fast and slow longitudinal and transverse waves excited by a midpoint source in porous solid medium; Step 2: Using the fluid-porous solid boundary conditions and the relationship between displacement and displacement potential, stress and strain, derive the equation relationship between the potential functions of the incident sound wave, reflected sound wave, transmitted fast and slow longitudinal wave, and transmitted shear wave excited by the point source; Step 3: Solve the incident and reflected acoustic wave displacement fields of the fluid medium at the fluid-porous solid seafloor interface excited by the point source; Step 4: Derive the analytical equation for the acoustic wave reflection coefficient excited by a point source at the fluid-porous solid seafloor interface.

2. The method for analyzing the reflection coefficient of acoustic waves excited by a source at a fluid-porous solid interface according to claim 1, characterized in that: The step 1 includes a solid displacement potential function and a pore fluid displacement potential function relative to the solid.

3. The method for analyzing the reflection coefficient of acoustic waves excited by a source at a fluid-porous solid interface according to claim 1, characterized in that: The step 1 comprises: Step 1-1: Apply the Helmholtz decomposition theory to obtain the displacement vector of the solid skeleton , the displacement of the pore fluid relative to the solid skeleton , the body force acting on the volume material , the body force acting on the fluid term ,in, represents the gradient, represents the curl, represents the solid displacement longitudinal wave potential function, represents the solid displacement shear wave potential function, represents the longitudinal wave potential function of the fluid relative to the solid displacement, represents the shear wave potential function of the fluid relative to the solid displacement, The longitudinal wave potential function representing the body force acting on the volume material, is the shear wave potential function representing the body force acting on the volume material, represents the longitudinal wave potential function of the body force acting on the fluid term, The shear wave potential function representing the body force acting on the fluid term; Step 1-2: Construct the displacement equation of porous solid media, expressed as: ， in represents partial differential, represents the second-order differential, t Indicates time, , represents the porosity, represents the density of the bulk material, represents the density of the pore fluid, represents the density of solid particles, , represents the fluid viscosity coefficient, represents the rock permeability coefficient, , S represents the structure factor, , , represents the second Lamé parameter, represents the first Lamé parameter of the dry rock skeleton, The first Lamé parameter representing the fluid rock, α is the biot coefficient, , , K S represents the bulk modulus of solid particles, K fl represents the bulk modulus of the fluid, K dry represents the bulk modulus of the dry rock skeleton, represents the divergence, represents the Laplace operator; Step 1-3: Substitute the potential function in step 1-1 into the displacement equation of the porous solid medium to obtain, Longitudinal wave potential function: ， Shear wave potential function: ， in F p , f p , F s and f s is a constant, i represents the imaginary unit, represents the angular frequency, yes , , and The spatial Dirac's delta function, x represents the position vector; Step 1-4: f p and f s Set it to 0, perform Fourier transform on the longitudinal wave potential function and the transverse wave potential function, and get a transformation function: ， in , , v p1 Indicates the fast longitudinal wave velocity of porous solid media, v p2 represents the slow longitudinal wave velocity in porous solid media, v s represents the shear wave velocity of porous solid media; Step 1-5: Perform inverse Fourier transform on the formula in step 1-4 and use the residue theorem to obtain: The displacement potential of a spherical transmission fast longitudinal wave of a solid skeleton is expressed as ,in, , represents the 0th order Bessel function, r Indicates the horizontal distance between the source and the receiver point. z represents the ordinate of the detection point, and represents the horizontal and vertical slowness in porous media, represents the zero-order Bessel function; The displacement potential of a solid skeleton through a spherical transmission slow longitudinal wave is expressed as ,in, ; The displacement potential of the spherical transmission shear wave of the solid skeleton is expressed as ,in, , ; The spherical transmission fast longitudinal wave displacement potential of the pore fluid relative to the solid phase is expressed as ,in, , ; The spherical transmission slow longitudinal wave displacement potential of the pore fluid relative to the solid phase is expressed as ,in, , ; The spherical transmission shear wave displacement potential of the pore fluid relative to the solid phase is expressed as ,in, , ; The displacement potential of a spherical incident longitudinal wave in a fluid medium is expressed as ,in, , , represents the plane wave incident angle, v p represents the speed of sound waves, h Indicates the vertical distance between the earthquake source and the reflection interface; The displacement potential of a spherical reflected longitudinal wave in a fluid medium is expressed as ,in Indicates the intensity of longitudinal waves reflected from the spherical surface.

4. The method for analyzing the reflection coefficient of acoustic waves excited by a source at a fluid-porous solid interface according to claim 3, characterized in that: The step 2 comprises: Step 2-1: Use the continuity boundary condition of the fluid entering and exiting the solid skeleton in the z direction ,in, , and represent the displacements of seawater, solid and pore fluid in the z direction, respectively; Step 2-2: Using the continuity boundary condition for normal stress ,in, represents the fluid pressure, represents the fluid density, , , ; Step 2-3: Using the Continuity Boundary Condition for Fluid Pressure ,in, ; Step 2-4: Using the boundary condition of zero shear stress ,in, represents the shear stress on the solid skeleton, ; Step 2-5: Combine the above four boundary conditions to establish: ,in , It represents the plane acoustic wave reflection coefficient of the fluid-porous solid seafloor interface without considering the point source.

5. The method for analyzing the reflection coefficient of acoustic waves excited by a source at a fluid-porous solid interface according to claim 4, characterized in that: The step 3 comprises: The displacement field of the incident acoustic wave of the fluid medium at the interface between the fluid and porous solid seabed excited by a point source is: ,in is the incident angle of the acoustic wave excited by the point source; The displacement field of the reflected acoustic wave of the fluid medium at the interface between the fluid and porous solid seabed excited by a point source is: .

6. The method for analyzing the reflection coefficient of acoustic waves excited by a source at a fluid-porous solid interface according to claim 5, characterized in that: The step 4 comprises: Step 4-1: Define the acoustic wave reflection coefficient equation of the fluid-porous solid seafloor interface excited by a point source as the ratio of the reflected acoustic wave excited by the point source to the incident acoustic wave; Step 4-2: The analytical equation for the acoustic wave reflection coefficient excited by a point source at the fluid-porous solid seafloor interface can be expressed as: ， in, represents the first-order Bessel function, .

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