An analytical method for the reflection coefficient of acoustic waves excited by a fluid-porous solid interface seismic source

Abstract

An analytical method for the reflection coefficient of acoustic waves excited by a fluid-porous solid interface seismic source, including Step 1: deriving the general forms of the potential functions of the fast and slow longitudinal waves and the transverse wave excited by a point source in a porous solid medium; Step 2: using the fluid-porous solid boundary conditions and the relationships between displacement and displacement potential, and stress and strain, to derive the equation relationships between the potential functions of the incident acoustic wave, the reflected acoustic wave, the transmitted fast and slow longitudinal waves, and the transmitted transverse wave excited by a point source; Step 3: solving the displacement fields of the incident and reflected acoustic waves in the fluid medium at the fluid-porous solid seabed interface excited by a point source; Step 4: deriving the analytical equation for the reflection coefficient of acoustic waves excited by a point source at the fluid-porous solid seabed interface. It can accurately characterize the reflection characteristics of acoustic waves excited by a point source at the fluid-porous solid seabed interface, and is of great significance for seabed sound field simulation, underwater target detection, and seabed resource exploration.

Description

Technical Field

[0001] The present invention relates to the field of marine geophysical technologies, and particularly to an analytical method for the acoustic wave reflection coefficient excited by a source at the fluid-porous solid interface. Background Art

[0002] Approximately 71% of the Earth's surface is covered by the ocean, so it is particularly important to study the reflection characteristics of the underwater acoustic field. The assumption of a point source in the ocean is quite common. For example, surface ships and underwater submarines, within a relatively large scale range, and air guns used for the exploration of undersea oil and gas, combustible ice, minerals, etc. can all be considered as point sources. Studying the acoustic wave reflection coefficient and acoustic wave reflection characteristics excited by a point source at the fluid-porous solid seabed interface is of great significance for improving the simulation of the underwater acoustic field, geoacoustic inversion, and the detection accuracy of underwater targets. In the field of marine geophysics, the plane wave reflection coefficient at 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 applied to geoacoustic inversion to improve the simulation of the underwater acoustic field and the detection accuracy of underwater targets. However, under very low frequency and short distance conditions, the plane wave reflection coefficient encounters some fundamental difficulties and is difficult to accurately describe the acoustic field and acoustic wave reflection characteristics at the fluid-porous solid seabed interface, which limits the accuracy of geoacoustic inversion, underwater acoustic field simulation, and underwater target detection.

[0003] Currently, there is no technical solution in the prior art to realize the analysis of the acoustic wave reflection coefficient excited by a point source at the fluid-porous solid seabed interface. There is an urgent need to propose an analytical method for the acoustic wave reflection coefficient excited by a point source at the fluid-porous solid seabed interface to realize the simulation of the acoustic wave reflection characteristics and acoustic field modeling at the fluid-porous solid seabed interface. Summary of the Invention

[0004] Aiming at the problems existing in the prior art, the purpose of the present invention is to provide an analytical method for the acoustic wave reflection coefficient excited by a point source at the fluid-porous solid seabed interface, which can describe the acoustic wave reflection characteristics excited by a point source at the fluid-porous solid seabed interface and is helpful for improving the accuracy of underwater wave field modeling, geoacoustic parameter inversion, and underwater target detection.

[0005] To achieve the above purpose, the technical solution adopted by the present invention is: an analytical method for the acoustic wave reflection coefficient excited by a source at the fluid-porous solid interface, comprising the following steps:

[0006] Step 1: Based on the Helmholtz decomposition theory, establish the relationships between the displacement and body force vectors and the potential functions. Substitute the displacement and body force vectors expressed by the potential functions into the displacement equation of the porous solid medium, and perform a spatial Fourier transform on it to obtain the spherical acoustic wave displacement potential integral equation in the wavenumber domain. Apply the residue theorem to derive the general forms of the potential functions of the fast and slow longitudinal waves and the transverse wave excited by a point source in the porous solid medium;

[0007] Step 2: Utilize the fluid-porous solid boundary conditions and the relationships between displacement and displacement potential, and between stress and strain to derive the equation relationships among the potential functions of the incident acoustic wave, reflected acoustic wave, transmitted fast and slow longitudinal waves, and transmitted transverse wave excited by a point source;

[0008] Step 3: Solve the displacement fields of the incident and reflected acoustic waves in the fluid medium at the fluid-porous solid seabed interface excited by a point source;

[0009] Step 4: Derive the analytical equation of the acoustic wave reflection coefficient excited by a point source at the fluid-porous solid seabed interface.

[0010] For the above analytical method of the acoustic wave reflection coefficient excited by a source at the fluid-porous solid interface, Step 1 includes the solid displacement potential function and the displacement of the pore fluid relative to the solid displacement potential function.

[0011] For the above analytical method of the acoustic wave reflection coefficient excited by a source at the fluid-porous solid interface, Step 1 includes:

[0012] 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 , where represents the gradient, represents the curl, represents the longitudinal wave potential function of the solid displacement, represents the transverse wave potential function of the solid displacement, represents the longitudinal wave potential function of the fluid relative to the solid displacement, represents the transverse wave potential function of the fluid relative to the solid displacement, represents the longitudinal wave potential function of the body force acting on the volume material, represents the transverse wave potential function of the body force acting on the volume material, represents the longitudinal wave potential function of the body force acting on the fluid term, represents the transverse wave potential function of the body force acting on the fluid term;

[0013] Step 1-2: Construct the displacement equation of the porous solid medium, expressed as:

[0014] , where denotes the partial derivative, denotes the second-order derivative, t denotes time, , denotes porosity, denotes the density of the bulk material, denotes the density of the pore fluid, denotes the density of the solid grains, , denotes the fluid viscosity coefficient, denotes the rock permeability coefficient, , S denotes the structure factor, , , denotes the second Lamé parameter, denotes the first Lamé parameter of the dry rock skeleton, denotes the first Lamé parameter of the fluid-rock, α is the Biot coefficient, , , K S denotes the bulk modulus of the solid grains, K fl denotes the bulk modulus of the fluid, K dry denotes the bulk modulus of the dry rock skeleton, denotes the divergence, denotes the Laplace operator;

[0015] Steps 1 - 3: Substitute the potential function in Step 1 - 1 into the displacement equation of the porous solid medium to obtain

[0016] Longitudinal wave potential function:

[0017] ,

[0018] Transverse wave potential function:

[0019] , where F p , f p , F s and f s are constants, i denotes the imaginary unit, denotes the angular frequency, is , , and The spatial Dirac's delta function, where x represents the position vector;

[0020] Steps 1 - 4: Set f p and f s to 0, and perform Fourier transforms on the longitudinal wave potential function and the transverse wave potential function to obtain the first - order transformed functions:

[0021] , where , , v p1 represents the fast longitudinal wave velocity of the porous solid medium, v p2 represents the slow longitudinal wave velocity of the porous solid medium, v s represents the transverse wave velocity of the porous solid medium;

[0022] Step 1 - 5: Perform an inverse Fourier transform on the formula in Step 1 - 4 and use the residue theorem to obtain

[0023] the spherical - transmitted fast longitudinal wave displacement potential of the solid skeleton, denoted as , where, , represents the Bessel function of the first kind of order zero, r represents the horizontal distance between the source and the geophone, z represents the ordinate of the geophone, and represent the horizontal and vertical slownesses in the porous medium, represents the Bessel function of the first kind of order zero;

[0024] The spherical - transmitted slow longitudinal wave displacement potential of the solid skeleton, denoted as, , where, ;

[0025] The spherical - transmitted transverse wave displacement potential of the solid skeleton, denoted as , where, , ;

[0026] The spherical - transmitted fast longitudinal wave displacement potential of the pore fluid relative to the solid phase, denoted as , where, , ;

[0027] The spherical - transmitted slow longitudinal wave displacement potential of the pore fluid relative to the solid phase, denoted as , where, , ;

[0028] The spherical transmitted shear wave displacement potential of the pore fluid relative to the solid phase, expressed as , where , ;

[0029] The spherical incident compressional wave displacement potential in the fluid medium, expressed as , where , , represents the plane wave incident angle, v p represents the acoustic wave velocity, h represents the vertical distance between the source and the reflection interface;

[0030] The spherical reflected compressional wave displacement potential in the fluid medium, expressed as , where represents the spherical reflected compressional wave intensity.

[0031] The above analytical method for the acoustic wave reflection coefficient excited by a source at the fluid-porous solid interface, the step 2 includes:

[0032] Step 2-1: Using the continuity boundary condition of the fluid flowing in and out of the solid skeleton in the z direction , where , and respectively represent the displacements of seawater, solid and pore fluid in the z direction;

[0033] Step 2-2: Using the continuity boundary condition of the normal stress , where represents the fluid pressure, represents the fluid density, , , ;

[0034] Step 2-3: Using the continuity boundary condition of the fluid pressure , where ;

[0035] Step 2-4: Using the boundary condition that the shear stress is zero , where represents the shear stress of the solid skeleton, ;

[0036] Step 2-5: Combining the above four boundary conditions, establish:

[0037] , where , represents the plane acoustic wave reflection coefficient at the fluid-porous solid seabed interface without considering the point source.

[0038] The above method for analyzing the acoustic wave reflection coefficient excited by a fluid-porous solid interface source, wherein step 3 includes:

[0039] The incident acoustic wave displacement field of the fluid medium at the fluid-porous solid seabed interface excited by a point source is , where is the incident angle of the acoustic wave excited by the point source;

[0040] The reflected acoustic wave displacement field of the fluid medium at the fluid-porous solid seabed interface excited by a point source is .

[0041] The above method for analyzing the acoustic wave reflection coefficient excited by a fluid-porous solid interface source, wherein step 4 includes:

[0042] Step 4-1: Define the acoustic wave reflection coefficient equation at the fluid-porous solid seabed interface excited by a point source as the ratio of the reflected acoustic wave to the incident acoustic wave excited by the point source;

[0043] Step 4-2: The analytical equation of the acoustic wave reflection coefficient excited by a point source at the fluid-porous solid seabed interface can be expressed as:

[0044] , where, represents the Bessel function of the first order, .

[0045] The beneficial effect of the method for analyzing the acoustic wave reflection coefficient excited by a fluid-porous solid interface source of the present invention is that, compared with the prior art, the present invention takes into account the spherical wavefront propagation and reflection theory at the fluid-porous solid seabed interface, and can accurately characterize the acoustic wave reflection characteristics excited by a point source at the fluid-porous solid seabed interface. Under the conditions of low-frequency point source excitation, near-shallow sea, and environments with a small distance from the seabed such as bottom-mounted buoys / hydrophones, there are certain errors in the plane wave theory, and it is impossible to accurately describe and characterize the underwater reflection sound field. The acoustic wave reflection coefficient of the fluid-porous solid interface source of the present invention can accurately describe the underwater reflection sound field in the above environments, which is of great significance for improving the accuracy of seabed sound field simulation, underwater target detection, and seabed resource exploration. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 is the overall flow schematic diagram in the embodiment of the present invention;

[0047] Figure 2 is the first schematic diagram of the spherical wave reflection coefficient at the fluid-porous solid seabed interface calculated in the embodiment;

[0048] Figure 3 is the second schematic diagram of the spherical wave reflection coefficient at the fluid-porous solid seabed interface calculated in the embodiment. Detailed implementation manners

[0049] For the convenience of understanding the present invention, the present invention will be 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 disclosed content of the present invention more thorough and comprehensive.

[0050] Embodiment 1

[0051] As Figure 1 shown, a method for analyzing the acoustic wave reflection coefficient excited by a fluid-porous solid interface seismic source includes the following steps.

[0052] Step 1: Derive the general forms of the potential functions of the fast and slow longitudinal waves and the transverse wave excited by a point seismic source in a porous solid medium, including the solid displacement potential function and the potential function of the pore fluid relative to the solid displacement potential function.

[0053] Specifically, apply the Helmholtz decomposition theory to establish the relationship between the displacement and body force vectors and the potential functions; substitute the displacement and body force vectors expressed by the potential functions into the displacement equation of the porous solid medium, and perform a spatial Fourier transform on it to obtain the spherical acoustic wave displacement potential integral equation in the wavenumber domain; apply the residue theorem to derive the general forms of the potential functions of the fast and slow longitudinal waves and the transverse wave excited by a point seismic source in a porous solid medium, including the solid displacement potential function and the potential function of the pore fluid relative to the solid displacement potential function.

[0054] Step 2: Use the fluid-porous solid boundary conditions and the relationships between displacement and displacement potential, and stress and strain to derive the equation relationships between the potential functions of the incident acoustic wave, the reflected acoustic wave, the transmitted fast and slow longitudinal waves, and the transmitted transverse wave excited by a point seismic source.

[0055] Step 3: Solve the incident and reflected acoustic wave displacement fields of the fluid medium at the fluid-porous solid seabed interface excited by a point seismic source.

[0056] Specifically, use the relationship between displacement and displacement potential, and based on the displacement potential functions of the incident acoustic wave and the reflected acoustic wave excited by a point seismic source, solve the incident and reflected acoustic wave displacement fields of the fluid medium at the fluid-porous solid seabed interface excited by a point seismic source. Finally, derive the analytical equation of the acoustic wave reflection coefficient excited by a point seismic source at the fluid-porous solid seabed interface.

[0057] Step 4: Derive the analytical equation of the acoustic wave reflection coefficient excited by a point seismic source at the fluid-porous solid seabed interface.

[0058] Embodiment 2

[0059] This embodiment specifically describes Embodiment 1.

[0060] As Figure 1As shown, an analytical method for the acoustic wave reflection coefficient excited by a fluid-porous solid interface source includes the following steps.

[0061] Step 1: Derive the general forms of the potential functions of the fast and slow longitudinal waves and the transverse wave excited by a point source in a porous solid medium, including the solid displacement potential function and the potential function of the pore fluid relative to the solid displacement potential function.

[0062] The displacement motion equation in a porous solid medium can be expressed as:

[0063] (1),

[0064] where, represents partial differentiation, represents second-order differentiation, t represents time; , represents porosity, , and respectively represent the densities of the bulk material, pore fluid, and solid particles; , u represents the displacement vector of the solid skeleton; and w respectively represent the displacements of the pore fluid and the pore fluid relative to the solid skeleton; , and represent the fluid viscosity and the rock permeability coefficient; , S represents the structure factor, which can be obtained through ; F and f represent the body forces acting on the bulk material and fluid terms; , , represents the second Lamé parameter (shear modulus), and respectively represent the first Lamé parameters of the dry rock skeleton and the saturated fluid rock, , ; K S , K fl and K dry represent the bulk moduli of the solid particles, fluid, and dry rock skeleton; , and represent divergence, gradient, and curl; represents the Laplace operator.

[0065] Applying the Helmholtz decomposition theory, we can obtain: , and respectively represent the longitudinal and transverse wave potential functions of solid displacement; , and respectively represent the longitudinal and transverse wave potential functions of fluid relative to solid displacement; , and respectively represent the longitudinal and transverse wave potential functions of the body force acting on the volume material; , where and respectively represent the longitudinal and transverse wave potential functions of the body force acting on the fluid term. , , and are time - steady - state oscillations. , , and are spatial Dirac’s delta functions, expressed as , where x represents the position vector.

[0066] Substituting the potential functions into Equation (1), the longitudinal wave potential function can be obtained:

[0067] (2),

[0068] and the transverse wave potential function:

[0069] (3),

[0070] where, F p , f p , F s and f s are constants, i represents the imaginary unit, represents the angular frequency.

[0071] We set f p and f s to 0 to study the perturbations caused when the body force acts only on the volume material. Performing Fourier transforms on Equations (2) and (3), we can finally obtain:

[0072] (4),

[0073] where, ; ; v p1 , vp2 and v s represent the fast longitudinal wave, slow longitudinal wave and transverse wave velocities of the porous solid medium.

[0074] Performing the Fourier inverse transform on Equation (4) and using the residue theorem, the spherical transmitted fast longitudinal wave displacement potential of the solid skeleton can be obtained, expressed as:

[0075] (5),

[0076] where ; represents the Bessel function of the first kind of order zero; r represents the horizontal distance between the source and the geophone; z represents the ordinate of the geophone; and represent the horizontal and vertical slownesses in the porous medium; represents the Bessel function of the first kind of order zero.

[0077] The spherical transmitted slow longitudinal wave displacement potential of the solid skeleton is:

[0078] (6),

[0079] where ; .

[0080] The spherical transmitted transverse wave displacement potential of the solid skeleton is:

[0081] (7),

[0082] where ; .

[0083] The spherical transmitted fast longitudinal wave displacement potential of the pore fluid relative to the solid phase is:

[0084] (8),

[0085] where ; .

[0086] The spherical transmitted slow longitudinal wave displacement potential of the pore fluid relative to the solid phase is:

[0087] (9),

[0088] where ; .

[0089] The spherical transmitted transverse wave displacement potential of the pore fluid relative to the solid phase is:

[0090] (10),

[0091] Among them, and .

[0092] The spherical incident longitudinal wave displacement potential in the fluid medium is:

[0093] (11),

[0094] Among them, ; ; represents the plane wave incident angle; v p represents the sound wave velocity; h represents the vertical distance between the seismic source and the reflection interface.

[0095] The spherical reflected longitudinal wave displacement potential in the fluid medium is:

[0096] (12),

[0097] Among them, represents the spherical reflected longitudinal wave intensity (displacement potential amplitude).

[0098] Step 2: Use the fluid-porous solid boundary conditions and the relationships between displacement and displacement potential, and stress and strain to derive the equation relationships among the potential functions of the incident sound wave, reflected sound wave, transmitted fast and slow longitudinal waves, and transmitted shear wave excited by a point seismic source.

[0099] By using the boundary conditions of the continuity of the fluid entering and leaving the solid skeleton in the z direction, the continuity of the normal stress, the continuity of the fluid pressure, and the shear stress being zero, as well as the relationships between displacement and displacement potential, and stress and strain, the following can be established:

[0100] (13),

[0101] Among them, ; represents the plane sound wave reflection coefficient at the fluid-porous solid seabed interface without considering the point seismic source.

[0102] Through formula (13), the relationship between the displacement potential amplitude of the incident sound wave and the displacement potential amplitude of the reflected sound wave excited by the seismic source at the fluid-porous solid interface is established, and then the sound wave reflection coefficient excited by the seismic source at the fluid-porous solid interface is obtained.

[0103] Step 3: Solve the incident and reflected sound wave displacement fields of the fluid medium at the fluid-porous solid seabed interface excited by the point seismic source;

[0104] The incident acoustic wave displacement field of the fluid medium at the fluid-porous solid seabed interface excited by a point source is , where is the incident angle of the acoustic wave excited by the point source.

[0105] The reflected acoustic wave displacement field of the fluid medium at the fluid-porous solid seabed interface excited by a point source is . The displacement fields of the incident acoustic wave and the reflected acoustic wave can be obtained from these two formulas.

[0106] Step 4, derive the analytical equation of the acoustic wave reflection coefficient excited by a point source at the fluid-porous solid seabed interface.

[0107] Define the acoustic wave reflection coefficient equation at the fluid-porous solid seabed interface excited by a point source as the ratio of the reflected acoustic wave to the incident acoustic wave excited by the point source.

[0108] Therefore, the analytical equation of the acoustic wave reflection coefficient excited by a point source at the fluid-porous solid seabed interface can be expressed as:

[0109] (14),

[0110] where represents the Bessel function of the first order; .

[0111] Example 3

[0112] In this example, the method provided in the above example is used to calculate the acoustic wave reflection coefficient excited by a point source at the fluid-porous solid seabed interface by using the model parameters of the fluid-porous solid seabed interface. The frequency of the acoustic wave excited by the point source and the seabed depth are set to 10 Hz and 500 m respectively.

[0113] The first case: The upper layer is seawater and the lower layer is a porous solid medium filled with pore water. Parameters of the upper layer seawater fluid medium: velocity 1414 (m / s), density 1000 (kg / m3); Parameters of the lower layer porous solid medium: solid particle bulk modulus 3.6*1010 (pa), pore fluid bulk modulus 22.5*109 (pa), dry rock skeleton bulk modulus 4.36*107 (pa), shear modulus 2.61*107 (pa), porosity 0.47, void fluid density 1000 (kg / m3), solid particle density 2650 (kg / m3), permeability 10-10 (cm2), fluid viscosity 10-3 (Pa*s). Figure 2 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 2On the left side (a) 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 condition of far-distance high frequency.

[0114] The second case: The upper layer is seawater, and the lower layer is a porous solid medium with pores filled with gases such as natural gas and carbon dioxide. Different from the parameters in Embodiment 1: The density of the pore fluid in the lower 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 set the same as in Embodiment 1. Figure 3 It is a schematic diagram of the reflection coefficient of the acoustic wave 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) 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 Embodiment 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.

[0115] 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 the acoustic wave excited by a point source at the fluid-porous solid seabed interface. As shown in Figure 2 and Figure 3 , compared with the prior art, the present invention considers the theory of spherical wavefront propagation and reflection at the fluid-porous solid seabed interface, can accurately describe the reflection characteristics of the acoustic wave excited by a point source at the fluid-porous solid seabed interface, and is of great significance for improving the accuracy of seabed sound field simulation, underwater target detection and seabed resource exploration.

[0116] The above embodiments are only for explaining the inventive concept and features of the present invention, and their purpose is to enable those of ordinary skill in the art to understand the content of the present invention and implement it accordingly, and cannot be used to limit the protection scope of the present invention. Any equivalent changes or modifications made according to the essence of the content of the present invention should be covered within the protection scope of the present invention.

Claims

1. An analytical method for the acoustic wave reflection coefficient excited by a fluid-porous solid interface source, characterized in that, It includes the following steps: Step 1: Based on the Helmholtz decomposition theory, establish the relationships between displacement and body force vectors and potential functions, including the solid displacement potential function and the potential function of pore fluid relative to the solid displacement potential function. Substitute the displacement and body force vectors expressed by the potential functions into the displacement equation of porous solid media, and perform spatial Fourier transform on it to obtain the spherical acoustic wave displacement potential integral equation in the wavenumber domain. Apply the residue theorem to deduce the general forms of the potential functions of fast and slow longitudinal waves and transverse waves excited by a point source in porous solid media, including: 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 , where represents the gradient, represents the curl, represents the longitudinal wave potential function of the solid displacement, represents the transverse wave potential function of the solid displacement, represents the longitudinal wave potential function of the fluid relative to the solid displacement, represents the transverse wave potential function of the fluid relative to the solid displacement, represents the longitudinal wave potential function of the body force acting on the volume material, represents the transverse wave potential function of the body force acting on the volume material, represents the longitudinal wave potential function of the body force acting on the fluid term, represents the transverse wave potential function of the body force acting on the fluid term; Step 1-2: Construct the displacement equation of porous solid media, expressed as: , where represents the partial derivative, represents the second-order derivative, t represents time, , represents porosity, represents the density of the bulk material, represents the density of the pore fluid, represents the density of the 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, represents the first Lamé parameter of the fluid-rock, α is the Biot coefficient, , , K S represents the bulk modulus of the 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; Step 1-3: Substitute the potential function in Step 1-1 into the displacement equation of porous solid media to obtain Longitudinal wave potential function: ， Transverse wave potential function: , where , , and are constants, i denotes the imaginary unit, denotes the angular frequency, is , , and is the spatial Dirac’s delta function, x represents the position vector, denotes the Laplace operator; Step 1-4: Set and to 0, perform Fourier transform on the longitudinal wave potential function and the transverse wave potential function to obtain a first transformed function: , where , , v p1 represents the fast longitudinal wave velocity of the porous solid medium, v p2 represents the slow longitudinal wave velocity of the porous solid medium, v s represents the shear wave velocity of the porous solid medium, k represents the wave number; Step 1-5: Perform inverse Fourier transform on the formula in Step 1-4 and use the residue theorem to obtain: The spherical transmission fast longitudinal wave displacement potential of the solid skeleton, expressed as , where , r represents the horizontal distance between the source and the geophone, z represents the ordinate of the geophone, represents the horizontal slowness in the porous medium, represents the vertical slowness of the fast longitudinal wave in the porous medium, represents the zero-order Bessel function; The spherical transmission slow longitudinal wave displacement potential of the solid skeleton, expressed as , where , , represents the vertical slowness of the slow longitudinal wave; The spherical transmission shear wave displacement potential of the solid skeleton is expressed as , where , ; The spherical transmission fast longitudinal wave displacement potential of pore fluid relative to the solid phase, expressed as , where , ; The spherical transmission slow P-wave displacement potential of pore fluid relative to the solid phase, expressed as , where , ; The spherical transmitted shear wave displacement potential of the pore fluid relative to the solid phase, expressed as , where , ; The spherical incident longitudinal wave displacement potential in a fluid medium, expressed as , where , , represents the incident angle of the plane wave, v p represents the sound wave velocity, h represents the vertical distance between the source and the reflection interface, A represents the amplitude of the incident longitudinal wave displacement potential in the fluid medium; The spherical reflected longitudinal wave displacement potential in a fluid medium, expressed as , where represents the spherical reflected longitudinal wave intensity; Step 2: Utilize the fluid-porous solid boundary conditions and the relationships between displacement and displacement potential, and between stress and strain to deduce the equation relationships among the potential functions of incident acoustic wave, reflected acoustic wave, transmitted fast and slow longitudinal waves, and transmitted transverse wave excited by a point source; Step 3: Solve the displacement fields of incident and reflected acoustic waves in the fluid medium at the fluid-porous solid seabed interface excited by a point source; Step 4: Deduce the analytical equation of the acoustic wave reflection coefficient excited by a point source at the fluid-porous solid seabed interface.

2. The analytical method for the acoustic wave reflection coefficient excited by a fluid-porous solid interface source according to claim 1, characterized in that, The said Step 2 includes: Step 2-1: Utilize the continuity boundary condition for the fluid flowing in and out of the solid skeleton in the z direction , where , and represent the displacements of seawater, solid, and pore fluid in the z direction, respectively; Step 2-2: Using the continuity boundary condition of the normal stress , where represents the fluid pressure, represents the density of the seawater fluid, , , ; Step 2-3: Utilize the continuity boundary condition of fluid pressure , where ; Step 2-4: Utilize the boundary condition of zero shear stress , where denotes the shear stress of the solid skeleton, ; Step 2-5: Combine the above four boundary conditions to establish: , where , represents the plane acoustic wave reflection coefficient at the fluid-porous solid seabed interface without considering the point source.

3. The analytical method for the acoustic wave reflection coefficient excited by a fluid-porous solid interface source according to claim 2, characterized in that, The said Step 3 includes: The incident acoustic wave displacement field of the fluid medium at the fluid-porous solid seabed interface excited by a point source is , where is the incident angle of the acoustic wave excited by the point source; The reflected acoustic wave displacement field of the fluid medium at the fluid-porous solid seabed interface excited by a point source is .

4. The method for analyzing the acoustic wave reflection coefficient excited by a fluid-porous solid interface source according to claim 3, wherein The said Step 4 includes: Step 4-1: Define the acoustic wave reflection coefficient equation at the fluid-porous solid seabed interface excited by a point source as the ratio of the reflected acoustic wave to the incident acoustic wave excited by the point source; Step 4-2: The analytical equation of the acoustic wave reflection coefficient at the fluid-porous solid seabed interface excited by a point source is expressed as: , where represents the first-order Bessel function.

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