Deep-sea t-phase calculation method and system based on seafloor seismic source mechanism

Abstract

The application provides a deep-sea T-phase calculation method and system based on a seafloor seismic source mechanism, and the method comprises the following steps: determining calculation physical quantities in an elastic multilayer ocean crust medium and a fluid deep-sea sound channel for a deep-sea seafloor seismic T-phase propagation process, and establishing an acoustic wave-seismic wave combined elliptical differential equation in a two-dimensional cylindrical coordinate system; the elliptical differential equation is converted into an acoustic wave-seismic wave combined parabolic differential equation, a horizontal recursive equation in a root form of the acoustic wave-seismic wave combined parabolic differential equation is given, an initial field horizontal recursive equation in the root form suitable for a seafloor seismic event is established, the horizontal recursive equation in the root form is converted into an N p step loop recursive equation, numerical discrete processing is performed on operator action in the loop recursive equation, a representation form of calculation quantities of virtual points in a discrete process is given, and a seismic wave field in an ocean crust medium and an acoustic wave field in a deep-sea sound channel are obtained according to the loop recursive equation.

Description

Technical Field

[0001] This invention belongs to the field of underwater acoustic physics technology, specifically relating to a deep-sea T-phase calculation method and system based on the mechanism of seafloor seismic sources. Background Technology

[0002] T-phase, as a low-frequency acoustic signal carrier form of seismic waves from the seabed that transforms at a horizontally non-uniform seabed interface and propagates over long distances in deep-sea acoustic channels, can be effectively used for underwater acoustic monitoring of activities such as submarine earthquakes and submarine volcanic eruptions, as well as for research on the geological structure of the seabed. Deep-sea T-phase propagation simulation requires comprehensive consideration of the characterization of the seabed earthquake source, the propagation process of the seismic wave field in the elastic oceanic crust, the transformation process of the seismic wave to the acoustic field at the fluid-elastic interface, and the low-frequency acoustic propagation process in the deep-sea acoustic channel. Factors such as the horizontally non-uniform elastic oceanic crust / fluid-ocean interface, the multi-layered elastic properties of the seabed medium, the sound velocity profile of the seawater channel, and the low-frequency acoustic band all significantly limit the application of existing underwater acoustic propagation models in T-phase simulation. Although underwater acoustic field calculation methods have been extended to T-phase simulation, these extended models lack physically meaningful representations of the elastic seabed source, and the source characterization methods used cannot effectively reflect the physical mechanisms and characteristics of the seabed source. Summary of the Invention

[0003] To address the problems existing in the prior art, this invention proposes a deep-sea T-phase calculation method and system based on the mechanism of submarine seismic sources. This method comprehensively considers the characterization and elasticity of submarine seismic sources, the propagation of seismic waves and acoustic waves in fluid media and their mutual conversion process, and realizes the simulation of deep-sea T-phase propagation under submarine seismic events.

[0004] To achieve the above objectives, this invention provides a deep-sea T-phase calculation method based on the submarine seismic source mechanism, which specifically includes:

[0005] Step 1) For the propagation process of the T phase of deep-sea seafloor earthquake, determine the physical quantities to be calculated in the elastic multilayer oceanic crust medium and the fluid deep-sea acoustic waveguide, and establish the joint elliptic differential equation of acoustic wave-seismic wave in a two-dimensional cylindrical coordinate system.

[0006] Step 2) Based on operator theory and factorization, the joint elliptic differential equation of acoustic wave and seismic wave is transformed into a joint parabolic differential equation of acoustic wave and seismic wave, and its radical form horizontal recursive equation is given.

[0007] Step 3) Based on the volumetric coefficient, rotation vector and line source-point source analogy of deep-sea submarine earthquakes, establish the initial field horizontal recursive equation in radical form suitable for submarine earthquake events;

[0008] Step 4) Based on the split-step theory and the higher-order Padé rational approximation, transform the horizontal recurrence equation in radical form into N pStep-by-step horizontal recursive equation;

[0009] Step 5) Based on virtual point technology and fluid-elastic interface boundary conditions, the operator action in the cyclic horizontal recursive equation is discretized, and the representation form of the physical quantity calculated by virtual point is given.

[0010] Step 6) Calculate the seismic wave field in the oceanic crust medium and the acoustic wave field in the deep-sea acoustic channel based on the cyclic horizontal recursive equation and its discrete processing results, and realize the simulation of the T phase of the seafloor earthquake.

[0011] As an improvement to the above method, step 1) specifically includes:

[0012] For the propagation process of deep-sea seafloor earthquake phase T, the volumetric strain coefficient Δ and vertical displacement w are selected as the physical quantities for calculation in a fluid medium, and the sound pressure field in the fluid is p = -λΔ, where λ is the Lamé coefficient of the medium; in an elastic medium, the horizontal displacement derivative is selected. The vertical displacement w is a physical quantity used in the calculation;

[0013] For a single-frequency harmonic point source problem with a time factor of exp(-iωt), we establish the equations of motion satisfied by the physical quantities; where i is the imaginary number, ω is the angular frequency, and t is time; in a two-dimensional cylindrical coordinate system (r,z), we extract the factors. Ignoring higher-order terms, we establish a joint elliptic differential equation for sound waves and seismic waves:

[0014]

[0015]

[0016] The vertical displacement w in the fluid medium is calculated based on the volumetric strain coefficient Δ and the Euler equation, while the vertical displacement w in the elastic medium is calculated by relating it to the derivative of the horizontal displacement u. r Jointly solve the equations for calculation, operator L l and M l and matrix operator L s and M s for:

[0017]

[0018]

[0019] Where, λ l Let ρ be the Lamé coefficient of the fluid medium, seawater. l Let C be the density of the fluid seawater medium, and let Lamé coefficient of the fluid seawater medium be related to the speed of sound in seawater, c. w The relationship is: λ s and μ s Let ρ be the Lamé coefficient of the elastomeric oceanic crust medium.s Let be the density of the elastomeric oceanic crust medium, and let be the Lamé coefficient of the elastomeric oceanic crust medium and the longitudinal wave velocity c of the oceanic crust. p and transverse wave velocity c s The relationship is:

[0020] As an improvement to the above method, step 2) specifically includes:

[0021] Based on factorization and operator theory, and neglecting the errors generated during operator commutation, taking only the forward field, the elliptic differential equations satisfied by the calculated physical quantities in fluid and elastic media are transformed into parabolic differential equations:

[0022]

[0023]

[0024] Where ω is the angular frequency, k l0 =ω / c l0 and k s0 =ω / c s0 The reference wavenumbers for the fluid and elastomer are c, respectively. l0 and c s0 These represent the fluid reference sound velocity and the elastic body reference wave velocity, respectively, with specific values ​​determined based on the medium parameters and the type of wave field within the medium. I is a 2×2 dimension identity matrix, and the operator X... l And matrix operator X s for:

[0025]

[0026] Discretize the radial coordinate r into r m =md r m = 1, 2, ..., M, where m represents the m-th radial discrete point, M is the number of radial discrete points, and d r Given the radial dispersion step length, the parabolic differential equation is transformed into a horizontal recurrence equation in radical form:

[0027]

[0028]

[0029] As an improvement to the above method, step 3) specifically includes:

[0030] For T-phase signals from ultra-long-range monitoring, the resulting seismic source can be nearly a point source, located at depth z. s The δ function is used for characterization, ignoring its deformation and nonlinear processes in the local three-dimensional space; considering both physical meaning and model derivation, the volumetric strain coefficient is selected. With rotation vector As an intermediate quantity The displacement vector of the particle. and These are vector operations of the Laplace operator;

[0031] For submarine earthquake sources dominated by shear type, an analogy between line sources in rectangular coordinates and point sources in cylindrical coordinates is adopted to establish a radical-form initial field horizontal recursive equation suitable for submarine earthquake events; the volumetric coefficient Δ and rotation vector are then used for shear-type line sources in a two-dimensional rectangular coordinate system (x,z). The non-homogeneous differential equation satisfied by the intermediate quantity is:

[0032]

[0033] Among them, Ω y Rotation vector The rotational component of the torque is in the y-axis direction, A s k is the focal intensity constant. p =ω / c p and k s =ω / c s These are the P-wave number and S-wave number of the elastic medium in the vicinity of the earthquake source, respectively, where ω is the angular frequency and c is the wave number of the P-wave. p and c s These are the longitudinal wave number and the transverse wave number of the medium, respectively; δ(x) and δ(zz) s Let be a Dirac generalized function, used to represent a location at a horizontal distance x = 0 and a depth z = z. s The epicenter was located at [location missing].

[0034] Based on the continuity of the half-side integral and the field, the expressions for the derivative of the horizontal displacement and the initial field of the vertical displacement of the elastic medium in a two-dimensional rectangular coordinate system are obtained:

[0035]

[0036] Wherein, δ(zz) s ) and δ′(zz s ) are the Dirac generalized function and its vertical derivative in the z-direction, respectively, which are approximated by trigonometric functions or e-exponential forms to achieve numerical calculation;

[0037] Based on the analogy between line sources in rectangular coordinates and point sources in cylindrical coordinates, and combining the parabolic equations and their horizontal recursive forms under elastic media, we obtain the initial field horizontal recursive equations in radical form suitable for submarine earthquake events:

[0038]

[0039]

[0040] Where Δ(r1,z) is the horizontal distance r1=d r The volumetric coefficient of a calculated physical quantity in a fluid medium; u r (r1, z) represents the horizontal distance r1 = d r The physical quantity of horizontal displacement is calculated in an elastic medium; w(r1,z) is the horizontal distance r1 = d. r The calculated physical quantity of the medium is the vertical displacement; d r Let n be the radial distance from the walk length. u The invertible operator constant introduced to enhance computational stability takes the value i, where i is an imaginary number; Z s (z,z s ) and Z s (z,z s The source function of the submarine earthquake source, obtained based on analogy and invertible operators, is as follows:

[0041] Z s (z,z s )=(1-n u X l ) -2 δ(zz s ),

[0042] As an improvement to the above method, step 4) specifically includes:

[0043] The higher-order Padé rational approximation method is used to transform the horizontal recurrence equation in radical form into a horizontal recurrence equation in basic algebraic form.

[0044]

[0045]

[0046] Where, when m=0, Δ(r0,z) and [u r [r0,z] and w(r0,z) are respectively equal to Z. s (z,z s ) and Z s (z,z s );α j and β j N represents the higher-order Padé rational approximation coefficients obtained from the horizontal recursive equation in radical form. p It is the order of the higher-order Padé rational approximation;

[0047] Based on horizontal distance r m =md r Solving for the physical quantity r at the location m+1 =(m+1)d rWhen calculating physical quantities, the split-step method is used to transform the basic algebraic form of the horizontal recursive equation into N. p Step-by-step horizontal recurrence equation:

[0048]

[0049]

[0050] Where j = 1, 2, ..., N p Let r be the order of each order of the higher-order Padé rational approximation of the radical operator. The input quantity of the cyclic horizontal recursion is given by r. m =md r The physical quantity at the location is given, let Δ 0 (r m ,z)=Δ(r m ,z)u r 0 (r m ,z)=u r (r m ,z)w 0 (r m ,z)=w(r m ,z), according to the first step of the horizontal recursive form from [Δ 0 (r m ,z),u r 0 (r m ,z),w 0 (r m The first step output [Δ] is obtained from z)] 1 (r m ,z),u r 1 (r m ,z),w 1 (r m ,z)], then [Δ 1 (r m ,z),u r 1 (r m ,z),w 1 (r m [,z)] is used as the input for the next step of the horizontal recursive form to obtain the output [Δ] for the second step. 2 (r m ,z),u r 2 (r m ,z),w 2 (r m ,z)], and so on to obtain the Nth p Step output r m+1=(m+1)d r The physical quantity calculated at the distance is:

[0051]

[0052] As an improvement to the above method, step 5) specifically includes:

[0053] When calculating physical quantities based on the formed cyclic horizontal recursive equation, the vertical coordinate z is discretized into zi. n =nd z n = 0, 1, ..., I z ,I z +1,...,N z , and These are the vertically discrete points at the fluid-elastic lower and upper interfaces, respectively. To truncate the boundary position, d z For vertical distance from walking length;

[0054] At the vertical discrete point Introducing virtual fluid points and their virtual computational load. At the vertical discrete point Introducing elastic virtual points and their virtual computational load With the introduction of vertical discrete point partitioning and virtual points, Galerkin discretization of operators is implemented for the cyclic horizontal recursive equations in fluid and elastic media, respectively.

[0055] Based on the fluid-elastic boundary conditions and the central finite difference method, the computational cost of the fluid-elastic virtual point is replaced by the computational cost at the actual discrete point, realizing the joint calculation of the sound field in the fluid medium and the seismic wave field in the oceanic crust medium based on the cyclic recursive equation; for the fluid medium, the j-th virtual point The representation form is:

[0056]

[0057] Where, parameter a 11 and a 12 They are respectively:

[0058]

[0059] in, and Discrete points and Lamé coefficient of the fluid medium, This represents the density of the fluid medium at the corresponding discrete locations;

[0060] For elastic media, virtual points The representation form is:

[0061]

[0062]

[0063] Where, parameter a 21 a 22 a 23 and parameter a 31 a 32 a 33 a 34 a 35 They are respectively:

[0064]

[0065]

[0066]

[0067]

[0068] in, For discrete points The density of the elastomeric medium, and Discrete points and Lamé coefficient of the elastic medium.

[0069] As an improvement to the above method, step 6) specifically includes:

[0070] Based on the initial field representation of the submarine seismic source and the cyclic horizontal recursive equation, the radial r is realized sequentially. m Vertically to each point z at coordinates n The physical quantities are calculated; for fluid media, the volumetric strain coefficient Δ and vertical displacement w are calculated; for elastic media, the derivative of horizontal displacement u is calculated. r The result of the calculation of the vertical displacement w;

[0071] The propagation loss of sound pressure in fluid media or vertical normal stress in elastic media is used as the descriptive quantity, based on the generalized Hooke's law and the extracted factors. (r m ,z n Fluid sound field propagation loss TL at () w and the propagation loss TL of seismic wave field in elastic bodies s Represented as:

[0072]

[0073]

[0074] Where, λ l (r m ,z n ) is a discrete point (r) m ,z n Lamé coefficient of the fluid medium at ) For discrete points (r) m ,z n Lamé coefficient of the elastic medium at ().

[0075] On the other hand, this invention proposes a deep-sea T-phase calculation system based on the mechanism of seafloor seismic sources, the system comprising:

[0076] The wave field equation establishment module is used to determine the physical quantities in elastic multilayer oceanic crust media and fluid deep-sea acoustic waveguides, and to establish the joint elliptic differential equation of acoustic waves and seismic waves in a two-dimensional cylindrical coordinate system.

[0077] The parabolic equation transformation module is used to transform the joint elliptic differential equation of acoustic waves and seismic waves into a joint parabolic differential equation of acoustic waves and seismic waves based on operator theory and factorization, and gives its horizontal recursive equation in radical form.

[0078] The initial field equation establishment module is used to establish a radical-form initial field horizontal recursive equation adapted to submarine earthquake events based on the volumetric coefficient, rotation vector and line source-point source analogy of deep-sea submarine earthquakes.

[0079] The cyclic recursion module is used to transform horizontal recursive equations in radical form into N-order equations based on split-step theory and higher-order Padé rational approximations. p Step-by-step horizontal recursive equation;

[0080] The operator processing module is used to discretize the operator actions in the cyclic horizontal recursive equations based on virtual point technology and fluid-elastic interface boundary conditions, and to provide a representation of the physical quantities calculated using virtual points; and

[0081] The T-phase solution module is used to calculate the seismic wave field in the oceanic crust and the acoustic wave field in the deep-sea acoustic channel based on the cyclic horizontal recursive equation and its discretization results, thereby simulating the T-phase of seafloor earthquakes. Compared with existing technologies, the advantages of this invention are:

[0082] This invention employs a source mechanism-based and robust operator approximation method to establish a deep-sea T-phase calculation method adapted to submarine earthquake events. It effectively characterizes the source mechanism of long-range T-phase low-frequency acoustic waves and the propagation and conversion processes of seismic waves and acoustic waves in the medium, ensuring the stability of the multi-layered elastic oceanic crust medium environment and the ultra-long-range propagation process of deep-sea acoustic waveguides. It solves the limitation of fully characterizing submarine seismic sources on T-phase propagation simulation and can effectively provide the mechanism of T-phase formation under submarine earthquake events. Attached Figure Description

[0083] Figure 1 This is a flowchart of the deep-sea T-phase calculation method based on the submarine seismic source mechanism of the present invention;

[0084] Figure 2 This is a schematic diagram of the ocean-oceanic crust waveguide environment model in Embodiment 1 of the present invention;

[0085] Figure 3 The deep-sea waveguide acoustic velocity profile is vertically distributed in Embodiment 1 of the present invention;

[0086] Figure 4 The results of the T-phase propagation loss distribution calculation using the method of this invention;

[0087] Figure 5 The method of this invention is used to receive the sound field propagation loss curve at a depth of 0.2 km. Detailed Implementation

[0088] This invention provides a deep-sea T-phase calculation method based on the mechanism of submarine seismic sources. This method mainly establishes a deep-sea T-phase calculation method adapted to submarine seismic events based on submarine seismic source characterization, parabolic equation theory and reliable interface processing methods.

[0089] The method includes:

[0090] Taking the ultra-long-range propagation process of the T phase of submarine seismic events as a starting point, the physical quantities of calculation in elastic multilayer oceanic crust media and fluid deep-sea acoustic waveguides are determined, and a joint parabolic equation model of acoustic waves and seismic waves is established.

[0091] Starting from the full characterization of submarine earthquake source characteristics and the study of long-range T-phase, the volumetric strain coefficient and rotation vector are selected as source characteristic characterization quantities, and an initial field model is established based on the analogy between line source and point source.

[0092] Based on the split-step theory and higher-order rational approximation, a finite-step horizontal recursive form adapted to the multi-layered elastic oceanic crust-deep-sea acoustic waveguide environment is established.

[0093] Based on virtual point technology, the operator effects in the cyclic horizontal recursive equation are discretized, and the representation of physical quantities calculated by virtual points is given. This enables joint calculation of acoustic waves and seismic waves, and obtains an effective simulation of the T-phase propagation process under submarine seismic events.

[0094] The simulation of the T-phase propagation process under typical submarine earthquake events shows that this method can effectively calculate the propagation process of seismic waves inside the oceanic crust, the conversion process of seismic waves and acoustic waves at the fluid-elastic interface, and the propagation process of low-frequency acoustic waves in the deep-sea channel under submarine earthquake events. It can be effectively used for the characteristic analysis and signal prediction of submarine earthquake T-phase signals.

[0095] The method specifically includes:

[0096] Based on the propagation process of the T-phase of deep-sea seafloor earthquakes, the physical quantities for calculation in elastic multilayer oceanic crust media and fluid deep-sea acoustic waveguides are determined, and a joint elliptic differential equation of acoustic wave and seismic wave is established in a two-dimensional cylindrical coordinate system.

[0097] Specifically, considering that the main excitation and propagation of the T-phase signal includes the seismic wave propagation process in the elastic multilayered oceanic crust medium, the seismic wave-sound wave conversion process at the non-uniform seabed interface, and the low-frequency sound transmission process in the deep-sea fluid acoustic channel, to avoid additional processing of the boundary conditions of the internal interfaces of the layered fluid medium and the layered elastic medium, the volumetric strain coefficient Δ and the vertical displacement w are selected as the physical quantities for calculation in the fluid medium, and the sound pressure field in the fluid is p = -λΔ, where λ is the Lamé coefficient of the medium; in the elastic medium, the horizontal displacement derivative is used. The vertical displacement w is a physical quantity used in the calculation;

[0098] For a single-frequency harmonic point source problem with a time factor of exp(-iωt), we establish the equations of motion satisfied by the physical quantities; where i is the imaginary number; ω is the angular frequency; and t is time. In a two-dimensional cylindrical coordinate system (r,z), we extract the factors... Ignoring higher-order terms, the differential equations satisfied by the calculated physical quantities in fluid and elastic media are:

[0099]

[0100]

[0101] In fluid media, the vertical displacement w can be calculated independently based on the volumetric strain coefficient Δ and the Euler equation. In elastic media, the vertical displacement w needs to be calculated in conjunction with the derivative of the horizontal displacement u. r Jointly solve the equations for calculation, operator L l and M l and matrix operator L s and M s for:

[0102]

[0103]

[0104] Where, λ l Let ρ be the Lamé coefficient of the fluid medium, seawater. l Let C be the density of the fluid seawater medium, and let Lamé coefficient of the fluid seawater medium be related to the speed of sound in seawater, c. w The relationship is: λ s and μ s Let ρ be the Lamé coefficient of the elastomeric oceanic crust medium.s Let be the density of the elastomeric oceanic crust medium, and let be the Lamé coefficient of the elastomeric oceanic crust medium and the longitudinal wave velocity c of the oceanic crust. p and transverse wave velocity c s The relationship is:

[0105] The calculated physical quantities of the fluid medium and the elastic medium are used as the calculated physical quantities of the differential equations of acoustic waves and seismic waves, respectively, to complete the determination of the calculated physical quantities in the elastic multilayer oceanic crust medium and the fluid deep-sea acoustic waveguide; the differential equations satisfied by the above acoustic wave field and seismic wave field are used as the acoustic-seismic wave joint elliptic differential equations to complete the establishment of the acoustic-seismic wave field differential equations.

[0106] Based on operator theory and factorization, the joint differential equation of acoustic wave and seismic wave is transformed into a joint parabolic differential equation of acoustic wave and seismic wave, and its radical form horizontal recursive equation is given.

[0107] Specifically, based on factorization and operator theory, and neglecting the errors generated during operator commutation, taking only the forward field, the elliptic equations of motion satisfied by the physical quantities in fluid and elastic media can be transformed into parabolic differential equations:

[0108]

[0109]

[0110] Where ω is the angular frequency, k l0 =ω / c l0 and k s0 =ω / c s0 The reference wavenumbers for the fluid and elastomer are c, respectively. l0 and c s0 These are the fluid reference sound velocity and the elastic body reference wave velocity, respectively. Their values ​​should be determined based on the medium parameters and the type of wave field within the medium. I is a 2×2 dimension identity matrix, and the operator X... l And matrix operator X s for:

[0111]

[0112] Discretize the radial coordinate r into r m =md r (m = 1, 2, ..., M), where M is the number of radial discrete points and the radial discrete step size is d. r Transform the parabolic differential equation into a horizontal recursive equation in radical form:

[0113]

[0114]

[0115] Based on the volumetric coefficient, rotation vector and line source-point source analogy of deep-sea submarine earthquakes, a radical form of the initial field horizontal recursive equation is established to adapt to submarine earthquake events.

[0116] Specifically, for the T-phase signal from ultra-long-range monitoring, the resulting seismic source can be almost a point source, located at depth z. s The δ function is used for characterization, ignoring its deformation and nonlinear processes in the local three-dimensional space; considering both physical meaning and model derivation, the volumetric strain coefficient is selected. With rotation vector As an intermediate quantity The displacement vector of the particle. and These are vector operations of the Laplace operator;

[0117] For submarine earthquake sources where shear is the dominant type, the rotation vector in cylindrical coordinates Characterizing and simplifying the differential equations is quite difficult. Therefore, an analogy between a line source in a rectangular coordinate system and a point source in a cylindrical coordinate system is adopted to establish a radical-form initial field horizontal recursive equation suitable for submarine earthquake events. The volumetric coefficient Δ and rotation vector are then used in a two-dimensional rectangular coordinate system (x,z) for shear-type line sources. The non-homogeneous differential equation satisfied by the intermediate quantity is:

[0118]

[0119] Among them, Ω y Rotation vector The rotational component of the torque is in the y-axis direction, A s k is the focal intensity constant. p =ω / c p and k s =ω / c s These are the P-wave number and S-wave number of the elastic medium in the vicinity of the earthquake source, respectively, where ω is the angular frequency and c is the wave number of the P-wave. p and c s These are the longitudinal wave number and the transverse wave number of the medium, respectively.

[0120] Based on the continuity of the half-integral and the field, we can obtain the expressions for the derivative of the horizontal displacement and the initial field of the vertical displacement of the elastic medium in a two-dimensional rectangular coordinate system:

[0121]

[0122] Wherein, δ(zz) s ) and δ′(zz s ) are the Dirac generalized function and its vertical derivative, which can be approximated by trigonometric functions or e-exponential forms to achieve numerical calculation;

[0123] Based on the analogy between line sources in rectangular coordinate systems and point sources in cylindrical coordinate systems, and combining the parabolic equations and their horizontal recursive forms under elastic media, we can obtain the initial field horizontal recursive equations in radical form suitable for submarine earthquake events:

[0124]

[0125]

[0126] Where Δ(r1,z) is the horizontal distance r1=d r The volumetric coefficient of a calculated physical quantity in a fluid medium; u r (r1, z) represents the horizontal distance r1 = d r The physical quantity of horizontal displacement is calculated in an elastic medium; w(r1,z) is the horizontal distance r1 = d. r The calculated physical quantity of the medium is the vertical displacement; d r For radial discrete length, n u The reversible operator constant introduced to enhance computational stability is generally taken as i, where i is an imaginary number; Z represents the source of submarine earthquakes. s (z,z s ) and Z s (z,z s They are respectively:

[0127]

[0128] Based on the split-step theory and the higher-order Padé rational approximation, the horizontal recurrence equation in radical form is transformed into N p Step-by-step horizontal recursive equation;

[0129] Specifically, based on the established horizontal recurrence equation in radical form, the higher-order Padé rational approximation method is used to transform the horizontal recurrence equation in radical form into a horizontal recurrence equation in basic algebraic form.

[0130]

[0131]

[0132] Where, when m=0, Δ(r0,z) and [u r [r0,z] and w(r0,z) are respectively equal to Z. s (z,z s ) and Z s (z,z s );α j and β j N represents the higher-order Padé rational approximation coefficients obtained from the horizontal recursive equation in radical form. pIt is the order of the higher-order Padé rational approximation;

[0133] Based on horizontal distance r m =md r Solving for the physical quantity r at the location m+1 =(m+1)d r When calculating physical quantities, the split-step method is used to transform the basic algebraic form of the horizontal recursive equation into N. p Step-by-step horizontal recurrence equation:

[0134]

[0135]

[0136] Where j = 1, 2, ..., N p Let r be the order of each order of the higher-order Padé rational approximation of the radical operator. The input quantity of the cyclic horizontal recursion is given by r. m =md r The physical quantity at the location is given, let Δ 0 (r m ,z)=Δ(r m ,z)u r 0 (r m ,z)=u r (r m ,z)w 0 (r m ,z)=w(r m ,z), according to the first step of the horizontal recursive form from [Δ 0 (r m ,z),u r 0 (r m ,z),w 0 (r m The first step output [Δ] is obtained from z)] 1 (r m ,z),u r 1 (r m ,z),w 1 (r m ,z)], then [Δ 1 (r m ,z),u r 1 (r m ,z),w 1 (r m [,z)] is used as the input for the next step of the horizontal recursive form to obtain the output [Δ] for the second step. 2 (r m ,z),u r2 (r m ,z),w 2 (r m ,z)], and so on to obtain the Nth p Step output r m+1 =(m+1)d r The physical quantity calculated at the distance is:

[0137]

[0138] Based on the virtual point technique, the operator actions in the cyclic horizontal recursive equation are discretized, and the representation form of physical quantities calculated by virtual points is given:

[0139] Specifically, when calculating physical quantities based on the formed cyclic horizontal recursive equation, the vertical coordinate z is discretized into zi. n =nd z (n = 0, 1, ..., I) z ,I z +1,...,N z ), and These are the vertically discrete points at the fluid-elastic lower and upper interfaces, respectively. To truncate the boundary position, d z For vertical distance from walking length;

[0140] At the vertical discrete point Introducing virtual fluid points and their virtual computational load. At the vertical discrete point Introducing elastic virtual points and their virtual computational load With the introduction of vertical discrete point partitioning and virtual points, the Galerkin discretization of the operator can be realized for the cyclic horizontal recursive equations in fluid and elastic media respectively.

[0141] To represent useless computational physical quantities at virtual points using actual discrete point computational physical representations, and to achieve a global joint solution of the fluid and elastic level recursive equations, fluid-elastic boundary conditions and central finite difference methods are used. For the fluid medium, virtual points... and The representation form is:

[0142]

[0143] Where, parameter a 11 and a 12 They are respectively:

[0144]

[0145] in, and Discrete points and Lamé coefficient of the fluid medium, This represents the density of the fluid medium at the corresponding discrete locations;

[0146] For elastic media, virtual points The representation form is:

[0147]

[0148]

[0149] Where, parameter a 21 a 22 a 23 and parameter a 31 a 32 a 33 a 34 a 35 They are respectively:

[0150] a 23 =1,

[0151] a 32 =4,

[0152]

[0153]

[0154] in, For discrete points Lamé coefficient of the fluid medium, For discrete points The density of the elastomeric medium, and Discrete points and Lamé coefficient of the elastic medium.

[0155] Based on the cyclic horizontal recursive equation and its discrete results, the seismic wave field in the oceanic crust medium and the acoustic wave field in the deep-sea acoustic channel are calculated to realize the simulation of the T phase of the seafloor earthquake.

[0156] Specifically, based on the initial field representation of the submarine seismic source and the cyclic horizontal recursive equation, the radial r can be realized sequentially. m =md r Vertical points z at coordinates (m=1,2,...,M) n =nd z (n = 0, 1, ..., I) z,I z +1,...,N z The method calculates the physical quantities of the fluid medium and provides the results for the volumetric strain coefficient Δ and vertical displacement w. For the elastic medium, the method provides the derivative of the horizontal displacement u. r The result of the calculation of the vertical displacement w;

[0157] To describe the propagation process of submarine earthquake phase T and its influence on the waveguide environment, the propagation loss of acoustic pressure in fluid media or vertical normal stress in elastic media is used as the descriptive quantity, based on the generalized Hooke's law and the extracted factors. (r m ,z n Fluid sound field propagation loss TL at () w and the propagation loss TL of seismic wave field in elastic bodies s It can be represented as:

[0158]

[0159]

[0160] Where, λ l (r m ,z n ) is a discrete point (r) m ,z n Lamé coefficient of the fluid medium at )

[0161] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0162] Example 1

[0163] like Figure 1As shown, this invention provides a deep-sea T-phase calculation method based on the mechanism of submarine seismic sources. This method, based on submarine seismic source characterization, parabolic equation theory, and reliable interface processing, establishes a deep-sea T-phase calculation method adapted to submarine seismic events. The method includes: taking the ultra-long-range propagation process of the T-phase of a submarine seismic event as a starting point, determining the physical quantities to be calculated in the elastic multilayer oceanic crust medium and the fluid deep-sea acoustic waveguide, and establishing a joint parabolic equation model of acoustic waves and seismic waves; taking the full characterization of submarine seismic source characteristics and the study of long-range T-phase as a starting point, selecting the volumetric coefficient and rotation vector as source characteristic characterization quantities, and establishing an initial field model based on the line source-point source analogy; establishing a finite-step horizontal recursive form adapted to the multilayer elastic oceanic crust-deep-sea acoustic waveguide environment based on the splitting-stepping theory and higher-order rational approximation; and using virtual point technology to discretize the operator action in the cyclic horizontal recursive equation, giving the characterization form of the virtual point calculated physical quantities, realizing the joint calculation of acoustic waves and seismic waves in the fluid seawater-elastic oceanic crust environment, and obtaining an effective simulation of the T-phase propagation process under submarine seismic events.

[0164] Ocean-oceanic crust waveguide environment model, such as Figure 2 As shown: A two-dimensional cylindrical coordinate system (r, z) is established, with the z-axis taken as positive downwards. The Lamé coefficient and density of the fluid seawater medium are λ. l and ρ l The Lamé coefficient and density of the elastomeric oceanic crust medium are λ. s μ s and ρ s For a single-frequency harmonic point source problem with a time factor of exp(-iωt), the factor The differential equations satisfied by the calculated physical quantities in fluid and elastomeric media are as follows:

[0165]

[0166]

[0167] In fluid media, the vertical displacement w can be calculated independently based on the volumetric strain coefficient Δ and the Euler equation. In elastic media, the vertical displacement w needs to be calculated in conjunction with the derivative of the horizontal displacement u. r Jointly solve the equations for calculation, operator L l and M l and matrix operator L s and M s for:

[0168]

[0169]

[0170] By employing factorization and operator theory, and neglecting the errors generated during operator commutation, and considering only the forward field, the elliptic equations of motion satisfied by the physical quantities in fluid and elastic media can be transformed into parabolic differential equations:

[0171]

[0172]

[0173] Where ω is the angular frequency, k l0 =ω / c l0 and k s0 =ω / c s0 The reference wavenumbers for the fluid and elastomer are c, respectively. l0 and c s0 These are the fluid reference sound velocity and the elastic body reference wave velocity, respectively. Their values ​​should be determined based on the medium parameters and the type of wave field within the medium. I is a 2×2 dimension identity matrix, and the operator X... l And matrix operator X s for:

[0174]

[0175] Discretize the radial coordinate r into r m =md r (m = 1, 2, ..., M), where M is the number of radial discrete points and the radial discrete step size is d. r The value d is generally taken as r ≤5λ, where λ is the wavelength, we can obtain the horizontal recurrence equation in radical form:

[0176]

[0177]

[0178] For the initial acoustic-seismic wave field generated by a submarine earthquake source, based on the analogy between line sources and point sources, and introducing the volumetric strain coefficient and rotation vector representation of the local source region, the radical form of the horizontal recursive equation for the initial field under submarine earthquake events is as follows:

[0179]

[0180]

[0181] Where, n u The reversible operator constant introduced to enhance computational stability is generally taken as i, where i is an imaginary number; Z represents the source of submarine earthquakes. s (z,z s ) and Z s (z,z s They are respectively:

[0182]

[0183] Using the higher-order Padé rational approximation method and the split-step method, the radical form of the horizontal recurrence equation is transformed into N p Step-by-step horizontal recurrence equation:

[0184]

[0185]

[0186] Where j = 1, 2, ..., N p Let r be the order of each order of the higher-order Padé rational approximation of the radical operator. The input quantity of the cyclic horizontal recursion is given by r. m =md r The physical quantity at the location is given, let Δ 0 (r m ,z)=Δ(r m ,z)u r 0 (r m ,z)=u r (r m ,z)w 0 (r m ,z)=w(r m ,z), according to the first step of the horizontal recursive form from [Δ 0 (r m ,z),u r 0 (r m ,z),w 0 (r m The first step output [Δ] is obtained from z)] 1 (r m ,z),u r 1 (r m ,z),w 1 (r m ,z)], then [Δ 1 (r m ,z),u r 1 (r m ,z),w 1 (r m [,z)] is used as the input for the next step of the horizontal recursive form to obtain the output [Δ] for the second step. 2 (r m ,z),u r 2 (r m ,z),w 2 (r m ,z)], and so on to obtain the Nthp Step output r m+1 =(m+1)d r The physical quantity calculated at the distance is:

[0187]

[0188] At the same time, the vertical coordinate z is discretized into z n =nd z (n = 0, 1, ..., I) z ,I z +1,...,N z ), and These are the vertically discrete points at the fluid-elastic lower and upper interfaces, respectively. To truncate the boundary position, d z The vertical discrete step length; at the vertical discrete point Introducing virtual fluid points and their virtual computational load. At the vertical discrete point Introducing elastic virtual points and their virtual computational load With the introduction of vertical discrete point partitioning and virtual points, the Galerkin discretization of the operator can be realized for the cyclic horizontal recursive equations in fluid and elastic media respectively.

[0189] To represent useless computational physical quantities at virtual points using actual discrete point computational physical representations, and to achieve a global joint solution of the fluid and elastic level recursive equations, fluid-elastic boundary conditions and central finite difference methods are used. For the fluid medium, virtual points... and The representation form is:

[0190]

[0191] For elastic media, virtual points The representation form is:

[0192]

[0193]

[0194] in, and Discrete points and Lamé coefficient of the fluid medium, This represents the density of the fluid medium at the corresponding discrete locations; For discrete points The density of the elastomeric medium, and Discrete points and Lamé coefficient of the elastic medium; parameter a 11 and a 12 Parameter a 21 a 22 a 23 and parameter a 31 a 32 a 33 a 34 a 35 They are respectively:

[0195]

[0196] a 23 =1,

[0197] a 32 =4,

[0198]

[0199]

[0200] Based on the calculations of acoustic wave fields in seawater waveguides and seismic waves in oceanic crust, this paper uses the propagation loss of acoustic pressure in fluid media or vertical normal stress in elastic media as a descriptive quantity to illustrate the deep-sea T-phase propagation process of submarine seismic events. m ,z n Fluid sound field propagation loss TL at () w and the propagation loss TL of seismic wave field in elastic bodies s It can be represented as:

[0201]

[0202]

[0203] Example 2.

[0204] Embodiment 2 of the present invention proposes a deep-sea T-phase calculation system based on the mechanism of seafloor seismic sources, implemented based on the method of Embodiment 1. The system includes:

[0205] The wave field equation establishment module is used to determine the physical quantities in elastic multilayer oceanic crust media and fluid deep-sea acoustic waveguides, and to establish the joint elliptic differential equation of acoustic waves and seismic waves in a two-dimensional cylindrical coordinate system.

[0206] The parabolic equation transformation module is used to transform the joint differential equation of acoustic waves and seismic waves into the joint parabolic differential equation of acoustic waves and seismic waves and its radical form horizontal recursive equation based on operator theory and factorization.

[0207] The initial field equation establishment module is used to establish a radical-form initial field horizontal recursive equation adapted to submarine earthquake events based on the volumetric coefficient, rotation vector and line source-point source analogy of deep-sea submarine earthquakes.

[0208] The cyclic recursion module is used to transform horizontal recursive equations in radical form into N-order equations based on split-step theory and higher-order Padé rational approximations. p Step-by-step horizontal recursive equation;

[0209] The operator processing module is used to discretize the operator action in the cyclic horizontal recursive equation based on virtual point technology and fluid-elastic interface boundary conditions, and to give the representation form of the physical quantity calculated by virtual point.

[0210] The T-phase solver module is used to calculate the seismic wave field in the oceanic crust medium and the acoustic wave field in the deep-sea acoustic channel using cyclic horizontal recursive equations, thereby simulating the T-phase of seafloor earthquakes.

[0211] Simulation example:

[0212] Considering the oceanic-oceanic crust waveguide with ideal submarine mountain topography, and referring to the actual deep-sea water and oceanic crust structure, the water sound velocity c is taken. w For example Figure 3 The Munk deep-sea sound velocity profile and density ρ shown are shown. w =1.0g / cm 3 Environmental and geometric parameters of oceanic crust and submarine mountains, such as Figure 2 As shown, the submarine mountains reach a height of 4 km and a radial dimension of 50 km, the deep-sea plain region has a depth of 5 km, the wave velocity inside the elastic medium exhibits a positive gradient distribution, and the Lamé coefficient λ of the fluid medium... l Lamé coefficient of elastic media [λ] s ,μ s The earthquake can be calculated based on sound speed or wave speed, density, and absorption. The submarine source is located at the oceanic crust-mantle interface, 10 km directly below the origin. The calculation frequency is 10 Hz, the receiving depth is 0.2 km, and the radial distance step length is d. r =50m, vertical distance from the walking distance d z =2m, maximum horizontal distance r max =500km, calculate the maximum depth z max =20km, the propagation loss distribution of phase T signal is as follows Figure 4 As shown, the propagation loss of the sound pressure field at the receiving depth is as follows: Figure 5 As shown.

[0213] like Figure 4 and Figure 5As shown, the deep-sea T-phase calculation method established in this invention can effectively simulate the T-phase propagation process of submarine seismic events. It demonstrates the propagation process of seismic waves in elastic multilayered oceanic crust, the seismic wave-sound wave conversion at the oceanic crust-seawater interface, and the low-frequency sound wave propagation process in the deep-sea channel. It can effectively give the effect of the non-horizontal oceanic crust-seawater interface on the formation of T-phase, and has high stability and accuracy.

[0214] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for calculating deep-sea T-phase based on the mechanism of submarine seismic sources, the method comprising: Step 1) For the propagation process of the T phase of deep-sea seafloor earthquake, determine the physical quantities to be calculated in the elastic multilayer oceanic crust medium and the fluid deep-sea acoustic waveguide, and establish the joint elliptic differential equation of acoustic wave-seismic wave in a two-dimensional cylindrical coordinate system. Step 2) Based on operator theory and factorization, the joint elliptic differential equation of acoustic wave and seismic wave is transformed into a joint parabolic differential equation of acoustic wave and seismic wave, and its radical form horizontal recursive equation is given. Step 3) Based on the volumetric coefficient, rotation vector and line source-point source analogy of deep-sea submarine earthquakes, establish the initial field horizontal recursive equation in radical form suitable for submarine earthquake events; Step 4) Based on the split-step theory and the higher-order Padé rational approximation, transform the horizontal recurrence equation in radical form into N p Step-by-step horizontal recursive equation; Step 5) Based on virtual point technology and fluid-elastic interface boundary conditions, the operator action in the cyclic horizontal recursive equation is discretized, and the representation form of the virtual point physical quantity is given. Step 6) Calculate the seismic wave field in the oceanic crust medium and the acoustic wave field in the deep-sea acoustic channel based on the cyclic horizontal recursive equation and its discrete processing results, and realize the simulation of the T phase of the seafloor earthquake.

2. The deep-sea T-phase calculation method based on the submarine seismic source mechanism according to claim 1, characterized in that, Step 1) specifically includes: For the propagation process of deep-sea seafloor earthquake phase T, the volumetric strain coefficient Δ and vertical displacement w are selected as the physical quantities for calculation in a fluid medium, and the sound pressure field in the fluid is p = -λΔ, where λ is the Lamé coefficient of the medium; in an elastic medium, the horizontal displacement derivative is selected. The vertical displacement w is a physical quantity used in the calculation; For a single-frequency harmonic point source problem with a time factor of exp(-iωt), we establish the equations of motion satisfied by the physical quantities; where i is the imaginary number, ω is the angular frequency, and t is time; in a two-dimensional cylindrical coordinate system (r,z), we extract the factors. Ignoring higher-order terms, we establish a joint elliptic differential equation for sound waves and seismic waves: The vertical displacement w in the fluid medium is calculated based on the volumetric strain coefficient Δ and the Euler equation, while the vertical displacement w in the elastic medium is calculated by relating it to the derivative of the horizontal displacement u. r Jointly solve the equations and calculate the operator L. l and M l and matrix operator L s and M s for: L l =λ l , Where, λ l Let ρ be the Lamé coefficient of the fluid medium, seawater. l Let C be the density of the fluid seawater medium, and let Lamé coefficient of the fluid seawater medium be related to the speed of sound in seawater, c. w The relationship is: λ s and μ s Let ρ be the Lamé coefficient of the elastomeric oceanic crust medium. s Let be the density of the elastomeric oceanic crust medium, and let be the Lamé coefficient of the elastomeric oceanic crust medium and the longitudinal wave velocity c of the oceanic crust. p and transverse wave velocity c s The relationship is:

3. The deep-sea T-phase calculation method based on the submarine seismic source mechanism according to claim 2, characterized in that, Step 2) specifically includes: Based on factorization and operator theory, and neglecting the errors generated during operator commutation, taking only the forward field, the elliptic differential equations satisfied by the calculated physical quantities in fluid and elastic media are transformed into parabolic differential equations: Where ω is the angular frequency, k l0 =ω / c l0 and k s0 =ω / c s0 The reference wavenumbers for the fluid and elastomer are c, respectively. l0 and c s0 These represent the fluid reference sound velocity and the elastic body reference wave velocity, respectively, with specific values ​​determined based on the medium parameters and the type of wave field within the medium. I is a 2×2 dimension identity matrix, and the operator X... l And matrix operator X s for: Discretize the radial coordinate r into r m =md r m = 1, 2, ..., M, where m represents the m-th radial discrete point, M is the number of radial discrete points, and d r Given the radial dispersion step length, the parabolic differential equation is transformed into a horizontal recurrence equation in radical form:

4. The deep-sea T-phase calculation method based on the submarine seismic source mechanism according to claim 3, characterized in that, Step 3) specifically includes: For T-phase signals from ultra-long-range monitoring, the resulting seismic source can be nearly a point source, located at depth z. s The δ function is used for characterization, ignoring its deformation and nonlinear processes in the local three-dimensional space; considering both physical meaning and model derivation, the volumetric strain coefficient is selected. With rotation vector As an intermediate quantity The displacement vector of the particle. and These are vector operations of the Laplace operator; For submarine earthquake sources dominated by shear type, an analogy between line sources in rectangular coordinates and point sources in cylindrical coordinates is adopted to establish a radical-form initial field horizontal recursive equation suitable for submarine earthquake events; the volumetric coefficient Δ and rotation vector are then used for shear-type line sources in a two-dimensional rectangular coordinate system (x,z). The non-homogeneous differential equation satisfied by the intermediate quantity is: Among them, Ω y Rotation vector The rotational component of the torque is in the y-axis direction, A s k is the focal intensity constant. p =ω / c p and k s =ω / c s These are the P-wave number and S-wave number of the elastic medium in the vicinity of the earthquake source, respectively, where ω is the angular frequency and c is the wave number of the P-wave. p and c s These are the longitudinal wave number and the transverse wave number of the medium, respectively; δ(x) and δ(zz) s Let be a Dirac generalized function, used to represent a location at a horizontal distance x = 0 and a depth z = z. s The epicenter was located at [location missing]. Based on the continuity of the half-side integral and the field, the expressions for the derivative of the horizontal displacement and the initial field of the vertical displacement of the elastic medium in a two-dimensional rectangular coordinate system are obtained: Wherein, δ(zz) s ) and δ′(zz s ) are the Dirac generalized function and its vertical derivative in the z-direction, respectively, which are approximated by trigonometric functions or e-exponential forms to achieve numerical calculation; Based on the analogy between line sources in rectangular coordinates and point sources in cylindrical coordinates, and combining the parabolic equations and their horizontal recursive forms under elastic media, we obtain the initial field horizontal recursive equations in radical form suitable for submarine earthquake events: Where Δ(r1,z) is the horizontal distance r1=d r The volumetric coefficient of a calculated physical quantity in a fluid medium; u r (r1, z) represents the horizontal distance r1 = d r The physical quantity of horizontal displacement is calculated in an elastic medium; w(r1,z) is the horizontal distance r1 = d. r The calculated physical quantity of the medium is the vertical displacement; d r Let n be the radial distance from the walk length. u The invertible operator constant introduced to enhance computational stability takes the value i, where i is an imaginary number; Z s (z,z s ) and Z s (z,z s The source function of the submarine earthquake source, obtained based on analogy and invertible operators, is as follows: WITH s (with,with s )=(1-n u X l ) -2 δ(zz s ), 5. The deep-sea T-phase calculation method based on the submarine seismic source mechanism according to claim 4, characterized in that, Step 4) specifically includes: The higher-order Padé rational approximation method is used to transform the horizontal recurrence equation in radical form into a horizontal recurrence equation in basic algebraic form. Where, when m=0, Δ(r0,z) and [u r [r0,z] and w(r0,z) are respectively equal to Z. s (z,z s ) and Z s (z,z s );α j and β j N represents the higher-order Padé rational approximation coefficients obtained from the horizontal recursive equation in radical form. p It is the order of the higher-order Padé rational approximation; Based on horizontal distance r m =md r Solving for the physical quantity r at the location m+1 =(m+1)d r When calculating physical quantities, the split-step method is used to transform the basic algebraic form of the horizontal recursive equation into N. p Step-by-step horizontal recurrence equation: Where j = 1, 2, ..., N p Let r be the order of each order of the higher-order Padé rational approximation of the radical operator. The input quantity of the cyclic horizontal recursion is given by r. m =md r The physical quantity at the location is given, let Δ 0 (r m ,z)=Δ(r m ,z)u r 0 (r m ,z)=u r (r m ,z)w 0 (r m ,z)=w(r m ,z), according to the first step of the horizontal recursive form from [Δ 0 (r m ,z),u r 0 (r m ,z),w 0 (r m The first step output [Δ] is obtained from z)] 1 (r m ,z),u r 1 (r m ,z),w 1 (r m ,z)], then [Δ 1 (r m ,z),u r 1 (r m ,z),w 1 (r m [,z)] is used as the input for the next step of the horizontal recursive form to obtain the output [Δ] for the second step. 2 (r m ,z),u r 2 (r m ,z),w 2 (r m ,z)], and so on to obtain the Nth p Step output r m+1 =(m+1)d r The physical quantity calculated at the distance is:

6. The deep-sea T-phase calculation method based on the submarine seismic source mechanism according to claim 5, characterized in that, Step 5) specifically includes: When calculating physical quantities based on the formed cyclic horizontal recursive equation, the vertical coordinate z is discretized into zi. n =nd z n = 0, 1, ..., I z ,I z +1,...,N z , and These are the vertically discrete points at the fluid-elastic lower and upper interfaces, respectively. To truncate the boundary position, d z For vertical distance from walking length; At the vertical discrete point Introducing virtual fluid points and their virtual computational load. At the vertical discrete point Introducing elastic virtual points and their virtual computational load With the introduction of vertical discrete point partitioning and virtual points, Galerkin discretization of operators is implemented for the cyclic horizontal recursive equations in fluid and elastic media, respectively. Based on the fluid-elastic boundary conditions and the central finite difference method, the computational cost of the fluid-elastic virtual point is replaced by the computational cost at the actual discrete point, realizing the joint calculation of the sound field in the fluid medium and the seismic wave field in the oceanic crust medium based on the cyclic recursive equation; for the fluid medium, the j-th virtual point The representation form is: Where, parameter a 11 and a 12 They are respectively: in, and Discrete points and Lamé coefficient of the fluid medium, This represents the density of the fluid medium at the corresponding discrete locations; For elastic media, virtual points The representation form is: Where, parameter a 21 a 22 a 23 and parameter a 31 a 32 a 33 a 34 a 35 They are respectively: a 23 ＝1， a 32 ＝4， in, For discrete points The density of the elastomeric medium, and Discrete points and Lamé coefficient of the elastic medium.

7. The deep-sea T-phase calculation method based on the submarine seismic source mechanism according to claim 6, characterized in that, Step 6) specifically includes: Based on the initial field representation of the submarine seismic source and the cyclic horizontal recursive equation, the radial r is realized sequentially. m Vertically to each point z at coordinates n The physical quantities are calculated; for fluid media, the volumetric strain coefficient Δ and vertical displacement w are calculated; for elastic media, the derivative of horizontal displacement u is calculated. r The result of the calculation of the vertical displacement w; The propagation loss of sound pressure in fluid media or vertical normal stress in elastic media is used as the descriptive quantity, based on the generalized Hooke's law and the extracted factors. (r m ,z n Fluid sound field propagation loss TL at () w and the propagation loss TL of seismic wave field in elastic bodies s Represented as: Where, λ l (r m ,z n ) is a discrete point (r) m ,z n Lamé coefficient of the fluid medium at ) For discrete points (r) m ,z n Lamé coefficient of the elastic medium at ().

8. A deep-sea T-phase calculation system based on the mechanism of submarine seismic sources, characterized in that, The system includes: The wave field equation establishment module is used to determine the physical quantities in elastic multilayer oceanic crust media and fluid deep-sea acoustic waveguides, and to establish the joint elliptic differential equation of acoustic waves and seismic waves in a two-dimensional cylindrical coordinate system. The parabolic equation transformation module is used to transform the joint elliptic differential equation of acoustic waves and seismic waves into a joint parabolic differential equation of acoustic waves and seismic waves based on operator theory and factorization, and gives its horizontal recursive equation in radical form. The initial field equation establishment module is used to establish a radical-form initial field horizontal recursive equation adapted to submarine earthquake events based on the volumetric coefficient, rotation vector and line source-point source analogy of deep-sea submarine earthquakes. The cyclic recursion module is used to transform horizontal recursive equations in radical form into N-order equations based on split-step theory and higher-order Padé rational approximations. p Step-by-step horizontal recursive equation; The operator processing module is used to discretize the operator actions in the cyclic horizontal recursive equations based on virtual point technology and fluid-elastic interface boundary conditions, and to provide a representation of the physical quantities calculated using virtual points; and The T-phase solution module is used to calculate the seismic wave field in the oceanic crust medium and the acoustic wave field in the deep-sea acoustic channel based on the cyclic horizontal recursive equation and its discrete processing results, so as to realize the simulation of the T-phase of seafloor earthquake.

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