VTI medium ray tracing method and device, electronic equipment and medium

Abstract

The application discloses a VTI medium ray tracing method and device, electronic equipment and medium. The method can comprise: for a VTI medium, solving a Christoffel equation according to Thomsen parameters by an eigenvalue method to obtain an eikonal equation of a longitudinal wave; solving the eikonal equation of the longitudinal wave to obtain a kinematic ray tracing equation of the VTI medium; and solving the kinematic ray tracing equation by a Runge-Kutta method to realize ray tracing of the VTI medium. The application can establish the travel time required by depth domain migration imaging of the underground medium by ray tracing of the VTI medium according to the VTI medium Thomsen parameters obtained in actual seismic velocity modeling, thereby improving the efficiency and effect of depth domain migration imaging of the VTI medium.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of seismic exploration, and more particularly to a VTI medium ray tracing method and device, an electronic equipment and a medium. BACKGROUND

[0002] With the increase of the difficulty of oil reservoir exploration, the conventional seismic exploration cannot meet the demand of oil exploration, so the theoretical assumption of seismic exploration is modified from the commonly used isotropic medium to anisotropic medium. At present, the vertical symmetry transverse isotropy (VTI) medium, commonly known as VTI medium, is widely used. In order to accurately pre-stack depth migration imaging of VTI medium, accurate travel time needs to be extracted. In order to improve the calculation speed and efficiency, the ray tracing method is usually used to calculate the travel time of the underground VTI medium.

[0003] In theory, the accurate travel time can be calculated by using the accurate ray tracing theory calculation method from the elastic stiffness coefficient matrix of the VTI medium. This calculation method does not use any approximation, so accurate calculation results can be obtained after the elastic stiffness coefficient matrix is given. Although the time field of the underground VTI medium can be established by using this method, the accurate elastic stiffness coefficient matrix of the VTI medium cannot be obtained in actual application, so the ray tracing forward is usually used to study the theoretical model.

[0004] Therefore, it is necessary to develop a VTI medium ray tracing method, device, electronic equipment and medium.

[0005] The information disclosed in the background section of the present application is only intended to deepen the understanding of the general background of the present application, and should not be regarded as acknowledging or implying in any form that the information constitutes prior art known to those skilled in the art. SUMMARY

[0006] The present application provides a VTI medium ray tracing method, device, electronic equipment and medium, which can obtain the travel time required for the depth domain migration imaging of the underground medium by the VTI medium Thomsen parameter obtained in the actual seismic velocity modeling, and can improve the efficiency and effect of the depth domain migration imaging of the VTI medium.

[0007] In a first aspect, the present application provides a VTI medium ray tracing method, comprising:

[0008] For the VTI medium, the Christoffel equation is solved by the eigenvalue method according to the Thomsen parameter to obtain the eikonal equation of the longitudinal wave;

[0009] solving the eikonal equation of the P-wave, obtaining the kinematic ray tracing equation of the VTI medium;

[0010] solving the kinematic ray tracing equation by Runge-Kutta method, realizing the ray tracing of the VTI medium.

[0011] Preferably, for VTI medium, solving the Christoffel equation by eigenvalue method according to Thomsen parameters, obtaining the eikonal equation of P-wave includes:

[0012] simplifying the eigenvalue expression corresponding to the Christoffel matrix of P-wave in the VTI medium into a stiffness coefficient function;

[0013] obtaining the expression of stiffness-density coefficient about the Thomsen parameters, and then obtaining the Thomsen form of the stiffness coefficient function according to the Thomsen parameters;

[0014] obtaining the simplified expression of the stiffness coefficient function according to the Thomsen form of the stiffness coefficient function, and then calculating the eikonal equation of the P-wave.

[0015] Preferably, by solving the eigenvalue equation of the Christoffel matrix of VTI medium, the analytical expression of eigenvalue G is obtained, which is expressed as a function of the stiffness coefficient:

[0016]

[0017] The expression of stiffness-density coefficient about the Thomsen parameters is:

[0018]

[0019] wherein, A ij is the stiffness-density coefficient, A ij =C ij / ρ, C 11 , C 13 , C 33 , C 55 , C 66 is the stiffness coefficient, ρ is the density, p1 and p3 respectively represent the slowness in x1 and x3 directions, V p0 , ε and δ are Thomsen parameters, V p0 represents the P-wave velocity in the symmetry axis direction, V s0 represents the P-wave velocity in the symmetry axis direction, ε and δ are anisotropy parameters, and G represents the eigenvalue of the Christoffel matrix.

[0020] Preferably, the Thomsen form of the stiffness coefficient function is:

[0021]

[0022] wherein p1 and p3 represent slowness in x1 and x3 directions respectively, V p0 ε and δ are Thomsen parameters, V p0 denotes P-wave velocity in the symmetry axis direction, and ε and δ are anisotropy parameters,

[0023] Preferably, the simplified expression of the stiffness coefficient function is:

[0024]

[0025] Preferably, the eikonal equation of the P-wave is:

[0026]

[0027] wherein p1 and p3 represent slowness in x1 and x3 directions respectively, V p0 ε and δ are Thomsen parameters, V p0 denotes P-wave velocity in the symmetry axis direction, and ε and δ are anisotropy parameters.

[0028] Preferably, the kinematic ray tracing equation of the VTI medium is:

[0029]

[0030] wherein p1 and p3 represent slowness in x1 and x3 directions respectively, V p0 ε and δ are Thomsen parameters, V p0 denotes P-wave velocity in the symmetry axis direction, and ε and δ are anisotropy parameters, p i and x i represent p1, p3 and x1, x3 respectively.

[0031] As a specific implementation manner of the embodiments of the present disclosure,

[0032] In a second aspect, the embodiments of the present disclosure further provide a VTI medium ray tracing device, comprising:

[0033] An eikonal equation determination module is configured to, for a VTI medium, solve a Christoffel equation by an eigenvalue method according to Thomsen parameters, and obtain an eikonal equation of a P-wave.

[0034] A ray tracing equation determination module is configured to solve the eikonal equation of the P-wave, and obtain a kinematic ray tracing equation of the VTI medium.

[0035] The ray tracing module solves the kinematic ray tracing equation by the Runge-Kutta method to realize ray tracing in the VTI medium.

[0036] Preferably, for the VTI medium, the Christoffel equation is solved by an eigenvalue method according to Thomsen parameters to obtain the eikonal equation of the longitudinal wave comprises:

[0037] The eigenvalue expression corresponding to the Christoffel matrix of the longitudinal wave in the VTI medium is simplified as a stiffness coefficient function;

[0038] According to the Thomsen parameters, the stiffness-density coefficient is expressed as a function of the Thomsen parameters, and then the Thomsen form of the stiffness coefficient function is obtained;

[0039] According to the Thomsen form of the stiffness coefficient function, a simplified expression of the stiffness coefficient function is obtained, and then the eikonal equation of the longitudinal wave is calculated.

[0040] Preferably, by solving the eigenvalue equation of the Christoffel matrix of the VTI medium, the analytical expression of the eigenvalue G is obtained, which is expressed as a function of the stiffness coefficient:

[0041]

[0042] The stiffness-density coefficient is expressed as a function of the Thomsen parameters as:

[0043]

[0044] Wherein, A ij is the stiffness-density coefficient, A ij =C ij / ρ, C 11 , C 13 , C 33 , C 55 , C 66 is the stiffness coefficient, ρ is the density, p1 and p3 respectively represent the slowness in x1 and x3 directions, V p0 , ε and δ are Thomsen parameters, V p0 represents the P-wave velocity in the symmetry axis direction, V s0 represents the P-wave velocity in the symmetry axis direction, ε and δ are anisotropy parameters, and G represents the eigenvalue of the Christoffel matrix.

[0045] Preferably, the Thomsen form of the stiffness coefficient function is:

[0046]

[0047] where p1 and p3 represent the slowness in x1 and x3 directions, respectively, V p0 , ε and δ are Thomsen parameters, and V p0 represents the P-wave velocity in the symmetry axis direction, and ε and δ are anisotropy parameters.

[0048] Preferably, the simplified expression of the stiffness coefficient function is:

[0049]

[0050] Preferably, the eikonal equation of the P-wave is:

[0051]

[0052] where p1 and p3 represent the slowness in x1 and x3 directions, respectively, V p0 , ε and δ are Thomsen parameters, and V p0 represents the P-wave velocity in the symmetry axis direction, and ε and δ are anisotropy parameters.

[0053] Preferably, the kinematic ray tracing equation of the VTI medium is:

[0054]

[0055] where p1 and p3 represent the slowness in x1 and x3 directions, respectively, V p0 , ε and δ are Thomsen parameters, and V p0 represents the P-wave velocity in the symmetry axis direction, and ε and δ are anisotropy parameters, and p i and x i represent p1, p3 and x1, x3, respectively.

[0056] In a third aspect, the embodiments of the present disclosure further provide an electronic device, which comprises:

[0057] a memory, which stores executable instructions;

[0058] a processor, which runs the executable instructions in the memory to implement the VTI medium ray tracing method.

[0059] In a fourth aspect, the embodiments of the present disclosure further provide a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to implement the VTI medium ray tracing method.

[0060] The method and device of the present application have other characteristics and advantages, which will be apparent from or will be set forth in more detail in the accompanying drawings and the subsequent detailed description, which together serve to explain certain principles of the present application. BRIEF DESCRIPTION OF DRAWINGS

[0061] The above and other objects, features and advantages of the present application will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings in which like reference characters refer to like parts throughout the figures, and in which:

[0062] Figure 1 A flow chart showing steps of a VTI medium ray tracing method according to one embodiment of the present application is shown.

[0063] Figure 2 A schematic diagram showing a three-layer forward model according to one embodiment of the present application is shown.

[0064] Figure 3 A schematic diagram showing depth domain migration imaging results without considering VTI medium anisotropy according to one embodiment of the present application is shown.

[0065] Figure 4 A schematic diagram showing results of extracting VTI medium subsurface travel time for depth domain migration imaging according to one embodiment of the present application is shown.

[0066] Figure 5 A block diagram of a VTI medium ray tracing device according to one embodiment of the present application is shown.

[0067] BRIEF DESCRIPTION OF DRAWINGS

[0068] 201, eikonal equation determining module; 202, ray tracing equation determining module; 203, ray tracing module. DETAILED DESCRIPTION

[0069] Preferred embodiments of the present application will be described in more detail below. Although the preferred embodiments of the present application are described below, it is understood that the present application can be implemented in various forms and should not be limited by the embodiments set forth herein.

[0070] The present application provides a VTI medium ray tracing method, comprising:

[0071] For VTI medium, the Christoffel equation is solved by eigenvalue method according to Thomsen parameters to obtain the eikonal equation of longitudinal wave;

[0072] Solving the eikonal equation of the P-wave, the kinematic ray tracing equation of the VTI medium is obtained.

[0073] Solving the kinematic ray tracing equation by the Runge-Kutta method, the ray tracing of the VTI medium is realized.

[0074] In one example, for the VTI medium, the Christoffel equation is solved by the eigenvalue method according to the Thomsen parameters, and the eikonal equation of the P-wave is obtained, including:

[0075] The eigenvalue expression corresponding to the Christoffel matrix of the P-wave in the VTI medium is simplified as a stiffness coefficient function;

[0076] According to the Thomsen parameters, the stiffness-density coefficient is expressed in terms of the Thomsen parameters, and the Thomsen form of the stiffness coefficient function is obtained;

[0077] According to the Thomsen form of the stiffness coefficient function, the simplified expression of the stiffness coefficient function is obtained, and the eikonal equation of the P-wave is calculated.

[0078] In one example, by solving the characteristic equation of the Christoffel matrix of the VTI medium, the analytical expression of the eigenvalue G is obtained, which is expressed as a function of the stiffness coefficient:

[0079]

[0080] The stiffness-density coefficient is expressed in terms of the Thomsen parameters as:

[0081]

[0082] where A ij is the stiffness-density coefficient, A ij =C ij / ρ, C 11 , C 13 , C 33 , C 55 , C 66 are stiffness coefficients, ρ is density, p1 and p3 represent the slowness in x1 and x3 directions, V p0 , ε and δ are Thomsen parameters, V p0 represents the P-wave velocity in the symmetry axis direction, V s0 represents the P-wave velocity in the symmetry axis direction, ε and δ are anisotropy parameters, and G represents the eigenvalue of the Christoffel matrix.

[0083] In one example, the Thomsen form of the stiffness coefficient function is:

[0084]

[0085] where p1 and p3 represent the slowness in x1 and x3 directions, respectively, V p0 , ε and δ are Thomsen parameters, and V p0 represents the P-wave velocity in the symmetry axis direction, and ε and δ are anisotropy parameters.

[0086] In one example, the simplified form of the stiffness coefficient function is:

[0087]

[0088] In one example, the eikonal equation of the P-wave is:

[0089]

[0090] where p1 and p3 represent the slowness in x1 and x3 directions, respectively, V p0 , ε and δ are Thomsen parameters, and V p0 represents the P-wave velocity in the symmetry axis direction, and ε and δ are anisotropy parameters.

[0091] In one example, the kinematic ray tracing equation of the VTI medium is:

[0092]

[0093] where p1 and p3 represent the slowness in x1 and x3 directions, respectively, V p0 , ε and δ are Thomsen parameters, and V p0 represents the P-wave velocity in the symmetry axis direction, and ε and δ are anisotropy parameters, and p i and x i represent p1, p3 and x1, x3, respectively.

[0094] Specifically, for anisotropic media, the eikonal equation of the P-wave can be obtained by solving the Christoffel equation using the eigenvalue method. For VTI media, since it has only 5 independent elastic stiffness coefficients C 11 , C 13 , C 33 , C 55 , C 66 , the eigenvalue expression corresponding to the Christoffel matrix of the P-wave in the VTI medium can be simplified as a function of these 5 stiffness coefficients, i.e., formula (1).

[0095] In actual seismic data processing, three anisotropic Thomsen parameters V p0 , ε and δ of the VTI medium are usually obtained, where V p0P-wave velocity in the direction of the symmetry axis, and epsilon and delta are dimensionless anisotropy parameters. In addition, the rocks in practice are all weakly anisotropic, so the theoretical calculation method of the VTI medium can be derived and simplified by using the two conditions, thereby obtaining a calculation method beneficial to practical application.

[0096] Firstly, by using the definition of the Thomsen parameter, A ij The expression of the formula (2) is formula (2), and the formula (1) can be further expressed in the form of the Thomsen parameter as formula (3).

[0097] Under the condition of weak anisotropy, epsilon is much smaller than 1, so the last term in the square root in the above formula can be directly eliminated. At the same time, the square root is removed by using the Taylor series expansion, so as to be simplified as formula (4), and further calculation can obtain the eikonal equation corresponding to the P wave as formula (5).

[0098] As can be seen from the formula (5), the eikonal equation of the P wave is changed into only depending on V p0 , epsilon and delta. By using the method of characteristics to solve the simplified eikonal equation, the final kinematic ray tracing system of the VTI medium is formula (6).

[0099] After the initial conditions are given, the problem is specific to solve the initial value problem of the ordinary differential equation. For a first-order ordinary differential equation, the Runge-Kutta method can be used to solve. Due to the axial symmetry of the VTI medium, only the propagation of the ray in the x1-x3 plane needs to be studied. In the specific calculation, the calculation of the ray tracing is very different for the homogeneous medium and the inhomogeneous medium. In the inhomogeneous medium, Therefore, p i ≠0. The ray changes not only the position but also the direction in the process of propagation. Therefore, the entire ray tracing equation set needs to be solved at the same time, and the Runge-Kutta method is used to solve the ray tracing equation to realize the ray tracing of the VTI medium.

[0100] The application also provides a VTI medium ray tracing device, which comprises:

[0101] An eikonal equation determination module, which obtains the eikonal equation of the longitudinal wave by solving the Christoffel equation through the eigenvalue method according to the Thomsen parameter for the VTI medium;

[0102] A ray tracing equation determination module, which obtains the kinematic ray tracing equation of the VTI medium by solving the eikonal equation of the longitudinal wave;

[0103] A ray tracing module, which realizes the ray tracing of the VTI medium by solving the kinematic ray tracing equation through the Runge-Kutta method.

[0104] In one example, for VTI medium, the Christoffel equation is solved by eigenvalue method according to Thomsen parameters, and the eikonal equation of the longitudinal wave is obtained, including:

[0105] The eigenvalue expression corresponding to the Christoffel matrix of the longitudinal wave in the VTI medium is simplified as a stiffness coefficient function;

[0106] According to the Thomsen parameters, the stiffness-density coefficient is expressed as a function of the Thomsen parameters, and then the Thomsen form of the stiffness coefficient function is obtained;

[0107] According to the Thomsen form of the stiffness coefficient function, a simplified expression of the stiffness coefficient function is obtained, and then the eikonal equation of the longitudinal wave is calculated.

[0108] In one example, by solving the characteristic equation of the Christoffel matrix of the VTI medium, the analytical expression of the eigenvalue G is obtained, which is expressed as a function of the stiffness coefficient:

[0109]

[0110] The stiffness-density coefficient is expressed as a function of the Thomsen parameters:

[0111]

[0112] where A ij is the stiffness-density coefficient, A ij =C ij / ρ, C 11 , C 13 , C 33 , C 55 , C 66 are stiffness coefficients, ρ is density, p1 and p3 represent slowness in x1 and x3 directions respectively, V p0 , ε and δ are Thomsen parameters, V p0 represents P-wave velocity in the symmetry axis direction, V s0 represents P-wave velocity in the symmetry axis direction, ε and δ are anisotropy parameters, and G represents the eigenvalue of the Christoffel matrix.

[0113] In one example, the Thomsen form of the stiffness coefficient function is:

[0114]

[0115] where p1 and p3 represent slowness in x1 and x3 directions respectively, V p0 , ε and δ are Thomsen parameters, V p0P-wave velocity in the symmetry axis direction, and ε and δ are anisotropy parameters,

[0116] In one example, the simplified form of the stiffness coefficient function is:

[0117]

[0118] In one example, the eikonal equation of the P-wave is:

[0119]

[0120] where p1 and p3 represent the slowness in the x1 and x3 directions, respectively, V p0 , ε and δ are Thomsen parameters, and V p0 represents the P-wave velocity in the symmetry axis direction, and ε and δ are anisotropy parameters.

[0121] In one example, the kinematic ray tracing equation of the VTI medium is:

[0122]

[0123] where p1 and p3 represent the slowness in the x1 and x3 directions, respectively, V p0 , ε and δ are Thomsen parameters, and V p0 represents the P-wave velocity in the symmetry axis direction, and ε and δ are anisotropy parameters, and p i and x i represent p1, p3 and x1, x3, respectively.

[0124] Specifically, for anisotropic media, the eikonal equation of the P-wave can be obtained by solving the Christoffel equation using the eigenvalue method. For VTI media, since it has only 5 independent elastic stiffness coefficients C 11 , C 13 , C 33 , C 55 , C 66 , the eigenvalue expression corresponding to the Christoffel matrix of the P-wave in the VTI medium can be simplified as a function of these 5 stiffness coefficients, i.e., formula (1).

[0125] In actual seismic data processing, three anisotropy Thomsen parameters V p0 , ε and δ of the VTI medium are usually obtained, where V p0 represents the P-wave velocity in the symmetry axis direction, and ε and δ are dimensionless anisotropy parameters. In addition, the rocks in practice are all weakly anisotropic, so the theoretical calculation method of the VTI medium can be derived and simplified by using these two conditions, thereby obtaining a calculation method that is beneficial to practical application.

[0126] First, using the definition of Thomsen parameters, A ij The expression of formula (2) is formula (2), and formula (1) can be further expressed in the form of Thomsen parameters as formula (3).

[0127] Under the condition of weak anisotropy, ε << 1, so the last term in the square root in the above formula can be directly eliminated. At the same time, the square root is removed by using Taylor series expansion, so it can be simplified as formula (4), and further calculation can obtain the eikonal equation corresponding to the P wave as formula (5).

[0128] As can be seen from formula (5), the P wave eikonal equation is changed to only depend on V p0 , ε, δ. By using the method of characteristics to solve this simplified eikonal equation, the final kinematic ray tracing system of VTI medium is formula (6).

[0129] After the initial conditions are given, the problem is specific to solve the initial value problem of ordinary differential equation. For a first-order ordinary differential equation, Runge-Kutta method can be used to solve. Due to the axial symmetry of VTI medium, only the propagation of rays in the x1-x3 plane needs to be studied. In the specific calculation, the calculation of ray tracing is very different for homogeneous medium and inhomogeneous medium. In the inhomogeneous medium, Therefore, p i ≠ 0. The ray changes not only the position but also the direction during propagation. Therefore, the entire ray tracing equation set needs to be solved simultaneously, and the Runge-Kutta method is used to solve the ray tracing equation to realize the ray tracing of VTI medium.

[0130] The application also provides an electronic device, which comprises a memory storing executable instructions, and a processor running the executable instructions in the memory to realize the VTI medium ray tracing method.

[0131] The application also provides a computer readable storage medium storing a computer program, which is executed by a processor to realize the VTI medium ray tracing method.

[0132] In order to facilitate the understanding of the scheme and effects of the embodiments of the application, four specific application examples are given below. Those skilled in the art should understand that the examples are only for the convenience of understanding the application, and any specific details are not intended to limit the application in any way.

[0133] Example 1

[0134] Figure 1A flow chart showing steps of a VTI medium ray tracing method according to an embodiment of the present application is shown.

[0135] As shown in Figure 1 , the VTI medium ray tracing method comprises: step 101, for a VTI medium, solving Christoffel equation by eigenvalue method according to Thomsen parameters to obtain eikonal equation of a longitudinal wave; step 102, solving the eikonal equation of the longitudinal wave to obtain kinematic ray tracing equation of the VTI medium; and step 103, solving the kinematic ray tracing equation by Runge-Kutta method to realize ray tracing of the VTI medium.

[0136] The present method is used to calculate travel time of a weak anisotropic Taylor sandstone model, and the calculation result is compared with that of a standard ray tracing system, and the result shows that the calculation result of the present application can meet the requirement of actual seismic exploration depth migration imaging.

[0137] Figure 2 A schematic diagram of a three-layer forward model according to an embodiment of the present application is shown.

[0138] A forward model as shown in Figure 2 is designed, wherein the first layer is a horizontal layer, and the second layer has a large syncline structure. The Thomsen parameters of the first layer medium are V p0 = 3000 m / s, V s0 = 1500 m / s, ε = 0.11, and δ = 0.04; the Thomsen parameters of the second layer medium are V p0 = 4000 m / s, V s0 = 2000 m / s, ε = -0.19, and δ = -0.23; and the Thomsen parameters of the third layer medium are V p0 = 6000 m / s, V s0 = 3000 m / s, ε = 0.08, and δ = 0.43. Travel time calculation and depth imaging are performed on the seismic record obtained by forward calculation.

[0139] Figure 3 A schematic diagram of depth domain migration imaging result without considering anisotropy of a VTI medium according to an embodiment of the present application is shown.

[0140] Figure 4 A schematic diagram of result of extracting VTI medium underground travel time for depth domain migration imaging according to an embodiment of the present application is shown.

[0141] Figure 3 It is shown that without considering anisotropy, the imaging result is quite different from the model, and there is a great error in structure imaging position; Figure 4After imaging using the travel time of the VTI medium calculated by the application, results consistent with the model are obtained, proving that the application can give the correct travel time of the VTI medium.

[0142] Example 2

[0143] Figure 5 A block diagram of a VTI medium ray tracing device is shown according to an embodiment of the application.

[0144] As Figure 5 shown, the VTI medium ray tracing device comprises:

[0145] A eikonal equation determination module 201 obtains the eikonal equation of the longitudinal wave by solving the Christoffel equation through the eigenvalue method according to the Thomsen parameters for the VTI medium.

[0146] A ray tracing equation determination module 202 obtains the kinematic ray tracing equation of the VTI medium by solving the eikonal equation of the longitudinal wave.

[0147] A ray tracing module 203 realizes the ray tracing of the VTI medium by solving the kinematic ray tracing equation through the Runge-Kutta method.

[0148] As an optional solution, obtaining the eikonal equation of the longitudinal wave by solving the Christoffel equation through the eigenvalue method according to the Thomsen parameters for the VTI medium comprises:

[0149] simplifying the eigenvalue expression corresponding to the Christoffel matrix of the longitudinal wave in the VTI medium into a stiffness coefficient function;

[0150] obtaining the expression of the stiffness-density coefficient with respect to the Thomsen parameters according to the Thomsen parameters, and further obtaining the Thomsen form of the stiffness coefficient function;

[0151] obtaining the simplified expression of the stiffness coefficient function according to the Thomsen form of the stiffness coefficient function, and further calculating the eikonal equation of the longitudinal wave.

[0152] As an optional solution, the analytical expression of the eigenvalue G is obtained by solving the characteristic equation of the Christoffel matrix of the VTI medium, and is expressed as a function of the stiffness coefficient:

[0153]

[0154] The stiffness-density coefficient is written as an expression with respect to the Thomsen parameters as:

[0155]

[0156] where A ij is the stiffness-density coefficient, A ij = C ij / p, C 11 , C 13 , C 33 , C 55 , C 66 is the stiffness coefficient, p is the density, p1and p3represent the slowness in the x1and x3directions, respectively, V p0 , e, and d are Thomsen parameters, V p0 represents the P-wave velocity in the symmetry axis direction, V s0 represents the P-wave velocity in the symmetry axis direction, e and d are anisotropy parameters, and G represents the eigenvalue of the Christoffel matrix.

[0157] As an alternative, the Thomsen form of the stiffness coefficient function is:

[0158]

[0159] where p1and p3represent the slowness in the x1and x3directions, respectively, V p0 , e, and d are Thomsen parameters, V p0 represents the P-wave velocity in the symmetry axis direction, e and d are anisotropy parameters,

[0160] As an alternative, the simplified form of the stiffness coefficient function is:

[0161]

[0162] As an alternative, the eikonal equation for the P-wave is:

[0163]

[0164] where p1and p3represent the slowness in the x1and x3directions, respectively, V p0 , e, and d are Thomsen parameters, V p0 represents the P-wave velocity in the symmetry axis direction, e and d are anisotropy parameters.

[0165] As an alternative, the kinematic ray tracing equation for a VTI medium is:

[0166]

[0167] where p1and p3represent the slowness in the x1and x3directions, respectively, V p0 , e, and d are Thomsen parameters, V p0 represents the P-wave velocity in the symmetry axis direction, e and d are anisotropy parameters, p i and xi p1, p3 and x1, x3, respectively.

[0168] Example 3

[0169] The electronic device includes a memory storing executable instructions, and a processor running the executable instructions in the memory to implement the VTI medium ray tracing method.

[0170] The electronic device according to an embodiment of the present disclosure includes a memory and a processor.

[0171] The memory is configured to store non-transitory computer-readable instructions. Specifically, the memory can include one or more computer program products that can include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may, for example, include random access memory (RAM), cache memory, and / or the like. The non-volatile memory may, for example, include read-only memory (ROM), hard disk, flash memory, and / or the like.

[0172] The processor can be a central processing unit (CPU) or other form of processing unit having data processing and / or instruction execution capabilities, and can control other components in the electronic device to perform desired functions. In an embodiment of the present disclosure, the processor is configured to run the computer-readable instructions stored in the memory.

[0173] Those skilled in the art will understand that, in order to solve the technical problem of how to obtain a good user experience effect, the present embodiment can also include well-known structures such as a communication bus, an interface, and the like, which should also be included in the protection scope of the present disclosure.

[0174] Detailed descriptions of the present embodiment can refer to the corresponding descriptions in the foregoing embodiments, which will not be repeated here.

[0175] Example 4

[0176] The present embodiment of the present disclosure provides a computer-readable storage medium storing a computer program, which is executed by a processor to implement the VTI medium ray tracing method.

[0177] The computer-readable storage medium according to an embodiment of the present disclosure stores non-transitory computer-readable instructions. When the non-transitory computer-readable instructions are run by a processor, all or part of the steps of the method according to the embodiments of the present disclosure are performed.

[0178] The above computer readable storage medium includes, but is not limited to, an optical storage medium (for example, a CD-ROM and a DVD), a magneto-optical storage medium (for example, an MO), a magnetic storage medium (for example, a magnetic tape or a magnetic hard disk), a medium having a built-in rewritable nonvolatile memory (for example, a memory card), and a medium having a built-in ROM (for example, a ROM cartridge).

[0179] It will be understood by those skilled in the art that the above description of the embodiments of the present application is given for the purpose of exemplifying the advantageous effects of the embodiments of the present application and is not intended to limit the embodiments of the present application to any of the examples given.

[0180] The above has described the embodiments of the present application, and the above description is exemplary and is not exhaustive and is not limited to the disclosed embodiments. Many modifications and changes are obvious to those skilled in the art without departing from the scope and spirit of the described embodiments.

Claims

1. A VTI medium ray tracing method, characterized by, The method comprises the following steps: For VTI medium, the Christoffel equation is solved by eigenvalue method according to Thomsen parameters to obtain the eikonal equation of the longitudinal wave; The eikonal equation of the longitudinal wave is solved to obtain the kinematic ray tracing equation of the VTI medium; The kinematic ray tracing equation is solved by Runge-Kutta method to realize the ray tracing of the VTI medium. For VTI medium, the Christoffel equation is solved by eigenvalue method according to Thomsen parameters to obtain the eikonal equation of the longitudinal wave, which comprises the following steps: The eigenvalue expression corresponding to the Christoffel matrix of the longitudinal wave in the VTI medium is simplified into a stiffness coefficient function; According to the Thomsen parameters, the stiffness-density coefficient is expressed in terms of the Thomsen parameters, and then the Thomsen form of the stiffness coefficient function is obtained; According to the Thomsen form of the stiffness coefficient function, the simplified form of the stiffness coefficient function is obtained, and then the eikonal equation of the longitudinal wave is calculated.

2. The VTI medium ray tracing method of claim 1, wherein, By solving the characteristic equation of the Christoffel matrix of the VTI medium, the analytical expression of the eigenvalue G is obtained, which is expressed as a function of the stiffness coefficient: （1） The stiffness-density coefficient is expressed in terms of the Thomsen parameters as: （2） wherein is a stiffness-density coefficient, , is a stiffness coefficient, is a density, and denote and slowness in the direction of the symmetry axis, denotes the P-wave velocity in the direction of the symmetry axis, V s0 denotes the S-wave velocity in the direction of the symmetry axis, and are anisotropy parameters, G denotes an eigenvalue of the Christoffel matrix.

3. The VTI medium ray tracing method of claim 2, wherein, The Thomsen form of the stiffness coefficient function is: （3） wherein and respectively represent and slowness in the direction of .

4. The VTI medium ray tracing method of claim 3, wherein, The simplified form of the stiffness coefficient function is: （4）。 5. The VTI medium ray tracing method of claim 1, wherein, The eikonal equation of the longitudinal wave is: （5） where and respectively represent and slowness in the direction of represents the P-wave velocity in the direction of the symmetry axis, and are anisotropy parameters.

6. The VTI medium ray tracing method of claim 2, wherein, The kinematic ray tracing equation of the VTI medium is: （6） wherein and respectively represent , and , .

7. A VTI medium ray tracing apparatus, characterized by The method comprises the following steps: An eikonal equation determination module, for VTI medium, solves the Christoffel equation by eigenvalue method according to Thomsen parameters to obtain the eikonal equation of the longitudinal wave; A ray tracing equation determination module, which solves the eikonal equation of the longitudinal wave to obtain the kinematic ray tracing equation of the VTI medium; A ray tracing module, which solves the kinematic ray tracing equation by Runge-Kutta method to realize the ray tracing of the VTI medium. For VTI medium, the Christoffel equation is solved by eigenvalue method according to Thomsen parameters to obtain the eikonal equation of the longitudinal wave, which comprises the following steps: The eigenvalue expression corresponding to the Christoffel matrix of the longitudinal wave in the VTI medium is simplified into a stiffness coefficient function; According to the Thomsen parameters, the stiffness-density coefficient is expressed in terms of the Thomsen parameters, and then the Thomsen form of the stiffness coefficient function is obtained; According to the Thomsen form of the stiffness coefficient function, the simplified form of the stiffness coefficient function is obtained, and then the eikonal equation of the longitudinal wave is calculated.

8. An electronic device, comprising: The electronic device comprises: A memory storing executable instructions; A processor running the executable instructions in the memory to implement the VTI medium ray tracing method of any one of claims 1-6.

9. A computer-readable storage medium, characterized in that, The computer readable storage medium stores a computer program which, when executed by a processor, implements the VTI medium ray tracing method of any one of claims 1-6.

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