Tunnel surrounding rock seismic wave rapid simulation method and device, electronic equipment and storage medium

Abstract

The invention discloses a tunnel surrounding rock seismic wave rapid simulation method and device, electronic equipment and a storage medium, and the method comprises the steps: decomposing a point seismic source function into a series of Gabor basis function linear expression forms, and obtaining a Gaussian wave packet in a Cartesian coordinate system for describing the propagation characteristics of seismic waves in a specific direction; calculating a Gaussian wave packet phase term and an amplitude term according to kinematics ray tracing and dynamics ray tracing, a given speed parameter model and a complex number initial value to obtain propagation characteristics of a single Gaussian wave packet at a single angle; repeating the propagation calculation process of the single-angle single Gaussian wave packet according to a set angle interval in a pre-selected angle range to obtain propagation characteristics of multiple multi-angle Gaussian wave packets; and superposing the propagation characteristics of the multiple Gaussian wave packets at multiple angles to obtain a point source wave field simulated by the Gaussian wave packets in a pre-selected angle range. The rapid simulation method has the advantages of high simulation precision, high calculation efficiency, small memory occupation, directivity and the like.

Description

Technical Field

[0001] The present application relates to the technical field of tunnel advanced geological prediction, and in particular, to a method, device, electronic equipment and storage medium for rapid simulation of tunnel surrounding rock seismic waves. Background Art

[0002] During tunnel construction, in order to ensure construction safety, optimize construction design and prevent large-scale machinery jams such as TBMs, it is necessary to conduct advance detection and forecast of the geological conditions in front of the tunnel face, such as fault fracture zones, boulders, changes in soft and hard rock layers and other unfavorable geological conditions. As one of the most widely used and effective advanced geological forecasting methods, the seismic wave method is increasingly valued by owners. Seismic waves mainly include data acquisition, data processing and geological interpretation. In order to ensure the effectiveness of the seismic wave method in tunnel advanced geological forecasting, it is often necessary to use accurate and fast numerical simulation of seismic wave propagation to analyze the laws of seismic wave propagation and obtain simulation data with accurate phase and amplitude.

[0003] In the prior art, numerical simulation of seismic wave field propagation is mainly divided into wave equation type and eikonal equation type. The former (wave equation type) solves the wave equation based on the finite difference method, and uses time and space extrapolation to obtain the seismic wave field at any time and any position. It is one of the simulation methods with the highest calculation accuracy at present. However, this seismic wave field simulation method not only occupies a large amount of memory, but also has low calculation efficiency. It is often necessary to improve the calculation efficiency through block calculation, parallel calculation and other strategies. In addition, the advanced geological prediction of tunnels focuses on the geological conditions in front of the face, and this method is based on the simulation of the seismic wave field in the whole space, and cannot perform directional propagation simulation, which easily leads to a large amount of computational cost waste. The latter (eikonal equation type) solves the eikonal equation after high-frequency approximation of the wave equation, and is widely used in background velocity modeling. Although this type of method has the advantages of high calculation efficiency and low memory usage, it can only obtain the arrival time of the front of the transmitted wave in the process of seismic wave propagation, and cannot obtain the amplitude and phase information of the seismic wave field.

[0004] The simulation of tunnel surrounding rock seismic waves has strong directionality, and also requires high simulation accuracy, high computational efficiency, and small memory usage. Directionality is mainly aimed at the propagation of seismic waves within a range of about 100m in front of the face, rather than focusing on the seismic wave field propagating in the entire space. The high simulation accuracy is due to the fact that compared with surface oil and gas exploration, underground tunnels are generally smaller in scale, and disaster-causing geological bodies such as fault fracture zones and isolated rock caves are smaller in scale, which requires high accuracy for tunnel advance geological prediction. High computational efficiency and small memory usage are based on the construction perspective, and tunnel advance geological prediction should be carried out as soon as possible to reduce the impact on tunnel construction.

[0005] Therefore, in the field of tunnel advanced geological prediction, inventing a method for rapid simulation of tunnel surrounding rock seismic waves, which takes into account both high simulation accuracy and high computational efficiency, has important practical significance and practical value. Summary of the invention

[0006] On the one hand, the present application provides a method for rapid simulation of tunnel surrounding rock seismic waves to solve the technical problem that existing rapid simulation methods of seismic waves cannot simultaneously take into account high simulation accuracy, high computing efficiency and low memory occupancy.

[0007] This application is implemented through the following scheme:

[0008] A method for rapid simulation of tunnel surrounding rock seismic waves, comprising the steps of:

[0009] The point source function is decomposed into a series of Gabor basis function linear expressions to obtain Gaussian wave packets in Cartesian coordinate system, which are used to describe the propagation characteristics of seismic waves in a specific direction.

[0010] According to kinematic ray tracing and dynamic ray tracing, the phase term T and amplitude term of the Gaussian wave packet are calculated with a given velocity parameter model and complex initial values, so as to calculate the propagation characteristics of a single Gaussian wave packet at a single angle;

[0011] Repeat the propagation calculation process of a single Gaussian wave packet at a single angle at a set angle interval within the preselected angle range to obtain the propagation characteristics of multiple Gaussian wave packets at multiple angles;

[0012] The propagation characteristics of multiple Gaussian wave packets at multiple angles are superimposed to obtain the point source wave field simulated by the Gaussian wave packets within the pre-selected angle range.

[0013] Furthermore, the given velocity parameter model includes the phase velocity v of a given known point on the central ray, and the complex initial value includes Let the complex initial value of the Gaussian wave packet and the parameters of the Gabor point source function satisfy the relationship:

[0014]

[0015]

[0016] in, represents the value of the second-order partial derivative of the phase term T with respect to the wavefront orthogonal coordinate y1 at the initial point of the central ray, represents the value of the second-order partial derivative of the phase term T with respect to the wavefront orthogonal coordinate y1 and travel time t at the initial point of the central ray, represents the value of the second-order partial derivative of the phase term T with respect to the travel time t at the initial point of the central ray, ψ0 is a constant coefficient, M ttrepresents the value of the second-order partial derivative of the phase term T with respect to the travel time t at a certain point on the central ray, and ω represents the central frequency of the Gaussian wave packet at a certain point on the central ray.

[0017] Furthermore, the expression of the Gaussian wave packet in the Cartesian coordinate system is:

[0018] u GP (x,z,t)=A(x,z,t)exp(iω0T(x,z,t))

[0019] Among them, u GP is a Gaussian wave packet, ω0 is the center frequency of the Gaussian wave packet, the amplitude term A(x,z,t) and the phase term T(x,z,t) are both complex-valued functions of the spatial coordinates (x,z) and time t, and i is an imaginary unit.

[0020] Furthermore, the phase term and amplitude term of the Gaussian wave packet are calculated according to the kinematic ray tracing and the dynamic ray tracing, the given velocity parameter model and the complex initial value, so as to calculate the propagation characteristics of a single Gaussian wave packet at a single angle, specifically including the steps of:

[0021] According to the given velocity parameter model, kinematic ray tracing and dynamic ray tracing are performed respectively to obtain dynamic ray parameters;

[0022] According to the given velocity parameter model, dynamic ray parameters and complex initial values, the second-order partial derivative matrix M of the phase term T in the wavefront orthogonal coordinate system with respect to the wavefront orthogonal coordinates and time in the two-dimensional space is calculated along the central ray, and then the amplitude term A is obtained according to the second-order partial derivative matrix M, the given velocity parameter model and dynamic ray parameters;

[0023] The second-order partial derivative matrix N in the Cartesian coordinate system is obtained through the second-order partial derivative matrix M and coordinate transformation, and then the phase term T is obtained;

[0024] Substitute the obtained phase term T and amplitude term A into the Gaussian wave packet in the Cartesian coordinate system to calculate the propagation characteristics of a single Gaussian wave packet at a single angle.

[0025] Furthermore, the method calculates the second-order partial derivative matrix M of the phase term T in the wavefront orthogonal coordinate system with respect to the wavefront orthogonal coordinates and time in the two-dimensional space along the central ray according to the given velocity parameter model, dynamic ray parameters and complex initial values, and then obtains the amplitude term A according to the second-order partial derivative matrix M, the given velocity parameter model and dynamic ray parameters, specifically comprising the steps of:

[0026] In the two-dimensional space, the expression of the second-order partial derivative matrix M of the phase term T with respect to the wavefront orthogonal coordinates and time in the wavefront orthogonal coordinate system (y1, y2, y3) is:

[0027]

[0028] Wherein, the second-order partial derivative matrix M is a diagonal matrix;

[0029] Calculate each element in the second-order partial derivative matrix M:

[0030]

[0031]

[0032]

[0033]

[0034]

[0035]

[0036] Where V represents the group velocity of a point on the central ray, v represents the phase velocity, the group velocity V is calculated by the phase velocity v, Q1, Q2, P1 and P2 are the dynamic ray parameters;

[0037] The amplitude term A is obtained based on the calculated second-order partial derivative matrix M, the given velocity parameter model, and the dynamic ray parameters:

[0038]

[0039] Among them, A 0 and V 0 represent the amplitude and group velocity of the initial point of the central ray respectively.

[0040] Furthermore, the second-order partial derivative matrix N in the Cartesian coordinate system is obtained by calculating the second-order partial derivative matrix M and coordinate transformation, and then the phase term T is obtained, which specifically includes the steps of:

[0041] In the case of two-dimensional space, the phase term T is at a point (x 1c , x 2c , x 3c ) is expanded by the second-order Taylor to obtain the calculation formula of the phase term T:

[0042]

[0043] Among them, (x1, x2, x3, t) are the coordinates of the central ray in the space-time domain, p t represents the first-order partial derivative of the seismic wave travel time with respect to the coordinates of the central ray in the space-time domain, are the second-order partial derivatives of the phase term T along the coordinates of the central ray in the space-time domain, and

[0044] According to the conversion relationship between the second-order partial derivative matrix M and the second-order partial derivative matrix N in the Cartesian coordinate system (x1, x2, x3), the second-order partial derivative matrix N in the Cartesian coordinate system (x1, x2, x3) is calculated:

[0045]

[0046] in:

[0047]

[0048] The phase term T is obtained by substituting each element in the calculated second-order partial derivative matrix N into the calculation formula of the phase term T obtained by performing the second-order Taylor expansion.

[0049] Furthermore, the propagation characteristics of multiple Gaussian wave packets at multiple angles are superimposed to obtain a point source wave field simulated by Gaussian wave packets within a preselected angle range, which specifically includes the steps of:

[0050] Gaussian wave packets are used to integrate different central ray exit angles to obtain the seismic wave field within the pre-selected angle range:

[0051]

[0052] Among them, ψ0 is a constant coefficient, represents the Gaussian wave packet when the central ray emits at an angle of θ, and w represents the angle weighting coefficient.

[0053] On the other hand, the present application also provides a tunnel surrounding rock seismic wave rapid simulation device, comprising:

[0054] Point source function decomposition module, used to decompose the point source function into a series of Gabor basis function linear expressions to obtain Gaussian wave packets in Cartesian coordinate system, which are used to describe the propagation characteristics of seismic waves in a specific direction;

[0055] The single Gaussian wave packet propagation characteristic calculation module is used to calculate the phase term T and amplitude term of the Gaussian wave packet according to kinematic ray tracing and dynamic ray tracing, given velocity parameter model and complex initial value, so as to calculate the propagation characteristics of a single Gaussian wave packet at a single angle;

[0056] The multi-Gaussian wave packet propagation characteristic calculation module is used to repeat the propagation calculation process of a single-angle single Gaussian wave packet at a set angle interval within a pre-selected angle range to obtain the propagation characteristics of multiple Gaussian wave packets at multiple angles;

[0057] The point source wave field superposition calculation module is used to superimpose the propagation characteristics of multiple Gaussian wave packets at multiple angles to obtain a point source wave field simulated by Gaussian wave packets within a pre-selected angle range.

[0058] On the other hand, the present application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method for rapid simulation of tunnel surrounding rock seismic waves when executing the computer program.

[0059] On the other hand, the present application further provides a storage medium, which includes a stored program, and when the program is run, controls the device where the storage medium is located to execute the steps of the method for rapid simulation of tunnel surrounding rock seismic waves.

[0060] On the other hand, the present application also provides a computer program product, including a computer program or computer executable instructions, which, when executed by a processor, implements the steps of the method for rapid simulation of tunnel surrounding rock seismic waves.

[0061] Compared with the prior art, this application has the following beneficial effects:

[0062] The present application provides a method, device, electronic device, and storage medium for rapid simulation of tunnel surrounding rock seismic waves. The method comprises the following steps: decomposing a point source function into a series of Gabor basis function linear expressions to obtain a Gaussian wave packet in a Cartesian coordinate system, which is used to describe the propagation characteristics of seismic waves in a specific direction; calculating the phase term and amplitude term of the Gaussian wave packet according to kinematic ray tracing and dynamic ray tracing, a given velocity parameter model, and a complex initial value, thereby calculating the propagation characteristics of a single Gaussian wave packet at a single angle; repeating the propagation calculation process of a single Gaussian wave packet at a single angle at a set angle interval within a preselected angle range to obtain the propagation characteristics of multiple Gaussian wave packets at multiple angles; and superimposing the propagation characteristics of multiple Gaussian wave packets at multiple angles to obtain a point source wave field simulated by the Gaussian wave packet within the preselected angle range. The method for rapid simulation of tunnel surrounding rock seismic waves of the present application realizes the simulation of point source wave field based on the propagation of a single Gaussian wave packet and angular superposition, discretizes the continuous calculation process, and realizes the simulation of the entire point source wave field by superimposing multiple Gaussian wave packets. It not only maintains the high simulation accuracy of the finite difference method of wave equations, but also includes the computational efficiency of the ray tracing method for solving the eikonal equation, while avoiding the disadvantage that the finite difference method of wave equations requires a large amount of memory. The present application can calculate the seismic wave field within a specific direction range according to a pre-selected angle range, rather than calculating the wave field in the entire space, which reduces the computing cost and waste of computing resources and saves computing memory usage.

[0063] In addition to the above-described purposes, features and advantages, the present application also has other purposes, features and advantages. The present application will be further described in detail with reference to the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application.

[0065] Figure 1 It is a schematic flow chart of a method for rapid simulation of seismic waves in surrounding rock of a tunnel according to a preferred embodiment of the present application.

[0066] Figure 2 It is a schematic diagram of the sub-step flow of step S2 of the preferred embodiment of the present application.

[0067] Figure 3 A schematic diagram of the propagation characteristics of a single Gaussian wave packet according to a preferred embodiment of the present application.

[0068] Figure 4 This is a schematic diagram of a point source wave field with multiple Gaussian wave packets superimposed at multiple angles according to a preferred embodiment of the present application.

[0069] Figure 5 It is a schematic diagram of a module of a rapid simulation device for seismic waves in surrounding rocks of a tunnel according to a preferred embodiment of the present application.

[0070] Figure 6 It is a schematic block diagram of an electronic device entity of a preferred embodiment of the present application.

[0071] Figure 7 It is a diagram of the internal structure of a computer device of a preferred embodiment of the present application. DETAILED DESCRIPTION

[0072] The embodiments of the present application are described in detail below in conjunction with the accompanying drawings, but the present application can be implemented in a variety of different ways defined and covered below.

[0073] like Figure 1 As shown, the preferred embodiment of the present application provides a method for rapid simulation of tunnel surrounding rock seismic waves, comprising the steps of:

[0074] S1. Decompose the point source function into a series of Gabor basis function linear expressions to obtain Gaussian wave packets in Cartesian coordinate system, which are used to describe the propagation characteristics of seismic waves in a specific direction;

[0075] S2. According to kinematic ray tracing and dynamic ray tracing, the phase term T and amplitude term of the Gaussian wave packet are calculated with a given velocity parameter model and complex initial values, so as to calculate the propagation characteristics of a single Gaussian wave packet at a single angle;

[0076] S3, repeating the propagation calculation process of a single Gaussian wave packet at a single angle at a set angle interval within the preselected angle range to obtain the propagation characteristics of multiple Gaussian wave packets at multiple angles;

[0077] S4. Superimpose the propagation characteristics of multiple Gaussian wave packets at multiple angles to obtain a point source wave field simulated by the Gaussian wave packets within a preselected angle range.

[0078] The present embodiment provides a method for rapid simulation of tunnel surrounding rock seismic waves. The method for rapid simulation of tunnel surrounding rock seismic waves realizes simulation of point source wave field based on the propagation of a single Gaussian wave packet and angular superposition, discretizes the continuous calculation process, and realizes simulation of the entire point source wave field by superimposing multiple Gaussian wave packets. It not only maintains the high simulation accuracy of the finite difference method of wave equations, but also includes the computational efficiency of the ray tracing method for solving the eikonal equation, while avoiding the disadvantage that the finite difference method of wave equations requires a large amount of memory. The present application can calculate the seismic wave field within a specific direction range according to a preselected angle range, rather than calculating the full-space wave field, thereby reducing the computational cost and waste of computational resources, and saving computational memory usage.

[0079] Preferably, in step S1, the given velocity parameter model includes the phase velocity v of a given known point on the central ray, and the complex initial value includes Let the complex initial value of the Gaussian wave packet and the parameters of the Gabor point source function satisfy the relationship:

[0080]

[0081]

[0082] in, represents the value of the second-order partial derivative of the phase term T with respect to the wavefront orthogonal coordinate y1 at the initial point of the central ray, represents the value of the second-order partial derivative of the phase term T with respect to the wavefront orthogonal coordinate y1 and travel time t at the initial point of the central ray, represents the value of the second-order partial derivative of the phase term T with respect to the travel time t at the initial point of the central ray, ψ0 is a constant coefficient, M tt represents the value of the second-order partial derivative of the phase term T with respect to the travel time t at a certain point on the central ray, and ω represents the central frequency of the Gaussian wave packet at a certain point on the central ray.

[0083] In this embodiment, a specific velocity parameter model is given, such as the phase velocity v of a given known point on the central ray, and the complex initial value includes This provides the necessary basic data for the subsequent calculation of the second-order partial derivative matrix M of the phase term T in the wavefront orthogonal coordinate system with respect to the wavefront orthogonal coordinates and time in the two-dimensional space along the central ray, the second-order partial derivative matrix N in the Cartesian coordinate system, the phase term T and the amplitude term A. The given physical parameter field and complex initial value are the necessary system inputs for providing Gaussian wave packets to simulate seismic wave propagation, including velocity parameter fields such as phase velocity v, complex initial value Different initial values ​​of complex numbers have different effects on the propagation form of Gaussian wave packets, as shown in Table 1:

[0084] Table 1: Physical meaning and selection of complex initial values

[0085]

[0086] Since only the velocity parameter model and the complex initial value need to be given Through kinematic ray tracing and dynamic ray tracing, all calculations of the rapid simulation method of tunnel surrounding rock seismic waves can be completed, which greatly simplifies the data required for calculation, simplifies the calculation process, and improves the calculation efficiency.

[0087] In addition, since the Gabor decomposition point source function uses a series of Gabor functions to establish the connection between the source sub-wave function and the Gaussian wave packet, it is only necessary to make the complex initial value of the Gaussian wave packet and the parameters of the Gabor point source function satisfy the above relationship at the same time. At this time, the Gabor function is used to decompose any point source function into a linear superposition of a series of Gabor functions. The superposition of the Gaussian wave packet according to the central ray emission angle can be equivalent to the point source wave field generated by the Gabor function. In subsequent calculations, the continuous calculation process is discretized, and the simulation of the entire wave field is realized through integral superposition, thereby taking into account both calculation accuracy and calculation efficiency.

[0088] Preferably, the expression of the Gaussian wave packet in the Cartesian coordinate system is:

[0089] u GP (x,z,t)=A(x,z,t)exp(iω0T(x,z,t))

[0090] Among them, u GP is a Gaussian wave packet, ω0 is the center frequency of the Gaussian wave packet, the amplitude term A(x,z,t) and the phase term T(x,z,t) are both complex-valued functions of the spatial coordinates (x,z) and time t, and i is an imaginary unit.

[0091] This embodiment specifically adopts a high-frequency asymptotic solution of the wave equation - Gaussian wave packet, also known as Gaussian beam in the space-time domain, which can be used to describe the propagation characteristics of seismic waves in a specific direction (including amplitude and phase). As long as the amplitude term A and the phase term T are known, the Gaussian wave packet in the Cartesian coordinate system can be calculated. Among them, the advantages of using propagation in a specific direction include: 1. It is helpful to observe and analyze the propagation characteristics of seismic waves in the target direction and reduce interference from non-target directions; 2. It can be used for target-oriented imaging; 3. It greatly reduces the amount of calculation and improves calculation efficiency.

[0092] Preferably, if Figure 2 As shown, the method calculates the phase term and amplitude term of the Gaussian wave packet according to kinematic ray tracing and dynamic ray tracing, a given velocity parameter model and a complex initial value, thereby calculating the propagation characteristics of a single Gaussian wave packet at a single angle, specifically including the steps of:

[0093] S21, according to the given velocity parameter model, kinematic ray tracing and dynamic ray tracing are performed respectively to obtain dynamic ray parameters;

[0094] S22, according to the given velocity parameter model, dynamic ray parameters and complex initial values, calculate the second-order partial derivative matrix M of the phase term T in the wavefront orthogonal coordinate system with respect to the wavefront orthogonal coordinates and time in the two-dimensional space along the central ray, and then obtain the amplitude term A according to the second-order partial derivative matrix M, the given velocity parameter model and dynamic ray parameters;

[0095] S23, obtaining a second-order partial derivative matrix N in a Cartesian coordinate system through a second-order partial derivative matrix M and coordinate transformation calculation, and then obtaining a phase term T;

[0096] S24, the obtained phase term T and amplitude term A are substituted into the Gaussian wave packet in the Cartesian coordinate system to calculate the propagation characteristics of a single Gaussian wave packet at a single angle (see Figure 3 ).

[0097] This embodiment provides a specific process for calculating the phase term and amplitude term of Gaussian wave packets according to kinematic ray tracing and dynamic ray tracing, a given velocity parameter model and a complex initial value, so as to calculate the propagation characteristics of a single Gaussian wave packet at a single angle. The advantages include: using an analytical formula to solve the wave equation, the wave field at any time can be directly obtained, avoiding the trouble of having to calculate the wave field sequentially for wave field extrapolation; the analytical solution has high calculation efficiency and small memory usage.

[0098] Preferably, the method calculates the second-order partial derivative matrix M of the phase term T in the wavefront orthogonal coordinate system with respect to the wavefront orthogonal coordinates and time in the two-dimensional space along the central ray according to the given velocity parameter model, dynamic ray parameters and complex initial values, and then obtains the amplitude term A according to the second-order partial derivative matrix M, the given velocity parameter model and the dynamic ray parameters, specifically comprising the steps of:

[0099] S221. The expression of the second-order partial derivative matrix M of the phase term T with respect to the wavefront orthogonal coordinates and time in the wavefront orthogonal coordinate system (y1, y2, y3) in two-dimensional space is:

[0100]

[0101] Wherein, the second-order partial derivative matrix M is a diagonal matrix;

[0102] S222. Calculate each element in the second-order partial derivative matrix M:

[0103]

[0104]

[0105]

[0106]

[0107]

[0108]

[0109] Where V represents the group velocity of a point on the central ray, v represents the phase velocity, the group velocity V is calculated by the phase velocity v, Q1, Q2, P1 and P2 are the dynamic ray parameters;

[0110] S223. Obtain the amplitude term A according to the calculated second-order partial derivative matrix M, the given velocity parameter model, and the dynamic ray parameters:

[0111]

[0112] Among them, A 0 and V 0 represent the amplitude and group velocity of the initial point of the central ray respectively.

[0113] In the above embodiment, since the group velocity V can be calculated from the phase velocity v, the above formula only needs to give the phase velocity v of the known point and the complex initial value and the dynamic ray parameters Q1, Q2, P1 and P2, the second-order partial derivative matrix M of the phase term T in the wavefront orthogonal coordinate system with respect to the wavefront orthogonal coordinates and time in the two-dimensional case can be calculated along the central ray. On this basis, according to the characteristic that the amplitude term A of the Gaussian wave packet changes continuously along the central ray, the amplitude term A is further obtained by combining the given velocity parameter model and dynamic ray parameters. The calculation is simple and fast.

[0114] Preferably, the second-order partial derivative matrix N in the Cartesian coordinate system is obtained by calculating the second-order partial derivative matrix M and coordinate transformation, and then the phase term T is obtained, which specifically includes the steps of:

[0115] S231, in the case of two-dimensional space, the phase term T is calculated at a point (x 1c , x 2c , x 3c ) is expanded by the second-order Taylor to obtain the calculation formula of the phase term T:

[0116]

[0117] Among them, (x1, x2, x3, t) are the coordinates of the central ray in the space-time domain, p t represents the first-order partial derivative of the seismic wave travel time with respect to the coordinates of the central ray in the space-time domain, are the second-order partial derivatives of the phase term T along the coordinates of the central ray in the space-time domain, and

[0118] S232. Calculate the second-order partial derivative matrix N in the Cartesian coordinate system (x1, x2, x3) according to the conversion relationship between the second-order partial derivative matrix M and the second-order partial derivative matrix N in the Cartesian coordinate system (x1, x2, x3):

[0119]

[0120] in:

[0121]

[0122] S233. Substitute each element in the calculated second-order partial derivative matrix N into the phase term T calculation formula obtained by performing second-order Taylor expansion to obtain the phase term T.

[0123] In the above embodiment, in order to calculate the phase term T, in the two-dimensional space, the phase term T is calculated at a point (x 1c , x 2c , x 3c ) is used to perform a second-order Taylor expansion to obtain the phase term T calculation formula to approximate the phase term T. Secondly, compared with performing a second-order Taylor expansion in three-dimensional space, obtaining the phase term T calculation formula only in two-dimensional space can make the obtained calculation formula simpler and at the same time, the calculation result can also meet the accuracy requirements.

[0124] The second-order partial derivative matrix N in the Cartesian coordinate system (x1, x2, x3) corresponds to the second-order partial derivative matrix M in the wavefront orthogonal coordinate system (y1, y2, y3). The two reflect the curvature of the wavefront in different coordinate systems. The above embodiment uses the coordinate conversion matrix According to the conversion relationship satisfied by the second-order partial derivative matrix M in the wavefront orthogonal coordinate system in the two-dimensional case and the second-order partial derivative matrix N in the Cartesian coordinate system, the second-order partial derivative matrix N in the Cartesian coordinate system (x1, x2, x3) is calculated. At the same time, according to the relationship between each element in the calculated second-order partial derivative matrix N and the second-order partial derivatives of the phase term T along the coordinates of the central ray in the space-time domain in the calculation formula of the phase term T obtained by the second-order Taylor expansion, the elements in the calculated second-order partial derivative matrix N are substituted into the calculation formula of the phase term T obtained by the second-order Taylor expansion to obtain the phase term T, and the phase term T can be obtained.

[0125] Preferably, the method of superimposing the propagation characteristics of multiple Gaussian wave packets at multiple angles to obtain a point source wave field simulated by Gaussian wave packets within a preselected angle range specifically comprises the following steps:

[0126] S41. Use Gaussian wave packets to integrate different central ray exit angles to obtain the seismic wave field within the preselected angle range:

[0127]

[0128] Among them, ψ0 is a constant coefficient, represents the Gaussian wave packet when the central ray emits at an angle of θ, and w represents the angle weighting coefficient.

[0129] In this embodiment, multiple Gaussian wave packets with different central ray emission angles are integrated and superimposed to obtain a point source wave field simulated by Gaussian wave packets within a preselected angle range (see Figure 4 ), since the present embodiment performs point source wave field simulation in a specific direction to obtain the seismic wave field within a preselected angle range, the simulation is directional rather than a full-space simulation, thereby satisfying the characteristic that the tunnel surrounding rock seismic wave simulation has strong directionality, reducing the amount of calculation, and greatly reducing the memory usage while ensuring high simulation accuracy and high calculation efficiency.

[0130] like Figure 5 As shown, another preferred embodiment of the present application further provides a tunnel surrounding rock seismic wave rapid simulation device, comprising:

[0131] Point source function decomposition module, used to decompose the point source function into a series of Gabor basis function linear expressions to obtain Gaussian wave packets in Cartesian coordinate system, which are used to describe the propagation characteristics of seismic waves in a specific direction;

[0132] The single Gaussian wave packet propagation characteristic calculation module is used to calculate the phase term T and amplitude term of the Gaussian wave packet according to kinematic ray tracing and dynamic ray tracing, given velocity parameter model and complex initial value, so as to calculate the propagation characteristics of a single Gaussian wave packet at a single angle;

[0133] The multi-Gaussian wave packet propagation characteristic calculation module is used to repeat the propagation calculation process of a single-angle single Gaussian wave packet at a set angle interval within a pre-selected angle range to obtain the propagation characteristics of multiple Gaussian wave packets at multiple angles;

[0134] The point source wave field superposition calculation module is used to superimpose the propagation characteristics of multiple Gaussian wave packets at multiple angles to obtain a point source wave field simulated by Gaussian wave packets within a pre-selected angle range.

[0135] like Figure 6 As shown, a preferred embodiment of the present application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method for rapid simulation of tunnel surrounding rock seismic waves in the above-mentioned embodiment when executing the computer program.

[0136] like Figure 7 As shown, the preferred embodiment of the present application also provides a computer device, which can be a terminal or a liveness detection server, and its internal structure diagram can be as shown in Figure 7 As shown. The computer device includes a processor, a memory and a network interface connected through a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the computer device is used to communicate with other external computer devices through a network connection. When the computer program is executed by the processor, the steps of the above-mentioned method for rapid simulation of tunnel surrounding rock seismic waves are implemented.

[0137] Those skilled in the art will understand that Figure 7 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0138] A preferred embodiment of the present application further provides a storage medium, which includes a stored program, and when the program is executed, controls the device where the storage medium is located to execute the steps of the method for rapid simulation of tunnel surrounding rock seismic waves in the above embodiment.

[0139] The preferred embodiment of the present application provides a computer program product or a computer program, which includes computer instructions stored in a computer-readable storage medium. The processor of the electronic device reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, so that the electronic device executes the inertia closed system inertia hydraulic loading self-adjustment control method of the embodiment of the present application, for example, Figure 1 The fast simulation method of seismic waves in tunnel surrounding rock is shown.

[0140] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0141] If the functions described in the method of this embodiment are implemented in the form of software functional units and sold or used as independent products, they can be stored in one or more computing devices readable storage media. Based on this understanding, the part of the embodiment of the present application that contributes to the prior art or the part of the technical solution can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions to enable a computing device (which can be a personal computer, server, mobile computing device or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk and other media that can store program code.

[0142] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of complete hardware embodiments, complete software embodiments, or embodiments in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code. The scheme in the embodiments of the present application can be implemented in various computer languages, for example, object-oriented programming language Java and literal scripting language JavaScript, etc.

[0143] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0144] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0145] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0146] Although the preferred embodiments of the present application have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0147] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

Claims

1. A method for rapid simulation of tunnel surrounding rock seismic waves, characterized in that: Includes steps: The point source function is decomposed into a series of Gabor basis function linear expressions to obtain Gaussian wave packets in Cartesian coordinate system, which are used to describe the propagation characteristics of seismic waves in a specific direction. According to kinematic ray tracing and dynamic ray tracing, the phase term T and amplitude term of the Gaussian wave packet are calculated with a given velocity parameter model and complex initial values, so as to calculate the propagation characteristics of a single Gaussian wave packet at a single angle; Repeat the propagation calculation process of a single Gaussian wave packet at a single angle at a set angle interval within the preselected angle range to obtain the propagation characteristics of multiple Gaussian wave packets at multiple angles; The propagation characteristics of multiple Gaussian wave packets at multiple angles are superimposed to obtain the point source wave field simulated by the Gaussian wave packets within the pre-selected angle range.

2. The method for rapid simulation of tunnel surrounding rock seismic waves according to claim 1, characterized in that: The given velocity parameter model includes the phase velocity v of a given known point on the central ray, and the complex initial value includes Let the complex initial value of the Gaussian wave packet and the parameters of the Gabor point source function satisfy the relationship: in, represents the value of the second-order partial derivative of the phase term T with respect to the wavefront orthogonal coordinate y1 at the initial point of the central ray, represents the value of the second-order partial derivative of the phase term T with respect to the wavefront orthogonal coordinate y1 and travel time t at the initial point of the central ray, represents the value of the second-order partial derivative of the phase term T with respect to the travel time t at the initial point of the central ray, ψ0 is a constant coefficient, M tt represents the value of the second-order partial derivative of the phase term T with respect to the travel time t at a certain point on the central ray, and ω represents the central frequency of the Gaussian wave packet at a certain point on the central ray.

3. The method for rapid simulation of tunnel surrounding rock seismic waves according to claim 1, characterized in that: The expression of the Gaussian wave packet in the Cartesian coordinate system is: u GP (x,z,t)=A(x,z,t)exp(iω0T(x,z,t)) Among them, u GP is a Gaussian wave packet, ω0 is the center frequency of the Gaussian wave packet, the amplitude term A(x,z,t) and the phase term T(x,z,t) are both complex-valued functions of the spatial coordinates (x,z) and time t, and i is an imaginary unit.

4. The method for rapid simulation of tunnel surrounding rock seismic waves according to claim 1, characterized in that: The method of calculating the phase term and amplitude term of the Gaussian wave packet according to kinematic ray tracing and dynamic ray tracing, a given velocity parameter model and a complex initial value, thereby calculating the propagation characteristics of a single Gaussian wave packet at a single angle, specifically includes the following steps: According to the given velocity parameter model, kinematic ray tracing and dynamic ray tracing are performed respectively to obtain dynamic ray parameters; According to the given velocity parameter model, dynamic ray parameters and complex initial values, the second-order partial derivative matrix M of the phase term T in the wavefront orthogonal coordinate system with respect to the wavefront orthogonal coordinates and time in the two-dimensional space is calculated along the central ray, and then the amplitude term A is obtained according to the second-order partial derivative matrix M, the given velocity parameter model and dynamic ray parameters; The second-order partial derivative matrix N in the Cartesian coordinate system is obtained through the second-order partial derivative matrix M and coordinate transformation, and then the phase term T is obtained; Substitute the obtained phase term T and amplitude term A into the Gaussian wave packet in the Cartesian coordinate system to calculate the propagation characteristics of a single Gaussian wave packet at a single angle.

5. The method for rapid simulation of tunnel surrounding rock seismic waves according to claim 4, characterized in that: The method calculates the second-order partial derivative matrix M of the phase term T in the wavefront orthogonal coordinate system with respect to the wavefront orthogonal coordinates and time in the two-dimensional space along the central ray according to the given velocity parameter model, dynamic ray parameters and complex initial values, and then obtains the amplitude term A according to the second-order partial derivative matrix M, the given velocity parameter model and dynamic ray parameters, specifically comprising the steps of: In the two-dimensional space, the expression of the second-order partial derivative matrix M of the phase term T with respect to the wavefront orthogonal coordinates and time in the wavefront orthogonal coordinate system (y1, y2, y3) is: Wherein, the second-order partial derivative matrix M is a diagonal matrix; Calculate each element in the second-order partial derivative matrix M: Where V represents the group velocity of a point on the central ray, v represents the phase velocity, the group velocity V is calculated by the phase velocity v, Q1, Q2, P1 and P2 are the dynamic ray parameters; The amplitude term A is obtained based on the calculated second-order partial derivative matrix M, the given velocity parameter model, and the dynamic ray parameters: Among them, A 0 and V 0 represent the amplitude and group velocity of the initial point of the central ray respectively.

6. The method for rapid simulation of tunnel surrounding rock seismic waves according to claim 5, characterized in that: The second-order partial derivative matrix N in the Cartesian coordinate system is obtained by calculating the second-order partial derivative matrix M and coordinate transformation, and then the phase term T is obtained, which specifically includes the steps of: In the case of two-dimensional space, the phase term T is at a point (x 1c , x 2c , x 3c ) is expanded by the second-order Taylor to obtain the calculation formula of the phase term T: Among them, (x1, x2, x3, t) are the coordinates of the central ray in the space-time domain, p t represents the first-order partial derivative of the seismic wave travel time with respect to the coordinates of the central ray in the space-time domain, N tt , are the second-order partial derivatives of the phase term T along the coordinates of the central ray in the space-time domain, and According to the conversion relationship between the second-order partial derivative matrix M and the second-order partial derivative matrix N in the Cartesian coordinate system (x1, x2, x3), the second-order partial derivative matrix N in the Cartesian coordinate system (x1, x2, x3) is calculated: The phase term T is obtained by substituting each element in the calculated second-order partial derivative matrix N into the calculation formula of the phase term T obtained by performing the second-order Taylor expansion.

7. The method for rapid simulation of tunnel surrounding rock seismic waves according to claim 1, characterized in that: The method of superimposing the propagation characteristics of multiple Gaussian wave packets at multiple angles to obtain a point source wave field simulated by Gaussian wave packets within a preselected angle range specifically includes the following steps: Gaussian wave packets are used to integrate different central ray exit angles to obtain the seismic wave field within the pre-selected angle range: Among them, ψ0 is a constant coefficient, represents the Gaussian wave packet when the central ray emits at an angle of θ, and w represents the angle weighting coefficient.

8. A rapid simulation device for seismic waves in tunnel surrounding rocks, characterized in that: include: Point source function decomposition module, used to decompose the point source function into a series of Gabor basis function linear expressions to obtain Gaussian wave packets in Cartesian coordinate system, which are used to describe the propagation characteristics of seismic waves in a specific direction; The single Gaussian wave packet propagation characteristic calculation module is used to calculate the phase term T and amplitude term of the Gaussian wave packet according to kinematic ray tracing and dynamic ray tracing, given velocity parameter model and complex initial value, so as to calculate the propagation characteristics of a single Gaussian wave packet at a single angle; The multi-Gaussian wave packet propagation characteristic calculation module is used to repeat the propagation calculation process of a single-angle single Gaussian wave packet at a set angle interval within a pre-selected angle range to obtain the propagation characteristics of multiple Gaussian wave packets at multiple angles; The point source wave field superposition calculation module is used to superimpose the propagation characteristics of multiple Gaussian wave packets at multiple angles to obtain a point source wave field simulated by Gaussian wave packets within a pre-selected angle range.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method for rapid simulation of tunnel surrounding rock seismic waves as described in any one of claims 1 to 7 are implemented.

10. A storage medium, comprising a stored program, which controls a device where the storage medium is located to execute the steps of the method for rapid simulation of tunnel surrounding rock seismic waves as claimed in any one of claims 1 to 7 when the program is executed.

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