Seismic vector wave field numerical simulation method, equipment and medium

Abstract

The invention discloses a seismic vector wave field numerical simulation method and device and a medium, and relates to the technical field of seismic vector wave field numerical simulation, and the method comprises the steps: determining a difference frequency dispersion relational expression containing a staggered grid finite difference coefficient according to a Nyquist sampling theorem; introducing an error limitation condition, and converting the staggered grid finite difference frequency division dispersion relational expression into a to-be-optimized target function; solving the objective function by using an improved zebra optimization algorithm to obtain an optimized staggered grid finite difference operator; the method comprises the following steps of: performing differential discrete processing on a first-order speed-stress elastic wave equation by utilizing an optimized staggered grid finite difference operator, and calculating to obtain a high-precision seismic vector wave field in a calculation region according to a medium parameter model of a test region, and according to a medium parameter model of the test region, optimizing the staggered grid finite difference operator by utilizing an improved zebra optimization algorithm, and obtaining a high-precision seismic vector wave field in the calculation region. The seismic vector wave field numerical simulation precision can be improved, and a foundation is laid for the subsequent seismic imaging inversion process.

Description

Technical Field

[0001] The present application relates to the technical field of numerical simulation of seismic vector wave fields, and in particular to a method, device and medium for numerical simulation of seismic vector wave fields. Background Art

[0002] The numerical simulation methods of seismic waves mainly include three types of methods: pseudospectral method, finite element method and finite difference method. Compared with pseudospectral method and finite element method, finite difference method is widely used in numerical simulation of seismic vector wave field because of its small memory usage and easy large-scale parallel calculation. This method realizes numerical simulation of seismic wave field by differential discretization of differential operators and then solving wave equations.

[0003] As the basis of seismic imaging and inversion, the computational accuracy of seismic vector wavefield numerical simulation plays a decisive role in the results of subsequent imaging and inversion. Although compared with the conventional finite difference method, the staggered grid finite difference method has higher computational accuracy and stability, and can further improve the accuracy of numerical simulation without increasing the amount of calculation. However, the essence of the staggered grid finite difference method is to approximate the differential operator with the differential operator, which inevitably causes numerical errors and leads to numerical dispersion, thereby reducing the accuracy of numerical simulation. Excessive numerical dispersion will lead to the inability to accurately calculate the waveform information during wavefield simulation. Even in the case of long-term wavefield simulation, the accumulation of errors caused by numerical dispersion may even lead to infinite computational anomalies in the wavefield. Therefore, optimizing the staggered grid finite difference operator and reducing the numerical error caused by the approximation of the differential operator by the differential operator is crucial for the rapid and accurate realization of seismic vector wavefield numerical simulation. Summary of the invention

[0004] The purpose of this application is to provide a method, device and medium for numerical simulation of seismic vector wavefields, which can improve the accuracy of numerical simulation of seismic vector wavefields by optimizing the staggered grid finite difference operator using an improved zebra optimization algorithm, thereby laying the foundation for subsequent seismic imaging inversion process.

[0005] To achieve the above objectives, this application provides the following solutions:

[0006] In a first aspect, the present application provides a method for numerical simulation of seismic vector wave fields, comprising:

[0007] According to the Nyquist sampling theorem, the first-order staggered grid finite difference operator is derived, and the difference dispersion relation including the staggered grid finite difference coefficients is constructed.

[0008] Introducing error limiting conditions, converting the differential dispersion relation including staggered grid finite difference coefficients into an objective function to be optimized, and converting the problem into a multi-parameter optimization problem; the solution of the objective function is the staggered grid finite difference coefficients;

[0009] An improved zebra optimization algorithm is constructed, and the objective function is solved by using the improved zebra optimization algorithm to obtain an optimized staggered grid finite difference operator; the improved zebra optimization algorithm is obtained by improving the zebra optimization algorithm by using a bacterial foraging optimization algorithm;

[0010] By using the optimized staggered grid finite difference operator, the first-order velocity-stress elastic wave equation is differentially discretized to obtain the numerical simulation scheme of seismic vector wave field.

[0011] The medium parameters, source parameters and observation system parameters of the test area are substituted into the seismic vector wave field numerical simulation scheme to obtain the seismic vector wave field numerical simulation results of the test area.

[0012] Optionally, an error limiting condition is introduced to transform the differential dispersion relation containing the staggered grid finite difference coefficients into an objective function to be optimized, and the problem is transformed into a multi-parameter optimization problem, including:

[0013] Calculate the first-order derivative of the original continuous signal to obtain the first-order derivative formula of the original continuous signal;

[0014] One half of the sampling interval is used as an independent variable, input into the first-order derivative formula of the original continuous signal and a finite sequence of a preset truncation length is intercepted to obtain an initial staggered grid finite difference operator;

[0015] Using the Fourier transform principle, the first-order derivative formula of the original continuous signal is transformed into the dispersion relation of the original continuous signal.

[0016] Based on the original continuous signal dispersion relation, the initial staggered grid finite difference operator dispersion relation is determined;

[0017] The error limit is introduced into the initial staggered grid finite difference operator dispersion relation, and the objective function including the staggered grid finite difference coefficients is constructed.

[0018] Optionally, the original continuous signal formula is:

[0019]

[0020] Among them, f(x) represents the original continuous signal, π is the circumference of a circle, and f n is a discrete signal, Δx represents the sampling interval, x is the independent variable, and n is the discrete signal f n The number of sampling times, f n =f(nΔx).

[0021] Optionally, the objective function is:

[0022]

[0023] Among them, k x is the wave number, k max is the maximum wave number, m is the spatial sampling position, M is half of the staggered grid finite difference length, c m is the staggered grid finite difference coefficient, and ε is the error limit.

[0024] Optionally, the objective function is solved by using an improved zebra optimization algorithm to obtain an optimized staggered grid finite difference operator, including:

[0025] Initialize zebra optimization algorithm parameters; the zebra optimization algorithm parameters include the total number of zebras in the population, the boundary of the population solution space and the maximum number of iterations T; the total number of zebras is an even number;

[0026] In the population solution space, the population is randomly initialized based on the total number of zebras;

[0027] The randomly initialized population is used as the optimized population at the 0th iteration;

[0028] Let the number of iterations num = 1;

[0029] The optimized population at the num-1th iteration is used as the initial population at the numth iteration;

[0030] Determine the evaluation value of the objective function value corresponding to each zebra in the initial population at the numth iteration;

[0031] Determine whether an end iteration condition is met and obtain a determination result; the end iteration condition is that the number of iterations num reaches the maximum number of iterations, or the evaluation value of the objective function corresponding to each zebra in the initial population at the numth iteration is less than the error limit;

[0032] If the judgment result is no, the foraging phase position of the initial population at the numth iteration is updated to obtain the first updated population at the numth iteration;

[0033] The first updated population at the numth iteration is updated in the defense phase to obtain the second updated population at the numth iteration;

[0034] Determine the objective function evaluation value corresponding to each zebra in the second updated population at the numth iteration;

[0035] After the defense phase, the evaluation value of each zebra has been determined. At this time, all zebras in the population are arranged in order from best to worst, and the zebras at the bottom half are eliminated to obtain the undetermined population at the numth iteration;

[0036] Copy the undetermined population at the numth iteration to obtain the copied population;

[0037] Merge the replicated population and the undetermined population at the numth iteration to ensure that the population size remains unchanged, and the zebras can move to a better position with a greater probability during the next optimization search, accelerate the movement of the population toward the optimal solution, and thus improve the convergence speed of the algorithm. In this way, the initial optimized population at the numth iteration can be obtained;

[0038] Based on the population dispersal mechanism, the zebra is randomly moved to a new position with a preset probability, thereby enhancing the randomness of its optimal neighborhood search and improving its ability to jump out of the local extreme value, thereby further enhancing the global search ability of the algorithm. Finally, the position of the zebra in the initial optimized population at the numth iteration is updated to obtain the optimized population at the numth iteration;

[0039] Increase the value of the iteration number num by 1, and return to the step "using the optimized population at the num-1th iteration as the initial population at the numth iteration";

[0040] If the judgment result is yes, all zebras in the initial population at the numth iteration are sorted from best to worst according to the evaluation value corresponding to each zebra, so as to determine the optimal solution of the objective function.

[0041] Optionally, the foraging phase position is updated as follows:

[0042]

[0043] Among them, X' l is the position of the lth zebra in the first updated population, is the position of the lth zebra in the initial population after the foraging phase position update, is the evaluation value of the objective function corresponding to the position update of the lth zebra in the initial population during the foraging phase, F l is the evaluation value of the objective function corresponding to the lth zebra before the foraging stage, X l is the position of the lth zebra in the initial population, m is the number of decision variables, is the y-th decision variable value after the position of the l-th zebra in the initial population is updated during the foraging phase, x l,y is the yth decision variable value of the lth zebra in the initial population, r is a random number between 0 and 1, PZ y is the optimal pioneer zebra y-th decision variable value in the initial population, and I is a random number between 1 and 2.

[0044] Optionally, the defense phase position is updated as follows:

[0045]

[0046] Among them, X' l ' is the position of the lth zebra in the second updated population, is the position of the lth zebra in the first updated population after the defense phase position update, is the evaluation value of the objective function corresponding to the position update of the lth zebra in the first updated population during the foraging phase, is the yth decision variable value after the position of the lth zebra in the first updated population is updated during the foraging phase, x' l,y is the value of the y-th decision variable of the l-th zebra in the first updated population, R is a constant, p s is the probability selection parameter, α is the probability threshold, AZ y Update the value of the y-th decision variable of the attacked zebra in the first population.

[0047] Optionally, the medium parameters include model size, grid spacing, longitudinal wave velocity model, shear wave velocity model and density model; the source parameters include source wavelet type, source main frequency and time step; the observation system parameters include source position and detector position.

[0048] In a second aspect, the present application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-mentioned seismic vector wavefield numerical simulation method.

[0049] In a third aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, which implements the above-mentioned seismic vector wavefield numerical simulation method when executed by a processor.

[0050] According to the specific embodiments provided in this application, this application discloses the following technical effects:

[0051] The present application provides a method, device and medium for numerical simulation of seismic vector wave fields. According to the Nyquist sampling theorem, a first-order staggered grid finite difference operator is derived, and a dispersion relation including differential coefficients is constructed; error limiting conditions are introduced to convert the staggered grid finite difference dispersion relation into an objective function to be optimized; an improved zebra optimization algorithm is constructed to solve the objective function to obtain an optimized staggered grid finite difference operator, and the obtained optimized staggered grid finite difference operator is used to perform differential discretization on the first-order velocity-stress elastic wave equation, and a high-precision and high-efficiency numerical simulation scheme based on the improved zebra optimization algorithm is established. According to the actual working area conditions, a medium parameter model of the test area is constructed, including a longitudinal wave velocity model, a shear wave velocity model, and a density model, and the source wavelet type and main frequency, grid spacing, and time step are determined, and a corresponding observation system is designed, such as the source location and the detector location. The set parameters are substituted into the staggered grid finite difference numerical simulation implementation plan based on the improved zebra optimization algorithm to achieve high-precision and high-efficiency numerical simulation of the seismic vector wave field, laying a solid foundation for subsequent seismic imaging and inversion. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0053] Figure 1 This is a flow chart of a numerical simulation method of seismic vector wave field in one embodiment of the present application;

[0054] Figure 2 This is a flow chart of improving the zebra optimization algorithm in one embodiment of the present application;

[0055] Figure 3 It is a numerical dispersion absolute error curve diagram of the optimized staggered grid finite difference operator based on the improved zebra optimization algorithm in one embodiment of the present application;

[0056] Figure 4 This is an absolute error curve diagram of the numerical dispersion of the optimized staggered grid finite difference operator based on the improved zebra optimization algorithm in one embodiment of the present application, which is magnified 1000 times;

[0057] Figure 5 This is a comparison diagram of staggered grid finite difference numerical simulation results before and after optimization in one embodiment of the present application;

[0058] Figure 6 A schematic diagram of the structure of a computer device provided in one embodiment of the present application. DETAILED DESCRIPTION

[0059] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0060] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0061] To optimize the staggered grid finite difference operator, the window function method and the optimization method can generally be used. The essence of the window function method is to design a window function with superior performance to minimize the spectrum leakage caused by using the window function to truncate the spatial convolution sequence of the pseudo-spectral method. The amplitude-frequency response of the designed window function needs to have the characteristics of narrow passband and large stopband attenuation at the same time. However, the contradiction between the bandwidth of the window function and the stopband attenuation is an obstacle that is difficult to overcome in the implementation of this method. Unlike the window function method, the optimization method converts the differential optimization problem into a multi-parameter optimization problem by constructing an objective function containing differential coefficients and using an optimization algorithm to solve it, thereby avoiding the trouble of window function design. The staggered grid finite difference operator optimized by the optimization method can effectively suppress numerical dispersion and lay a strong foundation for subsequent seismic imaging and inversion.

[0062] In an exemplary embodiment, Figure 1 As shown, a method for numerical simulation of seismic vector wave fields is provided, comprising:

[0063] Step 101: According to the Nyquist sampling theorem, a first-order staggered grid finite difference operator is derived, and a differential dispersion relation including staggered grid finite difference coefficients is constructed.

[0064] Step 102: Introduce error limiting conditions, transform the differential dispersion relation including the staggered grid finite difference coefficients into the objective function to be optimized, and transform the problem into a multi-parameter optimization problem. The solution of the objective function is the staggered grid finite difference coefficients.

[0065] Step 103: construct an improved zebra optimization algorithm, and use the improved zebra optimization algorithm to solve the objective function to obtain an optimized staggered grid finite difference operator. The improved zebra optimization algorithm is obtained by improving the zebra optimization algorithm using the bacterial foraging optimization algorithm.

[0066] Step 104: Using an optimized staggered grid finite difference operator, a differential discretization process is performed on the first-order velocity-stress elastic wave equation to obtain a numerical simulation scheme for the seismic vector wave field.

[0067] Step 105: Substitute the medium parameters, source parameters and observation system parameters of the test area into the seismic vector wave field numerical simulation scheme to obtain the seismic vector wave field numerical simulation results of the test area.

[0068] The medium parameters include model size, grid spacing, P-wave velocity model, S-wave velocity model and density model. The source parameters include source wavelet type, source dominant frequency and time step. The observation system parameters include source location and detector location.

[0069] Step 102 includes:

[0070] Take the first-order derivative of the original continuous signal and get the first-order derivative formula of the original continuous signal.

[0071] One half of the sampling interval is used as an independent variable, input into the first-order derivative formula of the original continuous signal, and a finite sequence of a preset truncation length is truncated to obtain an initial staggered grid finite difference operator.

[0072] Using the Fourier transform principle, the first-order derivative formula of the original continuous signal is Fourier transformed to obtain the dispersion relation of the original continuous signal.

[0073] Based on the original continuous signal dispersion relation, the initial staggered grid finite difference operator dispersion relation is determined.

[0074] The error limit is introduced into the initial staggered grid finite difference operator dispersion relation, and the objective function including the staggered grid finite difference coefficients is constructed.

[0075] Among them, the original continuous signal formula is:

[0076]

[0077] Among them, f(x) represents the original continuous signal, π is the circumference of a circle, and f n is a discrete signal, Δx represents the sampling interval, x is the independent variable, and n is the discrete signal f n The number of sampling times, f n =f(nΔx).

[0078] The objective function is:

[0079]

[0080] Among them, k x is the wave number, k maxis the maximum wave number, m is the spatial sampling position, M is half of the staggered grid finite difference length, c m is the staggered grid finite difference coefficient, and ε is the error limit.

[0081] Step 103 includes:

[0082] Initialize the zebra optimization algorithm parameters. The zebra optimization algorithm parameters include the total number of zebras in the population, the boundary of the population solution space, and the maximum number of iterations T. The total number of zebras is an even number.

[0083] In the population solution space, the population is randomly initialized based on the total number of zebras.

[0084] The randomly initialized population is used as the optimized population at the 0th iteration.

[0085] Let the number of iterations num=1.

[0086] The optimized population at the num-1th iteration is used as the initial population at the numth iteration.

[0087] Determine the evaluation value of the objective function corresponding to each zebra in the initial population at the numth iteration.

[0088] Determine whether the end iteration condition is met and obtain the judgment result. The end iteration condition is that the number of iterations num reaches the maximum number of iterations, or the evaluation value of the objective function corresponding to each zebra in the initial population at the numth iteration is less than the error limit.

[0089] If the judgment result is no, the foraging phase position of the initial population at the numth iteration is updated to obtain the first updated population at the numth iteration.

[0090] The first updated population at the numth iteration is updated in the defense phase position to obtain the second updated population at the numth iteration.

[0091] Determine the evaluation value of the objective function corresponding to each zebra in the second updated population at the numth iteration.

[0092] After the defense phase, the evaluation value of each zebra has been determined. At this time, all zebras in the population are arranged in order from best to worst, and the zebras at the bottom half are eliminated to obtain the undetermined population at the numth iteration;

[0093] Copy the undetermined population at the num-th iteration to obtain the copied population.

[0094] Merge the replicated population and the undetermined population at the numth iteration to ensure that the population size remains unchanged, and the zebras can move to a better position with a greater probability during the next optimization search, accelerate the movement of the population toward the optimal solution, and thus improve the convergence speed of the algorithm. In this way, the initial optimized population at the numth iteration can be obtained;

[0095] Based on the population dispersal mechanism, the zebra is randomly moved to a new position with a preset probability, thereby enhancing the randomness of its optimal neighborhood search and improving its ability to jump out of the local extreme value, thereby further enhancing the global search ability of the algorithm. Finally, the position of the zebra in the initial optimized population at the numth iteration is updated to obtain the optimized population at the numth iteration;

[0096] Increase the value of the iteration number num by 1, and return to the step "using the optimized population at the num-1th iteration as the initial population at the numth iteration".

[0097] If the judgment result is yes, all zebras in the initial population at the numth iteration are sorted from best to worst according to the evaluation value corresponding to each zebra, so as to determine the optimal solution of the objective function.

[0098] The position update during the foraging phase is:

[0099]

[0100] Among them, X' l is the position of the lth zebra in the first updated population, is the position of the lth zebra in the initial population after the foraging phase position update, is the evaluation value of the objective function corresponding to the position update of the lth zebra in the initial population during the foraging phase, F l is the evaluation value of the objective function corresponding to the lth zebra before the foraging stage, X l is the position of the lth zebra in the initial population, m is the number of decision variables, is the y-th decision variable value after the position of the l-th zebra in the initial population is updated during the foraging phase, x l,y is the yth decision variable value of the lth zebra in the initial population, r is a random number between 0 and 1, PZ y is the optimal pioneer zebra y-th decision variable value in the initial population, and I is a random number between 1 and 2.

[0101] The defense phase position is updated to:

[0102]

[0103] Among them, X' l' is the position of the lth zebra in the second updated population, is the position of the lth zebra in the first updated population after the defense phase position update, is the evaluation value of the objective function corresponding to the position update of the lth zebra in the first updated population during the foraging phase, is the yth decision variable value after the position of the lth zebra in the first updated population is updated during the foraging phase, x' l,y is the value of the y-th decision variable of the l-th zebra in the first updated population, R is a constant, p s is the probability selection parameter, α is the probability threshold, AZ y Update the value of the y-th decision variable of the attacked zebra in the first population.

[0104] Set the model to a uniform model, with the longitudinal wave velocity, shear wave velocity and density being 2000m / s, 1154.7m / s and 1800kg / m respectively. 3 The model size is 2km×2km, the grid spacing is dx=dz=5m, the source is located in the model, the detector is located on the surface, the source is Ricker wavelet, the main frequency is 40Hz, the time step is 0.0005s, and the simulation time is 2s. In order to avoid the influence of boundary reflection on the simulation results, the boundary condition is set to CPML (convolutional perfectly matched layer) boundary condition, and the method of this embodiment is specifically described.

[0105] (1) Optimized staggered grid finite difference operator based on improved zebra optimization algorithm

[0106] a. Staggered grid finite difference operator and dispersion relation

[0107] For a uniformly sampled discrete signal f n According to the Nyquist sampling theorem, the continuous signal f(x) of the original signal can be reconstructed by interpolating the sinc function:

[0108]

[0109] Where Δx represents the sampling interval, f n =f(nΔx).

[0110] Take the first-order derivative of both ends of formula (1) and convert Substituting in and truncating a finite sequence of length N (N is an even number), we can obtain the staggered grid finite difference operator:

[0111]

[0112] make w(n) is a truncation function, then c n represents the first-order staggered grid finite difference coefficients.

[0113] It can be seen that the staggered grid finite difference method truncates the infinite length spatial sequence and only uses the information of the finite length discrete points to approximate the differential operator, which is the source of numerical errors. From the perspective of spectrum analysis, this will inevitably lead to spectrum leakage and numerical dispersion. Therefore, in order to facilitate the intuitive analysis of the numerical dispersion of the staggered grid finite difference operator, Fourier transform is performed on both ends of formula (2):

[0114]

[0115] Among them, k x represents the wave number. Furthermore, the dispersion relation corresponding to the staggered grid finite difference operator can be obtained:

[0116]

[0117] Therefore, formula (4) can be used as an important basis for the dispersion analysis of the staggered grid finite difference method. For the optimization method, it is necessary to further transform the above formula into the objective function to be solved, so as to transform the staggered grid finite difference optimization problem into a multi-parameter optimization problem.

[0118] b. Objective function with staggered grid finite difference coefficients

[0119] On the basis of formula (4), the error limit ε is introduced and the error limit conditions are set, and then the optimization objective function including the staggered grid finite difference coefficients can be constructed:

[0120]

[0121] Among them, k max represents the maximum wave number to be solved, and the global optimal solution of the objective function is the optimized staggered grid finite difference coefficient. Therefore, it is necessary to construct a suitable optimization algorithm to optimize and solve the objective function, which has high requirements on the performance of the optimization algorithm, especially for high-order finite difference operators. It is necessary to seek an efficient optimization algorithm that can converge quickly and is suitable for high-dimensional multi-parameter optimization problems.

[0122] c. Improved Zebra optimization algorithm

[0123] As a probability calculation optimization algorithm, the swarm intelligence algorithm can obtain the optimal solution of the objective function by random search in the solution space. This solution method based on probability calculation enables it to have good performance in multi-parameter optimization problems. At the same time, it also has very good portability. Once the mathematical model of the problem to be solved is determined, this method can be used for optimization and solution. Therefore, according to the objective function constructed by formula (5), this application improves the algorithm on the basis of the traditional zebra optimization algorithm. Finally, the improved zebra optimization algorithm is used to solve the objective function to obtain the optimized staggered grid finite difference coefficients.

[0124] As a biologically inspired algorithm, the Zebra Optimization Algorithm (ZOA) is mainly based on the behavior pattern of zebras foraging on the grassland. By imitating the behavior of zebra populations in grouping, cooperation, and escaping predators during foraging, a mutual cooperation mechanism and dynamic update strategy between individuals are constructed to achieve the optimal solution of the objective function in the solution space. Since the ZOA algorithm adopts a mutual cooperation and guided aggregation method during search, it is easy to fall into local extreme values ​​during the optimization process. Therefore, this application combines the Bacterial Foraging Optimization Algorithm (BFOA) to improve it, and then constructs an improved Zebra Optimization Algorithm. Figure 2 In , E represents the evaluation value of the objective function. Figure 2 , the specific implementation is as follows:

[0125] The first step is to initialize the algorithm parameters, including initializing the population size, solution space boundary, maximum number of iterations, etc.

[0126] The zebra optimization algorithm is a group-optimization algorithm that considers zebras as members of a population. From a mathematical point of view, each zebra can be a candidate solution to the optimization problem, and the plain where the zebras are located is considered as the search space for the solution. The position of each zebra in the solution space determines the value of the decision variable. Therefore, each member zebra in the solution space can be modeled by a vector, and the elements of the vector represent the values ​​of the problem variables. The following population matrix can be constructed:

[0127]

[0128] Among them, X represents the population, X l represents the lth zebra in the population, x l,y represents the variable value of the lth zebra for the yth question, N represents the number of population members, and m is the number of decision variables.

[0129] In the zebra population, each zebra represents a candidate solution to the problem to be optimized. Therefore, the objective function can be evaluated based on the predicted value of each zebra for the problem variable. The evaluation value of the objective function can be expressed as the following vector:

[0130]

[0131] Among them, F is the vector of evaluation values ​​of the objective function, F l represents the objective function evaluation value obtained by the lth zebra. By comparing the objective function evaluation values ​​corresponding to each zebra, the quality of each candidate solution in this iteration can be effectively analyzed, thereby determining the best candidate solution to the problem to be solved. For minimization problems, the zebra with the smallest objective function evaluation value is the optimal solution, while for maximization problems, the opposite is true.

[0132] The second step is to randomly initialize the population in the solution space.

[0133] Similar to other optimization algorithms, at the beginning of the algorithm, it is necessary to randomly initialize the population in the solution space, as shown in formula (8):

[0134] x l,y =lb y +r·(ub y -lb y ) (8)

[0135] Among them, x l,y For individuals, lb y To find the lower bound of the optimal solution, ub y is the upper bound for optimization, and r represents a random number between [0, 1].

[0136] The third step is foraging and defense of the population.

[0137] In this step, the renewal mechanism of zebra members is determined based on two natural behaviors of zebras in nature - foraging and defense.

[0138] In the foraging stage of zebras (P1 stage), a pioneer zebra is first determined in the population, which will guide other members of the population to find their own position in the solution space. Therefore, the mathematical model of this stage can be expressed as:

[0139]

[0140] After the foraging stage, the population will enter the defense against predators. In nature, zebras will adopt different methods when facing different predators. For example, when facing the attack of lions, zebras will take zigzag escape routes and random sideways movements to avoid the lion's attack. When facing small predators such as hyenas, the zebra population will gather towards the attacked zebras, thereby confusing and scaring the enemy. Assuming that the probability threshold of these two situations is α, the mathematical model of the above process can be expressed as:

[0141]

[0142] Step 4: Replication mechanism.

[0143] The idea of ​​bacterial survival of the fittest in the BFOA algorithm is introduced into the zebra optimization algorithm. After the defense phase, the evaluation value corresponding to each zebra has been determined. Each zebra is sorted from best to worst, and the zebras in the bottom half are eliminated, and the retained population is replicated. This can not only ensure that the size of the population remains unchanged, but also enable the zebra to move to a better position with a greater probability during the next optimization search, accelerating the movement of the population toward the optimal solution, thereby improving the convergence speed of the algorithm.

[0144] Step 5: Dispersal mechanism.

[0145] During the defense and replication phases, the zebra population will aggregate, which may cause the algorithm to converge to the local optimal position prematurely. To prevent the algorithm from falling into the local extreme value, this application introduces the idea of ​​dispersal, which moves the zebras to new positions with a certain probability, thereby enhancing the randomness of its optimal neighborhood search and improving its ability to jump out of the local extreme value, thereby further enhancing the global search capability of the algorithm.

[0146] The numerical dispersion curve of the optimized staggered grid finite difference operator based on the improved zebra optimization algorithm is shown in Figure 3 As shown. Among them, the curves of different colors are the numerical dispersion curves of the 12 (red), 16 (blue), 20 (green) and 24 (purple) order optimized staggered grid finite difference operators, the black curves are the numerical dispersion curves of the conventional staggered grid finite difference operator, and the absolute error curve of the numerical dispersion of the optimized staggered grid finite difference operator based on the improved zebra optimization algorithm is magnified 1000 times as shown in Figure 4 As shown in the figure, by comparison, it is found that the optimized staggered grid finite difference coefficients have a higher spectral coverage while ensuring sufficient accuracy of the precision error, which can effectively suppress the spectrum leakage caused by the difference operator approximating the differential operator, thereby effectively reducing the calculation error in the numerical simulation process.

[0147] (2) A high-precision and high-efficiency numerical simulation scheme of seismic vector wave fields based on an improved zebra optimization algorithm

[0148] According to the optimized staggered grid finite difference operator obtained in step (1), the present application performs differential discretization on the first-order velocity-stress elastic wave equation, and then constructs a high-precision and high-efficiency seismic vector wave field numerical simulation scheme based on the improved zebra optimization algorithm.

[0149] Taking the two-dimensional case as an example, the first-order velocity-stress elastic wave equation can be expressed as:

[0150]

[0151] Among them, v x , v z represents the particle vibration velocity, σ xx , σ zz , σ xz is the stress component, x, z represent the spatial position. λ, μ are Lame constants, ρ is the density. t represents time.

[0152] The discretized form of formula (13) is as follows:

[0153]

[0154] Where k represents the time grid index, i and j represent the spatial grid index, h represents the spatial sampling interval, and c m represents the optimized staggered grid finite difference coefficient, and Δt represents the time sampling interval.

[0155] (3) According to the actual working conditions, construct the medium parameter model of the test area, including the longitudinal wave velocity model, the shear wave velocity model, and the density model, and determine the source wavelet type and main frequency, grid spacing, time step, and design the corresponding observation system, such as the source location and detector location.

[0156] The numerical simulation results of this implementation case are as follows Figure 5 As shown in the figure, the results are the X and Z components of the wave field snapshot at t = 0.4s, (a) The wave field snapshot of the X component obtained by the traditional staggered grid finite difference numerical simulation. (b) The wave field snapshot of the X component obtained by the optimized staggered grid finite difference numerical simulation. (c) The wave field snapshot of the Z component obtained by the traditional staggered grid finite difference numerical simulation. (d) The wave field snapshot of the Z component obtained by the optimized staggered grid finite difference numerical simulation. Observing the position indicated by the red arrow on the way, it can be found that the staggered grid finite difference operator optimized by the improved zebra optimization algorithm can effectively suppress numerical dispersion, realize high-precision and high-efficiency numerical simulation of seismic vector wave fields, and lay a strong foundation for the subsequent realization of high-precision seismic imaging and inversion.

[0157] According to the Nyquist sampling theorem, this application derives a first-order staggered grid finite difference operator and constructs a staggered grid finite difference dispersion relation containing a differential coefficient. Error limiting conditions are introduced to convert the staggered grid finite difference dispersion relation into an objective function to be optimized, and the problem is converted into a multi-parameter optimization problem. The solution of the objective function is the staggered grid finite difference coefficient. An improved zebra optimization algorithm is constructed to optimize the above objective function to obtain the optimized staggered grid finite difference coefficient, thereby reducing the calculation error caused by the differential operator approximating the differential operator and suppressing the numerical dispersion. According to the obtained staggered grid finite difference operator, the first-order velocity-stress elastic wave equation is differentially discretized, and a high-precision and high-efficiency numerical simulation scheme based on the improved zebra optimization algorithm is established. According to the work area conditions, a medium parameter model of the test area is constructed, including a longitudinal wave velocity model, a shear wave velocity model, and a density model, the source wavelet type and main frequency, grid spacing, and time step are determined, and the corresponding observation system is designed, such as the source location and the detector location. The set relevant parameters are substituted into the staggered grid finite difference numerical simulation implementation plan based on the improved zebra optimization algorithm to calculate the high-precision seismic vector wave field.

[0158] The present application also provides an application scenario, which applies the above-mentioned earthquake vector wave field numerical simulation method. Specifically: the earthquake vector wave field numerical simulation method provided in this embodiment can be applied in an earthquake protection and early warning scenario.

[0159] In an exemplary embodiment, a computer device is provided. The computer device may be a server or a terminal. The internal structure diagram thereof may be as follows: Figure 6 As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, referred to as I / O) and a communication interface. The processor, the memory and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. 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, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a method for numerical simulation of seismic vector wave fields is implemented.

[0160] Those skilled in the art will understand that Figure 6The 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. In an exemplary embodiment, a computer device is provided, including a memory and a processor, wherein a computer program is stored in the memory, and the processor implements the steps in the above-mentioned method embodiments when executing the computer program.

[0161] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program, and when the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0162] In an exemplary embodiment, a computer program product is provided, including a computer program, and when the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0163] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0164] Those of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0165] The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., but is not limited thereto. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but is not limited thereto.

[0166] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0167] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. At the same time, for those skilled in the art, according to the ideas of this application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A method for numerical simulation of seismic vector wave fields, characterized in that: include: According to the Nyquist sampling theorem, the first-order staggered grid finite difference operator is derived, and the difference dispersion relation including the staggered grid finite difference coefficients is constructed. Introducing error limiting conditions, converting the differential dispersion relation including staggered grid finite difference coefficients into an objective function to be optimized, and converting the problem into a multi-parameter optimization problem; the solution of the objective function is the staggered grid finite difference coefficients; Constructing an improved zebra optimization algorithm, and using the improved zebra optimization algorithm to solve the objective function, and obtaining an optimized staggered grid finite difference operator; The improved zebra optimization algorithm is obtained by improving the zebra optimization algorithm using the bacterial foraging optimization algorithm; By using the optimized staggered grid finite difference operator, the first-order velocity-stress elastic wave equation is differentially discretized to obtain the numerical simulation scheme of seismic vector wave field. The medium parameters, source parameters and observation system parameters of the test area are substituted into the seismic vector wave field numerical simulation scheme to obtain the seismic vector wave field numerical simulation results of the test area.

2. The method for numerical simulation of seismic vector wave fields according to claim 1, characterized in that: By introducing error limiting conditions, the differential dispersion relation containing staggered grid finite difference coefficients is transformed into the objective function to be optimized, and the problem is transformed into a multi-parameter optimization problem, including: Calculate the first-order derivative of the original continuous signal to obtain the first-order derivative formula of the original continuous signal; One half of the sampling interval is used as an independent variable, input into the first-order derivative formula of the original continuous signal and a finite sequence of a preset truncation length is intercepted to obtain an initial staggered grid finite difference operator; Using the Fourier transform principle, the first-order derivative formula of the original continuous signal is transformed into the dispersion relation of the original continuous signal. Based on the original continuous signal dispersion relation, the initial staggered grid finite difference operator dispersion relation is determined; The error limit is introduced into the initial staggered grid finite difference operator dispersion relation, and the objective function including the staggered grid finite difference coefficients is constructed.

3. The method for numerical simulation of seismic vector wave fields according to claim 2, characterized in that: The original continuous signal formula is: Among them, f(x) represents the original continuous signal, π is the circumference of a circle, and f n is a discrete signal, Δx represents the sampling interval, x is the independent variable, and n is the discrete signal f n The number of sampling times, f n =f(nΔx).

4. The method for numerical simulation of seismic vector wave fields according to claim 3, characterized in that: The objective function is: Among them, k x is the wave number, k max is the maximum wave number, m is the spatial sampling position, M is half of the staggered grid finite difference length, c m is the staggered grid finite difference coefficient, and ε is the error limit.

5. The method for numerical simulation of seismic vector wave fields according to claim 1, characterized in that: The objective function is solved by using the improved zebra optimization algorithm to obtain an optimized staggered grid finite difference operator, including: Initialize zebra optimization algorithm parameters; the zebra optimization algorithm parameters include the total number of zebras in the population, the boundary of the population solution space and the maximum number of iterations T; the total number of zebras is an even number; In the population solution space, the population is randomly initialized based on the total number of zebras; The randomly initialized population is used as the optimized population at the 0th iteration; Let the number of iterations num = 1; The optimized population at the num-1th iteration is used as the initial population at the numth iteration; Determine the objective function evaluation value corresponding to each zebra in the initial population at the numth iteration; Determine whether the end iteration condition is met and obtain a determination result; the end iteration condition is that the number of iterations num reaches the maximum number of iterations, or the objective function evaluation value corresponding to each zebra in the initial population at the numth iteration is less than the error limit; If the judgment result is no, the foraging phase position of the initial population at the numth iteration is updated to obtain the first updated population at the numth iteration; The first updated population at the numth iteration is updated in the defense phase to obtain the second updated population at the numth iteration; Determine the evaluation value of the objective function corresponding to each zebra in the second updated population at the numth iteration; After the defense phase, the evaluation value of each zebra has been determined. At this time, all zebras in the population are arranged in order from best to worst, and the zebras at the bottom half are eliminated to obtain the undetermined population at the numth iteration; Copy the undetermined population at the numth iteration to obtain the copied population; Merge the replicated population and the undetermined population at the numth iteration to ensure that the population size remains unchanged, and the zebras can move to a better position with a greater probability during the next optimization search, accelerate the movement of the population toward the optimal solution, and thus improve the convergence speed of the algorithm. In this way, the initial optimized population at the numth iteration can be obtained; Based on the population dispersal mechanism, the zebra is randomly moved to a new position with a preset probability, thereby enhancing the randomness of its optimal neighborhood search and improving its ability to jump out of the local extreme value, thereby further enhancing the global search ability of the algorithm. Finally, the position of the zebra in the initial optimized population at the numth iteration is updated to obtain the optimized population at the num+1th iteration. Increase the value of the iteration number num by 1, and return to the step "using the optimized population at the num-1th iteration as the initial population at the numth iteration"; If the judgment result is yes, all zebras in the initial population at the numth iteration are sorted from best to worst according to the evaluation value corresponding to each zebra, so as to determine the optimal solution of the objective function.

6. The method for numerical simulation of seismic vector wave fields according to claim 5, characterized in that: The position update in the foraging stage is: Among them, X' l is the position of the lth zebra in the first updated population, is the position of the lth zebra in the initial population after the foraging phase position update, is the evaluation value of the objective function corresponding to the position update of the lth zebra in the initial population during the foraging phase, F l is the evaluation value of the objective function corresponding to the lth zebra before the foraging stage, X l is the position of the lth zebra in the initial population, m is the number of decision variables, is the y-th decision variable value after the position of the l-th zebra in the initial population is updated during the foraging phase, x l,y is the yth decision variable value of the lth zebra in the initial population, r is a random number between 0 and 1, PZ y is the optimal pioneer zebra y-th decision variable value in the initial population, and I is a random number between 1 and 2.

7. The method for numerical simulation of seismic vector wave fields according to claim 6, characterized in that: The position update in the defense phase is: Among them, X' l ' is the position of the lth zebra in the second updated population, is the position of the lth zebra in the first updated population after the defense phase position update, is the evaluation value of the objective function corresponding to the position update of the lth zebra in the first updated population during the foraging phase, is the value of the lth decision variable after the position of the lth zebra in the first updated population is updated during the foraging phase, x' l,y is the value of the y-th decision variable of the l-th zebra in the first updated population, R is a constant, p s is the probability selection parameter, α is the probability threshold, AZ y Update the value of the y-th decision variable of the attacked zebra in the first population.

8. The method for numerical simulation of seismic vector wave fields according to claim 1, characterized in that: The medium parameters include model size, grid spacing, longitudinal wave velocity model, shear wave velocity model and density model; the source parameters include source wavelet type, source main frequency and time step; the observation system parameters include source location and detector location.

9. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the seismic vector wavefield numerical simulation method according to any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the seismic vector wave field numerical simulation method according to any one of claims 1 to 8 is implemented.

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