A seismic vector wavefield numerical simulation method, device and medium

Abstract

The application discloses a seismic vector wave field numerical simulation method, device and medium, relates to the technical field of seismic vector wave field numerical simulation, and comprises the following steps: according to the Nyquist sampling theorem, a difference dispersion relation formula containing staggered grid finite difference coefficients is determined; an error limiting condition is introduced, and the staggered grid finite difference dispersion relation formula is converted into a target function to be optimized; an improved zebra optimization algorithm is used to solve the target function, and an optimized staggered grid finite difference operator is obtained; the first-order velocity-stress elastic wave equation is subjected to difference dispersion processing by using the optimized staggered grid finite difference operator, and according to the medium parameter model of a test region, a high-precision seismic vector wave field in a calculation region can be calculated. The improved zebra optimization algorithm is used to optimize the staggered grid finite difference operator, the seismic vector wave field numerical simulation precision can be improved, and a foundation is laid for a 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] Seismic wave numerical simulation methods primarily include the pseudospectral method, the finite element method, and the finite difference method. Compared to the pseudospectral and finite element methods, the finite difference method is widely used in the numerical simulation of seismic vector wavefields due to its low memory usage and ease of large-scale parallel computation. This method achieves numerical simulation of seismic wavefields by discretizing differential operators and then solving the wave equation.

[0003] As the foundation of seismic imaging and inversion, numerical simulation of seismic vector wavefields relies on computational accuracy that decisively influences the results of subsequent imaging and inversion. Although the staggered-grid finite-difference method offers higher computational accuracy and stability than conventional finite-difference methods, it can further improve the accuracy of numerical simulations without increasing the computational effort. However, the essence of the staggered-grid finite-difference method is to approximate differential operators with differential operators, which inevitably leads to numerical errors and numerical dispersion, thereby reducing the accuracy of numerical simulations. Excessive numerical dispersion can prevent accurate calculation of waveform information during wavefield simulations. Even during long wavefield simulations, the accumulated errors caused by numerical dispersion can lead to infinite computational anomalies in the wavefield. Therefore, optimizing the staggered-grid finite-difference operator and, in turn, reducing the numerical errors caused by the approximation of differential operators by differential operators is crucial for the rapid and accurate implementation of numerical simulations of seismic vector wavefields. Summary of the Invention

[0004] The purpose of this application is to provide a method, device and medium for numerical simulation of seismic vector wave fields, which uses an improved zebra optimization algorithm to optimize the staggered grid finite difference operator, thereby improving the accuracy of numerical simulation of seismic vector wave fields and 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, the differential dispersion relation including staggered grid finite difference coefficients is converted 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 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 the bacterial foraging optimization algorithm;

[0010] The optimized staggered grid finite difference operator is used to perform differential discretization on the first-order velocity-stress elastic wave equation, and a numerical simulation scheme for seismic vector wave fields is obtained.

[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 constraint is introduced to transform the differential dispersion relation containing the staggered grid finite difference coefficients into the objective function to be optimized, thus transforming the problem 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] Taking half of the sampling interval as the independent variable, inputting it into the first-order derivative formula of the original continuous signal and intercepting a finite sequence of a preset interception length, an initial staggered grid finite difference operator is obtained;

[0015] 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;

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

[0017] An error limit is introduced into the dispersion relation of the initial staggered grid finite difference operator, and an objective function including 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, 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] where 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] initializing zebra optimization algorithm parameters; the zebra optimization algorithm parameters include the total number of zebras in a 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] randomly initializing the population in the population solution space based on the total number of zebras;

[0027] taking the randomly initialized population as the optimized population at the 0th iteration;

[0028] setting the iteration number num to 1;

[0029] taking the optimized population at the (num-1)th iteration as the initial population at the numth iteration;

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

[0031] determining whether an end iteration condition is met to obtain a determination result; the end iteration condition is that the iteration number 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 determination result is no, performing foraging stage position updating on the initial population at the numth iteration to obtain a first updated population at the numth iteration;

[0033] performing defense stage position updating on the first updated population at the numth iteration to obtain a second updated population at the numth iteration;

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

[0035] after the defense stage ends, the evaluation value corresponding to each zebra has been determined, at which time, all the zebras in the population are arranged in order from good to bad, and the zebras at the end half are eliminated to obtain a to-be-determined population at the numth iteration;

[0036] copying the to-be-determined population at the numth iteration to obtain a copied population;

[0037] Merge the replicated population and the undetermined population at the num-th iteration to ensure that the population size remains unchanged. This allows the zebras to move to a better position with a greater probability during the next optimization search, accelerating the population's movement toward the optimal solution and improving the algorithm's convergence speed. Thus, the initial optimized population at the num-th iteration can be obtained.

[0038] Based on the population dispersal mechanism, the zebras are randomly moved to new positions with a preset probability, thereby enhancing the randomness of their optimal neighborhood search and improving their ability to escape local extremes, thereby further enhancing the algorithm's global search capability. Finally, the positions of the zebras in the initial optimized population at the numth iteration are updated to obtain the optimized population at the numth iteration.

[0039] Increase the value of the number of iterations 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 num-th 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 position update in the foraging phase is:

[0042]

[0043] Among them, X' l is the position of the first zebra in the 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 first 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 value of the y-th decision variable of the l-th zebra in the initial population, r is a random number between 0 and 1, PZ y is the optimal value of the y-th decision variable of the pioneer zebra in the initial population, and I is a random number between 1 and 2.

[0044] Optionally, the position update in the defense phase is:

[0045]

[0046] Among them, X' l ' is the position of the first 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 y-th decision variable value after the position of the l-th 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; and the observation system parameters include source position and detector position.

[0048] In a second aspect, the present application provides 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 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] This application provides a method, device, and medium for numerical simulation of seismic vector wavefields. Based on the Nyquist sampling theorem, a first-order staggered grid finite difference operator is derived, and a dispersion relation containing the difference coefficients is constructed. Error constraints are introduced to transform 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. The resulting optimized staggered grid finite difference operator is used to differentially discretize the first-order velocity-stress elastic wave equation, establishing a high-precision, high-efficiency numerical simulation scheme based on the improved zebra optimization algorithm. Based on the actual work area, a medium parameter model of the test area is constructed, including a P-wave velocity model, a S-wave velocity model, and a density model. The source wavelet type and dominant frequency, grid spacing, and time step are determined, and a corresponding observation system, such as the source location and geophone location, is designed. 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 following briefly introduces the drawings required for use in the embodiments. 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 creative work.

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

[0054] Figure 2 This is a flowchart of the improved zebra optimization algorithm in one embodiment of the present application;

[0055] Figure 3 This is a numerical dispersion absolute error curve of an optimized staggered grid finite difference operator based on an 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 this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0060] In order to make the above-mentioned purposes, 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 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. 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 constructs an objective function containing differential coefficients and uses an optimization algorithm to solve it, thereby converting the differential optimization problem into a multi-parameter optimization problem, 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 numerical simulation method for earthquake vector wave fields is provided, comprising:

[0063] Step 101: Based on 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 constraints and transform the differential dispersion relation containing the staggered grid finite difference coefficients into the objective function to be optimized, thus transforming 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 it 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, perform differential discretization 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 wavefield numerical simulation scheme to obtain the seismic vector wavefield numerical simulation results of the test area.

[0068] Medium parameters include model size, grid spacing, P-wave velocity model, S-wave velocity model, and density model. Source parameters include source wavelet type, source dominant frequency, and time step. Observation system parameters include source location and receiver locations.

[0069] Step 102 includes:

[0070] The first-order derivative of the original continuous signal is calculated to obtain the first-order derivative formula of the original continuous signal.

[0071] 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.

[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] An error limit is introduced into the dispersion relation of the initial staggered grid finite difference operator, and an objective function including 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, 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 the length of the staggered grid finite difference, 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. These 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 must be 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 num-th iteration is updated to obtain the first updated population at the num-th iteration.

[0090] The first updated population at the num-th iteration is updated in the defense phase to obtain the second updated population at the num-th iteration.

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

[0092] After the defense phase, the evaluation value of each zebra has been determined. At this time, all zebras in the population are sorted from best to worst, and the zebras in 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 num-th iteration to ensure that the population size remains unchanged. This allows the zebras to move to a better position with a greater probability during the next optimization search, accelerating the population's movement toward the optimal solution and improving the algorithm's convergence speed. Thus, the initial optimized population at the num-th iteration can be obtained.

[0095] Based on the population dispersal mechanism, the zebras are randomly moved to new positions with a preset probability, thereby enhancing the randomness of their optimal neighborhood search and improving their ability to escape local extremes, thereby further enhancing the algorithm's global search capability. Finally, the positions of the zebras in the initial optimized population at the numth iteration are updated to obtain the optimized population at the numth iteration.

[0096] Increase the value of the number of iterations 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 num-th 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 first zebra in the 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 first 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 value of the y-th decision variable of the l-th zebra in the initial population, r is a random number between 0 and 1, PZ y is the optimal value of the y-th decision variable of the pioneer zebra in the initial population, and I is a random number between 1 and 2.

[0101] The defense phase positions are updated as follows:

[0102]

[0103] Among them, X' l' is the position of the first 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 y-th decision variable value after the position of the l-th 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 longitudinal wave velocity, shear wave velocity, and density as 2000 m / s, 1154.7 m / s, and 1800 kg / m 3 The model size is 2 km × 2 km, with a grid spacing of dx = dz = 5 m. The earthquake source is located in the model, and the detector is located on the surface. The earthquake source is a Ricker wavelet with a dominant frequency of 40 Hz, a time step of 0.0005 s, and a simulation duration of 2 s. To avoid the influence of boundary reflections on the simulation results, the boundary conditions are set to CPML (Convolutional Perfectly Matched Layer) boundary conditions. The method of this embodiment is described in detail.

[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] Calculate the first-order derivative of both ends of formula (1) and 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 the 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 error. From the perspective of spectrum analysis, this will inevitably lead to spectrum leakage and then 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 including 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. The global optimal solution of this objective function is the optimized staggered grid finite difference coefficients. Therefore, it is necessary to construct a suitable optimization algorithm to optimize and solve this objective function. This places high demands on the performance of the optimization algorithm, especially for high-order finite difference operators. It is necessary to find an efficient optimization algorithm that can converge quickly and is applicable to 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 through 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, based on the objective function constructed by formula (5), this application improves the traditional zebra optimization algorithm on the basis of the algorithm. Finally, the improved zebra optimization algorithm is used to solve the objective function to obtain the optimized staggered grid finite difference coefficients.

[0124] The Zebra Optimization Algorithm (ZOA) is a biologically inspired algorithm. Its idea is mainly derived from the behavior pattern of zebras foraging on the grassland. By imitating the behavior of zebra populations in grouping, cooperation, and escaping predators during foraging, it constructs a mutual cooperation mechanism and dynamic update strategy between individuals 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, a swarm optimization algorithm, treats zebras as members of a population. From a mathematical perspective, each zebra is a candidate solution to the optimization problem, and the plains where the zebras reside are considered the search space for solutions. Each zebra's position 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, whose elements 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 problem, 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, we can effectively analyze the quality of each candidate solution in this iteration and determine the best candidate solution to the problem. 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, the population needs to be randomly initialized 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 of the 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 zebra's foraging stage (P1 stage), a pioneer zebra is first identified in the population. This zebra 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 phase, the population will enter a defensive phase against predators. In nature, zebras adopt different strategies when facing different predators. For example, when facing an attack by a lion, zebras will adopt a zigzag escape route and random sideways movements to evade the lion's attack. When facing smaller predators like hyenas, the zebra population will gather around the attacked zebra to confuse and frighten the enemy. Assuming 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 bacterial survival of the fittest reproduction idea 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. The retained population is replicated. This not only ensures that the size of the population remains unchanged, but also allows the zebras to move to a better position with a greater probability during the next optimization search, accelerating the population's movement towards 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 a local optimal position prematurely. To prevent the algorithm from falling into a local extreme value, this application introduces the idea of ​​dispersal, which moves the zebras to a new position with a certain probability, thereby enhancing the randomness of its optimal neighborhood search, improving its ability to escape from local extreme values, and 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 as follows: 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 shown in Figure 4 As shown in the figure, the comparison shows 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) High-precision and high-efficiency numerical simulation scheme of seismic vector wavefield based on 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 wavefield 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 and z represent the spatial position. λ and μ are Lame constants, ρ is the density, and 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 area 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 wavefield snapshot at time t = 0.4s. (a) The wavefield snapshot of the X component obtained by the traditional staggered grid finite difference numerical simulation. (b) The wavefield snapshot of the X component obtained by the optimized staggered grid finite difference numerical simulation. (c) The wavefield snapshot of the Z component obtained by the traditional staggered grid finite difference numerical simulation. (d) The wavefield snapshot of the Z component obtained by the optimized staggered grid finite difference numerical simulation. Observing the position indicated by the red arrow, it can be found that the staggered grid finite difference operator optimized by the improved zebra optimization algorithm can effectively suppress numerical dispersion, achieve high-precision and high-efficiency seismic vector wavefield numerical simulation, and lay a solid foundation for the subsequent high-precision seismic imaging and inversion.

[0157] This application derives a first-order staggered grid finite difference operator based on the Nyquist sampling theorem, and constructs a staggered grid finite difference dispersion relation containing differential coefficients. By introducing error limiting conditions, the staggered grid finite difference dispersion relation is converted 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 coefficients, thereby reducing the calculation error caused by the difference operator approximating the differential operator and suppressing 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 wavefield numerical simulation method. Specifically, the earthquake vector wavefield numerical simulation method provided in this embodiment can be applied in earthquake protection and early warning scenarios.

[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, abbreviated as I / O) and a communication interface. The processor, memory and 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 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 merely a block diagram of a portion 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. A specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement. In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor implements the steps of 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. When the computer program is executed by a processor, the steps in the above-mentioned method embodiments are implemented.

[0162] In an exemplary embodiment, a computer program product is provided, including a computer program. 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 skilled in the art will understand that all or part of the processes in the above-mentioned embodiment methods can be implemented 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 memory, database or other media used in the embodiments provided in this application may include at least one of non-volatile and volatile memory. Non-volatile memory may 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 may 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 databases involved in the various embodiments provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchains. The processors involved in the various embodiments provided herein may include, but are not limited to, general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic units, data processing logic units based on quantum computing, and the like.

[0166] The technical features of the above embodiments can 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 document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may 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 earthquake 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, the differential dispersion relation including staggered grid finite difference coefficients is converted 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 coefficients; 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 using the bacterial foraging optimization algorithm; The optimized staggered grid finite difference operator is used to perform differential discretization on the first-order velocity-stress elastic wave equation, and a numerical simulation scheme for seismic vector wave fields is obtained. Substituting the medium parameters, source parameters and observation system parameters of the test area into the seismic vector wave field numerical simulation scheme, the seismic vector wave field numerical simulation results of the test area are obtained; The objective function is solved by using the improved zebra optimization algorithm to obtain the optimized staggered grid finite difference operator, including: 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; 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 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 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, then the foraging phase position of the initial population at the numth iteration is updated to obtain the first updated population at the numth iteration; Perform defense phase position update on the first updated population at the numth iteration 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 sorted from best to worst, and the zebras in the bottom half are eliminated to obtain the undetermined population at the numth iteration. Copy the undetermined population at the num-th iteration to obtain the copied population; Merge the replicated population and the undetermined population at the num-th iteration to ensure that the population size remains unchanged. This allows the zebras to move to a better position with a greater probability during the next optimization search, accelerating the population's movement toward the optimal solution and improving the algorithm's convergence speed. Thus, the initial optimized population at the num-th iteration can be obtained. Based on the population dispersal mechanism, the zebras are randomly moved to new positions with a preset probability, thereby enhancing the randomness of their optimal neighborhood search and improving their ability to escape local extremes, thereby further enhancing the algorithm's global search capability. Finally, the positions of the zebras in the initial optimized population at the numth iteration are updated to obtain the optimized population at the num+1th iteration. Increase the value of the number of iterations num by 1 and return to 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 num-th 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.

2. The method for numerical simulation of earthquake vector wavefield according to claim 1, characterized in that: By introducing error constraints, 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; Taking half of the sampling interval as the independent variable, inputting it into the first-order derivative formula of the original continuous signal and intercepting a finite sequence of a preset interception length, an initial staggered grid finite difference operator is obtained; 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; Based on the original continuous signal dispersion relation, the initial staggered grid finite difference operator dispersion relation is determined; An error limit is introduced into the dispersion relation of the initial staggered grid finite difference operator, and an objective function including staggered grid finite difference coefficients is constructed.

3. The method for numerical simulation of earthquake 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, 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 earthquake 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 the length of the staggered grid finite difference, c m is the staggered grid finite difference coefficient, and ε is the error limit.

5. The method for numerical simulation of earthquake vector wave fields according to claim 1, characterized in that: The position update in the foraging stage is: Among them, X' l is the position of the first zebra in the 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 first 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 value of the y-th decision variable of the l-th zebra in the initial population, r is a random number between 0 and 1, PZ y is the optimal value of the y-th decision variable of the pioneer zebra in the initial population, and I is a random number between 1 and 2.

6. The method for numerical simulation of earthquake vector wave fields according to claim 5, 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.

7. The method for numerical simulation of earthquake 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.

8. 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 7.

9. 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 wavefield numerical simulation method according to any one of claims 1 to 7 is implemented.

Images