Three-dimensional sound wave propagation simulation method based on multi-relaxation time lattice Boltzmann model

Abstract

The invention provides a three-dimensional sound wave propagation simulation method based on a multi-relaxation time lattice Boltzmann model, and belongs to the crossing field of geophysical exploration and computational acoustics. Comprising the following steps: 1) constructing a three-dimensional mathematical model based on an actual geological structure; 2) establishing a 3D-MLBM equation, and modifying a migration process to obtain an iterative computation format of the sound wave field quantity; 3) setting physical parameters, processing boundary conditions and initializing simulation conditions; 4) simulation of sound wave field propagation is carried out, and wave field information at different moments is recorded; and 5) carrying out quantitative comparison on the performance of the D3Q15-MLBM and the performance of the D3Q27-MLBM, optimizing model parameters, and analyzing and applying a result. And analyzing a model result, establishing a multi-dimensional performance evaluation system, and applying the multi-dimensional performance evaluation system to seismic wave field simulation and inversion of a large-scale three-dimensional geologic model.

Description

Technical Field

[0001] The present application proposes a three-dimensional acoustic wave propagation simulation method based on the multi-relaxation-time lattice Boltzmann model, belonging to the cross field of geophysical exploration and computational acoustics. Background Art

[0002] Currently, acoustic wave propagation simulation technology is a key means in fields such as geophysical exploration, seismology research, oil and gas resource exploration, and engineering geological evaluation. By accurately simulating the propagation law of acoustic waves in underground media, the formation structure can be inverted, lithology changes can be identified, reservoir characteristics can be evaluated, and a scientific basis can be provided for resource development.

[0003] Due to its unique mesoscopic modeling advantages and parallel computing potential, the lattice Boltzmann model (LBM) has gradually become a research hotspot in fluid mechanics, multiphase flow, and acoustic simulation. Different from traditional macroscopic continuum methods, LBM is based on the kinetic processes of microscopic particle collisions and migrations, describes the evolution of the particle distribution function through a discrete velocity model, and finally recovers macroscopic equations (such as the Navier-Stokes equation or the acoustic wave equation). Its explicit iterative characteristics, natural parallelism, and adaptability to complex boundaries make it show unique advantages in acoustic wave simulation. As in the following previously published domestic patent application, the application number is 202111166518.9, and the name is a viscous acoustic wave simulation method based on the single-relaxation-time lattice Boltzmann model. This method establishes a mathematical model of the area to be simulated according to the structural characteristics of the area to be simulated; establishes a discrete model based on the single-relaxation-time lattice Boltzmann equation, and constructs an iterative calculation format for each acoustic wave field parameter according to the physical parameters in the discrete model; assigns initial values to the wave field parameters in each preset direction in the discrete model, defines the source function, and formulates a wave impedance interface processing method, a fluid-solid boundary condition, and an external boundary condition of the calculation area; according to the iterative calculation format, uses the single-relaxation-time lattice Boltzmann equation to iteratively update and calculate the numerical values of the acoustic wave field parameters at the preset sampling time, thereby improving the accuracy of viscous acoustic wave simulation. However, the numerical stability of such LBM single-relaxation-time models is poor, and divergence problems are prone to occur especially under three-dimensional high Reynolds number or complex medium conditions.

[0004] As the prior art, the multi-relaxation-time lattice Boltzmann model (MLBM) was proposed. By separating the relaxation times of different modes, it aims to improve the stability and accuracy of the algorithm, becoming one of the core directions in current LBM research. However, MLBM still focuses on hydrodynamic simulations, such as pore flow or turbulence analysis, and the applicability and performance differences for acoustic wave propagation have not been fully explored. As in the following priorly published domestic patent application with the application number 201910281421.9 and the title "Large Eddy Simulation Method of Turbulence Based on Coherent Structure", it includes establishing a lattice Boltzmann method model to obtain the calculation formula for fluid viscosity; in the traditional Smagorinsky model, the eddy viscosity is determined by the filtered strain rate tensor, the filtering scale, and the Smagorinsky constant; in the lattice Boltzmann method - large eddy simulation method model, a uniform matrix grid is used to make the filtering scale △r the same as the lattice unit; in the multi-relaxation-time lattice Boltzmann model, the strain rate tensor is calculated; the Galilean invariant QLES in the sub-grid flow field is introduced, and the relationship equations between the Galilean invariant QLES and the strain rate tensor and the rotation rate tensor are defined. By defining the model parameter C, the relationship between the model parameter C and the coherent structure function is obtained; the eddy viscosity is obtained through the sub-grid kinetic energy kSGS, thereby establishing the relationship between the coherent structure function and the sub-grid kinetic energy; the eddy viscosity is obtained in the large eddy simulation. The above method is not applicable to three-dimensional acoustic wave simulation, difficult to solve the huge computational amount brought by three-dimensional acoustic wave simulation, and unable to achieve a balance between computational accuracy and efficiency at the same time.

[0005] In current acoustic wave propagation simulations, the choice of the discrete velocity model of MLBM directly affects the computational efficiency and accuracy. Commonly used discrete models in three-dimensional space include D3Q15-MLBM and D3Q27-MLBM. The D3Q15 model has a relatively small computational amount, but its anisotropy error is relatively high, which may introduce numerical dissipation in high-frequency acoustic wave or complex medium simulations; the D3Q27 model improves isotropy by increasing the number of discrete directions and has higher computational accuracy, but the computational cost increases significantly. There is still a lack of systematic comparative studies on these two models in acoustic applications.

[0006] Furthermore, the complexity of three-dimensional geological structures poses higher requirements for acoustic wave simulation. The actual formation often contains complex structures such as faults, fractures, and heterogeneous interlayers, which cause refraction, reflection, and scattering of the acoustic wave propagation paths. Traditional methods need to rely on grid encryption or adaptive algorithms to handle such problems, significantly increasing the computational burden. With its local evolution characteristics, MLBM can efficiently capture the characteristics of complex wave fields through simple collision and migration rules and is naturally compatible with parallel computing architectures such as GPUs, providing new ideas for large-scale three-dimensional simulations. However, existing MLBM acoustic models are mostly limited to two dimensions, and the adaptability to full three-dimensional geological models and the influence mechanism of discrete velocity models are not yet clear, restricting their application in actual exploration.

[0007] In view of this, this patent application is specifically proposed. Summary of the Invention

[0008] The three-dimensional acoustic wave propagation simulation method and device based on the multi-relaxation-time lattice Boltzmann model of the present invention aim to solve the problems existing in the above-mentioned prior art. By combining the D3Q15 and D3Q27 discrete velocity models, a three-dimensional acoustic wave field simulation framework is constructed, and then the performance differences between the two models are systematically compared to provide a numerical calculation tool for acoustic wave propagation analysis, oil and gas resource exploration, and engineering geological evaluation in complex geological structures, achieving the purpose of improving both computational efficiency and accuracy.

[0009] To achieve the above design purpose, the three-dimensional acoustic wave propagation simulation method based on the multi-relaxation-time lattice Boltzmann model includes the following steps:

[0010] 1) Construct a three-dimensional mathematical model based on the actual geological structure;

[0011] According to the actual geological data, analyze the geological structure characteristics of the target area, and determine the geometric range and resolution of the simulation area;

[0012] 2) Establish the 3D-MLBM equation and modify the migration process to obtain the iterative calculation format of the acoustic wave field quantity;

[0013] 3) Set physical parameters, handle boundary conditions, and initialize the simulation conditions;

[0014] 4) Conduct the simulation of the acoustic wave field propagation and record the wave field information at different times;

[0015] Realize the numerical simulation of the three-dimensional acoustic wave field propagation by iteratively solving the 3D-MLBM equation;

[0016] 5) Quantitatively compare the performance of D3Q15-MLBM and D3Q27-MLBM, optimize the model parameters, and analyze and apply the results;

[0017] Evaluate the performance of D3Q15-MLBM and D3Q27-MLBM in three-dimensional acoustic wave propagation simulation, including calculation accuracy, calculation efficiency, and stability;

[0018] Compare the sound pressure field and velocity field distributions of the two models at different times, and analyze their ability to capture the characteristics of acoustic wave propagation;

[0019] Calculate the error between the two models and the reference solution or experimental data, and compare the numerical stability;

[0020] Analyze the model results and establish a multi-dimensional performance evaluation system, and apply it to the seismic wave field simulation and inversion problems of large-scale three-dimensional geological models.

[0021] Furthermore, in step 1), according to the simulation target, geological complexity, computing resources, and accuracy requirements, select different discrete velocity models of 3D-MLBM; if the geological structure is simple and the computing resources are limited, select the D3Q15-MLBM model; if the geological structure is complex and high-precision simulation is required, select the D3Q27-MLBM model.

[0022] Furthermore, step 2) includes the following steps:

[0023] 2.1), Collision;

[0024] The expression of the collision process is:

[0025] f i colli (x,t) = f i (x,t) - M -1 S(m - m eq ) (5)

[0026] 2.2), Migration;

[0027] The expression of the migration process is:

[0028]

[0029] Among them, Z1 and Z2 respectively represent the wave impedances of the media on both sides of the interface, and are related to the actual physical parameters of the two sides of the media. The physical parameters include but are not limited to the density and acoustic wave velocity of the media;

[0030] 2.3), Update macroscopic quantities;

[0031] Calculate macroscopic quantities through the moments of the particle distribution function, and the expression is as follows:

[0032]

[0033] Among them, ρ is the density and u is the velocity;

[0034] 2.4), Calculate the sound pressure field;

[0035] The sound pressure p can be calculated through the density ρ:

[0036]

[0037] Through iterative calculation, the acoustic wave field quantities are gradually updated in time and space to simulate the propagation process of acoustic waves in geological media.

[0038] Furthermore, step 3) includes the following steps:

[0039] By reasonably reducing the s q value on the boundary to achieve the absorption of truncated reflection;

[0040] Adopt the rigid bounce boundary condition to implement the boundary condition processing;

[0041] Initializing the simulation conditions provides the initial state for the acoustic wave propagation simulation to ensure that the simulation starts from a reasonable starting point;

[0042] Initial density

[0043] The expression of the field distribution is:

[0044]

[0045] where, (x s , y s , z s ) is the source position, and rik(t) is the Ricker wavelet;

[0046] The expression of the initial velocity field distribution is:

[0047] u(x, y, z, t = 0) = 0 (13)

[0048] According to the initial density field and velocity field, the expression of the initial particle distribution function is:

[0049] f i (x, y, z, t = 0) = f i eq (ρ(x, y, z, t = 0), u(x, y, z, t = 0)) (14)

[0050] Furthermore, in step 4), record the wave field information at different times, including but not limited to the sound pressure field and velocity field.

[0051] Furthermore, step 5) includes analyzing the propagation characteristics of acoustic waves in geological media, visualizing the dynamic process of acoustic wave propagation through wave field snapshots and animations; calculating the energy distribution of the acoustic wave field and analyzing the energy attenuation characteristics during the acoustic wave propagation process.

[0052] Further, in step 5), quantitatively compare the differences in the waveform calculation accuracies of D3Q15-MLBM and D3Q27-MLBM. The expression is as follows:

[0053]

[0054] where A g is the wave amplitude at the g-th point calculated by 3D-FDM, B g is the wave amplitude at the g-th point calculated by D3Q15-MLBM, and C g is the wave amplitude at the g-th point calculated by D3Q27-MLBM.

[0055] In summary, the present application has the following advantages and beneficial effects:

[0056] 1. The present application proposes a comparative optimization method based on D3Q15-MLBM and D3Q27-MLBM. By constructing a three-dimensional geological mathematical model, systematically analyzing the performance differences between the two discrete velocity models in terms of calculation accuracy and numerical stability, and exploring parameter optimization strategies, it not only fills the technical gap of MLBM in three-dimensional acoustic simulation, but also provides a theoretical basis for model selection and calculation resource allocation in actual geological exploration, having important academic value and engineering significance.

[0057] 2. The unified simulation framework for three-dimensional acoustic wave propagation proposed in the present application can effectively support the rapid construction and high-precision calculation of complex geological models, proposes an MLBM parameter optimization method for acoustic wave propagation, balances the calculation resources and accuracy requirements, and thus can significantly promote the engineering application of LBM technology in the geophysical field.

[0058] 3. The present application provides a flexible and adjustable numerical simulation tool for fields such as geological exploration and earthquake prediction, and has the characteristics of strong adaptability and high result reliability. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 is a flow chart of the three-dimensional acoustic wave propagation simulation method based on the multi-relaxation-time lattice Boltzmann model according to the present application;

[0060] Figure 2 is a comparison diagram of two discrete models; wherein, Figure 2 (a) is a schematic diagram of the D3Q15 discrete velocity model, Figure 2 (b) is a schematic diagram of the D3Q27 discrete velocity model;

[0061] Figure 3 is a schematic diagram of the rigid bounce-back boundary treatment for the upper boundary of D3Q15-MLBM;

[0062] Figure 4 It is a comparison diagram of wave field slices of three models at t = 80 ms; among them, Figure 4 (a) is a schematic diagram of the wave field slice calculated by the D3Q15-MLBM model; Figure 4 (b) is a schematic diagram of the wave field slice calculated by the D3Q27-MLBM model; Figure 4 (c) is a schematic diagram of the wave field slice calculated by the 3D-FDM model;

[0063] Figure 5 It is a comparison diagram of wave profiles calculated by 3D-MLBM and 3D-FDM at different times and positions; among them, Figure 5 (a) is the wave profile at t = 50 ms, depth z = 100 m, and distance y = 100 m; Figure 5 (b) is the wave profile at t = 85 ms, distance y = 70 m, and distance x = 150 m; Figure 5 (c) is the wave profile at t = 70 ms, distance x = 70 m, and depth z = 120 m;

[0064] Figure 6 It is a schematic diagram of a three-dimensional heterogeneous velocity model;

[0065] Figure 7 It is a comparison diagram of wave field slices of three models at t = 105 ms; among them, Figure 7 (a) is a schematic diagram of the wave field slice calculated by the D3Q15-MLBM model; Figure 7 (b) is a schematic diagram of the wave field slice calculated by the D3Q27-MLBM model; Figure 7 (c) is a schematic diagram of the wave field slice calculated by the 3D-FDM model;

[0066] Figure 8 It is a comparison diagram of wave profiles calculated by 3D-MLBM and 3D-FDM at different times and positions; among them Figure 8 (a) is the wave profile at t = 80 ms, depth z = 125 m, and distance x = 125 m; Figure 8 (b) is the wave profile at t = 95 ms, distance y = 125 m, and distance x = 125 m; Figure 8 (c) is the wave profile at t = 60 ms, distance y = 125 m, and depth z = 125 m. Specific implementation manner

[0067] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0068] Example 1, as Figures 1 to 8 shown, the present application proposes a three-dimensional acoustic wave propagation simulation method based on the multi-relaxation time lattice Boltzmann model, including the following steps:

[0069] 1) Construct a three-dimensional mathematical model based on the actual geological structure;

[0070] Analyze the geological structure characteristics (including stratigraphic distribution, lithology, faults, fractures, etc.) of the target area according to the actual geological data (such as seismic exploration data, geological cross-sections, etc.), and determine the geometric range and resolution of the simulation area;

[0071] On the one hand, ensure that the model can accurately reflect the details of the geological structure, and use geological modeling software (such as Petrel, GOCAD, etc.) or numerical methods to convert the geological structure data into a three-dimensional mathematical model; the model is usually represented in the form of a grid, and the size and shape of the grid cells need to be reasonably selected according to the simulation accuracy and computing resources;

[0072] On the other hand, mark the physical parameters (such as density, sound velocity, viscosity, etc.) of different geological units in the model to provide a basis for subsequent acoustic wave propagation simulation.

[0073] LBM is a numerical simulation method based on the motion of microscopic particles, which is discretized in time, space, and velocity. The discrete velocity model of LBM can be denoted as DmQn, where m is the spatial dimension and n is the number of discrete velocities, describing the motion of fluids or acoustic waves in the grid. The discrete velocity model defines the possible directions and velocities of particles moving in the grid. Commonly used three-dimensional models include D3Q15 and D3Q27, as Figure 2 shown;

[0074] There is an inherent contradiction between the D3Q15 and D3Q27 models in terms of computational efficiency and physical accuracy. It is necessary to balance the selection of the discrete velocity model in complex inhomogeneous media to avoid acoustic wave anisotropy errors caused by simplified models (such as D3Q15) or excessive computational costs introduced by high-order models (such as D3Q27).

[0075] The lattice velocity information of D3Q15-MLBM and D3Q27-MLBM proposed in this application is recorded in Table 1 below:

[0076] Table 1---Comparison of discrete velocity sets and weight coefficients of D3Q15 and D3Q27

[0077]

[0078] Select different discrete velocity models of 3D-MLBM according to the simulation objectives, geological complexity, computing resources, and accuracy requirements;

[0079] If the geological structure is simple and the computing resources are limited, select the D3Q15-MLBM model; if the geological structure is complex and high-precision simulation is required, select the D3Q27-MLBM model;

[0080] 2) Establish the 3D-MLBM equation and modify the migration process to obtain the iterative calculation format of acoustic field quantities.

[0081] LBM is based on the statistical mechanics description of microscopic particle motion. By simulating the collision and migration processes of particles on a discrete grid, it macroscopically describes the propagation behavior of fluids or sound waves. MLBM is an improvement over the traditional single-relaxation-time LBM. By introducing multiple relaxation time parameters, it can more flexibly control the relaxation processes of different physical modes, thereby improving numerical stability and calculation accuracy. The parameters of the multi-relaxation-time model need to be precisely matched with the physical characteristics of the acoustic wave equation. How to optimize multiple relaxation parameters to stabilize the simulation process while ensuring the authenticity of physical phenomena such as acoustic wave attenuation and dispersion requires complex mathematical derivations and numerical verifications.

[0082] The propagation of sound waves can be regarded as the motion of a compressible fluid, and its governing equation can be approximately solved by LBM. In MLBM, the propagation of sound waves is described by the particle distribution function f i (x, t), where x = [x, y, z] is the three-dimensional spatial position and t is the time.

[0083] The governing equation of 3D-MLBM is

[0084] f i (x + c i Δt, t + Δt) = f i (x, t) + Ω i (x, t) (1)

[0085] where Ω i (x, t) is the collision operator, which describes the collision process of particles at the grid nodes; ci is the lattice velocity.

[0086] In MLBM, the collision operator is expressed in the moment space as:

[0087] Ω i = -M -1 S(m - m eq ) (2)

[0088] where M is the transformation matrix from the velocity space to the moment space, S is the relaxation matrix containing multiple relaxation time parameters, m is the moment vector, and m eq is the equilibrium moment vector.

[0089] The particle distribution function f i The distribution function is mapped to the moment space through the transformation matrix M to achieve the transformation between the moment space and the velocity space:

[0090] m = Mf (3)

[0091] where f = [f0, f1, L fN-1 T is the distribution function vector, and N is the number of discrete velocity directions;

[0092] The equilibrium distribution function f i eq in 3D-MLBM is derived from the Maxwell-Boltzmann velocity distribution in statistical mechanics:

[0093]

[0094] where c s is the lattice sound speed, determined by the lattice model, and is for both D3Q15 and D3Q27. u is the particle vibration velocity;

[0095] Therefore, 3D-MLBM realizes the iterative calculation of acoustic wave field quantities through the following steps;

[0096] 2.1), Collision;

[0097] The expression of the collision process is:

[0098] f i colli (x,t) = f i (x,t) - M -1 S(m - m eq ) (5)

[0099] 2.2), Migration;

[0100] Theoretically, the expression of the migration process of acoustic waves in a fluid is:

[0101] f i (x + c i Δt, t + Δt) = f i colli (x,t) (6)

[0102] Different from fluid flow, when depicting the wave phenomenon of acoustic waves, in order to adapt to media with different speeds and densities and fully consider the wave effects such as reflection and transmission of acoustic waves at the media interface, the above migration expression in this application is modified as:

[0103]

[0104] where Z1 and Z2 respectively represent the wave impedances of the media on both sides of the interface and are related to the actual physical parameters of the two sides of the media. The physical parameters include but are not limited to the density and acoustic wave velocity of the media;

[0105] Therefore, the modified migration step helps to improve the simulation accuracy of acoustic waves at the media interface;

[0106] ​2.3), Update macroscopic quantities;

[0107] Calculate macroscopic quantities through the moments of the particle distribution function, and the expressions are as follows:

[0108]

[0109] Among them, ρ is the particle perturbation density, and u is the particle vibration velocity;

[0110] 2.4), Calculate the sound pressure field;

[0111] The sound pressure p can be calculated from the particle perturbation density ρ:

[0112]

[0113] Through iterative calculation, the acoustic wave field quantities (such as sound pressure, velocity) are gradually updated in time and space to simulate the propagation process of sound waves in geological media;

[0114] 3), Set physical parameters, handle boundary conditions and initialize simulation conditions;

[0115] Physical parameters are the basis for simulating sound wave propagation and need to be reasonably set according to actual geological conditions and sound wave characteristics, including but not limited to density distribution, sound speed distribution, quality factor distribution, viscosity distribution, etc.

[0116] Boundary conditions are an important part of simulating sound wave propagation and directly affect the accuracy of simulation results. In this application, to solve the interference of truncated boundary reflections on simulation results, by changing the relaxation parameter s of the shear moment at the absorption boundary q to suppress the boundary reflected waves; Since the suppression of geological structure boundary reflection interference requires designing an efficient absorption boundary condition, the existing technology is difficult to directly apply under the MLBM framework, and a three-dimensional boundary processing algorithm with low numerical dissipation and high computational efficiency must be developed first.

[0117] In fact, both D3Q15-MLBM and D3Q27-MLBM have 6 shear moments, and their corresponding relaxation parameters s q are directly related to the shear viscosity υ, and the expression is:

[0118]

[0119] In this regard, this application reasonably reduces the s q value on the boundary to achieve the absorption of truncated reflections;

[0120] During the migration process, the particles have multi-directional motion characteristics, resulting in the lack of particle distribution functions at the boundary nodes in some directions. Therefore, it is necessary to implement boundary condition processing;

[0121] This application uses a rigid bounce-back boundary condition to solve this problem. Taking the upper boundary nodes of D3Q15-MLBM as an example Figure 3 As shown, the directions lacking the particle distribution function values are 4, 8, 10, 11, and 14:

[0122]

[0123] Initializing the simulation conditions provides an initial state for the acoustic wave propagation simulation, ensuring that the simulation starts from a reasonable starting point;

[0124] The expression for the initial density field distribution is:

[0125]

[0126] where (x s , y s , z s ) is the source position, and rik(t) is the Ricker wavelet;

[0127] The expression for the initial velocity field distribution is:

[0128] u(x, y, z, t = 0) = 0 (13)

[0129] According to the initial density field and velocity field, the expression for the initial particle distribution function is:

[0130] f i (x, y, z, t = 0) = f i eq (ρ(x, y, z, t = 0), u(x, y, z, t = 0)) (14)

[0131] 4) Perform the simulation of the acoustic wave field propagation and record the wave field information at different times;

[0132] By iteratively solving the 3D-MLBM equation, the numerical simulation of the three-dimensional acoustic wave field propagation is realized;

[0133] During the simulation process, record the wave field information at different times, including but not limited to the sound pressure field, velocity field, etc., providing data support for subsequent performance comparison and optimization;

[0134] 5) Quantitatively compare the performances of D3Q15-MLBM and D3Q27-MLBM, optimize the model parameters, and analyze and apply the results;

[0135] The main purpose of the performance comparison is to evaluate the performance of D3Q15-MLBM and D3Q27-MLBM in the three-dimensional acoustic wave propagation simulation, including aspects such as calculation accuracy, calculation efficiency, and stability;

[0136] Compare the sound pressure fields and velocity field distributions of the two models at different times, and analyze their abilities to capture the characteristics of acoustic wave propagation;

[0137] Calculate the errors between the two models and the reference solution (FDM) or experimental data, and compare the numerical stabilities;

[0138] Analyze the model results and establish a multi-dimensional performance evaluation system, and apply it to the seismic wave field simulation and inversion problems of large-scale three-dimensional geological models. For example, analyze the propagation characteristics of acoustic waves in geological media, such as reflection, refraction, attenuation, and scattering phenomena; visualize the dynamic process of acoustic wave propagation through wave field snapshots and animations; calculate the energy distribution of the acoustic wave field and analyze the energy attenuation characteristics during the propagation of acoustic waves, etc.

[0139] As Figure 8 shown, although the waveforms of D3Q15-MLBM and D3Q27-MLBM have the same starting points, there are slight amplitude differences at some reflection positions (as indicated by the arrows); thus, quantitatively compare Figure 8 (a) to Figure 8 (c) The difference results in the calculation accuracy of the waveforms shown, and the results are recorded in Table 2.

[0140]

[0141] Among them, A g is the wave amplitude at the gth point calculated by 3D-FDM, B g is the wave amplitude at the gth point calculated by D3Q15-MLBM, C g is the wave amplitude at the gth point calculated by D3Q15-MLBM.

[0142] Table 2---Comparison of wave field accuracies between D3Q15-MLBM and D3Q27-MLBM

[0143] <![CDATA[η1(D3Q15-MLBM)]]> <![CDATA[η2(D3Q27-MLBM) <!-- 8 -->]]> Figure 8 (a) Wave profile 0.2036％ 0.1150％ Figure 8 (b) Wave profile 0.3123％ 0.1776％ Figure 8 (c) Wave profile 0.1206％ 0.0580％

[0144] Based on the content of the above embodiments, the present application applies the relevant simulation methods to the following two models:

[0145] The first is a three-dimensional homogeneous model;

[0146] In the three-dimensional homogeneous model, the accuracies and stabilities of the wave field simulations of the D3Q15-MLBM and D3Q27-MLBM models are compared, and the three-dimensional finite difference method (3D-FDM) with a low time step is used as the reference solution.

[0147] The model consists of 200×200×200 discrete grids with a spatial step of 1m×1m×1m. The wave field recording time is 100 ms, where the time step of 3D - MLBM is 0.5 ms and that of 3D - FDM is 0.01 ms. The P - wave velocity of the homogeneous model is 2500 m / s, the density is 1000 kg / m 3 , and the quality factor is 25. A Ricker wavelet source with a dominant frequency of 35 Hz is applied at the center of the model.

[0148] As Figure 4 shown, at 80 ms, wave field snapshots at different positions calculated using the D3Q15 - MLBM, D3Q27 - MLBM, and 3D - FDM methods. By comparing Figure 4 (a) to Figure 4 (c) of the three sub - figures, it can be found that the wave fields of D3Q15 - MLBM and D3Q27 - MLBM are very close to the results of 3D - FDM in terms of waveform, polarity, and energy.

[0149] As Figure 5 shown, for further comparison, two sets of wave profiles are extracted from the same position; Figure 5 as indicated by the arrow in

[0150] there are some extra perturbations in the results of D3Q15 - MLBM, while the results of D3Q27 - MLBM are more consistent with those of 3D - FDM.

[0151] Second, the three - dimensional heterogeneous model;

[0152] As Figure 6 shown, the wave field simulations of D3Q15 - MLBM and D3Q27 - MLBM are tested in a three - dimensional non - uniform model with cavities; the size of this model is 250m×250m×250m, and the P - wave velocities from the inner layer to the outer layer are 1500 m / s, 2000 m / s, and 2500 m / s respectively; the medium density is 1500 kg / m 3 , and the total recording time is 120 ms; the remaining parameters are the same as those in the above three - dimensional homogeneous model example.

[0153] As Figure 7As shown, at the 105 ms moment, wave field snapshots extracted from different positions, which are calculated by D3Q15-MLBM, D3Q27-MLBM and 3D-FDM respectively. By comparing Figure 7 (a) to Figure 7 (c) of the three subfigures, it can be found that the wave field slices show high similarity in morphology, and only slight amplitude differences are observed in the internal reflection region.

[0154] This application focuses on these subtle differences and extracts two sets of wave profiles at different positions, as Figure 8 shown.

[0155] Based on Table 2 above, for this heterogeneous three-dimensional model, the accuracy error of D3Q27-MLBM is about half of that of D3Q15-MLBM. Compared with the results of 3D-FDM, the D3Q27-MLBM algorithm shows higher consistency. This may be because D3Q27-MLBM considers more discrete velocities in a wider range of directions than D3Q15-MLBM, thus theoretically improving its accuracy in modeling complex geological structures. As indicated by the arrow in Figure 8 c, small wave field jitters occur in the D3Q15-MLBM simulation, indicating that D3Q27-MLBM has better stability in this case.

[0156] Moreover, as shown in Table 3 below, quantitatively compare the memory occupancy and calculation time of D3Q15-MLBM and D3Q27-MLBM when simulating the acoustic wave field: The program is programmed in C language, and the running environment is a laptop with CPU: 16 AMD Ryzen7 5800H with Radeon Graphics; total memory: 15860 MiB.

[0157] By comparison, for a model of size 250×250×250, the memory occupancy and calculation time of D3Q27-MLBM are 1.21 and 1.37 times that of D3Q15-MLBM under the same conditions respectively. This indicates that D3Q27-MLBM consumes more computing resources.

[0158] Table 3---Quantitative comparison of D3Q15-MLBM and D3Q27-MLBM

[0159]

[0160]

[0161] Through the above quantitative comparison, it can be summarized that there are obvious differences between D3Q15-MLBM and D3Q27-MLBM in terms of calculation accuracy, memory occupancy, calculation time and algorithm stability.

[0162] As described above, similar technical solutions can be derived from the solution content given in combination with the accompanying drawings and description, and all of them still fall within the scope of the claims of the technical solution of the present invention.

Claims

1. A three-dimensional acoustic wave propagation simulation method based on the multi-relaxation time lattice Boltzmann model, characterized in that: including the following steps, 1), constructing a three-dimensional mathematical model based on the actual geological structure; According to the actual geological data, analyze the geological structure characteristics of the target area, and determine the geometric range and resolution of the simulation area; 2), establishing the 3D-MLBM equation and modifying the migration process to obtain the iterative calculation format of the acoustic field quantity; 3), setting physical parameters, processing boundary conditions and initializing simulation conditions; 4), performing the simulation of acoustic field propagation and recording the wave field information at different times; Through iterative solution of the 3D-MLBM equation, realizing the numerical simulation of three-dimensional acoustic field propagation; 5), quantitatively comparing the performances of D3Q15-MLBM and D3Q27-MLBM, optimizing the model parameters, and analyzing and applying the results; Evaluating the performances of D3Q15-MLBM and D3Q27-MLBM in the simulation of three-dimensional acoustic wave propagation, including calculation accuracy, calculation efficiency and stability; Comparing the sound pressure field and velocity field distributions of the two models at different times, and analyzing their abilities to capture the characteristics of acoustic wave propagation; Calculating the errors between the two models and the reference solution or experimental data, and comparing the numerical stabilities; Analyzing the model results and establishing a multi-dimensional performance evaluation system, and applying it to the seismic wave field simulation and inversion problems of large-scale three-dimensional geological models.

2. The three-dimensional acoustic wave propagation simulation method based on the multi-relaxation-time lattice Boltzmann model according to claim 1, wherein: In the said step 1), different discrete velocity models of 3D-MLBM are selected according to the simulation target, geological complexity, computing resources and accuracy requirements; If the geological structure is simple and the computing resources are limited, the D3Q15-MLBM model is selected; if the geological structure is complex and high-precision simulation is required, the D3Q27-MLBM model is selected.

3. The three-dimensional acoustic wave propagation simulation method based on the multi-relaxation time lattice Boltzmann model according to claim 1, characterized in that: The said step 2) includes the following steps; 2.1), collision; The expression of the collision process is: 2.2), migration; The expression of the migration process is: wherein, Z1 and Z2 respectively represent the wave impedances of the media on both sides of the interface, and are related to the actual physical parameters of the media on both sides. The said physical parameters include but are not limited to the density and acoustic wave velocity of the media; 2.3), updating macroscopic quantities; Calculating macroscopic quantities through the moments of the particle distribution function, and the expression is as follows: wherein, ρ is the density and u is the velocity; 2.4), calculating the sound pressure field; The sound pressure p can be calculated from the density ρ: Through iterative calculation, the acoustic field quantity is gradually updated in time and space to simulate the propagation process of acoustic waves in geological media.

4. The three-dimensional acoustic wave propagation simulation method based on the multi-relaxation time lattice Boltzmann model according to claim 1, characterized in that: The said step 3) includes the following steps, By reasonably reducing the s value on the boundary to achieve the absorption of truncated reflection; q ​ Adopting a rigid bounce boundary condition to implement boundary condition processing; Initializing the simulation conditions is to provide an initial state for the acoustic wave propagation simulation to ensure that the simulation starts from a reasonable starting point; the expression of the initial density field distribution is: Among them, (x s , y s , z s ) is the source location, and rik(t) is the Ricker wavelet; The expression of the initial velocity field distribution is: u(x,y,z,t=0)=0 (13) According to the initial density field and velocity field, the expression of the initial particle distribution function is:

5. The three-dimensional acoustic wave propagation simulation method based on the multi-relaxation-time lattice Boltzmann model according to claim 1, characterized in that: In the said step 4), recording the wave field information at different times, including but not limited to the sound pressure field and velocity field.

6. The three-dimensional acoustic wave propagation simulation method based on the multi-relaxation-time lattice Boltzmann model according to claim 1, characterized in that: The said step 5) includes analyzing the propagation characteristics of acoustic waves in geological media, visualizing the dynamic process of acoustic wave propagation through wave field snapshots and animations; calculating the energy distribution of the acoustic wave field and analyzing the energy attenuation characteristics during the acoustic wave propagation process.

7. The three-dimensional acoustic wave propagation simulation method based on the multi-relaxation-time lattice Boltzmann model according to claim 6, characterized in that: Quantitatively compare the differences in the waveform calculation accuracy between D3Q15-MLBM and D3Q27-MLBM. The expression is as follows: where A g is the wave amplitude at the g-th point calculated by 3D-FDM, B g is the wave amplitude at the g-th point calculated by D3Q15-MLBM, C g is the wave amplitude at the g-th point calculated by D3Q15-MLBM.

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