CN114089419A - Optimized variable grid earthquake forward modeling method - Google Patents
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Abstract
The invention provides an optimized variable grid earthquake forward modeling method, which comprises the following steps: step 1, carrying out space grid step length and time sampling interval which change step by step; step 2, carrying out multi-region variable space grid step length and time sampling interval; step 3, solving a difference coefficient according to a difference coefficient equation; and 4, performing forward modeling to obtain a simulation record of the complex geological target body. The optimized variable-grid earthquake forward simulation method realizes forward simulation of a millimeter-scale fractured reservoir, improves adaptability to complex geologic bodies and higher simulation precision and stability, can greatly reduce memory through combination of multilevel and block algorithms, improves calculation efficiency, and is applicable to numerical simulation of large-scale complex structures.
Description
Technical Field
The invention relates to the technical field of petroleum geophysical exploration, in particular to an optimized variable grid seismic forward modeling method.
Background
In the field of oil geophysical exploration, seismic forward modeling is the basis for reverse time migration and full waveform inversion.
The seismic wave propagation numerical simulation is a cornerstone for seismic data processing, is a powerful tool for researching a seismic wave propagation theory, guiding seismic data acquisition and explaining seismic data, and is also a key step in a plurality of seismic inversion algorithms. At present, the most common seismic wave numerical simulation method is a finite difference method. A general finite difference seismic simulation method is based on a regular grid in a Cartesian coordinate system and is an effective method for processing non-uniform media.
With the increasing complexity of geological conditions faced by seismic exploration, exploration objects comprise strong longitudinal and transverse speed change regions, low-speed zones, complex structural regions, small hole cracks of carbonate reservoirs and the like. When simulating seismic wavefields propagating in these regions, the grid spacing needs to be small to ensure simulation accuracy and computational stability, which results in a significant increase in numerical simulation storage and computation. The scholars have proposed the idea of variable meshing, i.e. simulating different regions using different mesh step sizes. Subsequently, a large number of scholars at home and abroad apply the idea to a numerical simulation method of the geological problem, so that the simulation precision is ensured, the memory requirement is reduced, and the adaptability and the practicability of a simulation algorithm are enhanced.
In the application No.: chinese patent application No. cn201710253444.x relates to a globally optimized staggered grid finite difference forward modeling method and apparatus, wherein the method includes: obtaining a staggered grid finite difference operator; establishing an objective function based on the maximized norm, and solving the objective function to obtain a staggered grid finite difference weight coefficient for optimizing a staggered grid finite difference operator, wherein the staggered grid finite difference weight coefficient is obtained by calculation within the maximum wave number coverage range of the optimized staggered grid finite difference operator and under the maximum spectrum error tolerance of the optimized staggered grid finite difference operator; and optimizing a space staggered grid finite difference operator by adopting the staggered grid finite difference weight coefficient obtained by solving and performing seismic wave forward modeling. But this method is computationally expensive.
In the application No.: the CN201610997235.1 chinese patent application relates to a space-time double-variation forward modeling method, which uses physical parameters of a depth domain velocity field representation to divide and grade the depth domain velocity field, establishes a background grid model of the depth domain velocity field, a variable grid model of a single-stage variable grid division and a variable grid model of a multi-stage variable grid division, and obtains a background grid seismic response wave field containing fine wave field characteristics of each division under different variable grid scales by using a space-time double-variation forward method through a corresponding background grid, two-dimensional sound wave pressure-velocity wave equation discrete difference formula under each single-stage variable grid and multi-stage variable grid. But for complex geological objects with different dimensions, the method has no way of performing accurate simulations.
In the application No.: CN201410298161.3, the present application relates to a finite difference forward method for a high-precision space and time arbitrary multiple variable grid, which includes: step 1, establishing a forward velocity model of an underground medium; step 2, carrying out two-dimensional grid discretization on the exercise speed model, and carrying out two-dimensional grid discretization on an acoustic wave field in the exercise speed model, wherein the acoustic wave field is positioned on grid nodes; step 3, discretizing the boundary condition grid of the optimal matching layer; and step 4, carrying out finite difference time domain forward modeling through a sound wave equation, wherein the time sampling step length is variable step length in grids with different sizes. Likewise, this method does not allow for fine modeling of complex geological targets.
Therefore, a new optimized variable-grid earthquake forward modeling method is invented, and the technical problems are solved.
Disclosure of Invention
The invention aims to provide an optimized variable grid seismic forward modeling method for realizing simultaneous exploration of multiple target areas.
The object of the invention can be achieved by the following technical measures: the optimized variable-grid earthquake forward modeling method comprises the following steps: step 1, carrying out space grid step length and time sampling interval which change step by step; step 2, carrying out multi-region variable space grid step length and time sampling interval; step 3, solving a difference coefficient according to a difference coefficient equation; and 4, performing forward modeling to obtain a simulation record of the complex geological target body.
The object of the invention can also be achieved by the following technical measures:
step 1a, exciting a wave field to normally propagate in a coarse grid area, and entering first-stage double-variation processing when the wave field in the coarse grid area propagates to a first-stage variable grid area, wherein grid spacing is reduced by n1Doubling;
step 1b, when the wave field in the first-level variable grid region is transmitted to the second-level variable grid region, the second-level double-variable processing is carried out, and the grid distance is reduced by n1×n2Doubling;
step 1c, when the wave field in the second-level variable grid region is transmitted to the third-level variable grid region, the distance is reduced by n again3Multiple, up to n1×n2×n3And (4) performing third-stage double-variable processing, so that n is realized through three-stage grid-variable processing1×n2×n3The grid change of the times is similar to that of the fourth-level and fifth-level variable grids which reach n1×n2×n3×n4Multiple and n1×n2×n3×n4×n5And (4) doubling.
In step 2, when a plurality of variable mesh areas exist, each area is independent and does not influence each other, that is, whether one area is encrypted or not is irrelevant to whether other areas are encrypted or not; assuming that there are only two variable mesh regions a and B, four cases are included: a encryption B is not encrypted, A encryption B is not encrypted, A encryption A and B are two independent events, and A and B are respectively and independently judged and processed.
In step 2, at each time step, the initial state is updated according to the conventional coarse grid, whether the wave field is transmitted to the fine area A or not is judged in the updating process, if the wave field is transmitted to the fine area A, fine processing is carried out by utilizing the variable space grid step length and variable time sampling interval principle, and if the wave field is not transmitted to the fine area A, the coarse grid updating is continuously adopted. Then judging whether the wave field is transmitted to a fine region B, if so, performing fine processing by utilizing a variable space grid step length and variable time sampling interval principle, and if not, updating by adopting a coarse grid; in the same way, the other areas (C, d.) are treated the same.
In step 3, a difference coefficient equation is deduced, and a difference coefficient is calculated according to the difference coefficient equation; the first-order velocity-stress equation of the 2D elastic wave based on the isotropic inhomogeneous medium is as follows:
wherein, vx，νzRepresenting the velocity, τ, of the horizontal and vertical components of the particle, respectivelyxx,τzz,τxzRepresenting a stress vector; ρ is density, λ, μ is Lame constant.
In step 3, unlike the conventional staggered grids, the grid spacing Δ x of the variable space step algorithm is no longer a constant value, and is denoted as Δix, the difference operator is spatially varying, which is a function of the grid step size; the resulting difference coefficient is expressed as:
wherein
Representing space of variationsStep size of grid, ci,jRepresenting a difference coefficient; and solving a difference coefficient according to the obtained difference coefficient equation.
In step 4, forward modeling is performed based on the difference coefficients obtained above, and a modeling record of the complex geological target is obtained.
The invention provides an optimized time-space double-transformation forward modeling algorithm, which aims at the defects existing in a variable grid algorithm, the diversity of the dimension of a seismic target body and the randomness of the appearance position. The method comprises the following steps: realizing space grid step length and time sampling interval which change step by step; realizing the spatial grid step length and the time sampling interval of multi-region change; and inputting a complex medium velocity field to obtain an accurate forward simulation result. Aiming at the defects in the variable grid algorithm, the diversity of the dimension of the seismic target body and the randomness of the appearance position, the invention provides an optimized space-time double-variable forward modeling algorithm. The method mainly comprises the following steps: the simulation of millimeter-scale cracks is realized through a multi-stage staggered grid-changing technology, so that small-scale geological exploration becomes possible; the method utilizes the block-to-grid concept to simulate the geologic body comprising a plurality of target areas with different scale series, and adopts different grid-variable multiples for each target area, thereby realizing the simultaneous exploration of multiple target areas.
The invention has the beneficial effects that: the invention provides an optimized variable-grid earthquake forward modeling method, which is used for solving the problem that the change rate of a thick grid and a thin grid of a current variable-grid algorithm cannot exceed 20 times, so that forward modeling of a millimeter-scale fractured reservoir is realized, the adaptability to a complex geologic body and higher modeling precision and stability are improved, the memory can be greatly reduced through the combination of multi-stage and block algorithms, the computing efficiency is improved, and the method is suitable for numerical modeling of large-scale complex tectonic bodies.
Drawings
FIG. 1 is a diagram illustrating an example of a block-by-block mesh velocity model in an embodiment of the present invention;
FIG. 2 is a schematic diagram of a multilevel variable mesh in accordance with an embodiment of the present invention;
FIG. 3 is a schematic diagram of a low velocity body model in an embodiment of the invention;
FIG. 4 is a schematic diagram of meshing according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of a shot record in an embodiment of the present invention: (a) a global fine grid method, (b) a block grid changing method, (c) a conventional grid changing method;
FIG. 6 is a comparison of waveforms in an embodiment of the present invention;
FIG. 7 is a comparison of time consumed for calculations in an embodiment of the present invention;
FIG. 8 is a diagram of a second stage multi-slit model in an embodiment of the present invention;
FIG. 9 is a schematic view of a 300ms wavefield snapshot of a fracture model in an embodiment of the present invention;
FIG. 10 is a schematic representation of a shot record of a fracture model in an embodiment of the present invention;
FIG. 11 is a flow chart of an embodiment of the optimized variable-grid seismic forward modeling method of the present invention.
Detailed Description
In order to make the aforementioned and other objects, features and advantages of the present invention comprehensible, preferred embodiments accompanied with figures are described in detail below.
As shown in fig. 11, fig. 11 is a flowchart of the optimized variable-grid seismic forward modeling method of the present invention.
In step 101, the excitation wave field is propagated normally in the coarse grid region, and when the wave field is propagated to the first-stage variable grid region in the coarse grid region, the first-stage double-variation processing is carried out (grid spacing is reduced by n)1Multiple);
at step 102, when the wave field in the first-level variable grid region propagates to the second-level variable grid region, a second-level double-variable processing is entered (grid spacing is reduced by n)1×n2Multiple);
at step 103, the spacing is again decreased by n as the wavefield passes in the second-level variable-grid region to the third-level variable-grid region3Multiple, up to n1×n2×n3Multiple, enter the third stageDouble-variable processing, thus realizing n by three-level variable-grid processing1×n2×n3The grid change of the times can reach n by four-level and five-level variable grids1×n2×n3×n4Multiple and n1×n2×n3×n4×n5Multiple, assume n1＝n2＝n3＝n4＝n5The change multiple can reach 3125 times as 5, and the accurate simulation of millimeter-scale cracks can be realized;
in step 104, a multi-region varying spatial grid step size and time sampling interval are performed. When a plurality of variable grid areas exist, each area is independent and does not influence each other, namely whether one area is encrypted or not is irrelevant to whether other areas are encrypted or not. Assuming that there are only two variable mesh regions a and B, four cases are included: a encrypts B and B, encrypts B and A, encrypts B and B, respectively judges A and B as two independent events, thus the four conditions are included;
and at each time step, updating the initial state according to the conventional coarse grid, judging whether the wave field is transmitted to the fine area A in the updating process, if so, performing fine processing by using a variable space grid step length and variable time sampling interval principle, and if not, continuously updating by using the coarse grid. And then judging whether the wave field is transmitted to a fine region B, if so, performing fine processing by utilizing a variable space grid step length and variable time sampling interval principle, and if not, updating by adopting a coarse grid. In the same way, the other areas (C, D.) are treated in the same way;
in step 105, the first order velocity-stress equation of the 2D elastic wave based on the isotropic inhomogeneous medium is:
wherein, vx，νzRepresenting the velocity, τ, of the horizontal and vertical components of the particle, respectivelyxx,τzz,τxzRepresenting the stress vector. ρ is density, λ, μ is Lame constant.
Unlike the conventional staggered grids, the grid spacing Δ x of the variable space step size algorithm is no longer a constant value and can be recorded as Δix, the difference operator is spatially varying, which is a function of the grid step size. The resulting difference coefficient is expressed as:
wherein
Representing variable space grid step size, ci,jRepresenting a difference coefficient;
solving a difference coefficient according to the obtained difference coefficient equation;
and step 106, finally performing forward modeling to obtain a simulation record of the complex geological target body.
In a specific embodiment to which the present invention is applied, a step-by-step varying spatial grid step size and time sampling interval algorithm based on an interleaved grid is implemented. Firstly, the excitation wave field normally propagates in a coarse grid region, and when the wave field propagates to a first-stage variable grid region in the coarse grid region, a first-stage double-variable processing is carried out (grid spacing is reduced by n1 times); when the wave field in the first-stage variable grid region is propagated to the second-stage variable grid region, the second-stage double-variable processing is carried out (the grid spacing is reduced by n1 multiplied by n2 times); when the wave field in the second-level variable grid region is transmitted to the third-level variable grid region, the spacing is reduced by n3 times again to reach n1 × n2 × n3 times, and the third-level dual-variable processing is performed, so that grid change of n1 × n2 × n3 times is realized through the third-level variable grid processing, and similarly, the four-level and five-level variable grids can reach n1 × n2 × n3 × n4 times and n1 × n2 × n3 × n4 × n5 times, and accurate simulation of the millimeter-level crack can be realized if n1 ═ n2 ═ n3 ═ n4 ═ n5 ═ 5 and the change multiple can reach 3125 times (as shown in fig. 1).
When a plurality of variable grid areas exist, each area is independent and does not influence each other, namely whether one area is encrypted or not is irrelevant to whether other areas are encrypted or not. Assuming that there are only two variable mesh regions a and B, four cases are included: a encryption B is not encrypted, A encryption B is not encrypted, A and B can be separately judged and processed because A and B are two independent events, and the A and B are included in the four conditions. The specific implementation steps of the blocking and grid changing are as follows: and at each time step, updating the initial state according to the conventional coarse grid, judging whether the wave field is transmitted to the fine area A in the updating process, if so, performing fine processing by using a variable space grid step length and variable time sampling interval principle, and if not, continuously updating by using the coarse grid. And then judging whether the wave field is transmitted to a fine region B, if so, performing fine processing by utilizing a variable space grid step length and variable time sampling interval principle, and if not, updating by adopting a coarse grid. Similarly, the other regions (C, d.) are treated the same (as shown in fig. 2).
To verify the correctness of the method of the present invention, we first build a model containing two distant low velocity bodies inside, as shown in fig. 3. In the model, the upper layer P wave speed is 3000m/s, the lower layer is 3500m/s, the speed of the upper left corner low-speed body is 1000m/s (3 times of variable grids are needed), and the speed of the lower right corner low-speed body is 600m/s (5 times of variable grids are needed). If a conventional algorithm is used, in order to meet the stability condition, the grid spacing and the sampling interval are both very small, so that oversampling on other calculation areas is caused, and the calculation efficiency is greatly reduced; however, if a conventional variable mesh algorithm is adopted, the same 5-fold variable mesh processing is adopted for the black dashed frame part in fig. 3, which may cause oversampling for the region between the low-speed volumes, and oversampling may also occur when the low-speed volumes at the upper left corner are calculated by adopting the 5-fold variable mesh. The optimal processing method is to adopt a block space-time double-variation algorithm, namely, to respectively carry out variable grid processing on two low-speed bodies, wherein the variable grid is adopted for the upper left corner by 3 times, and the variable grid is adopted for the lower right corner by 5 times (as shown in figure 4). For comparison analysis, the three methods (global fine grid, conventional 5-time variable grid, block variable grid) are respectively adopted for simulation trial calculation, the corresponding single shot record is shown in fig. 5, it can be seen from fig. 5 that shot records of the three methods are consistent, further, several single-channel waveforms are respectively extracted from the shot records for comparison, as shown in fig. 6 (direct wave is removed), it can be seen that the results obtained by the three methods are basically the same, only slight differences exist, and errors can be ignored. In conclusion, the results of fig. 5 and fig. 6 both verify the correctness of the block multi-level optimization space-time dual variant algorithm.
In order to verify the validity of the method of the invention. The results of trial calculation of the model prove that the results of the three methods are basically the same, but the storage amount and the calculation amount of the three methods are greatly different. FIG. 7 is a comparison of time consumption for three ways of calculating results. It can be found that: the efficiency of the conventional variable grid method is improved by 4.9 times compared with the efficiency of the global fine grid method, the efficiency of the block fine grid method is improved by 12.5 times compared with the conventional variable grid method, and the efficiency of the block variable grid method is improved by 61.2 times compared with the efficiency of the global fine grid method. Therefore, the numerical simulation efficiency can be greatly improved by adopting the block-to-grid algorithm, and only 8% of the time consumption of the grid is changed, and the time consumption of the global fine grid is 1.6%.
As is well known, the western carbonate reservoirs are generally buried deeper and require longer simulation time; and the crack size is small, and the seismic response is weak, so that a high-precision high-power variable grid simulation technology is required. The conventional variable grid algorithm is very easy to be unstable and has larger error under the conditions of large-time sampling and high-power grid change, and the multi-stage staggered variable grid algorithm relieves the grid change speed, so that the number of grid points is increased step by step, and the crack response characteristics can be stably and accurately simulated. For example, fig. 8 is a crack model, the opening is 2cm, the step length of the uniform grid is 4.5m, that is, the grid change multiple is more than 225 times, and the numerical simulation of the high power grid change algorithm is realized by adopting two-stage 15-time grid change. FIG. 9 is a snapshot of the wavefield of the fracture model at 300ms, from which it can be seen that the response of multiple fractures is very significant, appearing as a superposition of multiple diffracted wavefields. Figure 10 shows the shot record of the fracture model, and it can be found that the diffraction curve energy is stronger in the case of multiple fractures. False reflection errors can not be observed in the grid gradual change region, which shows that errors introduced by the multilevel variable grid are very small and can be ignored, and the effectiveness of the multilevel staggered variable grid algorithm is verified.
Therefore, in consideration of the defects of the variable grid technology, the invention provides an optimized variable grid forward modeling method, which provides a basis for researching the wave field propagation rule and characteristics of the complex underground medium and inversion imaging.
The optimized variable-grid earthquake forward simulation method is used for solving the problem that the change rate of a thick grid and a thin grid of the current variable-grid algorithm cannot exceed 20 times, so that forward simulation of a millimeter-scale fractured reservoir is realized, the adaptability to a complex geologic body and higher simulation precision and stability are improved, the memory can be greatly reduced through the combination of multi-stage and block algorithms, the calculation efficiency is improved, and the method is suitable for numerical simulation of large-scale complex structures. The method mainly comprises the following steps: the simulation of millimeter-scale cracks is realized through a multi-stage staggered grid-changing technology, so that small-scale geological exploration becomes possible; the method utilizes the block-to-grid concept to simulate the geologic body comprising a plurality of target areas with different scale series, and adopts different grid-variable multiples for each target area, thereby realizing the simultaneous exploration of multiple target areas.
It is to be understood that the above description is not intended to limit the present invention, and the present invention is not limited to the above examples, and those skilled in the art may make modifications, alterations, additions or substitutions within the spirit and scope of the present invention.
Claims (7)
1. The optimized variable-grid earthquake forward modeling method is characterized by comprising the following steps:
step 1, carrying out space grid step length and time sampling interval which change step by step;
step 2, carrying out multi-region variable space grid step length and time sampling interval;
step 3, solving a difference coefficient according to a difference coefficient equation;
and 4, performing forward modeling to obtain a simulation record of the complex geological target body.
2. The optimized variable-grid seismic forward modeling method according to claim 1, wherein step 1 comprises:
step 1a, exciting a wave field to normally propagate in a coarse grid area, and entering first-stage double-variation processing when the wave field in the coarse grid area propagates to a first-stage variable grid area, wherein grid spacing is reduced by n1Doubling;
step 1b, when the wave field in the first-level variable grid region is transmitted to the second-level variable grid region, the second-level double-variable processing is carried out, and the grid distance is reduced by n1×n2Doubling;
step 1c, when the wave field in the second-level variable grid region is transmitted to the third-level variable grid region, the distance is reduced by n again3Multiple, up to n1×n2×n3And (4) performing third-stage double-variable processing, so that n is realized through three-stage grid-variable processing1×n2×n3The grid change of the times is similar to that of the fourth-level and fifth-level variable grids which reach n1×n2×n3×n4Multiple and n1×n2×n3×n4×n5And (4) doubling.
3. The optimized variable-grid seismic forward modeling method according to claim 1, wherein in step 2, when a plurality of variable-grid regions exist, each region is independent and does not affect each other, that is, whether one region is encrypted or not is irrelevant to whether other regions are encrypted or not; assuming that there are only two variable mesh regions a and B, four cases are included: a encryption B is not encrypted, A encryption B is not encrypted, A encryption A and B are two independent events, and A and B are respectively and independently judged and processed.
4. The optimized variable-grid seismic forward modeling method according to claim 3, characterized in that in step 2, at each time step, the initial state is updated according to a conventional coarse grid, whether the wave field is transmitted to the fine area A is judged in the updating process, if the wave field is transmitted to the fine area A, the fine processing is performed by using the variable-space grid step size and variable-time sampling interval principle, and if the wave field is not transmitted to the fine area A, the coarse grid updating is continuously adopted. Then judging whether the wave field is transmitted to a fine region B, if so, performing fine processing by utilizing a variable space grid step length and variable time sampling interval principle, and if not, updating by adopting a coarse grid; in the same way, the other areas (C, d.) are treated the same.
5. The optimized variable-grid seismic forward modeling method according to claim 1, wherein in step 3, a difference coefficient equation is derived, and a difference coefficient is calculated according to the difference coefficient equation, wherein the 2D elastic wave first-order velocity-stress equation based on the isotropic inhomogeneous medium is:
wherein, vx，νzRepresenting the velocity, τ, of the horizontal and vertical components of the particle, respectivelyxx,τzz,τxzRepresenting a stress vector; ρ is density, λ, μ is Lame constant.
6. The optimized variable-grid seismic forward modeling method according to claim 5, wherein in step 3, unlike the conventional staggered grid, the grid interval Δ x of the variable-space-step algorithm is no longer a constant value and is noted as Δ xix, the difference operator is spatially varying, which is a function of the grid step size; the resulting difference coefficient is expressed as:
wherein
Representing variable space grid step size, ci,jRepresenting a difference coefficient;
and solving a difference coefficient according to the obtained difference coefficient equation.
7. The optimized variable-grid seismic forward modeling method according to claim 1, characterized in that in step 4, forward modeling is performed based on the difference coefficients obtained above, and a modeling record of a complex geological target is obtained.
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| CN115081267B (en) * | 2022-05-18 | 2023-08-29 | 内蒙古农业大学 | Optimization-based space-time variable step length finite difference seismic wave numerical simulation method |
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