CN114089419B - 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, performing step-by-step change of space grid step length and time sampling interval; step 2, performing space grid step length and time sampling interval of multi-region change; step 3, calculating a differential coefficient according to a differential coefficient equation; and 4, performing forward modeling to obtain a simulation record of the complex geological target. The optimized grid-variable seismic forward modeling method realizes forward modeling of the millimeter-scale fracture reservoir, improves adaptability to complex geologic bodies, has higher modeling precision and stability, can greatly reduce memory through combination of multistage and block algorithms, improves calculation efficiency, and is suitable for numerical simulation of large-scale complex structural bodies.
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 petroleum geophysical prospecting technology, seismic forward modeling is the basis for reverse time migration and full waveform inversion.
The seismic wave propagation numerical simulation is a basic stone for seismic data processing, is a powerful tool for researching seismic wave propagation theory, guiding seismic data acquisition and performing seismic data interpretation, and is a key step in many seismic inversion algorithms. Currently, the most commonly used seismic wave numerical simulation method is the finite difference method. The 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.
As the geological conditions faced by seismic exploration become increasingly complex, the exploration objects include strong longitudinal and transverse variable speed zones, low speed zones, complex structural zones, small hole and slot holes of carbonate reservoirs, and the like. When simulating the seismic wavefield propagating in these areas, the grid spacing needs to be small to ensure simulation accuracy and computational stability, which results in significant increases in numerical simulation storage and computation. The scholars have proposed the idea of a variable grid, i.e. simulating different areas with different grid steps. Subsequently, a large number of students at home and abroad apply the idea to the numerical simulation method of the geological problem, so that the simulation accuracy is ensured, the memory requirement is reduced, and the adaptability and the practicability of the simulation algorithm are enhanced.
In application number: in the chinese patent application of cn201710253444.X, a global optimized interleaved grid finite difference forward modeling method and apparatus are related, 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 an interleaving grid finite difference weight coefficient for optimizing an interleaving grid finite difference operator, wherein the interleaving grid finite difference weight coefficient is calculated within the coverage range of the maximum wave number of the optimized interleaving grid finite difference operator and under the maximum spectral error tolerance of the optimized interleaving 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 intensive.
In application number: in CN 201610997235.1's chinese patent application, a space-time double-varying forward modeling method is related, by using physical parameters represented by a depth domain velocity field, the depth domain velocity field is segmented and graded, a background grid model of the depth domain velocity field, a single-stage variable grid segmented variable grid model, and a multi-stage variable grid segmented variable grid model are established, and two-dimensional acoustic wave pressures under the corresponding background grid, each single-stage variable grid, and multi-stage variable grid? And obtaining a background grid seismic response wave field containing the fine wave field characteristics under different grid scales of each block by using a space-time double-varying forward modeling method according to the discrete difference of the velocity wave equation. But for complex geological targets with different scales, there is no way for this approach to accurately simulate.
In application number: in the chinese patent application CN201410298161.3, a high-precision space and time arbitrary multiple variable grid finite difference forward modeling method is related, where the high-precision space and time arbitrary multiple variable grid finite difference forward modeling method includes: step 1, establishing a forward speed model of an underground medium; step 2, performing two-dimensional grid discretization on the forward speed model, and performing two-dimensional grid discretization on an acoustic wave field in the forward 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, performing time domain finite difference forward modeling through an acoustic wave equation, wherein the time sampling step is a variable step in grids with different sizes. Likewise, this approach also fails to perform fine simulation of complex geologic targets.
Therefore, the invention discloses a new optimized variable grid earthquake forward modeling method, and solves the technical problems.
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 aim 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, performing step-by-step change of space grid step length and time sampling interval; step 2, performing space grid step length and time sampling interval of multi-region change; step 3, calculating a differential coefficient according to a differential coefficient equation; and 4, performing forward modeling to obtain a simulation record of the complex geological target.
The aim of the invention can be achieved by the following technical measures:
Step 1a, the excitation wave field normally propagates in the coarse grid area, when the wave field in the coarse grid area propagates to the first-stage variable grid area, the first-stage double-variable processing is carried out, and the grid spacing is reduced by n 1 times;
Step 1b, when the wave field in the first-stage variable grid area is transmitted to the second-stage variable grid area, entering second-stage double-variable processing, wherein the grid spacing is reduced by n 1×n2 times;
Step 1c, when the wave field in the second-level grid-changing area is transferred to the third-level grid-changing area, the distance is reduced again by n 3 times to n 1×n2×n3 times, and the third-level double-changing processing is performed, so that grid change of n 1×n2×n3 times is realized through the third-level grid-changing processing, and the fourth-level grid and the fifth-level grid-changing area reach n 1×n2×n3×n4 times and n 1×n2×n3×n4×n5 times in the same manner.
In step 2, when there are multiple variable grid areas, each area is independent and not affected, i.e. whether one area is encrypted or not is not related to other areas; assuming that there are only two variable grid areas a and B, four cases are included: a is not encrypted, B is not encrypted, and A and B are two independent events, and are respectively and independently judged.
In step 2, at each time step, the initial state is updated according to the conventional coarse grid, in the updating process, whether the wave field is transferred to the fine area A is judged, if so, the fine processing is performed by utilizing the principles of variable space grid step and variable time sampling interval, and if not, the coarse grid updating is continuously adopted. Then judging whether the wave field is transferred to a fine area B, if so, carrying out fine processing by utilizing the principle of utilizing the variable space grid step length and the variable time sampling interval, and if not, adopting coarse grid updating; the other areas (C, d.) were treated the same.
In step 3, a differential coefficient equation is deduced, and a differential coefficient is obtained according to the differential coefficient equation; the first-order velocity-stress equation of the 2D elastic wave based on the isotropic inhomogeneous medium is as follows:
Where v x,νz represents the velocity of the horizontal and vertical components of the particle, respectively, τ xx,τzz,τxz represents the stress vector; ρ is density, λ, μ is the lame constant.
In step 3, unlike the conventional staggered grid, the grid spacing Δx of the variable space step algorithm is no longer a constant value, noted as Δ i x, and the difference operator is spatially varying, which is a function of the grid step; the resulting differential coefficients are expressed as:
Wherein the method comprises the steps of Representing a variable space grid step size, c i,j representing a differential coefficient; and obtaining a differential coefficient according to the obtained differential coefficient equation.
In step 4, forward modeling is performed according to the differential coefficient obtained in the previous step, and a modeling record of the complex geological target is obtained.
Aiming at the defects existing in the variable grid algorithm, the diversity of the seismic target body scale and the randomness of the appearance position, the invention provides an optimized space-time double-variation forward modeling algorithm. Comprising the following steps: realizing the step-by-step change of the space grid step length and the time sampling interval; realizing the space grid step length and the time sampling interval of the multi-region change; inputting a complex medium velocity field to obtain an accurate forward modeling result. Aiming at the defects existing in the variable grid algorithm, the diversity of the scale of the seismic target and the randomness of the appearance position, the invention provides an optimized space-time double-variation forward simulation algorithm. Mainly comprises the following steps: simulation of millimeter-scale cracks is realized through a multistage staggered grid-changing technology, so that small-scale geological exploration is possible; the geobody comprising a plurality of target areas with different scale levels is simulated by utilizing the blocking grid-changing thought, and different grid-changing multiples are adopted for each target area, so that simultaneous exploration of multiple target areas is realized.
The beneficial effects of the invention are as follows: the invention provides an optimized variable grid seismic forward modeling method, which is used for solving the problem that the change rate of the coarse grid and the fine grid of the current variable grid algorithm cannot exceed 20 times so as to realize forward modeling of a millimeter-level fracture reservoir, improve the adaptability to complex geologic bodies and the modeling precision and stability, greatly reduce the memory and improve the calculation efficiency through the combination of multi-stage and block algorithms, and can be suitable for numerical modeling of large-scale complex structural bodies.
Drawings
FIG. 1 is a schematic diagram of an example of a block-variable grid speed model in accordance with an embodiment of the present invention;
FIG. 2 is a schematic diagram of a multi-level variational mesh in accordance with an embodiment of the present invention;
FIG. 3 is a schematic diagram of a low-speed volume model according to an embodiment of the invention;
FIG. 4 is a diagram illustrating meshing in accordance with an embodiment of the present invention;
FIG. 5 is a schematic diagram of a single 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 waveform comparison diagram of an embodiment of the present invention;
FIG. 7 is a graph showing a comparison of computing time consumption in accordance with an embodiment of the present invention;
FIG. 8 is a schematic diagram of a second stage multi-seam model in accordance with an embodiment of the present invention;
FIG. 9 is a diagram of a 300ms time wavefield snapshot of a crack model in an embodiment of the invention;
FIG. 10 is a schematic diagram of a single shot record of a crack model in an embodiment of the 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
The foregoing and other objects, features and advantages of the invention will be apparent from the following more particular description of preferred embodiments, as illustrated in the accompanying drawings.
As shown in FIG. 11, FIG. 11 is a flow chart of the optimized variable grid seismic forward modeling method of the invention.
In step 101, the excitation wave field normally propagates in the coarse grid region, and when the wave field in the coarse grid region propagates to the first-stage double-transformation processing (the grid spacing is reduced by n 1 times) is entered;
At step 102, when the wavefield in the primary variogram region propagates to the secondary variogram region, entering a secondary double variogram process (n 1×n2 times the grid spacing reduction);
In step 103, when the wave field in the second-level grid-changing area is transferred to the third-level grid-changing area, the distance is reduced again by n 3 times to n 1×n2×n3 times, and the third-level double-changing processing is performed, so that grid change of n 1×n2×n3 times is realized through the third-level grid-changing processing, and in the same way, the fourth-level and fifth-level grid-changing areas can reach n 1×n2×n3×n4 times and n 1×n2×n3×n4×n5 times, and the change multiple can reach 3125 times under the assumption that n 1＝n2＝n3＝n4＝n5 =5, so that the accurate simulation of millimeter-level cracks can be realized;
At step 104, a spatial grid step size and a temporal sampling interval of the multi-region variation are performed. When there are multiple variable grid areas, each area is independent and not affected, i.e. whether one area is encrypted or not is irrelevant to other areas. Assuming that there are only two variable grid areas a and B, four cases are included: the A encryption B does not encrypt, the A does not encrypt, and the B encrypts, and as A and B are two independent events, the A and the B can be respectively and independently judged, so that the four conditions comprise;
and updating the initial state according to a conventional coarse grid at each time step, judging whether the wave field is transmitted to a fine area A in the updating process, if so, carrying out fine processing by utilizing the principles of variable space grid step and variable time sampling interval, and if not, continuing to update by adopting the coarse grid. And judging whether the wave field is transferred to a fine area B, if so, carrying out fine processing by utilizing the principle of utilizing the variable space grid step length and the variable time sampling interval, and if not, adopting coarse grid updating. Similarly, other areas (C, d.) were treated the same;
In step 105, the 2D elastic wave first order velocity-stress equation based on the isotropic inhomogeneous medium is:
Where v x,νz represents the velocity of the horizontal and vertical components of the particle, respectively, and τ xx,τzz,τxz represents the stress vector. ρ is density, λ, μ is the lame constant.
Unlike conventional interleaved grids, the grid spacing Δx of the variable space-step algorithm is no longer a constant value, which can be noted as Δ i x, and the difference operator is spatially variable, which is a function of the grid step. The resulting differential coefficients are expressed as:
Wherein the method comprises the steps of Representing a variable space grid step size, c i,j representing a differential coefficient;
according to the obtained differential coefficient equation, a differential coefficient is obtained;
And in step 106, finally, forward modeling is performed to obtain a simulation record of the complex geological target.
In a specific embodiment to which the invention is applied, a step-by-step spatial grid step length and time sampling interval algorithm based on staggered grids is realized. Firstly, the excitation wave field normally propagates in a coarse grid area, and when the wave field in the coarse grid area propagates to a first-stage variable grid area, the first-stage double-variable processing is performed (the grid spacing is reduced by n1 times); when the wave field in the first-level variable grid area propagates to the second-level variable grid area, the second-level double-variable processing (the grid spacing is reduced by n1 multiplied by n 2) is entered; when the wave field in the second-level grid-changing area is transferred to the third-level grid-changing area, the distance is reduced by n3 times again to reach n1 multiplied by n2 multiplied by n3, and the third-level double-changing processing is performed, so that grid change of n1 multiplied by n2 multiplied by n3 is realized through the third-level grid-changing processing, and similarly, four-level and five-level grid-changing can reach n1 multiplied by n2 multiplied by n3 multiplied by n4 and n1 multiplied by n2 multiplied by n3 multiplied by n4 multiplied by n5, and assuming that n1 = n2 = n3 = n4 = n5 = 5, the change multiple can reach 3125 times, and the accurate simulation of millimeter-level cracks can be realized (as shown in fig. 1).
When there are multiple variable grid areas, each area is independent and not affected, i.e. whether one area is encrypted or not is irrelevant to other areas. Assuming that there are only two variable grid areas a and B, four cases are included: the A encryption B does not encrypt, the A does not encrypt, and the B encrypts, and because the A and the B are two independent events, the A and the B can be respectively and independently judged, and thus, all the four conditions are included. The specific implementation steps of the blocking grid change are as follows: and updating the initial state according to a conventional coarse grid at each time step, judging whether the wave field is transmitted to a fine area A in the updating process, if so, carrying out fine processing by utilizing the principles of variable space grid step and variable time sampling interval, and if not, continuing to update by adopting the coarse grid. And judging whether the wave field is transferred to a fine area B, if so, carrying out fine processing by utilizing the principle of utilizing the variable space grid step length and the variable time sampling interval, and if not, adopting coarse grid updating. Similarly, the other areas (C, d.) are treated identically (as shown in fig. 2).
To verify the correctness of the method of the present invention, we first set up a model with two low-speed volumes at a distance from each other inside, as shown in fig. 3. In the model, the P wave speed of the upper layer is 3000m/s, the lower layer is 3500m/s, the speed of the lower-left-angle low-speed body is 1000m/s (3 times of grid change is needed), and the speed of the lower-right-angle low-speed body is 600m/s (5 times of grid change is needed). If a conventional algorithm is used, in order to meet the stability condition, the grid spacing and the sampling interval are very small, so that over-sampling of other calculation areas is caused, and the calculation efficiency is greatly reduced; if the conventional grid-changing algorithm is adopted, the same 5 times grid-changing processing is adopted for the black dotted line frame part in fig. 3, so that the area between the low-speed bodies is oversampled, and the oversampling occurs when the upper left corner low-speed body is calculated by adopting the 5 times grid-changing. The optimal processing method is to adopt a block space-time double-transformation algorithm, namely, respectively carrying out grid transformation processing on two low-speed bodies, wherein the grid transformation is adopted by 3 times in the upper left corner, and the grid transformation is adopted by 5 times in the lower right corner (as shown in figure 4). For comparison analysis, the three methods (global fine grid, conventional 5 times variable grid and blocking variable grid) are adopted to carry out simulation trial calculation respectively, corresponding single gun records are shown in fig. 5, the gun records of the three methods are consistent, further, a plurality of single waveforms are extracted from the gun records respectively for comparison, and as shown in fig. 6 (direct waves are removed), the results obtained by the three methods are basically the same, only slight difference exists, and errors are negligible. Taken together, the results of fig. 5 and 6 verify the correctness of the block-wise multistage optimization spatiotemporal double-varying algorithm herein.
In order to verify the effectiveness of the method of the invention. The result of the model trial calculation proves that the results of the three methods are basically the same, but the storage amount and the calculated amount of the three methods are greatly different. FIG. 7 is a time-consuming comparison of the results calculated in three ways. It can be found that: the efficiency of the conventional grid-changing method is improved by 4.9 times compared with that of the global fine grid method, the efficiency of the block fine grid-changing method is improved by 12.5 times compared with that of the conventional grid-changing method, and the efficiency of the block fine grid-changing method is improved by 61.2 times compared with that of the global fine grid. Therefore, the numerical simulation efficiency can be greatly improved by adopting a blocking grid-changing algorithm, and the time consumption of the grid-changing algorithm is only 8% of the time consumption of the grid-changing algorithm, and the time consumption of the global fine grid is only 1.6%.
It is well known that western carbonate reservoirs are generally buried deeper, requiring longer simulation times; and the crack size is smaller, and the earthquake response is weak, so that a high-precision high-power grid simulation technology is required. The conventional grid-changing algorithm is extremely unstable and has larger error under the condition of large time sampling and high-power grid change, and the multistage staggered grid-changing 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. As shown in FIG. 8, which is a crack model, the opening is 2cm, the step length of the uniform grid is 4.5m, namely, the grid change multiple is more than 225 times, and the numerical simulation of the high-power grid algorithm is realized by adopting two-stage 15 times of 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 pronounced, representing a superposition of multiple diffracted wavefields. FIG. 10 is a gun record of a fracture model, and it can be seen that the diffraction curve is more energy-efficient in the case of multiple fractures. The false reflection error cannot be observed in the grid gradual change region, so that the error introduced by the multistage grid change is very small and can be ignored, and the effectiveness of the multistage staggered grid change algorithm is verified.
Therefore, considering the defects of the grid-variable technology, the invention provides an optimized grid-variable forward modeling method, which provides a basis for researching wave field propagation rules and characteristics of complex underground media and inversion imaging.
The optimized variable grid seismic forward modeling method is used for solving the problem that the variation rate of the thick and thin grids of the current variable grid algorithm cannot exceed 20 times, so that forward modeling of a millimeter-level fracture reservoir is realized, adaptability to a complex geologic body is improved, modeling precision and stability are high, memory can be greatly reduced through combination of multistage and block algorithms, calculation efficiency is improved, and the method is applicable to numerical modeling of a large-scale complex structure. Mainly comprises the following steps: simulation of millimeter-scale cracks is realized through a multistage staggered grid-changing technology, so that small-scale geological exploration is possible; the geobody comprising a plurality of target areas with different scale levels is simulated by utilizing the blocking grid-changing thought, and different grid-changing multiples are adopted for each target area, so that simultaneous exploration of multiple target areas is realized.
It should be understood that the above description is not intended to limit the invention to the particular embodiments disclosed, but to limit the invention to the particular embodiments disclosed, and that the invention is not limited to the particular embodiments disclosed, but is intended to cover modifications, adaptations, additions and alternatives falling within the spirit and scope of the invention.
Claims (4)
1. The optimized variable grid seismic forward modeling method is characterized by comprising the following steps of:
Step 1, performing step-by-step change of space grid step length and time sampling interval;
Step 2, performing space grid step length and time sampling interval of multi-region change;
Step 3, calculating a differential coefficient according to a differential coefficient equation;
step 4, forward modeling is carried out to obtain a simulation record of the complex geological target body;
The step 1 comprises the following steps:
Step 1a, the excitation wave field normally propagates in the coarse grid area, when the wave field in the coarse grid area propagates to the first-stage variable grid area, the first-stage double-variable processing is carried out, and the grid spacing is reduced by n 1 times;
Step 1b, when the wave field in the first-stage variable grid area is transmitted to the second-stage variable grid area, entering second-stage double-variable processing, wherein the grid spacing is reduced by n 1×n2 times;
Step 1c, when the wave field in the second-level variable grid area is transferred to the third-level variable grid area, the distance is reduced again by n 3 times to n 1×n2×n3 times, and the third-level double-variable processing is performed; thus, grid change of n 1×n2×n3 times is realized through three-level grid change processing; similarly, the four-stage and five-stage variable grids reach n 1×n2×n3×n4 times and n 1×n2×n3×n4×n5 times;
In step 2, when there are multiple variable grid areas, each area is independent and not affected, i.e. whether one area is encrypted or not is not related to other areas; assuming that there are only two variable grid areas a and B, four cases are included: a is not encrypted, B is not encrypted, and A and B are two independent events, and are respectively and independently judged;
In each time step, the initial state is updated according to a conventional coarse grid, whether the wave field is transmitted to a 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 principles of variable space grid step and variable time sampling interval, and if the wave field is not transmitted, the coarse grid is continuously adopted for updating; then judging whether the wave field is transferred to a fine area B, if so, carrying out fine processing by utilizing the principle of utilizing the variable space grid step length and the variable time sampling interval, and if not, adopting coarse grid updating; and the other areas are treated in the same way.
2. The optimized variable grid seismic forward modeling method of claim 1, wherein in step 3, the differential coefficient is calculated according to a differential coefficient equation, and the 2D elastic wave first-order velocity-stress equation based on the isotropic inhomogeneous medium is:
Wherein: v x、νz represents the velocity of the horizontal x-axis and vertical z-axis components of the particle, respectively, τ xx、τzz、τxz represents the stress vector; ρ is density, λ, μ is the lame constant.
3. The optimized variable grid seismic forward modeling method of claim 2, wherein in step 3, unlike the conventional staggered grid, the grid spacing Δx of the variable space-step algorithm is no longer a constant value, denoted as Δ i x, and the difference operator is spatially varying, which is a function of the grid step; the resulting differential coefficients are expressed as:
Wherein the method comprises the steps of Representing a variable space grid step size, c i,j representing a differential coefficient;
and obtaining a differential coefficient according to the obtained differential coefficient equation.
4. The optimized variable grid seismic forward modeling method as claimed in claim 1, wherein in step 4, forward modeling is performed according to the obtained differential coefficients to obtain a modeling record of the complex geological target.
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