CN110795882A - Wave field simulation method based on improved quantum particle swarm algorithm - Google Patents
Wave field simulation method based on improved quantum particle swarm algorithm Download PDFInfo
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Abstract
The method provides a finite difference numerical simulation method based on an improved quantum particle swarm method, and belongs to the technical field of seismic exploration. Specifically, an objective function containing finite difference coefficients is optimized and solved through an improved quantum particle swarm algorithm, the optimized finite difference coefficients are obtained through searching, then finite difference operators are constructed through the finite difference coefficients, an elastic wave equation is dispersed, and seismic wave field numerical simulation is carried out, so that the precision and the efficiency of the seismic wave field numerical simulation are improved.
Description
Technical Field
The invention belongs to the technical field of seismic exploration, particularly relates to a seismic numerical simulation technology, and particularly relates to a seismic wave field numerical simulation method based on finite difference.
Background
At present, a method for simulating a seismic wave field by using a finite difference method is one of mainstream methods, is widely applied to the processes of seismic wave forward inversion imaging, migration imaging and geophysical inversion, and is used for performing numerical simulation on the seismic wave field by using the finite difference method. The numerical dispersion is generated because a differential operator is used for approximating the differential operator, errors are caused after truncation, and the three methods are used for solving the problems, namely finer grid, wavelet dominant frequency reduction and optimization of a differential format by using various optimization methods, so that the differential operator is approximated to the differential operator as much as possible. The finer mesh increases the amount of computation, reduces the wavelet dominant frequency, loses high frequency components, and reduces resolution. The most used method is to optimize the differential format. The most common methods for optimizing the difference format are a window function method and an optimization method, and the theoretical essence of the optimization method is to calculate finite difference coefficients within a maximum tolerable error range so as to obtain the maximum wave number coverage range. The optimized finite difference operator is derived by adopting different window functions to truncate the space convolution sequence of the pseudo-spectrum method by the optimized window function method; the optimization method applies various intelligent algorithms, finds the optimal solution through a machine learning method, continuously improves the self limitation of the algorithm, improves the capability of the algorithm for searching the optimal solution, and finds more finite difference operators. The two methods are essentially the same, and both methods are to obtain finite difference coefficients, and only have one difference, the optimization method is to obtain the finite difference coefficients by 'calculating' through various optimization methods, and the preferred window function method is to obtain the finite difference coefficients by 'designing'.
The optimized finite difference coefficient obtained by the calculation of the optimization method is actually a problem of multi-parameter optimization, and the optimization methods widely used for optimizing finite difference operators at present comprise a least square method, a simulated annealing method, a Remez algorithm and the like. In the process of searching the optimal solution in the space to meet the requirement of the error limit by the least square method, the simulated annealing method and the Remez algorithm, the problems of slow convergence and incapability of converging to the global optimal solution generally exist, and even the problem of non-convergence can occur under some extreme conditions.
Therefore, how to provide a finite difference operator with higher precision to be applied to the seismic wave field numerical simulation to realize the numerical simulation of the seismic wave field with high precision and high efficiency is a technical problem to be solved in the field.
Disclosure of Invention
In the process of carrying out numerical simulation on a seismic wave field by a finite difference method, numerical dispersion is inevitably generated when a differential operator is replaced by the differential operator, and the numerical dispersion can cause great influence on wave field imaging. Aiming at the problem, the method for reducing errors by finding out better finite difference coefficients through an intelligent algorithm is the most economical method, so the invention provides an improved quantum particle swarm optimization-based finite difference numerical simulation method.
The technical scheme adopted by the invention is a wave field simulation method based on an improved quantum particle swarm algorithm intelligent algorithm, and the method is realized by the following steps:
firstly, defining the solving range of finite difference coefficients, and then solving the optimal solution through an improved quantum particle swarm algorithm. The obtained finite difference coefficients are used in numerical simulation of the seismic wavefield. The solving method is as follows: firstly, recording the current coefficient of each particle, determining the best one of the current coefficients of all the particles through comparison and recording, then adjusting the coefficient of each particle according to the optimal coefficient, comparing the current position with the previous position again, selecting a more excellent coefficient as the result of the adjustment, and updating the global optimal coefficient. This is a loop, called an iteration. After successive iteration, the finite difference coefficient meets the requirement, and the finite difference coefficient is returned by the algorithm as the final result.
Aiming at the characteristics of finite difference coefficients, such as small numerical value, large variation amplitude, complex coupling relation between high-order problems and the like, in the process of applying the quantum particle swarm optimization method to solving the finite difference coefficients, the search formula of the quantum particle swarm optimization method needs to be changed, and through multiple experimental determination, β is added in the step 3 to serve as a correction coefficient to improve the search of the quantum particle swarm, so that the search speed of the method can be greatly improved, the capability of preventing the quantum particle swarm from falling into the local optimal problem can be greatly improved, and the better capability of the finite difference coefficients can be found.
Advantageous effects
The method can search the optimal finite difference coefficient more quickly, improve the search performance, is not easy to fall into a local optimal solution, and constructs the optimized finite difference operator by utilizing the finite difference coefficient to realize the high-precision and high-efficiency numerical simulation of the seismic wave field.
Drawings
FIG. 1 is a flow chart of the method of the present invention
FIG. 2 is a numerical dispersion curve obtained by using an improved quantum-behaved particle swarm optimization method
FIG. 3 is an enlarged view of the numerical dispersion obtained by using the modified quantum-behaved particle swarm optimization method
FIG. 4 forward simulated shot records obtained using conventional methods
FIG. 5 is a forward simulated cannon record using an improved quantum-behaved particle swarm optimization method
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As will be appreciated by one skilled in the art, embodiments of the present invention may be embodied as a system, apparatus, method or computer program product. Accordingly, the present disclosure may be embodied in the form of: entirely hardware, entirely software (including firmware, resident software, micro-code, etc.), or a combination of hardware and software.
The principles and spirit of the present invention are explained in detail below with reference to several representative embodiments of the invention.
The invention uses a desktop computer as a computing platform (the computer adopts an i3-9100 processor which is a four-core eight-thread processor with a main frequency of 3.6GHz and an installed Win10 professional operating system), and uses MATLAB software to compute, wherein the version is 2016 b.
Fig. 1 is a flowchart of the algorithm of the present invention, which specifically includes the following steps: the method comprises the following steps:
the method comprises the following steps: the random position and velocity of the quantum particle population, the best position of the population, the best position of each particle, the particle search range, and the population size are initialized.
Step two: the fitness value for each particle is calculated. The adaptive value in the method is an error value from a differential equation to a differential equation when the finite difference coefficient is applied to carry out numerical dispersion calculation. The smaller the error value, the higher the adaptation value corresponding to the coefficient, and the larger the error value, the lower the error value corresponding to the coefficient. At present, there are various methods for obtaining an adaptive value by performing numerical dispersion calculation, such as a taylor series expansion method, which is a known technique.
Step three: calculating the average position of all the positions of the current particle, and updating the positions of all the particles according to the following formula
Wherein
Is the central expected coordinate value of the jth dimension position of the ith particle in the t iteration under quantum theory, and 'a' is the central expected coordinate value belonging toThe random number of (a) is set,
representing the historical optimal position of the ith particle of the t-th iteration, namely the position with the minimum corresponding fitness in the ith particle position in the previous t iterations;
x(i,:)tcoordinates of the ith particle in the t iteration are represented, β represents the optimization coefficient provided by the invention, β is 1/ln (1/u), u is a random number from 0 to 1, b is a contraction expansion coefficient, and mbestj(t) is the average position of all particles in the jth dimension for the tth iteration,
step four: range detection is carried out on the updated particle position, and when the difference between the updated particle position and the position before updating is larger than a threshold value, the particle position is corrected, wherein a specific correction formula is as follows: adding a threshold value on the basis of the coordinates of the original position according to the displacement direction of the particles; if the threshold value is not exceeded, not correcting; the threshold value is set by verifying the result through a plurality of experiments, and the specific results are shown in the following table:
| part below 8 th order | Portion above 8 |
|
| 8 th order | 0.06-0.1 | - |
| 12 th order | 0.2 | 0.01 |
| 16 steps | 0.2 | 0.01 |
| 20 th order | 0.2 | 0.003 |
| 24 steps | 0.2 | 0.002 |
Step five: detecting the positions of all the particles on the basis of the fourth step, and taking a boundary value as the updated particle position of the particle when the updated particle position exceeds the quantum particle swarm searching range; if the search range of the quantum particle swarm is not exceeded, the correction is not carried out;
step six: and if the ending condition is met, searching for the maximum cycle number, and exiting. Otherwise, returning to the second step, recalculating the adaptive value of the particles, and starting the next cycle.
Step seven: and the global optimal solution after the two corrections is a finite difference coefficient, and the obtained finite difference coefficient is used for constructing a finite difference operator and is applied to a Marmousi model for numerical simulation.
And constructing an optimized finite difference operator by using the finite difference coefficient obtained in the steps, performing frequency dispersion analysis, and theoretically analyzing the performance of the optimized finite difference operator. By observing the dispersion diagrams of each order, it can be seen that the higher the order, the larger the spectrum coverage. As shown in fig. 3, in which 8 th order can reach 56%, 12 th order can reach 68%, 16 th order can reach 75%, 20 th order can reach 80%, the fluctuation range is concentrated within one thousandth, and the maximum fluctuation occurs at 24 th order, reaching three thousandth. Compared with a frequency dispersion diagram of a traditional method in the diagram, the frequency spectrum coverage is obviously improved, and meanwhile, the fluctuation range is suppressed to a smaller range, so that the stability is greatly improved.
And selecting an 8-order finite difference operator, carrying out numerical simulation on the Marmousi model, and analyzing the performance of the coefficient through the obtained shot record diagram. As shown in fig. 4 and 5, it can be seen from the comparison of the two graphs that the method based on the improved finite difference quantum particle swarm optimization has lower dispersion and better imaging effect in the imaging of the edge region.
Claims (1)
1. A wave field simulation method based on an improved quantum particle swarm algorithm is characterized in that:
the method comprises the steps of carrying out optimization solving on an objective function containing finite difference coefficients by improving a quantum particle swarm algorithm to obtain optimized finite difference coefficients, and then carrying out seismic wave field numerical simulation by utilizing the finite difference coefficients, wherein the finite difference coefficients correspond to the positions of particles; the specific process is as follows:
the method comprises the following steps: initializing random positions and speeds of quantum particle swarms, the best position of a swarm, the best position of each particle, a particle search range and swarm scales;
step two: calculating an adaptation value of each particle;
step three: calculating the average position of all the positions of the current particle, and updating the positions of all the particles according to the following formula
WhereinIs the central expected coordinate value of the jth dimension position of the ith particle in the t iteration under quantum theory,"a" is a
The random number of (a) is set,
representing the historical optimal position of the ith particle by the tth iteration,
represents the global optimal position of all particles by the tth iteration, i.e.:
x(i,:)tcoordinates of the ith particle in the t iteration are represented, β represents the optimization coefficient provided by the invention, β is 1/ln (1/u), u is a random number from 0 to 1, b is a contraction expansion coefficient, and mbestj(t) is the average position of all particles in the jth dimension for the tth iteration,
step four: range detection is performed on the updated particle position when the updated particle position x (i:)tAnd the position x (i,: before updating)t-1If the difference is greater than the threshold, the position of the particle is corrected, and the specific correction method comprises the following steps: adding a threshold value on the basis of the coordinates of the original position according to the displacement direction of the particles; if the threshold value is not exceeded, not correcting;
step five: detecting the positions of all the particles on the basis of the fourth step, and taking a boundary value as the updated particle position of the particle when the updated particle position exceeds the quantum particle swarm searching range; if the search range of the quantum particle swarm is not exceeded, the correction is not carried out;
step six: if the end condition is met, namely the searching reaches the maximum cycle number, exiting; otherwise, returning to the second step, recalculating the adaptive value of the particles, and starting the next cycle;
step seven: and the global optimal solution after twice correction is the optimal finite difference coefficient obtained by searching, the obtained finite difference coefficient is used for constructing a finite difference operator and a discrete elastic wave equation, and the finite difference operator and the discrete elastic wave equation are applied to a Marmousi model for numerical simulation to obtain an optimized elastic wave numerical simulation result.
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| CN113534246A (en) * | 2020-04-17 | 2021-10-22 | 中国石油化工股份有限公司 | Pre-stack AVO inversion method based on bee colony optimization algorithm |
| CN113534246B (en) * | 2020-04-17 | 2023-11-24 | 中国石油化工股份有限公司 | Pre-stack AVO inversion method based on bee colony optimization algorithm |
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