CN115270579A - Second-order acoustic wave equation finite difference numerical simulation parameter selection method - Google Patents
Second-order acoustic wave equation finite difference numerical simulation parameter selection method Download PDFInfo
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Abstract
The invention discloses a second-order sound wave equation finite difference numerical simulation parameter selection method. It comprises the following steps: the method comprises the following steps: adding frequency dispersion to the seismic source wavelet; step two: setting a frequency dispersion error evaluation criterion and an error threshold; step three: screening finite difference parameter combinations according to an error evaluation criterion and a proper error threshold value; step four: performing finite difference dispersion on a second-order sound wave constant density wave equation to establish a calculated quantity target function; step five: and calculating a finite difference parameter corresponding to the minimum value of the objective function according to the calculated target function. The method has the advantage of realizing the selection of the finite difference parameters under the principle of minimum calculated amount of the second-order acoustic wave equation.
Description
Technical Field
The invention relates to the field of finite difference forward modeling numerical simulation of seismic exploration, in particular to a method for selecting finite difference numerical simulation parameters, and more particularly to a method for selecting finite difference numerical simulation parameters of a second-order acoustic wave equation.
Background
Finite difference methods are widely used for numerical simulation of seismic wavefields. Finite difference numerical simulation results in different propagation velocities of wavefields of different frequencies due to the difference discrete numerical calculation of differential equations. The greater the frequency of the wave field, the greater the numerical simulation dispersion error, and the more serious the dispersion phenomenon. The numerical simulation results corresponding to different difference parameters are different. The fine grid division precision corresponds to high-precision numerical simulation precision and huge calculation amount cost. At present, a high-order difference operator and an optimized high-order difference operator coefficient can be compromised to save the calculation cost, and a wave field can be simulated by high-efficiency and high-precision numerical values. But the finite difference parameter selection under the principle of minimum high-order calculated quantity can not be realized, and the method has the advantages of large calculated quantity, low efficiency and long time consumption; at present, reports about parameter selection theory guidance of the finite difference numerical simulation of the wave equation are not found.
Therefore, it is necessary to develop a method for selecting finite difference parameters that can realize the minimum calculation amount of the second-order acoustic wave equation.
Disclosure of Invention
The invention aims to provide a second-order sound wave equation finite difference numerical simulation parameter selection method, which realizes the finite difference parameter selection under the minimum calculated quantity principle of a second-order sound wave equation, gives theoretical guidance of the finite difference parameter selection under the minimum calculated quantity principle of the second-order sound wave equation, and has small calculated quantity and high efficiency; the method overcomes the defects that the prior art can not realize the finite difference parameter selection under the principle of minimum calculated amount of a second-order acoustic wave equation, and has large calculated amount, low efficiency and long time consumption.
In order to realize the purpose, the technical scheme of the invention is as follows: the method for selecting the finite difference numerical simulation parameters of the second-order acoustic wave equation is characterized by comprising the following steps of: comprises the following steps of (a) carrying out,
the method comprises the following steps: the seismic source wavelet is added with frequency dispersion and used for comparing with a reference wave field without frequency dispersion, in the second step, the waveform with frequency dispersion and the reference wave field without frequency dispersion are used for carrying out error evaluation, and the waveform with frequency dispersion is the waveform added with frequency dispersion in the first step;
step two: and setting a frequency dispersion error evaluation criterion and an error threshold value, wherein the final waveform is influenced by frequency dispersion, and the influence degrees of different frequency dispersion degrees on the waveform are different. The error evaluation criterion is used for guiding and determining a more proper error threshold; if the frequency dispersion waveform corresponding to the error threshold value is determined to be invalid frequency dispersion, discarding, and if the corresponding finite difference parameter is determined to be invalid frequency dispersion, discarding; determining finite difference parameters corresponding to the frequency dispersion smaller than the error threshold value as effective frequency dispersion, and determining optimized finite difference parameters from the effective frequency dispersion;
step three: screening finite difference parameter combinations according to an error evaluation criterion and a proper error threshold, and determining finite difference parameters corresponding to frequency dispersion smaller than the error threshold as effective finite difference parameters, wherein the effective finite difference parameters comprise optimized finite difference parameters;
step four: performing finite difference dispersion on a second-order sound wave constant density wave equation, establishing a calculated quantity target function, establishing the calculated quantity target function by corresponding different finite difference parameters to different calculated quantities, and selecting a finite difference parameter combination which can minimize the calculated quantity;
step five: and calculating a finite difference parameter corresponding to the minimum value of the objective function according to the calculated target function.
In the technical scheme, in the step one, frequency dispersion is added to a theoretical seismic source wavelet or a field actual seismic source wavelet;
in step one, the selected source wavelet is a theoretical wavelet (e.g. gaussian function, first derivative wavelet of rake wavelet, etc.) with analytical expression or a wavelet extracted from field seismic data, and the source wavelet p (x', t) is selected 0 ) The method for carrying out the spatial numerical value adding dispersion operation comprises the following specific steps:
s11: for a reference wavefield (i.e., a wavefield without dispersion, here the wavefield with a pre-dispersion or source wavelet in step one), p (x', t) 0 ) Performing discrete Fourier transform to obtain frequency domain wave field P (k, t) 0 ) The formula is as follows:
in formula (1): t is t 0 Is a time variable; x is a space coordinate variable; x is the wave field propagation distance; k' is a second-order acoustic wave equation, the central difference format positive mapping wave number is as follows:
in formula (2): c. C l Is a high-order difference operator coefficient; Δ x is a spatial discrete step; k is the wave number; n is the finite difference operator length; Δ x is a spatial discrete step;
s12: for the frequency domain wave field P (k, t) 0 ) Performing fast Fourier algorithm, and performing inverse transformation to time domain to obtain wave field p' (x, t) with numerical dispersion 0 ) The formula is as follows:
in formula (3): t is t 0 Is a time variable; x is nullAn inter-coordinate variable; Δ x is a spatial discrete step; k is the wave number.
In the above technical solution, a frequency dispersion error evaluation criterion and an error threshold are set, and the specific method includes:
in step two, according to the reference wave field p (x', t) in step one 0 ) And the numerically dispersed wavefield p' (x, t) 0 ) Setting a normalized two-norm error evaluation criterion, wherein the expression is as follows:
and taking the error between the numerical frequency dispersion wave field and the real wave field as a basis for judging the frequency dispersion degree, and selecting a proper error threshold value according to the magnitude of the frequency dispersion error.
In the above technical solution, the threshold is selected to be 0.01.
In the above technical solution, in step three, all finite difference parameter combinations corresponding to errors smaller than or equal to an error threshold are screened out according to the normalized two-norm error evaluation criterion given in step two; the finite difference parameter combination comprises a space sampling step length delta h, a finite difference operator length N and a finite difference coefficient c l And so on.
In the above technical solution, in step four, finite difference dispersion is performed on a second-order sound wave constant density wave equation, and a calculated quantity objective function is established, specifically including the following steps:
s4.1: performing center difference format dispersion on a second-order constant density acoustic wave equation:
in formula (5): c. C l Is a high-order difference operator coefficient; Δ h is a spatial discrete step length; Δ t is a time discrete step; n is the finite difference operator length;
representing time point t = n Δ t, spatial coordinate positionIs (i Δ h) ,j Δ h, k Δ h); v. of i,j,k Representing the velocity magnitude at (i Δ h, j Δ h, k Δ h) at the spatial coordinate position;
the sum of the addition operation amount and the multiplication operation amount is referred to as a calculation amount. When the equation is discrete, the computation involved is as follows: in the center difference discrete calculation of the three-dimensional wave equation, at each time step, the multiplication operation amount at each grid point is N +3, the addition operation amount is 11 × N +3, and the calculation amount is 12 × N +6. And in the two-dimensional wave equation, the multiplication operation amount is N +3, the addition operation amount is 7 multiplied by N +3, and the calculation amount is 8 multiplied by N +6. And in the one-dimensional wave equation, the multiplication operation amount is N +3, the addition operation amount is 3 multiplied by N +3, and the calculation amount is 4 multiplied by N +6. With reference to the above calculated quantity analysis, similar calculated quantities can be obtained by different wave equations and different difference formats;
s4.2: and carrying out grid division on the speed model body, and establishing a calculated quantity objective function.
In the technical scheme, the speed model body comprises a three-dimensional cube speed model and a two-dimensional rectangular speed model;
the grid point number NUM of the speed model body = volume/grid interval;
the calculated amount Cost of the velocity model body is related to the number of grid points NUM and the difference order N.
In the above technical solution, when the speed model body is a three-dimensional cube speed model, mesh division with a mesh spacing of Δ h meters is performed on a three-dimensional cube with a length, width and height of L, W, H meters, and the number of divided mesh points NUM and the calculated amount Cost are respectively:
NUM＝L×W×H/Δh(6)
Cost＝NUM×(12×N+6)(7)
when the speed model body adopts a two-dimensional rectangular speed model, grid division with the grid spacing of delta h meters is carried out on rectangles with the length and the width of L, W meters respectively, and the number NUM of divided grid points and the calculated quantity Cost are respectively as follows:
NUM＝L×W/Δh(8)
Cost＝NUM×(8×N+6)(9)。
in the above technical solution, in step five, the finite difference parameter combination corresponding to the minimum value of the objective function is calculated according to all the finite difference parameter combinations corresponding to the error smaller than or equal to the threshold value screened out in step three and the calculated quantity objective function in step four, and the finite difference numerical simulation parameter under the principle of minimum calculated quantity is selected.
Due to the adoption of the technical scheme, the invention has the following advantages: according to the analytic expression of numerical dispersion in the wave field space direction, theoretical guidance is provided for selecting the finite difference parameters of the second-order acoustic wave equation on the basis of minimizing the calculated quantity of finite difference numerical simulation.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a diagram illustrating a proposed value of finite difference parameter selection when a wavelet is a ricker wavelet according to an embodiment of the present invention.
In fig. 2, G represents the number of wavelength sampling points corresponding to 2.5 times the main frequency of the theoretical Ricker wavelet.
Detailed Description
The embodiments of the present invention will be described in detail with reference to the accompanying drawings, which are not intended to limit the present invention, but are merely exemplary. While the advantages of the invention will be clear and readily understood by the description.
As shown in fig. 1, the present invention provides a method for selecting finite difference numerical simulation parameters of a second order acoustic wave equation of a calculated minimum objective function, which comprises the following steps:
1) Extracting a seismic source wavelet or a theoretical seismic source wavelet according to the real seismic record, and performing spatial direction frequency dispersion operation;
the method comprises the following specific steps:
setting a Source wavefield p (x', t) without numerical dispersion 0 ) For the reference wave field, performing a spatial Dispersion Forward Transform (FSDT) on the reference wave field, and performing a Dispersion operation:
in the formula, k' is a positive enantiomerNumber of rays, t 0 Is a time variable, X is a space coordinate variable, and X is a wave field propagation distance.
The specific implementation process of the spatial frequency dispersion is as follows:
1.1 For the reference wavefield p (x', t) 0 ) Performing discrete Fourier transform to obtain frequency domain wave field P (k, t) 0 ) The formula is as follows:
in formula (1): t is t 0 Is a time variable; x is a space coordinate variable; x is the wave field propagation distance; k' is a positive mapping wave number of a second-order acoustic wave equation center difference format, and the expression is as follows:
in formula (2): c. C l Is a high-order difference operator coefficient; Δ x is a spatial discrete step; k is the wave number; n is the finite difference operator length;
1.2 To the frequency domain wavefield P (k, t) 0 ) Performing fast Fourier algorithm, and performing inverse transformation to time domain to obtain wave field p' (x, t) with numerical dispersion 0 ) The formula is as follows:
in formula (3): t is t 0 Is a time variable; x is a space coordinate variable; k is the wave number.
2) Setting a frequency dispersion error evaluation criterion, and selecting an error threshold value of 0.01;
the method comprises the following specific steps:
the normalized two-norm between the numerical frequency-dispersion wavefield and the reference wavefield is proposed to measure the dispersion error:
and (3) the error between the numerical frequency dispersion wave field and the real wave field is used as a basis for judging the frequency dispersion degree, a proper error threshold value is selected according to the frequency dispersion error, and the recommended threshold value is selected to be 0.01.
3) And screening the finite difference parameters of different combinations according to the error threshold value of 0.01 to obtain the finite difference parameters under the given error threshold value: spatial sampling step length delta h, finite difference operator length N and finite difference coefficient c l And the like.
4) Establishing a calculated quantity objective function;
the specific implementation process is as follows:
4.1 The second-order sound wave constant density wave equation is subjected to center grid difference dispersion:
in formula (5): c. C l Is a high-order difference operator coefficient; Δ h is a spatial discrete step length; Δ t is a time discrete step; n is the finite difference operator length;
represents the wavefield variable at time point t = n Δ t, at spatial coordinate position (i Δ h, j Δ h, k Δ h); v. of i,j,k The velocity magnitude at (i Δ h, j Δ h, k Δ h) at the spatial coordinate position is represented. In the central difference discrete computation of the three-dimensional wave equation, the multiplication amount at each grid point is N +3, the addition amount is 11 × N +3, and the computation amount is 12 × N +6 (the sum of the addition amount and the multiplication amount is referred to as a computation amount) at each time step. In the two-dimensional wave equation, the multiplication amount is N +3, the addition amount is 7 × N +3, and the calculation amount is 8 × N +6 (the sum of the addition amount and the multiplication amount is referred to as a calculation amount). In the one-dimensional wave equation, the multiplication amount is N +3, the addition amount is 3 × N +3, and the calculation amount is 4 × N +6 (the sum of the addition amount and the multiplication amount is referred to as a calculation amount). With reference to the above calculation amount analysis, similar calculation amounts can be obtained for different wave equations and different difference formats.
4.2 Gridding the velocity model volume:
for example, a three-dimensional cube velocity model divides a three-dimensional cube with length, width and height of L, W, H meters into grids with a grid spacing of delta h meters, wherein the divided grid points NUM are as follows:
NUM＝L×W×H/Δh(6)
for example, a two-dimensional rectangular velocity model divides a rectangle with a length and a width of L, W meters into grids with a grid interval of Δ h meters, wherein the number NUM of the divided grids is as follows:
NUM＝L×W/Δh(8)
4.3 To establish a computation objective function Cost:
three-dimensional cube velocity model:
Cost＝NUM×(12×N+6)(7)
two-dimensional rectangular velocity model:
Cost＝NUM×(8×N+6)(9)
5) And screening different finite difference parameter sets according to the calculated amount objective function Cost, and calculating the finite difference parameter corresponding to the minimum value (the calculated amount is minimum) of the objective function (as shown in fig. 2).
In conclusion, the invention provides theoretical guidance for selecting the finite difference parameters of the second-order acoustic wave equation under the principle of minimum calculated quantity.
Examples
The invention is explained in detail by taking the finite difference parameter selection as an embodiment under the principle that the invention is used for realizing the minimum calculated amount of a second-order acoustic wave equation of a certain Ricker wavelet reference wave field, and has the guiding function for the application of the invention to the space numerical value dispersion simulation and the finite difference parameter optimization selection of other seismic source wavelets (such as theoretical wavelets (such as Gaussian functions and the like) with analytical expressions or wavelets extracted from field seismic data).
As shown in fig. 1, the optimization selection of the second-order acoustic wave equation finite difference parameter of the objective function with the minimum calculated quantity by using the method of the present invention in the embodiment includes the following steps:
1) Performing spatial direction frequency dispersion operation according to the Ricker wavelet;
the method comprises the following specific steps:
setting a Source wavefield p (x', t) without numerical dispersion 0 ) For a reference wave field, performing spatial dispersion forward transform on a reference wave field Ricker wavelet, and performing dispersion adding operation:
wherein k' is the positive mapping wave number, t 0 Is a time variable, X is a space coordinate variable, and X is a wave field propagation distance.
The specific implementation process of the spatial frequency dispersion is as follows:
1.1 For the reference wavefield p (x', t) 0 ) Performing discrete Fourier transform to obtain frequency domain wave field P (k, t) 0 ) The formula is as follows:
in formula (1): t is t 0 Is a time variable; x is a space coordinate variable; x is the wave field propagation distance; k' in formula (1) is a positive mapping wavenumber:
in the formula (2): c. C l Is a high-order difference operator coefficient; Δ x is a spatial discrete step; k is the wave number; n is the finite difference operator length;
1.2 To the frequency domain wavefield P (k, t) 0 ) Performing fast Fourier algorithm, and performing inverse transformation to time domain to obtain wave field p' (x, t) with numerical dispersion 0 ) The formula is as follows:
in formula (3): t is t 0 Is a time variable; x is a space coordinate variable; k is the wave number.
2) Setting a frequency dispersion error evaluation criterion, and selecting an error threshold value of 0.01 in the embodiment;
the Ricker wavelet in the embodiment is a second-order sound wave, and the method for setting the dispersion error evaluation criterion is specifically as follows:
the normalized two-norm between the numerical frequency-dispersive wavefield and the reference wavefield is proposed to measure the dispersion error:
in the embodiment, the error between the numerical frequency dispersion wave field and the real wave field is used as a basis for judging the frequency dispersion degree, and a proper error threshold value is selected according to the magnitude of the frequency dispersion error, wherein the threshold value is selected to be 0.01.
3) And screening the finite difference parameters of different combinations according to the error threshold value of 0.01 to obtain the finite difference parameters under the given error threshold value: spatial sampling step length delta h, finite difference operator length N and finite difference coefficient c l And the like.
4) Establishing a calculation target function;
the specific implementation process of this embodiment is as follows:
4.1 The second-order sound wave constant density wave equation is subjected to center grid difference dispersion:
in formula (5): c. C l Is a high-order difference operator coefficient; Δ h is a spatial discrete step length; Δ t is a time discrete step; n is the finite difference operator length;
represents the wavefield variable at time point t = n Δ t, at spatial coordinate position (i Δ h, j Δ h, k Δ h); v. of i,j,k The velocity magnitude at (i Δ h, j Δ h, k Δ h) at the spatial coordinate position is represented. Two-dimensional wave equation with multiplication amount of N +3, addition amount of 7 XN +3 and calculation amount of 8Xn +6 (the sum of the addition amount and the multiplication amount is referred to as a calculation amount).
4.2 Mesh partitioning of the velocity model volume:
the embodiment is a two-dimensional rectangular velocity model, and grid division with a grid interval of Δ h meters is performed on a rectangle with a length and a width of L, W meters, where the number of divided grid points NUM is as follows:
NUM＝L×W/Δh(8)
4.3 To establish a computation objective function Cost:
two-dimensional rectangular velocity model:
Cost＝NUM×(8×N+6)(9)
5) And screening different finite difference parameter sets according to the calculated amount objective function Cost, and calculating the finite difference parameter corresponding to the minimum value (the calculated amount is minimum) of the objective function (as shown in fig. 2).
And (4) conclusion: the finite difference parameter selection suggestion obtained by the method of the present invention in this embodiment is shown in fig. 2, where fig. 2 is a finite difference parameter value that is suggested to be selected based on the taylor series expansion method and the remitz exchange method with the theoretical Ricker wavelet as a reference wave field. In fig. 2, G represents the number of wavelength sampling points corresponding to 2.5 times the main frequency of the theoretical Ricker wavelet. Fig. 2 (a) is a diagram of a proposed value selected by a finite difference parameter under the target principle of a minimum calculated amount corresponding to a difference coefficient calculated based on a taylor series expansion method; in the graph (a) in fig. 2, it is suggested that the order of the difference operator calculated based on the taylor series expansion method is selected to be 16-20 orders, and the number of wavelength sampling points is selected to be 3-3.2 points; fig. 2 (b) is a diagram of a proposed value selected by a finite difference parameter under the target principle of minimum calculated amount corresponding to an optimized difference coefficient calculated by a remitz exchange method; in the diagram (b) in fig. 2, it is suggested that the order of the differential operator calculated based on the remitz exchange method is selected to be 14 to 18 orders, and the number of wavelength sampling points is selected to be 2.6 to 2.7 points. Any finite difference method, when the source wavelet is ricker, can refer to the finite difference parameter selection of fig. 2 in this embodiment.
Other source wavelets (e.g., theoretical wavelets with analytical expressions (e.g., gaussian functions, etc.) or wavelets extracted from field seismic data) reference wavefields may also be used to obtain optimized finite difference numerical simulation parameters according to the method.
The above embodiments are only for illustrating the present invention, and the steps may be changed, and any modification and equivalent changes of the individual steps based on the principle of the present invention should not be excluded from the protection scope of the present invention.
Other parts not described belong to the prior art.
Claims (9)
1. The method for selecting the finite difference numerical simulation parameters of the second-order acoustic wave equation is characterized by comprising the following steps of: comprises the following steps of (a) carrying out,
the method comprises the following steps: adding frequency dispersion to the seismic source wavelet;
step two: setting a frequency dispersion error evaluation criterion and an error threshold;
step three: screening finite difference parameter combinations according to an error evaluation criterion and a proper error threshold value;
step four: performing finite difference dispersion on a second-order sound wave constant density wave equation to establish a calculated quantity target function;
step five: and calculating a finite difference parameter corresponding to the minimum value of the objective function according to the calculated target function.
2. The method for selecting finite difference numerical simulation parameters of a second-order acoustic wave equation according to claim 1, wherein: in the first step, the seismic source wavelet is selected as a theoretical wavelet with an analytical expression or a wavelet extracted from field seismic data, and the seismic source wavelet p (x', t) is subjected to 0 ) The method for carrying out the spatial numerical value adding dispersion operation comprises the following specific steps:
s11: for the reference wavefield p (x', t) 0 ) Performing discrete Fourier transform to obtain frequency domain wave field P (k, t) 0 ) The formula is as follows:
in formula (1): t is t 0 Is a time variable; x is a space coordinate variable; x is the wave field propagation distance; k' is a second-order acoustic wave equation, the central difference format positive mapping wave number is as follows:
in the formula (2): c. C l Is a high-order difference operator coefficient; Δ x is a spatial discrete step; k is the wave number; n is the finite difference operator length;
s12: for the frequency domain wave field P (k, t) 0 ) Performing fast Fourier algorithm, and performing inverse transformation to obtain wave field p' (x, t) with numerical dispersion 0 ) The formula is as follows:
in formula (3): t is t 0 Is a time variable; x is a space coordinate variable; k is the wave number.
3. The method for selecting finite difference numerical simulation parameters of a second-order acoustic wave equation according to claim 1 or 2, wherein: setting a frequency dispersion error evaluation criterion and an error threshold, wherein the specific method comprises the following steps:
in step two, according to the reference wave field p (x', t) in step one 0 ) And the wavefield p' (x, t) with the numerical dispersion added 0 ) Setting a normalized two-norm error evaluation criterion, wherein the expression is as follows:
and taking the error between the numerical frequency dispersion wave field and the real wave field as a basis for judging the frequency dispersion degree, and selecting a proper error threshold value according to the magnitude of the frequency dispersion error.
4. The method for selecting finite difference numerical simulation parameters of a second-order acoustic wave equation according to claim 3, wherein: the threshold was chosen to be 0.01.
5. The method for selecting finite difference numerical simulation parameters of a second-order acoustic wave equation according to claim 4, wherein: in the third step, screening out all finite difference parameter combinations corresponding to errors smaller than or equal to an error threshold value according to the normalized two-norm error evaluation criterion given in the second step; the finite difference parameter combination comprises a space sampling step length delta h, a finite difference operator length N and a finite difference coefficient c l 。
6. The method for selecting finite difference numerical simulation parameters of a second-order acoustic wave equation according to claim 5, wherein: in the fourth step, finite difference dispersion is carried out on the second-order sound wave constant density wave equation, and a calculated quantity target function is established, wherein the method specifically comprises the following steps:
s4.1: performing center difference format dispersion on the second-order constant density acoustic wave equation:
in formula (5): c. C l Is a high-order difference operator coefficient; Δ h is a spatial discrete step length; Δ t is a time discrete step; n is the finite difference operator length;
represents the wavefield variable at time point t = n Δ t, at spatial coordinate position (i Δ h, j Δ h, k Δ h); v. of i,j,k Representing the velocity magnitude at (i Δ h, j Δ h, k Δ h) at the spatial coordinate position;
s4.2: and carrying out grid division on the speed model body, and establishing a calculated quantity objective function.
7. The method for selecting finite difference numerical simulation parameters of a second-order acoustic wave equation according to claim 6, wherein: the speed model body comprises a three-dimensional cube speed model and a two-dimensional rectangular speed model;
the number of mesh points NUM = volume/mesh pitch of the velocity model volume.
8. The method for selecting finite difference numerical simulation parameters of a second-order acoustic wave equation according to claim 7, wherein: when the speed model body selects a three-dimensional cube speed model, carrying out grid division with a grid spacing of delta h meters on a three-dimensional cube with a length, width and height of L, W, H meters respectively, wherein the divided grid point number NUM and the calculated quantity Cost are respectively as follows:
NUM＝L×W×H/Δh(6)
Cost＝NUM×(12×N+6)(7)
when the two-dimensional rectangular speed model is selected as the speed model body, grid division with the grid spacing of delta h meters is carried out on the rectangle with the length and the width of L, W meters, and the number NUM of divided grid points and the calculated quantity Cost are respectively as follows:
NUM＝L×W/Δh(8)
Cost＝NUM×(8×N+6)(9)。
9. the method for selecting finite difference numerical simulation parameters of a second-order acoustic wave equation according to claim 8, wherein: in the fifth step, all finite difference parameter combinations corresponding to errors smaller than or equal to the error threshold value are screened out in the third step and the finite difference parameter combinations corresponding to the minimum value of the objective function are calculated according to the calculated quantity objective function in the fourth step, and the finite difference numerical simulation parameters under the principle of minimum calculated quantity are selected.
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