CN109598094A - Earthquake vector wave field finite difference numerical simulation method, equipment and system - Google Patents
Earthquake vector wave field finite difference numerical simulation method, equipment and system Download PDFInfo
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Abstract
The present invention provides a kind of earthquake vector wave field finite difference numerical simulation method, system, computer equipment and computer readable storage mediums, are related to seismic exploration technique field.This method comprises: determining that mixing convolution optimizes window function according to the window function of a variety of different parameters and cosine combination window function；Optimize window function according to the mixing convolution space convolution sequence of pseudo- spectrometry is truncated, the finite difference operator optimized；Numerical simulation is carried out to earthquake vector wave field according to the finite difference operator of the optimization.The present invention constructs a kind of mixing convolution optimization window function based on least square combination, the space convolution sequence that pseudo- spectrometry is truncated is gone using the window function, the finite difference operator optimized, it recycles the finite difference operator to carry out earthquake vector wave field numerical, improves the precision and efficiency of earthquake vector wave field numerical.
Description
Technical field
The present invention is about seismic exploration technique field, especially with regard to the numerical simulation technology of seismic field, concretely
It is a kind of earthquake vector wave field finite difference numerical simulation method, system, computer equipment and computer readable storage medium.
Background technique
Seismic wave field numerical simulation is to be calculated based on wave theory by numerical value, simulates seismic wave in ball medium
Communication process.Wave field numerical is the basis of Geophysics Inversion and imaging technique, can use seismic wave Numerical Simulation
Means a connection is set up between elastic parameter and seismic response, known by way of wave field numerical known
A reservoir conditions under what kind of seismic response can be obtained.On the contrary, it is assumed that have a seismic response, can apply
Inversion algorithm obtains elastic parameter, there is these elastic parameters, and one can be done to inversion result based on petrophysical model
Explanation, obtain corresponding reservoir parameter.Differential equation method is based on continuous media differential volume member elastodynamics principle, commonly uses
Differential equation method include finite difference and FInite Element, be the important tool and method of seismic wave field numerical simulation.Cause
This, there is precision and more efficient finite-difference algorithm, so that it may the higher seismic wave field numerical simulation result of precision is obtained,
Preferably serve the needs of imaging and inverting.
Finite-difference algorithm is exactly to use difference operator approximate differential operator, and this approximation certainly will will lead to call number value frequency
It dissipates, that is, error.For numerical solidification, there are two types of methods to remove optimization finite-difference algorithm for existing mainstream, improves arithmetic accuracy,
One is optimal method, the second is window function metht.The essence of two methods be all to obtain maximum spectrum coverage area before
It puts, reduces the limits of error, only optimal method is to improve arithmetic accuracy by search optimal solution, and window function metht is to pass through interaction
Optimal solution is designed, to improve arithmetic accuracy.In recent years, domestic and international geophysics educational circles is for the optimization of finite-difference algorithm to mention
The precision of high seismic wave Numerical Simulation, has done many research work, achieves preferable effect.
It is calculated the finite difference coefficient of optimization using optimal method, actually multi-parameters optimization is asked
Topic, the optimal method for being widely used optimization finite difference operator at present have least square method, simulated annealing and Remez
Algorithm etc. is needed for different optimization methods using different objective functions.Pass through such as least square method, Remez algorithm
Optimal solution in removal search solution space, to meet the requirement of the limits of error, it is slow often to be faced with convergence, convergence less than globally optimal solution or
The problem of person does not restrain.It is preferred that window function metht is using different window functions, to go the space convolution sequence that pseudo- spectrometry is truncated to derive excellent
The finite difference operator of change.
Therefore, how a kind of new finite-difference algorithm is provided, is applied to earthquake vector wave field numerical, with reality
The numerical simulation of the high-accuracy high-efficiency rate of existing earthquake vector wave field is urgent technical problem to be solved in the field.
Summary of the invention
In view of this, the embodiment of the invention provides a kind of earthquake vector wave field finite difference numerical simulation method, system,
Computer equipment and computer readable storage medium carry out mixing convolution to a variety of window functions first, followed by mixing pleat
Multiple mixing convolution window functions and cosine combination window function after product carry out the optimum organization based on least square method, obtain
Optimize window function to a kind of mixing convolution based on least square combination, the space that pseudo- spectrometry is truncated finally is gone to using the window function
Convolution sequence, the finite difference operator optimized recycle the finite difference operator to carry out earthquake vector wave field numerical,
Improve the precision and efficiency of earthquake vector wave field numerical.
It is an object of the invention to provide a kind of earthquake vector wave field finite difference numerical simulation methods, comprising:
Determine that mixing convolution optimizes window function according to the window function of a variety of different parameters and cosine combination window；
The space convolution sequence of pseudo- spectrometry, the finite difference optimized are truncated according to the mixing convolution optimization window function
Operator；
Numerical simulation is carried out to earthquake vector wave field according to the finite difference operator of the optimization.
Preferably, described to determine that mixing convolution optimizes window letter according to the window function and cosine combination window of a variety of different parameters
Number includes:
Choose a variety of window functions；
Mixing convolution is carried out to the window function of a variety of different parameters, obtains multiple mixing convolution window functions；
Combination is optimized to the multiple mixing convolution window function and cosine combination window function, it is excellent to obtain mixing convolution
Change window function.
Preferably, the window function be cosine combination window and/or rectangular window and/or triumphant damp window and/or Chebyshev window and/
Or Gaussian window.
Preferably, a variety of window functions of selection include choosing window according to the main lobe and side lobe performance of window function amplitude-frequency response
Function.
Preferably, combination is optimized to the multiple mixing convolution window function and cosine combination window function, is mixed
Closing convolution optimization window function includes:
Optimization based on least square method is carried out to the multiple mixing convolution window function and cosine combination window function
Combination, error are limited to passband ripple and stopband ripple, obtain mixing convolution optimization window function.
It is an object of the invention to provide a kind of earthquake vector wave field finite difference numerical simulation systems, comprising:
It mixes convolution optimization window function and constructs module, for the window function and cosine combination window according to a variety of different parameters
Determine that mixing convolution optimizes window function；
Optimization module is truncated, for the space convolution sequence of pseudo- spectrometry to be truncated according to the mixing convolution optimization window function,
The finite difference operator optimized；
Earthquake vector wave field analog module, for being carried out according to the finite difference operator of the optimization to earthquake vector wave field
Numerical simulation.
Preferably, the mixing convolution optimization window function building module includes:
Window function chooses module, for choosing a variety of window functions；
Convolution module is mixed, mixing convolution is carried out for the window function to a variety of different parameters, obtains multiple mixing convolutions
Window function；
Optimum organization module, for optimizing group to the multiple mixing convolution window function and cosine combination window function
It closes, obtains mixing convolution optimization window function.
Preferably, the window function be cosine combination window and/or rectangular window and/or triumphant damp window and/or Chebyshev window and/
Or Gaussian window.
Preferably, it includes that window function obtains module that the window function, which chooses module, for according to window function amplitude-frequency response
Main lobe and side lobe performance choose window function
Preferably, the optimum organization module includes:
Least square method optimum organization module, for being carried out to multiple mixing convolution window functions and cosine combination window function
Optimum organization based on least square method, error are limited to passband ripple and stopband ripple, obtain mixing convolution optimization window function.
It is an object of the invention to provide a kind of computer equipments, comprising: be adapted for carrying out each instruction processor and
Equipment is stored, the storage equipment is stored with a plurality of instruction, and described instruction is suitable for being loaded by processor and being executed a kind of earthquake arrow
Measure wave field finite difference numerical simulation method.
It is an object of the invention to provide a kind of computer readable storage mediums, are stored with computer program, the meter
Calculation machine program is for executing a kind of earthquake vector wave field finite difference numerical simulation method.
The beneficial effects of the present invention are, provide a kind of earthquake vector wave field finite difference numerical simulation method, system,
Computer equipment and computer readable storage medium carry out mixing convolution to a variety of window functions first, followed by mixing pleat
Multiple mixing convolution window functions and cosine combination window function after product carry out the optimum organization based on least square method, obtain
Optimize window function to a kind of mixing convolution based on least square combination, the space that pseudo- spectrometry is truncated finally is gone to using the window function
Convolution sequence, the finite difference operator optimized recycle the finite difference operator to carry out earthquake vector wave field numerical,
Improve the precision and efficiency of earthquake vector wave field numerical.
For above and other objects, features and advantages of the invention can be clearer and more comprehensible, preferred embodiment is cited below particularly,
And cooperate institute's accompanying drawings, it is described in detail below.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
Some embodiments of invention for those of ordinary skill in the art without creative efforts, can be with
It obtains other drawings based on these drawings.
Fig. 1 is a kind of structural representation of earthquake vector wave field finite difference numerical simulation system provided in an embodiment of the present invention
Figure；
Fig. 2 is to mix convolution in a kind of earthquake vector wave field finite difference numerical simulation system provided in an embodiment of the present invention
Optimize the structural schematic diagram of window function building module；
Fig. 3 is window function choosing in a kind of earthquake vector wave field finite difference numerical simulation system provided in an embodiment of the present invention
The structural schematic diagram of modulus block；
Fig. 4 is optimum organization in a kind of earthquake vector wave field finite difference numerical simulation system provided in an embodiment of the present invention
The structural schematic diagram of module；
Fig. 5 is a kind of flow chart of earthquake vector wave field finite difference numerical simulation method provided in an embodiment of the present invention；
Fig. 6 is the specific flow chart of the step S101 in Fig. 5；
Fig. 7 is the dispersion curve of 1 order derivative of regular grid of the mixing convolution window function optimization based on Least-squares minimization
Schematic diagram；
Fig. 8 is the trueness error curve synoptic diagram amplified after 1000 times；
Fig. 9 is conventional staggering mesh finite-difference operator (using 8 rank operators) arteries and veins in specific embodiment provided by the invention
Rush the wave field schematic diagram of response；
Figure 10 is conventional staggering mesh finite-difference operator (using 12 rank operators) in specific embodiment provided by the invention
The wave field schematic diagram of impulse response；
Figure 11 is that the mixing convolution window function optimization in specific embodiment provided by the invention based on least square combination has
Limit the wave field schematic diagram of difference operator (using 8 rank operators) impulse response；
Figure 12 is that the mixing convolution window function optimization in specific embodiment provided by the invention based on least square combination has
Limit the wave field schematic diagram of difference operator (using 12 rank operators) impulse response.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
Those skilled in the art will understand that embodiments of the present invention can be implemented as a kind of system, device, method or
Computer program product.Therefore, disclose can be with specific implementation is as follows by the present invention, it may be assumed that complete hardware, complete software
The form that (including firmware, resident software, microcode etc.) or hardware and software combine.
Below with reference to several representative embodiments of the invention, the principle and spirit of the present invention are explained in detail.
The essence of window function metht is the design of FIR (having limit for length) filter, because finite difference calculus is pseudo- spectrometry space pleat
The truncation of product sequence is gone truncation to have different as a result, for finite difference optimization, is preferably truncated using different windows
Window function, it is required that cut-off frequecy of passband is small, stopband attenuation is big, meanwhile, passband ripple and stopband ripple want as small as possible.There is this
The optimization finite-difference algorithm that the truncation window function of sample goes the space convolution sequence that pseudo- spectrometry is truncated to obtain has maximum spectrum and covers
Lid range and trueness error are smaller.Existing auto convolution combination window function optimization method carries out certainly using to certain window function
Convolution is combined with another or several window functions again, to obtain best optimization performance, although auto convolution energy
Increase stopband attenuation, but also will increase cut-off frequecy of passband simultaneously, in addition, the size control to passband ripple and stopband ripple
System, without more effective scheme.
The basic idea of the invention is that carry out mixing convolution to a variety of window functions first, followed by mixing convolution after
Multiple mixing convolution window functions and cosine combination window function carry out the optimum organization based on least square method, obtain a kind of base
Optimize window function in the mixing convolution of least square combination, finally goes the space convolution sequence that pseudo- spectrometry is truncated using the window function
Column, the finite difference operator optimized recycle the finite difference operator to carry out earthquake vector wave field numerical, improve
The precision and efficiency of earthquake vector wave field numerical.
Fig. 1 is a kind of structural representation of earthquake vector wave field finite difference numerical simulation system provided in an embodiment of the present invention
Figure, referring to Figure 1, the seismic wave field numerical simulation system based on finite difference includes:
It mixes convolution optimization window function and constructs module 100, for the window function and cosine group according to a variety of different parameters
It closes window function and determines that mixing convolution optimizes window function.
One continuous signal f (x) with limit can be by with the signal f of a uniform samplingnPass through sinc function interpolation weight
It builds:
Wherein, Δ x is the sampling interval,To end wave number.
If asking first derivative and second dervative respectively to formula (1) the right and left, and the derivative value at x=0 is taken, it can be with
Formula (2) and formula (3) are obtained, if willIt substitutes into formula (1), formula (4) can be obtained:
There are the window functions that a length is N+1 point, and N is even number, remove truncation formula (2) and formula (3), and obtaining routine has
Limit difference operator:
Assuming that N is even number there are the window function that a length is N point, truncation formula (4) is gone, it is limited to obtain staggered-mesh
Difference operator:
W (n) is truncation window function.For conventional finite difference operator, w (n) is the window function of N+1 point, for being interleaved with
Difference operator is limited, w (n) is the window function of N point, and N is even number.
Fig. 2 is the structural schematic diagram for mixing convolution optimization window function building module 100, referring to Fig. 2, mixing convolution optimization
Window function constructs module 100
Window function chooses module 201, for choosing a variety of window functions.
Because finite difference calculus is the truncation of pseudo- spectrometry space convolution sequence, truncation is gone to have using different windows different
As a result, window function is preferably truncated, it is required that cut-off frequecy of passband is as small as possible, stopband declines for finite difference optimization
Subtract greatly, meanwhile, passband ripple and stopband ripple want as small as possible.There is such truncation window function to remove the space pleat that pseudo- spectrometry is truncated
The optimization finite-difference algorithm that product sequence obtains has maximum spectrum coverage area and trueness error is smaller.
In order to design this target window function, first have to that a variety of window functions is selected to carry out mixing convolution, in the present invention, base
This window function generally has cosine composite window, rectangular window, triumphant damp window, Chebyshev window, Gaussian window etc., only lists cosine group here
The general expression of window is closed, the expression formula of other window functions is omitted:
Wherein, N is window function length, and L is the item number of cosine combination window, alFor coefficient, L and alValue it is different, determine
Different cosine combination window functions.For example, being binomial Cosine Window, working as a as L=10=0.5, a1=0.5 is Hanning window.
Fig. 3 is the structural schematic diagram that window function chooses module 201, referring to Fig. 3, window function selection module 201 includes:
Window function obtains module 2011, for choosing window function according to the main lobe and side lobe performance of window function amplitude-frequency response.
Referring to Fig. 2, mixing convolution optimization window function constructs module 100 further include:
Convolution module 202 is mixed, mixing convolution is carried out for the window function to a variety of different parameters, obtains multiple mixing pleats
Product window function.
Mixing convolution between different type window function, can increase stopband attenuation, secondary lobe is made to become smaller, because of finite difference
Method is the truncation of pseudo- spectrometry space convolution sequence, and the stopband attenuation of window function is smaller, and the spectrum component of leakage is fewer, because
This, the precision of difference operator approximate differential operator is higher.But convolution operation will bring the increase of window function main lobe width,
Therefore selection mixing convolution scheme, i.e. the relatively narrow different window functions of selection main lobe carry out convolution, compared to window function auto convolution
The increase of scheme, main lobe width is less, thus, it is possible to obtain bigger spectrum coverage area.
Stopband attenuation can be greatly reduced, secondary lobe is made to become smaller under the premise of main lobe width increases less by mixing convolution,
Improve the precision of difference operator approximate differential operator.
Optimum organization module 203, it is excellent for being carried out to the multiple mixing convolution window function and cosine combination window function
Change combination, obtains mixing convolution optimization window function.
Fig. 4 is the structural schematic diagram of optimum organization module 203, referring to Fig. 4, optimum organization module 203 includes:
Least square method optimum organization module 2031, for multiple mixing convolution window functions and cosine combination window function
The optimum organization based on least square method is carried out, error is limited to passband ripple and stopband ripple, obtains mixing convolution optimization window
Function.
In the present invention, it is also necessary to consider that passband ripple and stopband ripple bring influence, passband ripple and stopband ripple
A degree of precision will be brought to influence, in order to obtain precision and more efficient finite difference operator, using least square
Combined mode sets passband ripple and stopband ripple limit, obtains best combined effect.
Referring to Figure 1, the earthquake vector wave field finite difference numerical simulation system further include:
Optimization module 200 is truncated, for the space convolution sequence of pseudo- spectrometry to be truncated according to the mixing convolution optimization window function
Column, the finite difference operator optimized.
By mix convolution optimization window function be applied to finite difference coefficient solution, i.e., solution objective function Equation (9),
(10), (11), to obtain the finite difference coefficient of optimization.The finite difference coefficient of optimization may make up finite difference operator.
Conventional second dervative:
Conventional first derivative:
Staggered-mesh:
Earthquake vector wave field analog module 300, for the finite difference operator according to the optimization to earthquake vector wave field
Carry out numerical simulation.Earthquake vector wave field numerical is carried out using the finite difference operator of optimization, can be improved earthquake vector
The precision and efficiency of wave field numerical.
It as above is a kind of earthquake vector wave field finite difference numerical simulation system provided by the invention, first to a variety of windows
Function carries out mixing convolution, followed by after mixing convolution multiple mixing convolution window functions and cosine combination window function into
Optimum organization of the row based on least square method obtains a kind of mixing convolution optimization window function based on least square combination, most
The space convolution sequence that pseudo- spectrometry is truncated is gone using the window function afterwards, the finite difference operator optimized recycles this limited
Difference operator carries out earthquake vector wave field numerical, improves the precision and efficiency of earthquake vector wave field numerical.
In addition, although being referred to several unit modules of system in the above detailed description, it is this to divide only simultaneously
Non-imposed.In fact, embodiment according to the present invention, the feature and function of two or more above-described units can
To embody in a unit.Equally, the feature and function of an above-described unit can also be served as reasons with further division
Multiple units embody.Terms used above " module " and " unit ", can be realize predetermined function software and/or
Hardware.Although module described in following embodiment is preferably realized with software, the group of hardware or software and hardware
The realization of conjunction is also that may and be contemplated.
After describing the earthquake vector wave field finite difference numerical simulation system of exemplary embodiment of the invention, connect
Get off, is introduced with reference to method of the attached drawing to exemplary embodiment of the invention.The implementation of this method may refer to above-mentioned whole
The implementation of body, overlaps will not be repeated.
Fig. 5 is a kind of process signal of earthquake vector wave field finite difference numerical simulation method provided in an embodiment of the present invention
Figure, refers to 5, which comprises
S101: determine that mixing convolution optimizes window letter according to the window function of a variety of different parameters and cosine combination window function
Number.
Fig. 6 is the specific flow chart of step S101, referring to Fig. 6, step S101 includes:
S201: a variety of window functions are chosen.
Because finite difference calculus is the truncation of pseudo- spectrometry space convolution sequence, truncation is gone to have using different windows different
As a result, window function is preferably truncated, it is required that cut-off frequecy of passband is as small as possible, stopband declines for finite difference optimization
Subtract greatly, meanwhile, passband ripple and stopband ripple want as small as possible.There is such truncation window function to remove the space pleat that pseudo- spectrometry is truncated
The optimization finite-difference algorithm that product sequence obtains has maximum spectrum coverage area and trueness error is smaller.
In order to design this target window function, first have to that a variety of window functions is selected to carry out mixing convolution, in the present invention, base
This window function generally has cosine composite window, rectangular window, triumphant damp window, Chebyshev window, Gaussian window etc..
In one embodiment of the invention, step S201 can according to window function amplitude-frequency response main lobe and secondary lobe
Performance chooses window function.
Referring to Fig. 6, step S102 further include:
S202: carrying out mixing convolution to the window function of a variety of different parameters, obtains multiple mixing convolution window functions.
Mixing convolution between different type window function, can increase stopband attenuation, secondary lobe is made to become smaller, because of finite difference
Method is the truncation of pseudo- spectrometry space convolution sequence, and the stopband attenuation of window function is smaller, and the spectrum component of leakage is fewer, because
This, the precision of difference operator approximate differential operator is higher.But convolution operation will bring the increase of window function main lobe width,
Therefore selection mixing convolution scheme, i.e. the relatively narrow different window functions of selection main lobe carry out convolution, compared to window function auto convolution
The increase of scheme, main lobe width is less, thus, it is possible to obtain bigger spectrum coverage area.
Stopband attenuation can be greatly reduced, secondary lobe is made to become smaller under the premise of main lobe width increases less by mixing convolution,
Improve the precision of difference operator approximate differential operator.
S203: optimizing combination to multiple mixing convolution window functions and cosine combination window function, obtains mixing convolution
Optimize window function.
In one embodiment of the invention, step S203 can be for multiple mixing convolution window functions and cosine group
It closes window function and carries out the optimum organization based on least square method, error is limited to passband ripple and stopband ripple, obtains mixing pleat
Product optimization window function.
In the present invention, it is also necessary to consider that passband ripple and stopband ripple bring influence, passband ripple and stopband ripple
A degree of precision will be brought to influence, in order to obtain precision and more efficient finite difference operator, using least square
Combined mode sets passband ripple and stopband ripple limit, obtains best combined effect.
Fig. 5 is referred to, the method also includes:
S102: the space convolution sequence of pseudo- spectrometry is truncated according to the mixing convolution optimization window function, what is optimized has
Limit difference operator.
By mix convolution optimization window function be applied to finite difference coefficient solution, i.e., solution objective function Equation (9),
(10), (11), to obtain the finite difference coefficient of optimization.
In one preferred embodiment of the invention, a kind of improved window function is constructed, is gone with such truncation window function
The optimization finite-difference algorithm that the space convolution sequence of the pseudo- spectrometry of truncation obtains has maximum spectrum coverage area and precision is missed
Difference is smaller.In this embodiment, the detailed step of the algorithm is as follows:
(1) main lobe and side lobe performance of more a variety of window function amplitude-frequency responses, selection carry out the window function of mixing convolution；
(2) change the parameter that the selected window function to convolution combines, carry out L mixing convolution, choose main lobe and side
The result of valve best performance.
(3) by the reorganization window function of the mixing convolution window function of step (1) output and cosine combination window and different parameters
Mixing convolution result carries out the combination based on least-squares algorithm, and error is limited to passband ripple and stopband ripple.
(4) the preliminary window function for obtaining truncation best performance, truncation optimization finite difference operator.
(5) finite difference operator that applying step (4) generates introduces approximate error function, calculates and draw approximate error
Curve, the stability of its spectral coverage of primary part observation and approximation accuracy, if effect is bad, return step (1), (2),
(3), restart to recycle, until satisfied result.
S103: numerical simulation is carried out to earthquake vector wave field according to the finite difference operator of the optimization.Utilize optimization
Finite difference operator carries out earthquake vector wave field numerical, can be improved the precision and effect of earthquake vector wave field numerical
Rate.
It as above is a kind of earthquake vector wave field finite difference numerical simulation method provided by the invention, first to a variety of windows
Function carries out mixing convolution, followed by after mixing convolution multiple mixing convolution window functions and cosine combination window function into
Optimum organization of the row based on least square method obtains a kind of mixing convolution optimization window function based on least square combination, most
The space convolution sequence that pseudo- spectrometry is truncated is gone using the window function afterwards, the finite difference operator optimized recycles this limited
Difference operator carries out earthquake vector wave field numerical, improves the precision and efficiency of earthquake vector wave field numerical.
The present invention also provides a kind of computer equipments, comprising: it is adapted for carrying out the processor and storage equipment of each instruction,
The storage equipment is stored with a plurality of instruction, and described instruction is limited suitable for being loaded by processor and executing a kind of earthquake vector wave field
Difference numerical analogy method.
The present invention also provides a kind of computer readable storage mediums, are stored with computer program, the computer program
For executing a kind of earthquake vector wave field finite difference numerical simulation method.
Below with reference to specific embodiment, technical solution of the present invention is discussed in detail.
In the embodiment 1, choose triumphant damp window and Chebyshev window carry out mixing convolution, and from the triumphant damp window of different coefficients
Convolution result is mixed with Chebyshev window, cosine combination window carries out the combination based on least-squares algorithm, obtains optimal truncation
Performance, and optimize finite difference operator, dispersion curve shows there is higher precision and spectrum coverage area.Fig. 7 is based on minimum two
Multiply the dispersion curve figure of the regular grid finite difference operator (1 order derivative) of the mixing convolution window function optimization of optimization, abscissa
It is Nyquist wavenumber percentage, ordinate is absolute error.Fig. 8 is the trueness error curve amplified after 1000 times, abscissa
It is Nyquist wavenumber percentage, ordinate is absolute error.As can see from Figure 7, the essence of the finite difference operator of optimization
Degree is significantly larger than conventional operator, and the precision of 12 rank operators is much larger than the precision of conventional 16 ranks, from Fig. 8 it can be found that precision is missed
The undulated control of difference is in lower range, and after long step-length is accumulative, stability is preferable, and therefore, algorithm provided by the present application is that have
Effect.
Using selecting triumphant damp window and Chebyshev window to carry out mixing convolution in the present embodiment 1, to single order regular grid, participate in
The window function parameter for mixing convolution is Chebyshev window (r=45), triumphant pool window (beta=3.3)；To second order regular grid, participate in
The window function parameter for mixing convolution is Chebyshev window (r=53,51), triumphant pool window (beta=3.3,3.1)；Interlock net to single order
Lattice, the window function parameter for participating in mixing convolution is Chebyshev window (r=21), triumphant pool window (beta=4.2).Mix convolution it
Afterwards, the combination based on least-squares algorithm is carried out, the Hanning window in cosine combination window, and the triumphant damp window of different coefficients are had chosen
With Chebyshev window mixing convolution result (Chebyshev window (r=65), triumphant pool window (beta=3.3)).Combination coefficient is a=
0.568, b=0.212, c=0.220.
The numerical simulation for doing an impulse response in example 2 compares the mixing convolution that 8 ranks are combined based on least square
Window function optimizes staggering mesh finite-difference operator and conventional 8 ranks, the effect of 12 rank staggering mesh finite-difference operator numerical simulations
Fruit.Two-dimentional isotropic medium is defined, sizing grid is 311 × 311, and grid spacing is 10m, velocity of longitudinal wave 2000ms-1,
Shear wave velocity is 1500ms-1, ρ=1000kgm-3.Point source is excited in centre, using concentrated force source, Ricker wavelet dominant frequency
For 30Hz, Δ t=1.5ms, nt=3000.Such as Fig. 9 to Figure 12, abscissa therein is distance, and unit is rice, and ordinate is deep
Degree, unit is rice.
In conclusion the present invention provides a kind of earthquake vector wave field finite difference numerical simulation methods, system, computer
Equipment and computer readable storage medium carry out mixing convolution to a variety of window functions first, followed by mixing convolution after
Multiple mixing convolution window functions and cosine combination window function carry out the optimum organization based on least square method, obtain one kind
Mixing convolution based on least square combination optimizes window function, finally goes the space convolution sequence that pseudo- spectrometry is truncated using the window function
Column, the finite difference operator optimized recycle the finite difference operator to carry out earthquake vector wave field numerical, improve
The precision and efficiency of earthquake vector wave field numerical.
It is improvement on hardware (for example, to diode, crystal that the improvement of one technology, which can be distinguished clearly,
Pipe, switch etc. circuit structures improvement) or software on improvement (improvement for method flow).However, with technology
The improvement of development, current many method flows can be considered as directly improving for hardware circuit.Designer is almost
All corresponding hardware circuit is obtained by the way that improved method flow to be programmed into hardware circuit.Therefore, it cannot be said that one
The improvement of a method flow cannot be realized with hardware entities module.For example, programmable logic device (Programmable
Logic Device, PLD) (such as field programmable gate array (Field Programmable Gate Array, FPGA)) just
It is such a integrated circuit, logic function determines device programming by user.It is voluntarily programmed by designer Lai one
Dedicated integrated circuit is designed without asking chip maker and made to a digital display circuit " integrated " on a piece of PLD
Chip.Moreover, nowadays, substitution manually makes IC chip, and " logic compiler (logic is also used in this programming instead mostly
Compiler) " software realizes that when it writes with program development software compiler used is similar, and before compiling
Also handy specific programming language is write for source code, this is referred to as hardware description language (Hardware Description
Language, HDL), and HDL is also not only a kind of, but there are many kinds, such as ABEL (Advanced Boolean
Expression Language)、AHDL(Altera Hardware Description Language)、Confluence、
CUPL(Cornell University Programming Language)、HDCal、JHDL(Java Hardware
Description Language)、Lava、Lola、MyHDL、PALASM、RHDL(Ruby Hardware Description
Language) etc., VHDL (Very-High-Speed Integrated Circuit is most generally used at present
Hardware Description Language) and Verilog2.Those skilled in the art also will be apparent to the skilled artisan that only needs will be square
Method process slightly programming in logic and is programmed into integrated circuit with above-mentioned several hardware description languages, so that it may be readily available reality
The now hardware circuit of the logical method process.
Controller can be implemented in any suitable manner, for example, controller can take such as microprocessor or processing
The computer for the computer readable program code (such as software or firmware) that device and storage can be executed by (micro-) processor can
Read medium, logic gate, switch, specific integrated circuit (Application Specific Integrated Circuit,
ASIC), the form of programmable logic controller (PLC) and insertion microcontroller, the example of controller includes but is not limited to following microcontroller
Device: ARC625D, Atmel AT91SAM, Microchip PIC18F26K20 and Silicone Labs C8051F320 are deposited
Memory controller is also implemented as a part of the control logic of memory.
It is also known in the art that other than realizing controller in a manner of pure computer readable program code, it is complete
Entirely can by by method and step carry out programming in logic come so that controller with logic gate, switch, specific integrated circuit, programmable
Logic controller realizes identical function with the form for being embedded in microcontroller etc..Therefore this controller is considered one kind
Hardware component, and the structure that the device for realizing various functions for including in it can also be considered as in hardware component.Or
Even, can will be considered as realizing the device of various functions either the software module of implementation method can be Hardware Subdivision again
Structure in part.
System, device, module or the unit that above-described embodiment illustrates can specifically realize by computer chip or entity,
Or it is realized by the product with certain function.
For convenience of description, it is divided into various units when description apparatus above with function to describe respectively.Certainly, implementing this
The function of each unit can be realized in the same or multiple software and or hardware when application.
As seen through the above description of the embodiments, those skilled in the art can be understood that the application can
It realizes by means of software and necessary general hardware platform.Based on this understanding, the technical solution essence of the application
On in other words the part that contributes to existing technology can be embodied in the form of software products, the computer software product
It can store in storage medium, such as ROM/RAM, magnetic disk, CD, including some instructions are used so that a computer system
(can be personal computer, server or network system etc.) executes the certain of each embodiment of the application or embodiment
Method described in part.
All the embodiments in this specification are described in a progressive manner, same and similar portion between each embodiment
Dividing may refer to each other, and each embodiment focuses on the differences from other embodiments.Especially for system reality
For applying example, since it is substantially similar to the method embodiment, so being described relatively simple, related place is referring to embodiment of the method
Part explanation.
The application can be used in numerous general or special purpose computing system environments or configuration.Such as: personal computer, clothes
Business device computer, hand system or portable system, plate system, multicomputer system, microprocessor-based system, set
Top box, programmable consumer electronics system, network PC, minicomputer, mainframe computer including any of the above system or system
Distributed computing environment etc..
The application can describe in the general context of computer-executable instructions executed by a computer, such as program
Module.Generally, program module includes routines performing specific tasks or implementing specific abstract data types, programs, objects, group
Part, data structure etc..The application can also be practiced in a distributed computing environment, in these distributed computing environments, by
Task is executed by the connected teleprocessing system of communication network.In a distributed computing environment, program module can be with
In the local and remote computer storage media including storage system.
Although depicting the application by embodiment, it will be appreciated by the skilled addressee that the application there are many deformation and
Variation is without departing from spirit herein, it is desirable to which the attached claims include these deformations and change without departing from the application's
Spirit.
Claims (12)
1. a kind of earthquake vector wave field finite difference numerical simulation method, which is characterized in that the described method includes:
Determine that mixing convolution optimizes window function according to the window function of a variety of different parameters and cosine combination window function；
The space convolution sequence of pseudo- spectrometry is truncated according to the mixing convolution optimization window function, the finite difference optimized is calculated
Son；
Numerical simulation is carried out to earthquake vector wave field according to the finite difference operator of the optimization.
2. the method according to claim 1, wherein the window function and cosine according to a variety of different parameters
Combination window function determines that mixing convolution optimization window function includes:
Choose a variety of window functions；
Mixing convolution is carried out to the window function of a variety of different parameters, obtains multiple mixing convolution window functions；
Combination is optimized to the multiple mixing convolution window function and cosine combination window function, obtains mixing convolution optimization window
Function.
3. according to the method described in claim 2, it is characterized in that, the window function be cosine combination window and/or rectangular window and/
Or triumphant damp window and/or Chebyshev window and/or Gaussian window.
4. according to the method described in claim 2, it is characterized in that, a variety of window functions of selection include according to window function amplitude-frequency
The main lobe and side lobe performance of response choose window function.
5. according to the method described in claim 2, it is characterized in that, to the multiple mixing convolution window function and cosine combination
Window function optimizes combination, obtains mixing convolution optimization window function and includes:
Optimum organization based on least square method is carried out to the multiple mixing convolution window function and cosine combination window function,
Error is limited to passband ripple and stopband ripple, obtains mixing convolution optimization window function.
6. a kind of earthquake vector wave field finite difference numerical simulation system, which is characterized in that the system comprises:
It mixes convolution optimization window function and constructs module, for the window function and cosine combination window function according to a variety of different parameters
Determine that mixing convolution optimizes window function；
Optimization module is truncated, for the space convolution sequence of pseudo- spectrometry to be truncated according to the mixing convolution optimization window function, obtains
The finite difference operator of optimization；
Earthquake vector wave field analog module, for carrying out numerical value to earthquake vector wave field according to the finite difference operator of the optimization
Simulation.
7. system according to claim 6, which is characterized in that the mixing convolution optimization window function constructs module and includes:
Window function chooses module, for choosing a variety of window functions；
Convolution module is mixed, mixing convolution is carried out for the window function to a variety of different parameters, obtains multiple mixing convolution window letters
Number；
Optimum organization module, for optimizing combination to the multiple mixing convolution window function and cosine combination window function,
Obtain mixing convolution optimization window function.
8. system according to claim 7, which is characterized in that the window function be cosine combination window and/or rectangular window and/
Or triumphant damp window and/or Chebyshev window and/or Gaussian window.
9. system according to claim 7, which is characterized in that it includes that window function obtains mould that the window function, which chooses module,
Block, for choosing window function according to the main lobe and side lobe performance of window function amplitude-frequency response.
10. system according to claim 7, which is characterized in that the optimum organization module includes:
Least square method optimum organization module, for being based on to multiple mixing convolution window functions and cosine combination window function
The optimum organization of least square method, error are limited to passband ripple and stopband ripple, obtain mixing convolution optimization window function.
11. a kind of computer equipment characterized by comprising it is adapted for carrying out the processor and storage equipment of each instruction, it is described
Storage equipment is stored with a plurality of instruction, and described instruction is suitable for being loaded by processor and being executed such as claim 1 to 5 any one institute
A kind of earthquake vector wave field finite difference numerical simulation method stated.
12. a kind of computer readable storage medium, which is characterized in that be stored with computer program, the computer program is used for
Execute a kind of earthquake vector wave field finite difference numerical simulation method as described in claim 1 to 5 any one.
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