CN106772585A - Analysis method and device is intended in a kind of optimization based on elastic wave decoupling equation - Google Patents
Analysis method and device is intended in a kind of optimization based on elastic wave decoupling equation Download PDFInfo
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Abstract
Intend analysis method and device the present invention relates to a kind of optimization based on elastic wave decoupling equation, wherein, method includes：Equivalent P ripples, the equations for elastic waves of S ripples decoupling are obtained, the equations for elastic waves decoupled according to equivalent P ripples, S ripples obtains accordingly P ripples, the optimization normalization of S ripples and intends Laplace operator respectively；Laplace operator is intended according to P ripples, the optimization normalization of S ripples and obtains the symbol that P ripples, S ripples optimize pseudo-differential operator；Symbol to P ripples, S ripples optimization pseudo-differential operator is decomposed respectively；The decomposition result of P ripples, the symbol of S ripples optimization pseudo-differential operator is updated in the expression formula of elastic wave optimization pseudo-differential operator, the final expression formula that elastic wave optimizes pseudo-differential operator is obtained；The equations for elastic waves that equivalent P ripples, S ripples are decoupled is calculated respectively using the final expression formula of elastic wave optimization differential operator, the horizontal component of P wave fields and the horizontal component and vertical component of vertical component and S wave fields is obtained.
Description
Technical field
The present invention relates to seismic wave wave-field simulation technical field, more particularly to a kind of optimization that equation is decoupled based on elastic wave
Quasi-solution is analysed.
Background technology
Seismic wave wave-field simulation (Seismic forward) and imaging (reverse-time migration) are that two, exploration geophysics field is important grinds
Study carefully direction.High-efficiency high-accuracy Seismic forward operator is the basic and key of seismic imaging and inverting.Conventional earthquake wave field mould
Plan method can be divided into：Finite difference calculus, pseudo- spectrometry etc..Wherein, conventional finite difference is just calculating son has precision low and shakiness
The shortcomings of determining, in order to suppress numerical solidification, the size of space lattice is generally smaller than earthquake wavelength 8 times~10 times.And in order to meet
Stability condition, time sampling interval need to obtain smaller.Therefore, in order to reach seismic wave wave-field simulation precision, based on Taylor's level
The finite difference method that number launches, because room and time sampling can not be too big, causes its amount of calculation very big.Composed for conventional pseudo
For method, Finite Difference Scheme of Second Order precision is relatively low on time orientation, and for big step-length time sampling interval, pseudo- spectrometry is unstable
It is fixed；Fast Flourier direct transform and inverse transformation, its amount of calculation is repeatedly utilized to be increased relative to finite difference due to pseudo- spectrometry.
Intend analytic method to be proposed in 2009 by Etgen and Brandsberg-Dahl first, similar to Lax-Wendroff side
The compensation thought of method：Utilization space derivative term, the error of the approximate compensation discrete generation of time second dervative.Lax-Wendroff side
The higher derivative of method utilization space approximately to replace high order time difference, compensates the approximately caused mistake of time second differnce
Difference, so as to improve time precision.Intending analytic method can be in wave-number domain amendment Laplace operator.In wave number-spatial domain, utilize
Intend Laplace operator, can compensate because time second differnce and caused by parsing error so that the jump of press time direction two
The error that cellular is caused.In the case of velocity variations are slow, intending analytic method can effectively eliminate the numerical value of time orientation
Frequency dispersion.It is not too violent model for velocity variations, intending analytic method can be drawn by cascading the plan of several constant compensation speed
General Laplacian operater, the error that compensation is caused due to second-order time difference.But when velocity variations are more violent, Etgen and
Brandsberg-Dahl points out that speed interpolation, the plan of approximate speed change can be carried out using the plan Laplace operator under multiple constant speeds
Laplace operator.Although can be obtained for isotropic medium using speed interpolation strategy (3~5 refer to compensation speed)
Better effects, but it is poor for anisotropic medium (VTI or TTI) effect, not only include speed because intending Laplace operator, and
And also comprising parameters such as anisotropy, it needs group speed and anisotropic parameters to enter row interpolation to intending Laplace operator,
Not only amount of calculation increase, and plan analytic method can produce larger error over time and space.
The content of the invention
The main purpose of the embodiment of the present invention is to propose that analytic method is intended in a kind of optimization based on elastic wave decoupling equation
And device, Laplace operator is intended into sound wave normalization and is improved to elastic wave optimization normalization plan Laplace operator, using bullet
Property ripple optimization pseudo-differential operator represent elastic wave optimization normalization intend Laplace operator, the operator not only include original quasi-differential
Operators spectrum estimation, but also comprising a time compensation item, will be in terms of time frequency dispersion and space frequency dispersion, better than traditional puppet
Spectrometry and plan analytic method.
To achieve the above object, the embodiment of the invention provides a kind of optimization quasi-solution analysis side that equation is decoupled based on elastic wave
Method, including：
The normal density elastic ripple decoupling equation of Second Order Displacements is decomposed, equivalent P ripples, the elastic wave of S ripples decoupling is obtained
Equation, and accordingly P ripples, S ripples optimization normalization plan are obtained respectively using the equations for elastic waves that the equivalent P ripples, S ripples are decoupled
Laplace operator；
P ripples, S ripples optimization normalization plan Laplace operator are carried out using the expression formula of elastic wave optimization pseudo-differential operator
Represent, obtain the symbol that P ripples, S ripples optimize pseudo-differential operator；
Symbol to P ripples, S ripples optimization pseudo-differential operator is decomposed respectively；
The decomposition result of P ripples, S ripples optimization pseudo-differential operator symbol is updated to the expression that elastic wave optimizes pseudo-differential operator
In formula, the final expression formula that elastic wave optimizes pseudo-differential operator is obtained；
The bullet decoupled to the equivalent P ripples, S ripples respectively using the final expression formula of elastic wave optimization differential operator
Property wave equation calculated, obtain the horizontal component of P wave fields and the horizontal component of vertical component and S wave fields and vertical point
Amount.
Optionally, in an embodiment of the present invention, the expression formula of the normal density elastic ripple decoupling equation of the Second Order Displacements is：
Wherein, x is space vector, three coordinates of vertical direction in x, y, z representation space vector x；Vp(x) and Vs(x)
Respectively velocity of longitudinal wave and shear wave velocity, u (x, t), v (x, t), w (x, t) are respectively particle under mixed recharge field action in space
The displacement component produced in three vertical direction in vector x.
Optionally, in an embodiment of the present invention, the expression formula of the P wave equations in the equations for elastic waves of the decoupling is：
In formula, up(x,t)、vp(x,t)、wpIt is vertical that (x, t) is respectively three under the effect of P ripples in space vector x of particle
The displacement component that direction produces；
The expression formula of the S wave equations in the equations for elastic waves of the decoupling is：
In formula, us(x,t)、vs(x,t)、wsIt is vertical that (x, t) is respectively three under the effect of S ripples in space vector x of particle
The displacement component that direction produces.
Optionally, in an embodiment of the present invention, the P ripples, the expression formula of S ripples optimization normalization plan Laplace operator
For：
In formula, kelaIt is space wave-number vector, wherein, kp、ksRespectively P ripples, S ripples space wave-number vector, ela=p, s table
Show P ripples and S ripples；For Laplace operator is intended in elastic wave optimization normalization, wherein,It is P ripples
Laplace operator is intended in optimization normalization,For Laplace operator is intended in the optimization normalization of S ripples；Δ t is to adopt the time
Sample is spaced.
Optionally, in an embodiment of the present invention, the expression formula of the elastic wave optimization pseudo-differential operator is：
Wherein, α (x, kela) it is referred to as the symbol of elastic wave optimization pseudo-differential operator A [E (x, t)], E (kela, t) for displacement is sweared
The spatial Fourier transform of amount E (x, t).
Optionally, in an embodiment of the present invention, the P ripples, the expression formula of the symbol of S ripples optimization pseudo-differential operator are：
In formula, αopt,ela(x,kela) in ela=p, s represent respectively P ripples optimization pseudo-differential operator symbol and S ripples optimization
The symbol of pseudo-differential operator.
Optionally, in an embodiment of the present invention, the final expression formula of the elastic wave optimization pseudo-differential operator is：
In formula, the maximum number of N representation space vectors；The number numbering of n representation space vectors；M representation space wave-number vectors
The maximum number of amount；The number numbering of m representation space wave-number vectors.
Optionally, in an embodiment of the present invention, the symbol to P ripples, S ripples optimization pseudo-differential operator is respectively adopted low-rank point
Solution approximation method is decomposed.
Optionally, in an embodiment of the present invention, after the P ripples, the symbol approximate factorization of S ripples optimization pseudo-differential operator
Expression formula be：
Wherein, W (x, km) it is symbol αopt,ela(x,kela) submatrix, its by with kmRelevant specific column element group
Into；W(xn,kela) it is symbol αopt,ela(x,kela) another submatrix, its by with xnRelevant specific row element composition；αmn
Coefficient matrix in the middle of representing.
Accordingly, to achieve the above object, the embodiment of the invention provides a kind of optimization that equation is decoupled based on elastic wave
Quasi-solution analysis apparatus, including：
Laplace operator computing unit is intended in elastic wave optimization normalization, for the normal density elastic ripple decoupling of Second Order Displacements
Equation is decomposed, and obtains equivalent P ripples, the equations for elastic waves of S ripples decoupling, and decouple using the equivalent P ripples, S ripples
Equations for elastic waves obtains accordingly P ripples, the optimization normalization of S ripples and intends Laplace operator respectively；
Elastic wave optimizes the symbol determining unit of pseudo-differential operator, for intending Laplce to P ripples, the optimization normalization of S ripples
Operator represents that acquisition P ripples, S ripples optimize the symbol of pseudo-differential operator using elastic wave optimization pseudo-differential operator；
Resolving cell, decomposes respectively for the symbol to P ripples, S ripples optimization pseudo-differential operator；
Elastic wave optimizes the final expression formula acquiring unit of pseudo-differential operator, for P ripples, S ripples to be optimized into pseudo-differential operator
The decomposition result of symbol is updated in elastic wave optimization pseudo-differential operator expression formula, obtains elastic wave optimization pseudo-differential operator most
Whole expression formula；
Wavefield component computing unit, for the final expression formula using elastic wave optimization differential operator respectively to described
Equivalent P ripples, the equations for elastic waves of S ripples decoupling are calculated, and obtain the horizontal component and vertical component and S ripples of P wave fields
The horizontal component and vertical component of wave field.
Above-mentioned technical proposal has the advantages that：
On the basis of sound wave intends analytic method, sound wave plan Laplace operator is improved to elastic wave optimization by the technical program
Laplace operator is intended in normalization, and elastic wave optimization normalization intends Laplace operator, medium constant compensation speed is replaced
It is the p-and s-wave velocity with the true medium of spatial alternation.Represent that elastic wave optimizes normalizing using elastic wave optimization pseudo-differential operator
Change and intend Laplace operator, relative to traditional pseudo- spectrometry and plan analytic method, elastic wave optimization pseudo-differential operator not only includes
The Power estimation of original pseudo-differential operator, but also comprising a time compensation item.Therefore, elastic wave optimization pseudo-differential operator can be with
On each mesh point of space, the error that second-order time difference causes is accurately compensated for.In the less situation in time sampling interval
Under, although traditional pseudo- spectrometry still has spatial accuracy very high, there is obvious time frequency dispersion.When sampling time interval is super
When having crossed CFL (condition of convergence) numbers, pseudo- spectrometry is unstable.Therefore, when time sampling interval becomes big, although the space of pseudo- spectrometry
Precision is very high, but easily time of occurrence frequency dispersion and wild effect.Although intending analytic method can effectively compensate for time mistake
Difference, reduces time frequency dispersion, but because compensation speed is more than real medium speed, space error can substantially increase.In velocity variations
In the case of acutely, even if Laplace operator is intended in the multiple constant speed compensation of cascade, intending analytic method can also produce space error.And it is sharp
The elastic wave proposed with the technical program optimizes pseudo-differential operator, will be in terms of time frequency dispersion and space frequency dispersion, better than traditional
Pseudo- spectrometry and plan analytic method.
Brief description of the drawings
In order to illustrate more clearly about the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing
The accompanying drawing to be used needed for having technology description is briefly described, it should be apparent that, drawings in the following description are only this
Some embodiments of invention, for those of ordinary skill in the art, on the premise of not paying creative work, can be with
Other accompanying drawings are obtained according to these accompanying drawings.
Fig. 1 is that the present embodiment proposes that a kind of optimization quasi-solution based on elastic wave decoupling equation analyses method flow diagram；
Fig. 2 is that the present embodiment proposes a kind of optimization quasi-solution analysis apparatus block diagram that equation is decoupled based on elastic wave；
The X-component schematic diagram that Fig. 3 a are obtained for pseudo- spectrometry in embodiment one；
The Z component schematic diagram that Fig. 3 b are obtained for pseudo- spectrometry in embodiment one；
The X-component schematic diagram that Fig. 3 c are obtained for plan analytic method in embodiment one；
The Z component schematic diagram that Fig. 3 d are obtained for plan analytic method in embodiment one；
Fig. 3 e intend the X-component schematic diagram that analytic method is obtained to optimize in embodiment one；
Fig. 3 f intend the Z component schematic diagram that analytic method is obtained to optimize in embodiment one；
Fig. 4 is inclination stratiform model schematic in embodiment two；
Fig. 5 a intend the X-component schematic diagram that analytic method is obtained to optimize in embodiment two；
Fig. 5 b intend the Z component schematic diagram that analytic method is obtained to optimize in embodiment two；
The X-component schematic diagram that Fig. 5 c are obtained for plan analytic method in embodiment two；
The Z component schematic diagram that Fig. 5 d are obtained for plan analytic method in embodiment two；
The X-component schematic diagram that Fig. 5 e are obtained for pseudo- spectrometry in embodiment two；
The Z component schematic diagram that Fig. 5 f are obtained for pseudo- spectrometry in embodiment two；
2. 1. black box partly need office in the horizontal component single shot record figure that Fig. 6 a are obtained for pseudo- spectrometry in embodiment two
Portion's enlarged diagram；
1. 2. part needs black box in the horizontal component single shot record figure that Fig. 6 b are obtained for plan analytic method in embodiment two
Close-up schematic view；
Fig. 6 c are to optimize in embodiment two to intend in the horizontal component single shot record figure that obtains of analytic method black box 1. 2. portion
Dividing needs close-up schematic view；
1. 2. part is local for black box in the horizontal component single shot record figure that Fig. 7 a are obtained for pseudo- spectrometry in embodiment two
Enlarged diagram；
Fig. 7 b are to intend in the horizontal component single shot record figure that obtains of analytic method black box 1. 2. part office in embodiment two
Portion's enlarged diagram；
Fig. 7 c are to optimize in embodiment two to intend in the horizontal component single shot record figure that obtains of analytic method black box 1. 2. portion
Divide close-up schematic view.
Specific embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete
Site preparation is described, it is clear that described embodiment is only a part of embodiment of the invention, rather than whole embodiments.It is based on
Embodiment in the present invention, it is every other that those of ordinary skill in the art are obtained under the premise of creative work is not made
Embodiment, belongs to the scope of protection of the invention.
The operation principle of the technical program is：From prior art it is understood that asking for intending micro- using constant compensation speed
Divide the plan analytic method scheme of operator, the technology of most critical is the selection of constant speed and the calculating of pseudo-differential operator.Because fast
The selection of degree and the result of calculation of plan Laplace operator, indirectly and directly determine the time and spatial accuracy just drilled.For
The different rate pattern of velocity variations, intending analytic method can solve plan Laplace operator using different schemes, can obtain
Preferably simulate effect.But, last simulation effect still has greater room for improvement.Existing plan analytic method is based on Chang Midu
ACOUSTIC WAVE EQUATION, and for isotropic medium, and do not meet practically matter situation.Therefore, for anisotropic medium, quasi-solution
Analysis method simulation effect is poor, and now, we carry out wave-field simulation using equations for elastic waves.Therefore, the technical program is by sound wave
Intend Laplace operator and be improved to elastic wave optimization normalization plan Laplace operator, pseudo-differential operator table is optimized using elastic wave
Show that Laplace operator is intended in elastic wave optimization normalization, the pseudo-differential operator not only includes the Power estimation of original pseudo-differential operator,
But also the error caused comprising a time compensation item, compensation second-order time difference.Elastic wave optimization pseudo-differential operator can not
Direct application space Fast Fourier Transform (FFT) is calculated, if directly calculating, its amount of calculation is larger.In order to reduce amount of calculation, this
Technical scheme is decomposed to the symbol in elastic wave optimization pseudo-differential operator using low-rank decomposition approximation method.Be finally reached with
Lower both sides effect：When time sampling interval is smaller, the time and spatial simulation precision that the technical program is just being drilled are superior to
Traditional pseudo- spectrometry and plan analytic method, but amount of calculation is not improved again；When time sampling interval is larger, the technical program exists
Better than pseudo- spectrometry in stability, and time and spatial accuracy will be better than pseudo- spectrometry and intend analytic method.
The expression formula of Second Order Displacements normal density elastic ripple decoupling equation is：
Wherein, x is space vector, three coordinates of vertical direction in x, y, z representation space vector x；Vp(x) and Vs(x)
Respectively velocity of longitudinal wave and shear wave velocity, u (x, t), v (x, t), w (x, t) are respectively particle space arrow under mixed recharge field action
The displacement component produced in three vertical direction in amount x.
In formula (1), the calculating of displacement component time second differnce, not only with velocity of longitudinal wave VpX () is relevant, go back and shear wave
Speed VsX () is relevant so that we can not directly using elastic wave optimization pseudo-differential operator set forth below, so by formula
(1) the P ripple equivalent with it, the equations for elastic waves of S ripples decoupling are decomposed into：
Wherein, formula (2) is the P wave equations in the equations for elastic waves of decoupling, and formula (3) is the S in the equations for elastic waves of decoupling
Wave equation.up(x,t)、vp(x,t)、wp(x, t) is respectively three vertical direction of the particle in space vector x under the effect of P ripples and produces
Raw displacement component；us(x,t)、vs(x,t)、wsIt is vertical that (x, t) is respectively three under the effect of S ripples in space vector x of particle
The displacement component that direction produces.So, three displacements of vertical direction of the particle in space vector x under mixed recharge field action with
And P ripples, S wave fields can be expressed as：
In formula 4, u (x, t), v (x, t), w (x, t) particle three in space vector x under mixed recharge field action is vertical
The displacement in direction；P (x, t), s (x, t) represent P ripples displacement component and S ripple displacement components respectively.Wherein, P ripples displacement component is P
Wave field, S ripple displacement components are S wave fields.
Space displacement vector is：
E (x, t)=p (x, t)+s (x, t) (5)
The equations for elastic waves of above-mentioned decoupling can be decomposed and the pure compressional wave of continuation and pure shear wave while continuation vector wave field
Wave field.
For the technical program, P wave field horizontal components are：up(x, t) and vp(x, t), P wave field vertical components
For：wp(x, t), S wave field horizontal components are：us(x, t) and vs(x, t), S wave fields vertical component is ws(x,t)；In mixing
Under wave field effect, u (x, t), v (x, t) are horizontal component, and w (x, t) is vertical component.Formula (2), formula (3) are asked
Solution, just can obtain the horizontal component and vertical component of P wave fields and the horizontal component and vertical component of S wave fields.Then root
According to formula (4), displacement components u (x, t), the v of three vertical direction of the particle in space vector x under mixed recharge field action just can be obtained
(x, t), w (x, t) and P ripples displacement component p (x, t), S ripples displacement component s (x, t), mixed recharge just can be obtained according to formula (5)
Displacement component E (x, t) of field.
Isotropism Chang Midu ACOUSTIC WAVE EQUATIONs can be written as：
Wherein, U (x, t) is earthquake acoustic pressure wave field, and v (x) is seismic wave velocity,It is Laplace operator.
Under the assumed condition of v (x)=v (constant), intending Laplace operator (second order wave number-Space Operators) F (k) is：
Wherein, k is space wave-number vector, and Δ t is time sampling interval.
Can obtain wave number-spatial domain plan analytic method expression formula by formula (6) and formula (7) is：
Intending analytic method expression formula in temporal-spatial field is：
Wherein, the direct transform of FFT representation spaces fast Fourier, FFT-1Representation space Fast Fourier Transform Inverse.
For uniform dielectric, the space Fast Fourier Transform Inverse in formula (9) can be applied directly, and formula (9) can be provided
Analytic solutions or approximate analytic solution；For non-uniform dielectric, when speed is with spatial variations, it is impossible to which direct hollow of applying equation (9) is fast
Fast Fourier inversion.
In order to more precisely compensate the time error that second order finite difference causes, Laplace operator will be intended in formula (7)
Constant compensation speed v replace with true velocity v (x) of spatial alternation.So, intend that Laplace operator is rewritable to be：
Wherein, FoptK () is the function of space wave-number vector k, and relevant with space grid coordinate, i.e., relevant with speed.This
Technical scheme is by FoptK () is referred to as optimization and intends Laplace operator.
Cosine function in formula (10) is used into Taylor expansion, then optimization intends that Laplace operator is rewritable to be：
By F (k) in formula (11) alternate form (8), correspondingly, Frequency-Space Domain optimization intends that analytic method is rewritable to be：
In temporal-spatial field, formula (12) can be written as arbitrary order Lax-Wendroff forms：
Wherein,
It is obvious that Lax-Wendroff form utilization spaces derivative term carrys out the approximate discrete mistake for compensating time second dervative
Difference.
Laplace operator is intended according to the normalization that Chu and Stoffa is proposed：
Laplace operator is intended into formula (10) optimization and is improved to optimization normalization plan Laplace operator：
Because formula (15) can be only applied to scalar ACOUSTIC WAVE EQUATION, and the technical program is applied to Seismic Wave Equation for elastic wave
Decoupling equation, then elastic wave optimization normalization is intended Laplace operator and is represented by：
Wherein, kp、ksRespectively P ripples, S ripples space wave-number vector, ela=p, s represent P ripples and S ripples.
Second Order Differential Operator is not only, and can also be in wave number-space discrete error for causing of domain compensation second-order time finite difference.This
When, compensation speed takes velocity of longitudinal wave V respectivelyp(x) and shear wave velocity Vs(x)。
Pseudo-differential operator can be regarded as popularization and the general type of Second Order Differential Operator, can use Fourier integral form
It is expressed as：
Wherein, α (x, kela) it is referred to as the symbol of elastic wave optimization pseudo-differential operator A [E (x, t)], E (kela, t) for displacement is sweared
The spatial Fourier transform of amount E (x, t).
For Second Order Differential Operator and elastic wave optimization pseudo-differential operator, the technical program will signify α (x, kela) rewrite
For：
Wherein,It is defined in formula (16).Correspondingly, by the α in formula (18)opt,ela(x,kela) replace
α (x, the k changed in formula (17)ela), elastic wave optimization pseudo-differential operator can be written as:
Elastic wave optimization pseudo-differential operator not only includes the Power estimation of original pseudo-differential operator, but also during comprising one
Between compensation term.The time compensation item can accurately compensate for the error that second-order time difference causes in wave number-spatial domain.Compensation speed
It is medium actual speed in formula (16), therefore, elastic wave optimization pseudo-differential operator can be on each mesh point of space, accurately
The error that compensation second-order time difference in ground causes.
We are by Aoptela[E (x, t)] is abbreviated as：
Aopt,ela[E (x, t)]=FT-1{αopt,ela(x,kela)FFT[E(x,t)]} (20)
Wherein, FT-1Representation space Fourier inversion.
So, in formula (2) (during ela=p) and formula (3) (during ela=s), Second Order Differential Operator With symbol αopt,ela(x,kela) between relation be represented by：
Due to including the P ripples, the S ripple compensation speeds v that change with space coordinates in elastic wave optimization pseudo-differential operatorp(x)、vs
(x), so equation (20) can not be calculated directly in application space Fast Fourier Transform (FFT).If direct accounting equation (20), its
Amount of calculation isWherein NxIt is 3-dimensional grid sum.In order to reduce amount of calculation, the technical program optimizes to elastic wave and intends
Symbol in differential operator, using low-rank decomposition approximation method.
The approximate main thought of low-rank decomposition can be divided is：Choose N number of representational space vector and M representational space wave
Number vector, approximate original wave number-spatial mixing domain operator.Symbol is approximately decomposed into following form by the technical program：
Wherein, W (x, km) it is symbol αopt,ela(x,kela) submatrix, its by with kmRelevant specific column element group
Into；W(xn,kela) it is symbol αopt,ela(x,kela) another submatrix, its by with xnRelevant specific row element composition；αmn
Coefficient matrix in the middle of representing.
By formula (22) by αopt,ela(x,kela) decomposed, during the result after decomposition is substituted into formula (20), that
Aopt,ela[E (x, t)] is rewritable to be：
Equivalent to the Fast Fourier Transform (FFT) of N × 2 time space is applied, its amount of calculation is O (NN to the amount of calculation of formula (23)x log
Nx)×2.N is generally an integer for very little, and its size is relevant with the order of formula (23) matrix decomposition.
P wave equations (correspondence formula 2) and the equivalent solution in Equivalent Decoupling equations for elastic waves can be obtained using formula (23)
The optimization pseudo-differential operator of Second Order Differential Operator, the P ripples that will be obtained in S wave equations (correspondence formula 3) in coupling equations for elastic waves
The optimization pseudo-differential operator of Second Order Differential Operator substitutes into formula (2) respectively, and the quasi-differential of the S ripple Second Order Differential Operators that will be obtained is calculated
Filial generation enters formula (3), and the P wave equations and S wave equations in Equivalent Decoupling equations for elastic waves are calculated respectively, obtains P ripple ripples
The horizontal component of field and the horizontal component and vertical component of vertical component and S wave fields.
The technical program is divided the symbol in elastic wave optimization pseudo-differential operator using low-rank decomposition approximation method
Solution, greatly reduces the amount of calculation for directly optimizing pseudo-differential operator application space Fast Fourier Transform (FFT) to elastic wave.For meter
Efficiency is calculated, in the case of uniform dielectric, each normalized plan Laplace operator is approximate by low-rank decomposition, and its order is 2.
This means conventional pseudo- spectrometry is compared to, calculating normalized plan Laplace operator needs extra 2 fast Fouriers
Conversion.But, analytic method is intended in elastic wave optimization can be applied to than larger time sampling interval, when this will save many calculating
Between.When time sampling interval is larger, pseudo- spectrometry is unstable, although intending analytic method stabilization, space frequency dispersion is serious；This technology
Scheme propose elastic wave optimization intend analytic method no matter time frequency dispersion or space frequency dispersion, be superior to traditional pseudo- spectrometry and quasi-solution
Analysis method；And in this case, optimization plan analytic method is just drilling the required time is less than pseudo- spectrometry and plan analytic method.
Based on above-mentioned operation principle, the present embodiment proposes that analytic method is intended in a kind of optimization based on elastic wave decoupling equation,
As shown in Figure 1.Including：
Step 101)：The normal density elastic ripple decoupling equation of Second Order Displacements is decomposed, equivalent P ripples, the decoupling of S ripples is obtained
Equations for elastic waves, and using the equivalent P ripples, S ripples decouple equations for elastic waves obtain respectively accordingly P ripples, S ripples optimize
Laplace operator is intended in normalization；
Step 102)：P ripples, the optimization normalization of S ripples are intended by Laplace operator and optimizes pseudo-differential operator table using elastic wave
Show, obtain the symbol that P ripples, S ripples optimize pseudo-differential operator；
Step 103)：P ripples, S ripples optimization pseudo-differential operator symbol are decomposed respectively；
Step 104)：Intend micro- by elastic wave optimization is updated to the decomposition result of P ripples, S ripples optimization pseudo-differential operator symbol
Divide in the expression formula of operator, obtain the final expression formula that elastic wave optimizes pseudo-differential operator；
Step 105)：Using the final expression formula of elastic wave optimization differential operator respectively to equivalent P ripples, the S
The equations for elastic waves of ripple decoupling is calculated, and obtains the horizontal component of P wave fields and the level point of vertical component and S wave fields
Amount and vertical component.
One of ordinary skill in the art will appreciate that all or part of flow in realizing above-described embodiment method, Ke Yitong
Computer program is crossed to instruct the hardware of correlation to complete, described program can be stored in general computer read/write memory medium
In, the program is upon execution, it may include such as the flow of the embodiment of above-mentioned each method.Wherein, described storage medium can be magnetic
Dish, CD, read-only memory (Read-Only Memory, ROM) or random access memory (Random Access
Memory, RAM) etc..
As shown in Fig. 2 for the present embodiment proposes a kind of optimization quasi-solution analysis apparatus block diagram that equation is decoupled based on elastic wave.Bag
Include：
Laplace operator computing unit 201 is intended in elastic wave optimization normalization, for the normal density elastic ripple of Second Order Displacements
Decoupling equation is decomposed, and obtains equivalent P ripples, the equations for elastic waves of S ripples decoupling, and using the equivalent P ripples, S ripple solutions
The equations for elastic waves of coupling obtains accordingly P ripples, the optimization normalization of S ripples and intends Laplace operator respectively；
Elastic wave optimizes the symbol determining unit 202 of pseudo-differential operator, for intending La Pula to P ripples, the optimization normalization of S ripples
This operator represents that acquisition P ripples, S ripples optimize the symbol of pseudo-differential operator using elastic wave optimization pseudo-differential operator；
Resolving cell 203, decomposes respectively for the symbol to P ripples, S ripples optimization pseudo-differential operator；
Elastic wave optimizes the final expression formula acquiring unit 204 of pseudo-differential operator, for P ripples, S ripples optimization quasi-differential to be calculated
The decomposition result of son symbol is updated in the expression formula of elastic wave optimization pseudo-differential operator, obtains elastic wave optimization pseudo-differential operator
Final expression formula；
Wavefield component computing unit 205, it is right respectively for the final expression formula using elastic wave optimization differential operator
The equivalent P ripples, S ripples decoupling equations for elastic waves calculated, obtain P wave fields horizontal component and vertical component and
The horizontal component and vertical component of S wave fields.
Those skilled in the art will also be appreciated that the various functions that the embodiment of the present invention is listed are by hardware or soft
Part realizes depending on the design requirement of specific application and whole system.Those skilled in the art can be specific for every kind of
Using, it is possible to use various methods realize described function, but this realization is understood not to be protected beyond the embodiment of the present invention
The scope of shield.
Although additionally, being referred to some units of device in above-detailed, this division is only not strong
Property processed.In fact, according to the embodiment of the present invention, the feature and function of above-described two or more units can be
Embodied in one unit.Equally, the feature and function of an above-described unit can also be further divided into by multiple
Unit embodies.
Embodiment
In order to more intuitively describe the features of the present invention and operation principle, come below in conjunction with practice scene
Description.
Embodiment one
The present embodiment uses 2D homogeneous models, and it is 10m in X-direction and Z-direction sampling interval.Shear wave and velocity of longitudinal wave
Respectively 1500m/s, 2500m/s.The dominant frequency of Ricker wavelets is 20Hz, and peak frequency is 50Hz.Focus is located at model center,
And compressional wave and shear wave are produced simultaneously.Each wave field accounts for minimum grid points：2, this has reached Nyquist sampling thheorems pole
Limit.This modeling computation does not use absorbing boundary condition.Intending analytic method using pseudo- spectrometry, plan analytic method and optimization respectively is carried out
Forward simulation, time sampling interval Δ t=2.5ms.Fig. 3 a and Fig. 3 b are respectively the X-component and Z component that pseudo- spectrometry is obtained, Fig. 3 c
It is respectively with Fig. 3 d and intends X-component and Z component that analytic method is obtained, Fig. 3 e and Fig. 3 f is that X-component and Z that analytic method is obtained are intended in optimization
Component.X-component and Z component that three kinds of method of testings are obtained are contrasted respectively, and observed result shows：When spatial sampling interval is
10m, when time sampling interval is 2.5ms, pseudo- spectrometry is unstable；Still stablize although intending analytic method, optimization and intending analytic method,
But space frequency dispersion (shown in black arrow) the analogy analytic method that analytic method is intended in optimization is less.
Embodiment two
The present embodiment uses two-dimensional layered model, and verifying it using the optimization plan analytic method of the technical program proposition has
Effect property.And contrasted with pseudo- spectrometry and plan analytic method.Two-dimensional layered model includes one, top flat reflector and bottom
One inclined reflection layer, inclined reflection layer is step-like interface.From top to bottom, every layer of velocity of longitudinal wave is：2000m/s、2350m/
S, 2500m/s, shear wave velocity is：1500m/s、1800m/s、2300m/s.Model area size is 250 × 250, horizontal direction
10m is with vertical direction grid spacing, as shown in Figure 4.Forward simulation uses Richer wavelets, and dominant frequency is 30HZ, can be simultaneously
Produce compressional wave and shear wave.The time sampling interval of wave-field simulation is 1.5ms, and the total time sampling points of earthquake record are 1501
It is individual.Shot point is located at model net lattice point (125,5) place, and wave detector is uniformly distributed in model whole surface.Fig. 5 a~Fig. 5 b are optimization
Intend X-component and Z component that analytic method is obtained, Fig. 5 c~Fig. 5 d are to intend X-component and Z component that analytic method is obtained, Fig. 5 e~Fig. 5 f
For X-component and Z component that pseudo- spectrometry is obtained.Fig. 5 a~Fig. 5 f are the X-component and Z component wave field snapshot plotting at t=1.2s moment.
X-component and Z component that three kinds of method of testings are obtained are contrasted respectively, and observed result shows：In time sampling interval during 1.5ms,
Pseudo- spectrometry has obvious time frequency dispersion (shown in black arrow)；Intend analytic method and although suppress time frequency dispersion (black arrow institute
Show), but because compensation speed is more than actual speed, space frequency dispersion can be produced (shown in light arrow)；Analytic method is intended in optimization,
On press time and space frequency dispersion, better than pseudo- spectrometry and plan analytic method.
2. 1. black box in horizontal component single shot record figure shown in Fig. 6 a is partly needed into partial enlargement, in corresponding diagram 7a
1. and 2., 2. 1. black box in the horizontal component single shot record figure shown in Fig. 6 b is partly needed into partial enlargement, corresponding diagram 7b
In 1. and 2., 2. 1. black box in the horizontal component single shot record figure shown in Fig. 6 c is partly needed into partial enlargement, corresponding diagram
In 7c 1. and 2..It is observed that square 1. in：Fig. 6 a puppet spectrometries, direct wave has obvious time frequency dispersion (black arrow institute
Show), Fig. 6 b intend analytic method, and time frequency dispersion has been suppressed well, but have more serious space frequency dispersion (shown in light arrow), scheme
Analytic method is intended in 6c optimizations, while press time frequency dispersion, also eliminates plan analytic method because compensation speed chooses excessive generation
Space frequency dispersion；Square 2. in it is same.
The numerical simulation for inclining stratified model is also demonstrated that：Optimization intend analytic method in press time frequency dispersion and space frequency dispersion,
Compared to traditional pseudo- spectrometry and intend analytic method, advantageously.
Above specific embodiment, has been carried out further specifically to the purpose of the present invention, technical scheme and beneficial effect
It is bright, should be understood that and these are only specific embodiment of the invention, the protection model being not intended to limit the present invention
Enclose, all any modification, equivalent substitution and improvements within the spirit and principles in the present invention, done etc. should be included in the present invention
Protection domain within.
Claims (10)
1. analytic method is intended in a kind of optimization based on elastic wave decoupling equation, it is characterised in that including：
The normal density elastic ripple decoupling equation of Second Order Displacements is decomposed, equivalent P ripples, the equations for elastic waves of S ripples decoupling is obtained,
And using the equivalent P ripples, S ripples decouple equations for elastic waves obtain respectively accordingly P ripples, S ripples optimization normalization intend draw it is general
Laplacian operater；
Table is carried out using the expression formula of elastic wave optimization pseudo-differential operator to P ripples, S ripples optimization normalization plan Laplace operator
Show, obtain the symbol that P ripples, S ripples optimize pseudo-differential operator；
Symbol to P ripples, S ripples optimization pseudo-differential operator is decomposed respectively；
The decomposition result of P ripples, the symbol of S ripples optimization pseudo-differential operator is updated to the expression formula that elastic wave optimizes pseudo-differential operator
In, obtain the final expression formula that elastic wave optimizes pseudo-differential operator；
The elastic wave decoupled to the equivalent P ripples, S ripples respectively using the final expression formula of elastic wave optimization differential operator
Equation is calculated, and obtains the horizontal component of P wave fields and the horizontal component and vertical component of vertical component and S wave fields.
2. the method for claim 1, it is characterised in that the normal density elastic ripple of Second Order Displacements decouples the expression of equation
Formula is：
Wherein, x is space vector, three coordinates of vertical direction in x, y, z representation space vector x；Vp(x) and Vs(x) difference
It is velocity of longitudinal wave and shear wave velocity, u (x, t), v (x, t), w (x, t) are respectively particle space vector x under mixed recharge field action
In three vertical direction on produce displacement component.
3. method as claimed in claim 2, it is characterised in that the expression of the P wave equations in the equations for elastic waves of the decoupling
Formula is：
In formula, up(x,t)、vp(x,t)、wp(x, t) is respectively three vertical direction of the particle in space vector x under the effect of P ripples
The displacement component of generation；
The expression formula of the S wave equations in the equations for elastic waves of the decoupling is：
In formula, us(x,t)、vs(x,t)、ws(x, t) is respectively three vertical direction of the particle in space vector x under the effect of S ripples
The displacement component of generation.
4. method as claimed in claim 3, it is characterised in that Laplace operator is intended in the P ripples, the optimization normalization of S ripples
Expression formula is：
In formula, kelaIt is space wave-number vector, wherein, kp、ksRespectively P ripples, S ripples space wave-number vector, ela=p, s represent P ripples
With S ripples；For Laplace operator is intended in elastic wave optimization normalization, wherein,For the optimization of P ripples is returned
One changes plan Laplace operator,For Laplace operator is intended in the optimization normalization of S ripples；Δ t is time sampling interval.
5. method as claimed in claim 4, it is characterised in that the expression formula of the elastic wave optimization pseudo-differential operator is：
Wherein, α (x, kela) it is referred to as the symbol of elastic wave optimization pseudo-differential operator A [E (x, t)], E (kela, t) it is displacement vector E
The spatial Fourier transform of (x, t).
6. method as claimed in claim 5, it is characterised in that the P ripples, the expression of the symbol of S ripples optimization pseudo-differential operator
Formula is：
In formula, αopt,ela(x,kela) in ela=p, s represent respectively P ripples optimization pseudo-differential operator symbol and S ripples optimization quasi-differential
The symbol of operator.
7. method as claimed in claim 6, it is characterised in that the elastic wave optimizes the final expression formula of pseudo-differential operator
For：
In formula, the maximum number of N representation space vectors；The number numbering of n representation space vectors；M representation space wave-number vectors
Maximum number；The number numbering of m representation space wave-number vectors.
8. method as claimed in claim 7, it is characterised in that the symbol to P ripples, S ripples optimization pseudo-differential operator is respectively adopted
Low-rank decomposition approximation method is decomposed.
9. method as claimed in claim 8, it is characterised in that the P ripples, the symbol of S ripples optimization pseudo-differential operator are approximately divided
Expression formula after solution is：
Wherein, W (x, km) it is symbol αopt,ela(x,kela) submatrix, its by with kmRelevant specific column element composition；W
(xn,kela) it is symbol αopt,ela(x,kela) another submatrix, its by with xnRelevant specific row element composition；αmnRepresent
Middle coefficient matrix.
10. it is a kind of based on elastic wave decouple equation optimization quasi-solution analysis apparatus, it is characterised in that including：
Laplace operator computing unit is intended in elastic wave optimization normalization, for the normal density elastic ripple decoupling equation of Second Order Displacements
Decomposed, obtained equivalent P ripples, the equations for elastic waves of S ripples decoupling, and the elasticity decoupled using the equivalent P ripples, S ripples
Wave equation obtains accordingly P ripples, the optimization normalization of S ripples and intends Laplace operator respectively；
Elastic wave optimizes the symbol determining unit of pseudo-differential operator, for intending Laplace operator to P ripples, the optimization normalization of S ripples
Represented using elastic wave optimization pseudo-differential operator, obtain the symbol that P ripples, S ripples optimize pseudo-differential operator；
Resolving cell, decomposes respectively for the symbol to P ripples, S ripples optimization pseudo-differential operator；
Elastic wave optimizes the final expression formula acquiring unit of pseudo-differential operator, for P ripples, S ripples optimization pseudo-differential operator to be signified
Decomposition result be updated to elastic wave optimization pseudo-differential operator expression formula in, obtain elastic wave optimize pseudo-differential operator final table
Up to formula；
Wavefield component computing unit, for the final expression formula using elastic wave optimization differential operator respectively to described equivalent
P ripples, S ripples decoupling equations for elastic waves calculated, obtain P wave fields horizontal component and vertical component and S wave fields
Horizontal component and vertical component.
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107340540A (en) * | 2017-07-05 | 2017-11-10 | 中国科学院地质与地球物理研究所 | Direction wave decomposition method, device and the computer-readable storage medium of elastic wave field |
| CN109212605A (en) * | 2018-09-28 | 2019-01-15 | 中国科学院地质与地球物理研究所 | pseudo-differential operator storage method and device |
| CN112505775A (en) * | 2020-10-16 | 2021-03-16 | 中国石油大学(华东) | Seismic wave forward modeling method and device, storage medium and processor |
| CN112859162A (en) * | 2019-11-28 | 2021-05-28 | 中国石油天然气集团有限公司 | Three-dimensional sound wave equation space domain forward modeling method and device based on pseudo-spectrum method |
| CN113139266A (en) * | 2020-01-18 | 2021-07-20 | 中国科学院地质与地球物理研究所 | Longitudinal wave and transverse wave numerical simulation method and system |
| CN113406698A (en) * | 2021-05-24 | 2021-09-17 | 中国石油大学(华东) | Dual-phase medium elastic wave reverse time migration imaging method based on longitudinal and transverse wave decoupling |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103412328A (en) * | 2013-08-01 | 2013-11-27 | 中国石油天然气集团公司 | Wave number field amplitude preservation wave field separation method based on staggered mesh finite difference algorithm |
| CN104122585A (en) * | 2014-08-08 | 2014-10-29 | 中国石油大学(华东) | Seismic forward modeling method based on elastic wave field vector decomposition and low-rank decomposition |
| CN104133241A (en) * | 2014-07-31 | 2014-11-05 | 中国科学院地质与地球物理研究所 | Wave field separating method and device |
| CN104749623A (en) * | 2014-10-20 | 2015-07-01 | 袁茂林 | Seismic data imaging processing method |
| WO2016060513A1 (en) * | 2014-10-17 | 2016-04-21 | 한국지질자원연구원 | Prestack egs migration method for seismic wave multi-component data |
| CN105807315A (en) * | 2016-03-14 | 2016-07-27 | 中国石油大学(华东) | Elastic vector reverse time migration imaging method |
-
2017
- 2017-01-26 CN CN201710057397.1A patent/CN106772585B/en not_active Expired - Fee Related
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103412328A (en) * | 2013-08-01 | 2013-11-27 | 中国石油天然气集团公司 | Wave number field amplitude preservation wave field separation method based on staggered mesh finite difference algorithm |
| CN104133241A (en) * | 2014-07-31 | 2014-11-05 | 中国科学院地质与地球物理研究所 | Wave field separating method and device |
| CN104122585A (en) * | 2014-08-08 | 2014-10-29 | 中国石油大学(华东) | Seismic forward modeling method based on elastic wave field vector decomposition and low-rank decomposition |
| WO2016060513A1 (en) * | 2014-10-17 | 2016-04-21 | 한국지질자원연구원 | Prestack egs migration method for seismic wave multi-component data |
| CN104749623A (en) * | 2014-10-20 | 2015-07-01 | 袁茂林 | Seismic data imaging processing method |
| CN105807315A (en) * | 2016-03-14 | 2016-07-27 | 中国石油大学(华东) | Elastic vector reverse time migration imaging method |
Non-Patent Citations (1)
| Title |
|---|
| 黄建平 等: "一种解耦的起伏地表弹性波高斯束偏移方法", 《石油地球物理勘探》 * |
Cited By (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107340540A (en) * | 2017-07-05 | 2017-11-10 | 中国科学院地质与地球物理研究所 | Direction wave decomposition method, device and the computer-readable storage medium of elastic wave field |
| CN107340540B (en) * | 2017-07-05 | 2019-05-07 | 中国科学院地质与地球物理研究所 | Direction wave decomposition method, device and the computer storage medium of elastic wave field |
| CN109212605A (en) * | 2018-09-28 | 2019-01-15 | 中国科学院地质与地球物理研究所 | pseudo-differential operator storage method and device |
| WO2020063131A1 (en) * | 2018-09-28 | 2020-04-02 | 中国科学院地质与地球物理研究所 | Method and device for storing pseudo-differential operator |
| CN112859162A (en) * | 2019-11-28 | 2021-05-28 | 中国石油天然气集团有限公司 | Three-dimensional sound wave equation space domain forward modeling method and device based on pseudo-spectrum method |
| CN112859162B (en) * | 2019-11-28 | 2024-04-30 | 中国石油天然气集团有限公司 | Three-dimensional acoustic wave equation space domain forward modeling method and device based on pseudo-spectrum method |
| CN113139266A (en) * | 2020-01-18 | 2021-07-20 | 中国科学院地质与地球物理研究所 | Longitudinal wave and transverse wave numerical simulation method and system |
| CN113139266B (en) * | 2020-01-18 | 2024-05-17 | 中国科学院地质与地球物理研究所 | Longitudinal and transverse wave numerical simulation method and system |
| CN112505775A (en) * | 2020-10-16 | 2021-03-16 | 中国石油大学(华东) | Seismic wave forward modeling method and device, storage medium and processor |
| CN113406698A (en) * | 2021-05-24 | 2021-09-17 | 中国石油大学(华东) | Dual-phase medium elastic wave reverse time migration imaging method based on longitudinal and transverse wave decoupling |
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