CN108196303A - Elastic wave field separation method, device, storage medium and equipment - Google Patents
Elastic wave field separation method, device, storage medium and equipment Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
- G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
- G01V1/36—Effecting static or dynamic corrections on records, e.g. correcting spread; Correlating seismic signals; Eliminating effects of unwanted energy
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
- G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
- G01V1/36—Effecting static or dynamic corrections on records, e.g. correcting spread; Correlating seismic signals; Eliminating effects of unwanted energy
- G01V1/364—Seismic filtering
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V2210/00—Details of seismic processing or analysis
- G01V2210/30—Noise handling
- G01V2210/32—Noise reduction
- G01V2210/324—Filtering
Abstract
The present invention provides a kind of elastic wave field separation method, device, storage medium and equipment.This method includes：In the case where avoiding shear wave singularity, the polarization vector of seismic wave type is obtained by solving Kelvin Christoffel equations；Utilize the polarization vector of simulated annealing optimization seismic wave type；Elastic wave field separation is carried out to seismic wave vector wave field using the polarization vector of the seismic wave type after optimization.The present invention can improve wave field separation precision and efficiency.
Description
Technical field
The present invention relates to Seismic Exploration Data Processing technical field more particularly to a kind of elastic wave field separation method, dresses
It puts, storage medium and equipment.
Background technology
Seismic prospecting is widely recognized in energy minerals exploration, and particularly, multi-wave seismic survey is carried because it has
The features such as abundant subsurface information and be greatly developed.However, being interfered with each other between different waves in multi-wave seismic data, reduce
Imaging resolution, so as to seriously affect the accuracy of geologic interpretation result.In order to improve imaging resolution, often need reasonably
Carry out vector wave field separation.
During based on polarization characteristic to vector wave field separation, it is inevitable the problem of be how ensure computational efficiency premise
Under, wave field is allowed more accurately to project on corresponding polarization direction, and (wave field separation is referred to as projecting in wave-number domain, and in spatial domain
It is referred to as space filtering).Because of the presence of S wave singularitys, on particular propagation direction, SH waves in three-dimensional TTI media and
Quasi-SV waves are inseparable, because the inclined of two kinds of wave modes can not possibly be obtained by solving Kelvin-Christoffel equations
Shake vector.Yan and Sava (Yan, J., and P.Sava, 2011, Improving the efficiency of elastic
wave-mode separation for heterogeneous tilted transverse isotropic media:
Geophysics,76,T65-T78,doi:10.1190/1.3581360.2011) in the conventional binomial window function of wave-number domain utilization
It is blocked with Gauss window functions and approaches pseudo-differential operator, and go the anisotropy of interpolation polarization vector using IDW algorithms in spatial domain
The efficiency and precision of wave field separation to reduce the calculation amount of wave field separation, is improved in part.Moreover, its algorithm is adapted to by force respectively
The situation of anisotropy.
It specifically, can be by optimizing to improve separating effect to vector wave field dividing operator.To dividing operator
The method optimized can be divided into window function optimization algorithm and Direct optimization method.Window function optimization method is suitable by selecting
Window function go to block pseudo- law popularization operator, the dividing operator so as to be optimized.Direct optimization method is then to utilize least square
The optimization methods such as method, Remez algorithms directly acquire the difference for making dividing operator in the error curve meet demand as far as possible of wave-number domain
Divide coefficient.The problem of such method makes the design of dividing operator be simplified to optimization dividing operator gives spectrum coverage area, with optimization
Method search makes as small as possible point of coefficient of error.
Invention content
The present invention provides a kind of elastic wave field separation method, device, storage medium and equipment, to improve wave field separation
Precision and efficiency.
The embodiment of the present invention provides a kind of elastic wave field separation method, including：In the case where avoiding shear wave singularity,
The polarization vector of seismic wave type is obtained by solving Kelvin-Christoffel equations；Optimize seismic wave using simulated annealing
The polarization vector of type；Elastic wave field point is carried out to seismic wave vector wave field using the polarization vector of the seismic wave type after optimization
From.
In one embodiment, seismic wave type includes quasi-P waves, quasi-SV involves SH waves, is avoiding shear wave singularity
In the case of, by solving the polarization vector of Kelvin-Christoffel equations acquisition seismic wave type, including：It solves three-dimensional each
The Kelvin-Christoffel equations of anisotropy medium obtain the normalization polarization vector of quasi-P waves；Based on quasi-P
Wave, SH involve the polarization vector orthogonality relation of quasi-SV waves, utilize the normalization polarization vector of quasi-P waves and earthquake wave vector
The polarization vectors of SH waves is calculated in the direction of propagation of amount wave field, utilizes the normalization polarization vector of quasi-P waves and SH waves
The polarization vector of quasi-SV waves is calculated in polarization vector.
In one embodiment, seismic wave type includes quasi-P waves, in the case where avoiding shear wave singularity, passes through solution
Kelvin-Christoffel equations obtain the polarization vector of seismic wave type, including：Solve 3-D elastic anisotropic media
Kelvin-Christoffel equations obtain the normalization polarization vector of quasi-P waves；Optimize seismic wave using simulated annealing
The polarization vector of type, including：Utilize the normalization polarization vector of simulated annealing optimization quasi-P waves；Based on quasi-P waves,
SH involves the polarization vector orthogonality relation of quasi-SV waves, utilizes the normalization polarization vector and ground of the quasi-P waves after optimization
The polarization vector of SH waves is calculated in the direction of propagation of seismic wave vector wave field, and the normalization using the quasi-P waves after optimization is inclined
The polarization vectors of quasi-SV waves is calculated in the polarization vector of vector sum SH waves of shaking, wherein, the seismic wave type after optimization includes
Optimize the polarization vector of the normalization polarization vectors of quasi-P waves, the polarization vector of SH waves and quasi-SV waves.
In one embodiment, optimize the polarization vector of seismic wave type using simulated annealing, including：It establishes based on maximization
The object function of norm sets the limits of error in maximum wave-number range in object function；Target letter is searched for using simulated annealing
The value of Optimizing operator coefficient variation in number, so that target function value meets the limits of error；The Optimizing operator coefficient obtained using search
The value structure Optimizing operator of variable；The polarization vector of seismic wave type is multiplied by by the Optimizing operator of structure, after optimization is calculated
Seismic wave type polarization vector.
In one embodiment, elastic wave is carried out to seismic wave vector wave field using the polarization vector of the seismic wave type after optimization
Wave field separation, including：The polarization vector of seismic wave type after optimization is converted by wave-number domain to spatial domain；Utilize the inclined of spatial domain
The vector that shakes carries out space filtering to seismic wave vector wave field, to carry out elastic wave field separation.
In one embodiment, object function is：
Wherein, kxFor wave number,For maximum wave number, N is Grid dimension, and 1≤n≤N/2, n are integer, bnIt is calculated for optimization
Subsystem number variable, Δ x are the sampling interval, and T is the limits of error.
In one embodiment, the value of Optimizing operator coefficient variation in object function is searched for using simulated annealing, so that mesh
Offer of tender numerical value meets the limits of error, including：By Optimizing operator coefficient absolute value of amplitude in [0,2] section and Optimizing operator coefficient amplitude
Around the condition of center damped oscillation, the value of Optimizing operator coefficient variation in object function is searched for using simulated annealing,
So that target function value meets the limits of error.
The embodiment of the present invention also provides a kind of elastic wave field separator, including：Polarization vector generation unit, is used for：
In the case where avoiding shear wave singularity, by solve Kelvin-Christoffel equations obtain seismic wave type polarization to
Amount；Polarization vector optimizes unit, is used for：Utilize the polarization vector of simulated annealing optimization seismic wave type；Vector wave field separation list
Member is used for：Elastic wave field separation is carried out to seismic wave vector wave field using the polarization vector of the seismic wave type after optimization.
Also a kind of computer readable storage medium of the embodiment of the present invention, is stored thereon with computer program, which is located
Manage the step of realizing the various embodiments described above the method when device performs.
Also a kind of computer equipment of the embodiment of the present invention, including memory, processor and storage on a memory and can be
The computer program run on processor, the processor realize the step of the various embodiments described above the method when performing described program
Suddenly.
Elastic wave field separation method, device, storage medium and the computer equipment of the present invention, is avoiding shear wave singularity
In the case of, the polarization vector that avoids singularity can be solved and polarization vector is optimized integration, can avoided in spy
Determine direction, it the problem of singularity of two shear waves leads to not separation, can be by solving Kelvin-Christoffel equations
The polarization vector of seismic wave type is obtained, successfully obtains the polarization vector of various wave modes.Optimize seismic wave type using simulated annealing
Polarization vector, can comparatively fast and successfully restrain, obtain optimal polarization vector, so can improve elastic wave field separation
Precision and efficiency.
Description of the drawings
In order to illustrate more clearly about the embodiment of the present invention or technical scheme of the prior art, to embodiment or will show below
There is attached drawing needed in technology 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
Other attached drawings are obtained according to these attached drawings.In the accompanying drawings：
Fig. 1 is the flow diagram of the elastic wave field separation method of one embodiment of the invention；
Fig. 2 is the polarization that seismic wave type is obtained by solving Kelvin-Christoffel equations of one embodiment of the invention
The method flow schematic diagram of vector；
Fig. 3 is that the method flow of the polarization vector using simulated annealing optimization seismic wave type in one embodiment of the invention shows
It is intended to；
Fig. 4 is the method flow of the polarization vector using simulated annealing optimization seismic wave type in another embodiment of the present invention
Schematic diagram；
Fig. 5 be in one embodiment of the invention using optimization after seismic wave type polarization vector to seismic wave vector wave field into
The method flow schematic diagram of row elastic wave field separation；
Fig. 6 to Fig. 8 is X-component, Y-component and Z points of pulse number of responses value analog result in one embodiment of the invention respectively
The wave field snapshot of amount；
Fig. 9 to Figure 11 is that quasi-P waves, quasi-SV after wave field separation shown in Fig. 6 to Fig. 8 involve SH waves respectively
Wave field snapshot；
Figure 12 is the structure diagram of the elastic wave field separator of one embodiment of the invention；
Figure 13 is the structure diagram of polarization vector generation unit in one embodiment of the invention；
Figure 14 is the structure diagram of polarization vector optimization unit in one embodiment of the invention；
Figure 15 is the structure diagram of polarization vector optimization unit in another embodiment of the present invention；
Figure 16 is the structure diagram of vector wave field separative element in one embodiment of the invention；
Figure 17 is the structure diagram of the computer equipment of one embodiment of the invention.
Specific embodiment
Purpose, technical scheme and advantage to make the embodiment of the present invention are more clearly understood, below in conjunction with the accompanying drawings to this hair
Bright embodiment is described in further details.Here, the illustrative embodiments of the present invention and their descriptions are used to explain the present invention, but simultaneously
It is not as a limitation of the invention.
Fig. 1 is the flow diagram of the elastic wave field separation method of one embodiment of the invention.As shown in Figure 1, this implementation
The elastic wave field separation method of example, it may include：
Step S110：In the case where avoiding shear wave singularity, obtained by solving Kelvin-Christoffel equations
The polarization vector of seismic wave type；
Step S120：Utilize the polarization vector of simulated annealing optimization seismic wave type；
Step S130：Elastic wave field is carried out to seismic wave vector wave field using the polarization vector of the seismic wave type after optimization
Separation.
In 3-D elastic anisotropic media, for example, three-dimensional TTI (Tilt Transversely Isotropic, laterally respectively to
The same sex) medium, for the special direction of propagation, for example, perpendicular or parallel TI (Transversely Isotropic, laterally respectively to
The same sex) medium symmetry axis direction, can be there are pure P waves and S waves, although S waves can also divide, two S wave phases of division
Speed is consistent, and is propagated with identical phase velocity, here it is the singularitys of S waves.Because there is the presence of S wave singularitys, in spy
The fixed direction of propagation, SH waves and quasi-SV waves in three-dimensional TTI media are inseparable, because can not possibly pass through solution
Kelvin-Christoffel equations obtain the polarization vector of two kinds of wave modes.In above-mentioned steps S110, singularity is being avoided
In the case of, such as in the case where avoiding shear wave (S waves) singularity, can be obtained by solving Kelvin-Christoffel equations
To the polarization vector of various seismic wave types.
In above-mentioned steps S120, simulated annealing can be based on Metropolis and be proposed in nineteen fifty-three in thermodynamics field
Simulated annealing obtain, belong to a kind of random algorithm.Simulated annealing finds new explanation using stochastical sampling mode, and with
Temperature declines and gradually smaller probability receives poor solution.Simulated annealing is the extension of local search algorithm, has energy
The advantages of enough jumping out local optimum trap can comparatively fast converge to globally optimal solution.With initial temperature during simulated annealing optimizing
The selection of (variable initial value) and final temperature (variable end value) is extremely important, directly determine search how long and can be into
Work(searches the solution for meeting the error upper limit.
In above-mentioned steps S130, it can be projected in wave-number domain or carry out space filtering in spatial domain, to realize
Elastic wave field detaches.
In the present embodiment, in the case where avoiding shear wave singularity, can by avoid singularity polarization vector solve and
The problem of polarization vector is optimized integration, and can be avoided in specific direction, and the singularity of two shear waves leads to not separation,
The polarization vector of seismic wave type can be obtained by solving Kelvin-Christoffel equations, successfully obtains the inclined of various wave modes
Shake vector.Using the polarization vector of simulated annealing optimization seismic wave type, it can comparatively fast and successfully restrain, obtain optimal polarization
Vector, and then the precision and efficiency of elastic wave field separation can be improved.
In some embodiments, it is believed that the quasi-P waves in 3-D elastic anisotropic media (such as TTI media) are not strange
Different in nature problem, and it is believed that the polarization vector of three kinds of wave modes (quasi-P waves, quasi-SV waves and SH waves) is mutually orthogonal.
The polarization vector of quasi-P waves can first be obtained, quasi-SV waves and SH waves then is obtained using the polarization vector of quasi-P waves
Polarization vector, then vector wave field is projected into corresponding direction to detach wave field.In the direction of propagation existing for singularity, find
The amplitude of the polarization vector of two S waves is zero, it is possible to avoid singularity problem.
In above-mentioned steps S110 and step S120, the polarization vector of various wave modes can first be obtained, then to various waves
The polarization vector of type optimizes, and finally carries out wavefield decomposition using the polarization vector after all optimizations.Alternatively, it can first be obtained
The polarization vector of the polarization vector of wave mode in certain, such as the polarization vector of quasi-P waves, then to the polarization vector of this kind of wave mode
It optimizes, and then the polarization vectors of other wave modes, such as quasi- is acquired using the polarization vector of this kind of wave mode after optimization
The polarization vector of SV waves and SH waves finally utilizes the polarization vector of this kind of wave mode after optimization and the polarization of other wave modes acquired
Vector carries out wavefield decomposition.
Fig. 2 is the polarization that seismic wave type is obtained by solving Kelvin-Christoffel equations of one embodiment of the invention
The method flow schematic diagram of vector.Seismic wave type may include that quasi-P waves, quasi-SV involve SH waves.As shown in Fig. 2, upper
It states in step S110, in the case where avoiding shear wave singularity, earthquake is obtained by solving Kelvin-Christoffel equations
The method of the polarization vector of wave mode, it may include：
Step S111：The Kelvin-Christoffel equations for solving 3-D elastic anisotropic media obtain quasi-P waves
Normalize polarization vector；
Step S112：Involve the polarization vector orthogonality relation of quasi-SV waves based on quasi-P waves, SH, utilize quasi-P
The polarization vector of SH waves is calculated in the normalization polarization vector of wave and the direction of propagation of seismic wave vector wave field, utilizes quasi-
The polarization vector of quasi-SV waves is calculated in the normalization polarization vector of P waves and the polarization vector of SH waves.
By above-mentioned steps S111~step S112 obtain the normalization polarization vector of quasi-P waves, the polarization of SH waves to
After amount and the polarization vector of quasi-SV waves, in above-mentioned steps S120, simulated annealing can be utilized to polarize those
(polarization vector of the normalization polarization vector of quasi-P waves, the polarization vector of SH waves and quasi-SV waves) optimizes.It is only sharp
The polarization vector of quasi-P waves is obtained with Kelvin-Christoffel equations, then quasi- is involved based on quasi-P waves, SH
The polarization vector of other wave modes is obtained using the normalization polarization vector of quasi-P waves in the polarization vector orthogonality relation of SV waves, can
To avoid shear wave singularity.
In embodiment, in above-mentioned steps S111, can by solving the characteristic values of Kelvin-Christoffel equations,
The polarization vector of quasi-P waves is obtained, then the polarization vector of quasi-P waves is normalized, obtains the normalizing of quasi-P waves
Change polarization vector.
In embodiment, seismic wave type may include quasi-P waves, above-mentioned steps S110, in the situation for avoiding shear wave singularity
Under, the method for the polarization vector by solving Kelvin-Christoffel equations acquisition seismic wave type, it may include：It solves three-dimensional
The Kelvin-Christoffel equations of anisotropic medium obtain the normalization polarization vector of quasi-P waves.Utilize Kelvin-
Christoffel equations only seek the normalization polarization vector of quasi-P waves, can be to avoid shear wave singularity.
Fig. 3 is that the method flow of the polarization vector using simulated annealing optimization seismic wave type in one embodiment of the invention shows
It is intended to.As shown in figure 3, above-mentioned steps S120, using the method for the polarization vector of simulated annealing optimization seismic wave type, can wrap
It includes：
Step S1211：Utilize the normalization polarization vector of simulated annealing optimization quasi-P waves；
Step S1212：Involve the polarization vector orthogonality relation of quasi-SV waves based on quasi-P waves, SH, after optimization
The normalization polarization vector of quasi-P waves and the direction of propagation of seismic wave vector wave field the polarization vectors of SH waves is calculated,
The polarization of quasi-SV waves is calculated using the normalization polarization vector of the quasi-P waves after optimization and the polarization vector of SH waves
Vector, wherein, seismic wave type after optimization include the normalization polarization vectors of optimization quasi-P waves, the polarization vector of SH waves and
The polarization vector of quasi-SV waves.
In the present embodiment, only the normalization polarization vector of quasi-P waves can be optimized, other waves are then obtained accordingly
The polarization vector of type, with this, it is possible to reduce the calculation amount of optimization process.
Fig. 4 is the method flow of the polarization vector using simulated annealing optimization seismic wave type in another embodiment of the present invention
Schematic diagram.As shown in figure 4, in above-mentioned steps S120, optimize the method for the polarization vector of seismic wave type using simulated annealing,
It may include：
Step S1221：It establishes based on the object function for maximizing norm, sets in object function in maximum wave-number range
The limits of error；
Step S1222：The value of Optimizing operator coefficient variation in object function is searched for using simulated annealing, so that target letter
Numerical value meets the limits of error；
Step S1223：Optimizing operator is built using the value of Optimizing operator coefficient variation that search obtains；
Step S1224：The polarization vector of seismic wave type is multiplied by by the Optimizing operator of structure, the ground after optimization is calculated
The polarization vector of seismic wave type.
In the present embodiment, by searching for the value of Optimizing operator coefficient variation met the requirements, it is possible to Optimizing operator is built,
Advanced optimize polarization vector.Wave field separation precision can be improved by reducing the limits of error.
In embodiment, for above-mentioned steps S1211, specific implementation can be analogous to Fig. 4, and by step S1224
In the polarization vector of seismic wave type replace with the normalization polarization vectors of quasi-P waves.
In embodiment, in above-mentioned steps S1221, object function can be：
Wherein, kxFor wave number,For maximum wave number, N is Grid dimension, and 1≤n≤N/2, n are integer, bnIt is calculated for optimization
Subsystem number variable, Δ x are the sampling interval, and T is the limits of error.
In embodiment, above-mentioned steps S1222 searches for Optimizing operator coefficient variation in object function using simulated annealing
Value, so that target function value meets the method for the limits of error, it may include：By Optimizing operator coefficient absolute value of amplitude in [0,2] section
The condition of center damped oscillation is surrounded with Optimizing operator coefficient amplitude, is searched in object function and optimized using simulated annealing
The value of operator coefficient variable, so that target function value meets the limits of error.In embodiment, Optimizing operator coefficient bnAmplitude should be
Be in the concussion of attenuation around center 0, i.e., | bn| ＞ | bn+1|, and | bn||bn+1| ＜ 0, n=1,2 ... N/2.The present embodiment,
Using above-mentioned condition chess game optimization operator coefficient, search range can be reduced, improve optimization efficiency.
Fig. 5 be in one embodiment of the invention using optimization after seismic wave type polarization vector to seismic wave vector wave field into
The method flow schematic diagram of row elastic wave field separation.As shown in figure 5, above-mentioned steps S130, utilizes the seismic wave type after optimization
Polarization vector to seismic wave vector wave field carry out elastic wave field separation method, it may include：
Step S131：The polarization vector of seismic wave type after optimization is converted by wave-number domain to spatial domain；
Step S132：Space filtering is carried out to seismic wave vector wave field using the polarization vector of spatial domain, to carry out elasticity
Wave field detaches.
Illustrate the reality of the wave field separation method of the embodiment of the present invention by taking quasi-P waves in three-dimensional non-homogeneous TTI media as an example
Under applying for example.
For non-uniform dielectric, the anisotropic parameters using each space lattice node are theoretically needed, to each section
Point all asks for dividing operator, then carries out space filtering to model in spatial domain to carry out vector wave field separation again：
QP=LPx[Ux]+LPy[Uz]+LPz[Uy] (1)
Wherein, the wave field of the quasi-P waves in qP representation spaces domain, Ux、UyAnd UzRepresent three directions of coupling vector wave field
Component, LPx、LPyAnd LPzX, the pseudo-differential operator in tri- directions of Y, Z are represented respectively；[] representation space convolution (filtering).
In spatial domain, space filtering is carried out to vector wave field using pseudo-differential operator, you can the quasi-P waves detached
Wave field.For accurately separating P wave from S wave field, it is required for being calculated the corresponding polarization vector of each wave mode, then by vector wave
Field projects to polarization vector direction, to detach wave field.
It, can be in the hope of quasi- by solving the Kelvin-Christoffel equations of three-dimensional TTI media under three-dimensional situation
P waves, quasi-SV waves and SH wave polarizations vector, respectively with pP、pSVAnd pSHIt represents, to normalize wave number vectorRepresent the direction of propagation of wave, wherein, kx、kyAnd kzRepresent wave number in x, y and z side respectively
Upward component, | k | represent the mould of wave number vector,Represent the wave number after normalization on x, y and z direction respectively
Component.
Wave field separation method in three-dimensional TTI media obtains quasi-P by crossing solution Kelvin-Christoffel equations
The normalization polarization vector of waveNormalization polarization vector is represented respectivelyIn x, y
And the component on z directions), the direction of propagation of wave isThen the polarization vector of quasi-SV waves and SH waves can be with
It is calculated by the normalization polarization vector of quasi-P waves and the direction of propagation.
In embodiment, can be obtained by solving Kelvin-Christoffel equations quasi-P waves normalization polarize to
Amount, is denoted asThe direction of propagation of wave isThe then polarization vector p of SH wavesSHIt can be by
The normalization polarization vector of quasi-P waves and the direction of propagation are calculated：
Wherein, pSHx、pSHyAnd pSHzThe polarization vector p of SH waves is represented respectivelySHComponent on x, y and z direction.
In embodiment, the polarization vectors of quasi-SV waves can be by the normalization polarization vector of quasi-P waves and SH waves
Polarization vector is calculated：
The fixed direction of propagation is the direction of propagation existing for S wave singularitys, it is assumed that the parallel TI media symmetry axis in the direction of propagation, then
On the direction of propagation, the polarization direction of P waves is parallel to the direction of propagation, is denoted as：
Formula (4) is substituted into formula (2) and formula (3), it can be in the hope of the polarization vector of two S waves on the direction of propagation：
pSV=(0,0,0), pSH=(0,0,0) (5)
In the direction of propagation existing for singularity it can be seen from formula (5), the amplitude of the polarization vector of two S waves is zero,
The problem of so as to avoid singularity.
In embodiment, solve Kelvin-Christoffel equations and obtain the normalization polarization vector needs of quasi-P waves
Optimize into row format to obtain higher precision, therefore, introduce the optimization that global optimization operator carries out dividing operator：
According to the sampling theory of discrete signal, a continuous signal f (x) with limit can be by with the letter of a uniform sampling
Number fnIt is rebuild by sinc function interpolations：
Wherein, Δ x is the sampling interval,To end wave number, x is continuity point position, and n represents n-th of sampled point.
If seeking first derivative, and take the derivative value at x=0 to formula (6) the right and left, can obtain：
There are the window functions that a length is N+1 points, and N is even number, goes to block formula (7), obtain the calculation of conventional finite difference
Son.
Wherein,
Because singular point n=0 exists, in order to avoid singularity, formula (7) is expressed as：
Wherein,fnAnd f-nRepresent the signal of uniform sampling, windowed function is cut
Having no progeny just has：
Wherein,bnRepresent Optimizing operator coefficient, w (n) tables
Show the window function blocked.
Fourier transformation is carried out to formula (10) to be obtained：
Wherein, the left side of formula (11) is analytic solutions, and the right is numerical solution.
In embodiment, in order to achieve the purpose that adapt to broadband seismic simulation needs, the wave number of difference operator can be covered
Lid range is widened.In some embodiments, error is absolutely composed using the maximum maximized in the certain wave-number range of Norm Control,
It is as follows to establish object function：
It is the covered maximum wave-number range of Optimizing operator, T is margin of error limit.It can be directly controlled by T
The error upper limit of finite difference operator (dividing operator).With the global optimization approach of Fast Convergent, fast search to the limits of error
Under global optimum's Optimizing operator coefficient.By constantly increasingIt can obtain the optimization staggered-mesh of spectrum coverage area bigger
Optimizing operator coefficient.So the present embodiment is built based on the object function for maximizing norm foundation than existing least squares method
Vertical object function is more flexible.
In embodiment, in order to achieve the purpose that reduce optimization cost, inventor has found according to sinc interpolation theories：(1) it is excellent
There is N/2 Optimizing operator coefficient in the limited operator of N dot grids (dividing operator) of change；(2) amplitude of each Optimizing operator coefficient
Absolute value is in [0,2] section；(3) amplitude of Optimizing operator coefficient should be the concussion in attenuation around center 0, i.e.,
|bn| ＞ | bn+1|, and | bn||bn+1| ＜ 0, n=1,2 ... N/2.It can be calculated according to a principle chess game optimization in above-mentioned (1)~(3)
Subsystem number.It thus, can be by only determining b1To bnAnd optimize entire operator.
For high-order grid finite difference operator, such as N=16, then there are 8 Optimizing operator coefficients to need to optimize, belong to high
Dimension complicated function seeks extreme-value problem.For the object function of such complexity, linear search method and least square method can not spirits
It is living to solve.And the embodiment of the present invention carries out this target problem to directly search optimal Optimizing operator system using simulated annealing
Number.And the value range of each Optimizing operator coefficient can be set according to above-mentioned (2), (3) condition, then with (2) condition to Optimizing operator
The solving result of coefficient is limited, and can greatly reduce search range, makes simulated annealing more efficient.
In embodiment, for second-order central finite difference operator (dividing operator), the transform of spatial differencing scheme has：
Wherein, Z is a complex variable, F2(Z) be second-order central finite difference operator transform represent, Z1And Z-1Table
Show the index of Z variables.
Formula (13) both sides are transformed into wave-number domain, and carry out Euler's expansion, can obtain：
F2(k)=- isin (k) (14)
Wherein, k represents wave number, F2(k) be second-order central finite difference operator wave number domain representation.
Formula (14) both sides with being multiplied by i, and divided by k, can obtain the second order Optimizing operator of wave-number domain：
Wherein, W2(k) it represents using wave number k as the second order Optimizing operator of variable.
Similar to the above method, the Optimizing operators such as quadravalence, six ranks can be obtained.Arbitrary exponent number Optimizing operator can be：
Wherein, W2n(k) using wave number k as the Optimizing operator (wave-number domain) of the 2n ranks of variable.bnTo be searched using simulated annealing
The Optimizing operator coefficient that rope is calculated.
In the embodiment of the present invention, by algorithm globally optimal with singularity three-dimensional wave separation algorithm is avoided to combine, profit
Globally optimal solution is solved, and optimize dividing operator using the optimal solution with simulated annealing method, inverse transformation back to spatial domain is intended
Differential operator, the advantage of this method are can to set the smaller limits of error, and the limits of error can be controlled in a ten thousandth, and are utilized
Simulated annealing solves the Optimal solution problem for maximizing norm, can obtain the spectrum coverage area of bigger, while can ensure essence
The stability for spending error is preferable.The dividing operator precision that optimization obtains is higher, and low order operator can reach the precision of high-order operator,
Effectively save calculation amount.It, can be with by first solving to obtain the normalization polarization vector of quasi-P waves and the known direction of propagation
The polarization vector of SH waves is acquired, recycles and is calculated by the normalization polarization vector of quasi-P waves and the polarization vector of SH waves
The polarization vector of quasi-SV waves.Can to avoid the singularity of three-dimensional TI media specific direction, shear wave cause two shear waves without
The problem of method detaches.
In embodiment, elastic wave field separation method may include (1) using global optimization method optimization dividing operator and (2)
Avoid two steps of three-dimensional wave separation algorithm of singularity.
In embodiment, it may include following steps using global optimization method optimization dividing operator：
(1) setting error upper limit T；
(2) wave number is existedIn the range of uniformly it is discrete afterSubsequent step is performed to each wave number
(3)~(4), search meet the optimal Optimizing operator coefficient of T；
(3) global search is carried out with simulated annealing, wherein, setting key parameter is needed to have：Marklov chain lengths,
Initial temperature, final temperature and step factor；In addition, also independent variable dimension M and each independent variable value range, i.e. 2M scales
The Optimizing operator coefficient number and the value range of each Optimizing operator coefficient that point operator to be optimized.
(4) if the Optimizing operator coefficient searched, makes target function value meet the limits of error, then (2) step, and k=k are returned to
+ 1, carry out the global optimizing of next wave number sampled point；If not satisfied, then terminating, the optimization for taking a wave number sampled point is excellent
Change operator coefficient to export as optimal solution.
(5) dividing operator is optimized using 2M rank optimum finite-difference operators.
In embodiment, the three-dimensional wave separation algorithm of singularity is avoided, flow can be as follows：
(1) Kelvin-Christoffel equations are solved and obtains the normalization polarization vector of quasi-P waves；
(2) polarization vector of SH waves is calculated by the normalization polarization vector of Quasi-P waves and the direction of propagation；
(3) the inclined of quasi-SV waves is calculated by the polarization vector of the normalization polarization vector of quasi-P waves and SH waves
Shake vector.
In embodiment, normalization polarization vector is asked in step (1) to be optimized using above-mentioned global optimization approach,
Step (2) and (3) is carried out, solves the polarization vector of SH waves and the polarization vector of quasi-SV waves.
In other embodiment, other dividing operator optimization algorithms, such as window function metht can be selected as needed, it is minimum
Square law etc..
Fig. 6 to Fig. 8 is X-component, Y-component and Z points of pulse number of responses value analog result in one embodiment of the invention respectively
The wave field snapshot of amount.Fig. 9 to Figure 11 is that quasi-P waves, quasi-SV after wave field separation shown in Fig. 6 to Fig. 8 involve respectively
The wave field snapshot of SH waves.Fig. 9 to Figure 11 illustrates wave field separation as a result, by Fig. 6 under three-dimensional uniformly TTI anisotropic mediums
To Fig. 8 and Fig. 9 to Figure 11, comparison can see, and quasi-P waves, quasi-SV involve SH waves and be cleanly separated out very much, do not have
There is the interference of another wave, detached the vector wave field under three-dimensional TTI media well.Therefore, the embodiment of the present invention is in three-dimensional
Separation strategy under model is effective.
Global optimization operator can optimize pseudo-differential operator first, pseudo-differential operator be made to have higher separation accuracy, simultaneously
Greatly improve computational efficiency.Next avoids the algorithm of three-dimensional wave field singularity can be to avoid in specific direction, two shear waves
Singularity problem lead to not separation the problem of.So the method for the embodiment of the present invention, introduces global optimization operator and keeps away
Exempt from the wave separation algorithm of three-dimensional wave field singularity, the precision and efficiency of trivector wave field separation can be improved.Wherein, it utilizes
Global optimization arithmetic operators optimization dividing operator can obtain the higher dividing operator of precision.It is detached using the algorithm of singularity is avoided
The problem of wave field can be avoided in specific direction, and the singularity of two shear waves leads to not separation.
Based on the inventive concept identical with elastic wave field separation method shown in FIG. 1, the embodiment of the present application additionally provides
A kind of elastic wave field separator, as described in example below.The original solved the problems, such as due to the elastic wave field separator
Reason is similar to elastic wave field separation method, therefore the implementation of the elastic wave field separator may refer to elastic wave field point
Implementation from method, overlaps will not be repeated.
Figure 12 is the structure diagram of the elastic wave field separator of one embodiment of the invention.As shown in figure 12, this reality
Apply the elastic wave field separator of example, it may include：Polarization vector generation unit 210, polarization vector optimization unit 220 and vector
Wave field separation unit 230, above-mentioned each unit are linked in sequence.
Polarization vector generation unit 210, is used for：In the case where avoiding shear wave singularity, by solving Kelvin-
Christoffel equations obtain the polarization vector of seismic wave type；
Polarization vector optimizes unit 220, is used for：Utilize the polarization vector of simulated annealing optimization seismic wave type；
Vector wave field separative element 230, is used for：Using the polarization vector of the seismic wave type after optimization to seismic wave vector wave
Field carries out elastic wave field separation.
Figure 13 is the structure diagram of polarization vector generation unit in one embodiment of the invention.Seismic wave type includes quasi-
P waves, quasi-SV involve SH waves, as shown in figure 13, polarization vector generation unit 210, it may include：Quasi-P wave polarizations vector
Generation module 211 and SH involve quasi-SV wave polarizations vector generation module 212, and the two is connected with each other.
Quasi-P wave polarizations vector generation module 211, is used for：Solve the Kelvin- of 3-D elastic anisotropic media
Christoffel equations obtain the normalization polarization vector of quasi-P waves；
SH involves quasi-SV wave polarizations vector generation module 212, is used for：Quasi-SV is involved based on quasi-P waves, SH
The polarization vector orthogonality relation of wave utilizes the normalization polarization vector of quasi-P waves and the direction of propagation of seismic wave vector wave field
The polarization vector of SH waves is calculated, is calculated using the normalization polarization vector of quasi-P waves and the polarization vector of SH waves
The polarization vector of quasi-SV waves.
In embodiment, seismic wave type may include quasi-P waves, polarization vector generation unit 210, it may include：Quasi-P waves
Polarization vector solves module, is used for：The Kelvin-Christoffel equations for solving 3-D elastic anisotropic media obtain quasi-P
The normalization polarization vector of wave.
Figure 14 is the structure diagram of polarization vector optimization unit in one embodiment of the invention.As shown in figure 14, polarize to
Amount optimization unit 220, it may include：Quasi-P wave polarization vector optimizations module 2211 and SH involve quasi-SV wave polarizations vector
Optimization module 2212, the two are connected with each other.
Quasi-P wave polarization vector optimizations module 2211, is used for：Utilize the normalizing of simulated annealing optimization quasi-P waves
Change polarization vector；
SH involves quasi-SV wave polarization vector optimizations module 2212, is used for：Quasi- is involved based on quasi-P waves, SH
The polarization vector orthogonality relation of SV waves utilizes the normalization polarization vector of the quasi-P waves after optimization and seismic wave vector wave field
The direction of propagation polarization vectors of SH waves is calculated, utilize the normalization polarization vector of the quasi-P waves after optimization and SH waves
Polarization vector the polarization vectors of quasi-SV waves is calculated, wherein, the seismic wave type after optimization includes optimization quasi-P waves
Normalization polarization vector, the polarization vector of the polarization vector of SH waves and quasi-SV waves.
Figure 15 is the structure diagram of polarization vector optimization unit in another embodiment of the present invention.As shown in figure 15, it polarizes
Vector optimization unit 220, it may include：Object function establishes module 2221, Optimizing operator coefficient determination module 2222, Optimizing operator
Build module 2223 and vector optimization computing module 2224, above-mentioned each sequence of modules connection.
Object function establishes module 2221, is used for：It establishes based on the object function for maximizing norm, sets in object function
The limits of error in maximum wave-number range；
Optimizing operator coefficient determination module 2222, is used for：Optimizing operator system in object function is searched for using simulated annealing
The value of number variable, so that target function value meets the limits of error；
Optimizing operator builds module 2223, is used for：Optimization is built using the value of Optimizing operator coefficient variation that search obtains
Operator；
Vector optimization computing module 2224, is used for：The polarization vector of seismic wave type is multiplied by by the Optimizing operator of structure, is counted
Calculate the polarization vector of the seismic wave type after being optimized.
In embodiment, object function establishes module 2221 and is additionally operable to perform：Object function is：
Wherein, kxFor wave number,For maximum wave number, N is Grid dimension, and 1≤n≤N/2, n are integer, bnIt is calculated for optimization
Subsystem number variable, Δ x are the sampling interval, and T is the limits of error.
In embodiment, Optimizing operator coefficient determination module 2222, it may include：Conditional search module, is used for：By Optimizing operator
Coefficient absolute value of amplitude surrounds the condition of center damped oscillation in [0,2] section and Optimizing operator coefficient amplitude, utilizes mould
Intend the value of Optimizing operator coefficient variation in annealing method search object function, so that target function value meets the limits of error.
Figure 16 is the structure diagram of vector wave field separative element in one embodiment of the invention.Vector wave field as shown in figure 16
Separative element 230, it may include：Domain modular converter 231 and wave field separation module 232, the two are connected with each other.
Domain modular converter 231, is used for：The polarization vector of seismic wave type after optimization is converted by wave-number domain to spatial domain；
Wave field separation module 232, is used for：Space filter is carried out to seismic wave vector wave field using the polarization vector of spatial domain
Wave, to carry out elastic wave field separation.
The embodiment of the present invention also provides a kind of computer readable storage medium, is stored thereon with computer program, the program
The step of the various embodiments described above the method is realized when being executed by processor.
The present invention also provides a kind of computer equipments.As shown in figure 17, computer equipment 300 includes memory 310, processing
Device 320 and the computer program that can be run on memory 310 and on the processor 320 is stored in, the processor 320 performs institute
The step of the various embodiments described above the method being realized when stating program.
In conclusion elastic wave field separation method, device, storage medium and the computer equipment of the present invention, are avoiding
In the case of shear wave singularity, the polarization vector that avoids singularity can be solved and polarization vector is optimized integration, energy
It enough avoids in specific direction, the problem of singularitys of two shear waves leads to not separation, it can be by solving Kelvin-
Christoffel equations obtain the polarization vector of seismic wave type, successfully obtain the polarization vector of various wave modes.Utilize simulated annealing
Method optimizes the polarization vector of seismic wave type, can comparatively fast and successfully restrain, obtain optimal polarization vector, and then can improve bullet
Property wave field separation precision and efficiency.
In the description of this specification, reference term " one embodiment ", " specific embodiment ", " some implementations
Example ", " such as ", the description of " example ", " specific example " or " some examples " etc. mean to combine the embodiment or example description
Particular features, structures, materials, or characteristics are contained at least one embodiment of the present invention or example.In the present specification,
Schematic expression of the above terms may not refer to the same embodiment or example.Moreover, the specific features of description, knot
Structure, material or feature can in an appropriate manner combine in any one or more embodiments or example.Each embodiment
Involved in the step of sequence for schematically illustrating the implementation of the present invention, sequence of steps therein is not construed as limiting, can be as needed
It appropriately adjusts.
It should be understood by those skilled in the art that, the embodiment of the present invention can be provided as method, system or computer program
Product.Therefore, the reality in terms of complete hardware embodiment, complete software embodiment or combination software and hardware can be used in the present invention
Apply the form of example.Moreover, the computer for wherein including computer usable program code in one or more can be used in the present invention
The computer program production that usable storage medium is implemented on (including but not limited to magnetic disk storage, CD-ROM, optical memory etc.)
The form of product.
The present invention be with reference to according to the method for the embodiment of the present invention, the flow of equipment (system) and computer program product
Figure and/or block diagram describe.It should be understood that it can be realized by computer program instructions every first-class in flowchart and/or the block diagram
The combination of flow and/or box in journey and/or box and flowchart and/or the block diagram.These computer programs can be provided
The processor of all-purpose computer, special purpose computer, Embedded Processor or other programmable data processing devices is instructed to produce
A raw machine so that the instruction performed by computer or the processor of other programmable data processing devices is generated for real
The device of function specified in present one flow of flow chart or one box of multiple flows and/or block diagram or multiple boxes.
These computer program instructions, which may also be stored in, can guide computer or other programmable data processing devices with spy
Determine in the computer-readable memory that mode works so that the instruction generation being stored in the computer-readable memory includes referring to
Enable the manufacture of device, the command device realize in one flow of flow chart or multiple flows and/or one box of block diagram or
The function of being specified in multiple boxes.
These computer program instructions can be also loaded into computer or other programmable data processing devices so that counted
Series of operation steps are performed on calculation machine or other programmable devices to generate computer implemented processing, so as in computer or
The instruction offer performed on other programmable devices is used to implement in one flow of flow chart or multiple flows and/or block diagram one
The step of function of being specified in a box or multiple boxes.
Particular embodiments described above has carried out the purpose of the present invention, technical solution and advantageous effect further in detail
Describe in detail it is bright, it should be understood that the above is only a specific embodiment of the present invention, the guarantor being not intended to limit the present invention
Range is protected, all within the spirits and principles of the present invention, any modification, equivalent substitution, improvement and etc. done should be included in this
Within the protection domain of invention.
Claims (10)
1. a kind of elastic wave field separation method, which is characterized in that including：
In the case where avoiding shear wave singularity, the polarization of seismic wave type is obtained by solving Kelvin-Christoffel equations
Vector；
Utilize the polarization vector of simulated annealing optimization seismic wave type；
Elastic wave field separation is carried out to seismic wave vector wave field using the polarization vector of the seismic wave type after optimization.
2. elastic wave field separation method as described in claim 1, which is characterized in that seismic wave type include quasi-P waves,
Quasi-SV involves SH waves, in the case where avoiding shear wave singularity, is obtained by solving Kelvin-Christoffel equations
The polarization vector of seismic wave type, including：
Solve 3-D elastic anisotropic media Kelvin-Christoffel equations obtain quasi-P waves normalization polarize to
Amount；
Involve the polarization vector orthogonality relation of quasi-SV waves based on quasi-P waves, SH, the normalization using quasi-P waves is inclined
The polarization vectors of SH waves is calculated in the shake direction of propagation of vector sum seismic wave vector wave field, utilizes the normalization of quasi-P waves
The polarization vector of quasi-SV waves is calculated in polarization vector and the polarization vector of SH waves.
3. elastic wave field separation method as described in claim 1, which is characterized in that
Seismic wave type includes quasi-P waves, in the case where avoiding shear wave singularity, by solving Kelvin-Christoffel
Equation obtains the polarization vector of seismic wave type, including：
Solve 3-D elastic anisotropic media Kelvin-Christoffel equations obtain quasi-P waves normalization polarize to
Amount；
Optimize the polarization vector of seismic wave type using simulated annealing, including：
Utilize the normalization polarization vector of simulated annealing optimization quasi-P waves；
Involve the polarization vector orthogonality relation of quasi-SV waves based on quasi-P waves, SH, utilize the quasi-P waves after optimization
The polarization vector of SH waves is calculated in the direction of propagation of normalization polarization vector and seismic wave vector wave field, after optimization
The polarization vector of quasi-SV waves is calculated in the normalization polarization vector of quasi-P waves and the polarization vector of SH waves, wherein, it is excellent
Seismic wave type after change includes optimizing the normalization polarization vector of quasi-P waves, the polarization vector of SH waves and quasi-SV waves
Polarization vector.
4. elastic wave field separation method as described in claim 1, which is characterized in that optimize seismic wave using simulated annealing
The polarization vector of type, including：
It establishes based on the object function for maximizing norm, sets the limits of error in maximum wave-number range in object function；
The value of Optimizing operator coefficient variation in object function is searched for using simulated annealing, so that target function value meets spectrum error
Limit；
Optimizing operator is built using the value of Optimizing operator coefficient variation that search obtains；
The polarization vector of seismic wave type is multiplied by by the Optimizing operator of structure, be calculated optimization after seismic wave type polarization to
Amount.
5. elastic wave field separation method as described in claim 1, which is characterized in that utilize the inclined of the seismic wave type after optimization
The vector that shakes carries out elastic wave field separation to seismic wave vector wave field, including：
The polarization vector of seismic wave type after optimization is converted by wave-number domain to spatial domain；
Space filtering is carried out to seismic wave vector wave field using the polarization vector of spatial domain, to carry out elastic wave field separation.
6. elastic wave field separation method as claimed in claim 4, which is characterized in that object function is：
Wherein, kxFor wave number,For maximum wave number, N is Grid dimension, and 1≤n≤N/2, n are integer, bnFor Optimizing operator coefficient
Variable, Δ x are the sampling interval, and T is the limits of error.
7. elastic wave field separation method as claimed in claim 4, which is characterized in that search for target letter using simulated annealing
The value of Optimizing operator coefficient variation in number, so that target function value meets the spectrum limits of error, including：
By Optimizing operator coefficient absolute value of amplitude center damped oscillation is surrounded in [0,2] section and Optimizing operator coefficient amplitude
Condition, using simulated annealing search for object function in Optimizing operator coefficient variation value so that target function value meet spectrum
The limits of error.
8. a kind of elastic wave field separator, which is characterized in that including：
Polarization vector generation unit, is used for：In the case where avoiding shear wave singularity, by solving Kelvin-Christoffel
Equation obtains the polarization vector of seismic wave type；
Polarization vector optimizes unit, is used for：Utilize the polarization vector of simulated annealing optimization seismic wave type；
Vector wave field separative element, is used for：Seismic wave vector wave field is carried out using the polarization vector of the seismic wave type after optimization
Elastic wave field detaches.
9. a kind of computer readable storage medium, is stored thereon with computer program, which is characterized in that the program is held by processor
The step of claim 1 to 7 the method is realized during row.
10. a kind of computer equipment including memory, processor and stores the meter that can be run on a memory and on a processor
Calculation machine program, which is characterized in that the step of processor realizes claim 1 to 7 the method when performing described program.
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