CN108196303B - Elastic wave field separation method, device, storage medium and equipment - Google Patents
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Abstract
The present invention provides a kind of elastic wave field separation method, device, storage medium and equipment.This method comprises: obtaining the polarization vector of seismic wave type by solving Kelvin-Christoffel equation in the case where avoiding shear wave singularity；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 be improved wave field separation precision and efficiency.
Description
Technical Field
The invention relates to the technical field of seismic exploration data processing, in particular to an elastic wave field separation method, an elastic wave field separation device, a storage medium and elastic wave field separation equipment.
Background
Seismic exploration is widely accepted in energy mineral exploration, and in particular, multi-wave seismic exploration is greatly developed due to the characteristics of carrying abundant underground information and the like. However, the mutual interference between different waves in the multi-wave seismic data reduces the imaging resolution, thereby seriously affecting the accuracy of the geological interpretation result. To improve imaging resolution, it is often necessary to perform vector wave field separation reasonably.
When vector wave fields are separated based on polarization characteristics, the inevitable problem is how to project wave fields into corresponding polarization directions more accurately on the premise of ensuring the calculation efficiency (wave field separation is called projection in the wave number domain, and spatial filtering in the spatial domain). Due to the presence of S-wave singularities, SH and quasi-SV waves in three-dimensional TTI media are inseparable in a particular propagation direction, since it is not possible to obtain polarization vectors for both modes by solving the Kelvin-Christoffel equation. Yan and Sava (Yan, J., and P. Sava,2011, Improving the efficiency of the wavefield separation for the heterologous separation of transformed isocratic media: Geophysics,76, T65-T78, doi:10.1190/1.3581360.2011) use a conventional binomial window function and a Gauss window function to cut off the approximate pseudo-differential operator in the wave number domain, and use an IDW algorithm to interpolate the anisotropic part of the polarization vector in the space domain to reduce the calculation amount of the wavefield separation and improve the efficiency and accuracy of the wavefield separation. Moreover, the algorithm can adapt to the strong anisotropy.
In particular, the separation effect can be improved by optimizing the vector wave field separation operator. Methods for optimizing the separating operator can be divided into a window function optimization algorithm and a direct optimization algorithm. The window function optimization method is to select a proper window function to truncate the pseudo-ordinary operator, so that an optimized separation operator is obtained. The direct optimization algorithm is to directly obtain a difference coefficient which enables an error curve of a separation operator in a wave number domain to meet requirements as much as possible by using optimization methods such as a least square method, a Remez algorithm and the like. The method simplifies the design of the separation operator into the problem of optimizing the separation operator, gives a spectrum coverage range, and searches the fractional coefficient which enables the error to be as small as possible by using an optimization method.
Disclosure of Invention
The invention provides an elastic wave field separation method, an elastic wave field separation device, a storage medium and elastic wave field separation equipment, which are used for improving the precision and the efficiency of wave field separation.
The embodiment of the invention provides an elastic wave field separation method, which comprises the following steps: under the condition of avoiding transverse wave singularity, obtaining a polarization vector of a seismic wave type by solving a Kelvin-Christoffel equation; optimizing the polarization vector of a seismic wave mode by using a simulated annealing method; and performing elastic wave field separation on the seismic wave vector wave field by using the optimized polarization vector of the seismic wave mode.
In one embodiment, the seismic modes include the quasi-P waves, the quasi-SV waves, and the SH waves, and the polarization vectors of the seismic modes are obtained by solving the Kelvin-christofel equation while avoiding transverse wave singularities, including: solving a Kelvin-Christoffel equation of the three-dimensional anisotropic medium to obtain a normalized polarization vector of the quasi-P wave; based on the orthogonal relation of the polarization vectors of the quasi-P wave, the SH wave and the quasi-SV wave, the polarization vector of the SH wave is obtained by calculation according to the normalized polarization vector of the quasi-P wave and the propagation direction of the seismic wave vector wave field, and the polarization vector of the quasi-SV wave is obtained by calculation according to the normalized polarization vector of the quasi-P wave and the polarization vector of the SH wave.
In one embodiment, the seismic mode comprises a quasi-P wave, and the polarization vector of the seismic mode is obtained by solving a Kelvin-christoflel equation while avoiding transverse wave singularities, comprising: solving a Kelvin-Christoffel equation of the three-dimensional anisotropic medium to obtain a normalized polarization vector of the quasi-P wave; optimizing polarization vectors of seismic modes using simulated annealing, comprising: optimizing the normalized polarization vector of the quasi-P wave by using a simulated annealing method; based on the orthogonal relation of the polarization vectors of the quasi-P wave, the SH wave and the quasi-SV wave, the polarization vector of the SH wave is obtained through calculation by utilizing the optimized normalized polarization vector of the quasi-P wave and the propagation direction of a seismic wave vector wave field, and the polarization vector of the quasi-SV wave is obtained through calculation by utilizing the optimized normalized polarization vector of the quasi-P wave and the optimized polarization vector of the SH wave, wherein the optimized seismic wave mode comprises the optimized normalized polarization vector of the quasi-P wave, the optimized polarization vector of the SH wave and the optimized polarization vector of the quasi-SV wave.
In one embodiment, optimizing the polarization vectors of seismic modes using simulated annealing comprises: establishing a target function based on the maximized norm, and setting an error limit in the maximum wave number range in the target function; searching the value of the optimized operator coefficient variable in the objective function by using a simulated annealing method so as to enable the objective function value to meet the error limit; constructing an optimization operator by using the value of the optimization operator coefficient variable obtained by searching; and multiplying the polarization vector of the seismic wave form by the constructed optimization operator to calculate and obtain the polarization vector of the optimized seismic wave form.
In one embodiment, elastic wave field separation of a seismic wave vector wavefield using polarization vectors of optimized seismic wave modes comprises: converting the polarization vector of the optimized seismic wave form from a wave number domain to a space domain; and carrying out spatial filtering on the seismic wave vector wave field by using the polarization vector of the spatial domain so as to carry out elastic wave field separation.
In one embodiment, the objective function is:
wherein k isxIn terms of the wave number, the number of waves,is the maximum wave number, N is the number of grid points, N is more than or equal to 1 and less than or equal to N/2, N is an integer, bnTo optimize operator coefficient variables, Δ x is the sampling interval and T is the error limit.
In one embodiment, searching for values of optimization operator coefficient variables in the objective function using a simulated annealing method such that the objective function values satisfy an error limit, comprises: and searching the value of an optimization operator coefficient variable in the objective function by using a simulated annealing method according to the condition that the absolute value of the amplitude of the optimization operator coefficient is in the interval of [0,2] and the attenuation oscillation of the amplitude of the optimization operator coefficient around the central position so as to enable the objective function value to meet the error limit.
An embodiment of the present invention further provides an elastic wave field separation apparatus, including: a polarization vector generation unit for: under the condition of avoiding transverse wave singularity, obtaining a polarization vector of a seismic wave type by solving a Kelvin-Christoffel equation; a polarization vector optimization unit to: optimizing the polarization vector of a seismic wave mode by using a simulated annealing method; a vector wave field separating unit for: and performing elastic wave field separation on the seismic wave vector wave field by using the optimized polarization vector of the seismic wave mode.
The embodiments of the present invention also provide a computer readable storage medium, on which a computer program is stored, which when executed by a processor implements the steps of the method described in the above embodiments.
The embodiment of the present invention further provides a computer device, which includes a memory, a processor, and a computer program stored in the memory and capable of running on the processor, and when the processor executes the computer program, the steps of the method described in each of the above embodiments are implemented.
According to the elastic wave field separation method, the device, the storage medium and the computer equipment, under the condition of avoiding transverse wave singularity, solving of polarization vectors avoiding singularity and optimization of the polarization vectors can be combined, the problem that the singularity of two transverse waves cannot be separated in a specific direction can be solved, the polarization vectors of seismic wave modes can be obtained through solving a Kelvin-Christoffel equation, and the polarization vectors of various wave modes can be successfully obtained. The polarization vector of the seismic wave mode is optimized by using a simulated annealing method, so that the convergence can be fast and successful, the optimal polarization vector can be obtained, and the precision and the efficiency of elastic wave field separation can be further improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts. In the drawings:
FIG. 1 is a schematic flow chart of an elastic wave field separation method according to an embodiment of the present invention;
FIG. 2 is a schematic flow diagram of a method for obtaining polarization vectors for seismic modes by solving the Kelvin-Christoffel equation in accordance with an embodiment of the present invention;
FIG. 3 is a schematic flow chart illustrating a method for optimizing polarization vectors of seismic modes using simulated annealing in accordance with an embodiment of the present invention;
FIG. 4 is a schematic flow chart of a method for optimizing polarization vectors of seismic modes using simulated annealing in accordance with another embodiment of the present invention;
FIG. 5 is a schematic flow chart illustrating a method for elastic wave field separation of a seismic wave vector wavefield using polarization vectors of optimized seismic wave patterns in accordance with an embodiment of the present invention;
FIGS. 6-8 are wave field snapshots of the X, Y, and Z components, respectively, of an impulse response numerical simulation result in accordance with an embodiment of the present invention;
FIGS. 9-11 are wavefield snapshots of the quasi-P, quasi-SV, and SH waves, respectively, after the wavefield separation shown in FIGS. 6-8;
fig. 12 is a schematic structural view of an elastic wave field separating apparatus according to an embodiment of the present invention;
FIG. 13 is a schematic structural diagram of a polarization vector generation unit according to an embodiment of the present invention;
FIG. 14 is a schematic structural diagram of a polarization vector optimization unit according to an embodiment of the present invention;
FIG. 15 is a schematic structural diagram of a polarization vector optimization unit according to another embodiment of the present invention;
figure 16 is a schematic diagram of the structure of a vector wave field separation unit in an embodiment of the invention;
fig. 17 is a schematic structural diagram of a computer device according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the embodiments of the present invention are further described in detail below with reference to the accompanying drawings. The exemplary embodiments and descriptions of the present invention are provided to explain the present invention, but not to limit the present invention.
Fig. 1 is a schematic flow chart of an elastic wave field separation method according to an embodiment of the present invention. As shown in fig. 1, the method for separating an elastic wave field according to the present embodiment may include:
step S110: under the condition of avoiding transverse wave singularity, obtaining a polarization vector of a seismic wave type by solving a Kelvin-Christoffel equation;
step S120: optimizing the polarization vector of a seismic wave mode by using a simulated annealing method;
step S130: and performing elastic wave field separation on the seismic wave vector wave field by using the optimized polarization vector of the seismic wave mode.
In three-dimensional anisotropic media, such as three-dimensional TTI (transverse Isotropic) media, for a particular propagation direction, such as a direction perpendicular or parallel to the TI (transverse Isotropic) media symmetry axis, there exist pure P-waves and S-waves, and the S-waves are split, but the split two S-waves have the same phase velocity and propagate with the same phase velocity, which is the singularity of the S-waves. Due to the presence of S-wave singularities, SH and quasi-SV waves in three-dimensional TTI media are inseparable in a particular propagation direction because it is not possible to obtain polarization vectors for both modes by solving the Kelvin-Christoffel equation. In the above step S110, in the case of avoiding singularity, for example, in the case of avoiding singularity of transverse wave (S-wave), polarization vectors of various seismic modes can be obtained by solving the Kelvin-christofel equation.
In the step S120, the simulated annealing method can be obtained based on the simulated annealing method proposed by Metropolis in 1953 in the thermodynamic field, and belongs to a random algorithm. The simulated annealing algorithm searches for new solutions in a random sampling manner and accepts poorer solutions with a probability that becomes progressively smaller as the temperature decreases. The simulated annealing algorithm is an extension of a local search algorithm, has the advantage of being capable of jumping out of a local optimal trap and can be quickly converged to a global optimal solution. The selection of the initial temperature (initial value of variable) and the final temperature (final value of variable) is very important when the simulated annealing method is used for optimization, and the length of the search is directly determined, and whether the solution meeting the upper limit of the error can be successfully searched.
In the above step S130, projection may be performed in a wave number domain, or spatial filtering may be performed in a spatial domain, so as to implement elastic wave field separation.
In this embodiment, under the condition of avoiding the singularity of the transverse wave, the solution of the polarization vector avoiding the singularity and the optimization of the polarization vector can be combined, the problem that the singularities of the two transverse waves cannot be separated in a specific direction can be avoided, the polarization vectors of seismic wave modes can be obtained by solving the Kelvin-christofel equation, and the polarization vectors of various wave modes can be successfully obtained. The polarization vector of the seismic wave mode is optimized by using a simulated annealing method, so that the convergence can be fast and successful, the optimal polarization vector can be obtained, and the precision and the efficiency of elastic wave field separation can be further improved.
In some embodiments, the quasi-P waves in three-dimensional anisotropic media (e.g., TTI media) can be considered to have no singularity problems, and the polarization vectors of the three modes (quasi-P waves, quasi-SV waves, and SH waves) can be considered to be mutually orthogonal. The polarization vectors of the quasi-P wave can be firstly obtained, then the polarization vectors of the quasi-SV wave and the SH wave are obtained by utilizing the polarization vectors of the quasi-P wave, and then the vector wave field is projected to the corresponding direction to separate the wave field. In the propagation direction of the singularity, the amplitude of the polarization vector of the two S waves is found to be zero, so that the problem of the singularity can be avoided.
In the above steps S110 and S120, the polarization vectors of various wave modes may be obtained first, then the polarization vectors of various wave modes are optimized, and finally the wave field decomposition is performed by using all the optimized polarization vectors. Alternatively, the polarization vector of a certain mode, for example, the polarization vector of a quasi-P wave, may be obtained first, then the polarization vector of the mode is optimized, and then the polarization vectors of other modes, for example, the polarization vectors of a quasi-SV wave and an SH wave, are obtained using the optimized polarization vector of the mode, and finally the wave field decomposition is performed using the optimized polarization vector of the mode and the obtained polarization vectors of other modes.
FIG. 2 is a schematic flow chart of a method for obtaining polarization vectors for seismic modes by solving the Kelvin-Christoffel equation in accordance with an embodiment of the present invention. Seismic modes may include the quasi-P wave, the quasi-SV wave, and the SH wave. As shown in fig. 2, in step S110, the method for obtaining the polarization vector of the seismic wave pattern by solving the Kelvin-christofel equation may include:
step S111: solving a Kelvin-Christoffel equation of the three-dimensional anisotropic medium to obtain a normalized polarization vector of the quasi-P wave;
step S112: based on the orthogonal relation of the polarization vectors of the quasi-P wave, the SH wave and the quasi-SV wave, the polarization vector of the SH wave is obtained by calculation according to the normalized polarization vector of the quasi-P wave and the propagation direction of the seismic wave vector wave field, and the polarization vector of the quasi-SV wave is obtained by calculation according to the normalized polarization vector of the quasi-P wave and the polarization vector of the SH wave.
After the normalized polarization vector of the quasi-P wave, the polarization vector of the SH wave, and the polarization vector of the quasi-SV wave are obtained in steps S111 to S112, the polarizations (the normalized polarization vector of the quasi-P wave, the polarization vector of the SH wave, and the polarization vector of the quasi-SV wave) can be optimized by the simulated annealing method in step S120. The polarization vector of the quasi-P wave is obtained by using only the Kelvin-Christoffel equation, and then the polarization vectors of other wave modes are obtained by using the normalized polarization vector of the quasi-P wave based on the orthogonal relation of the polarization vectors of the quasi-P wave, the SH wave and the quasi-SV wave, so that the singularity of transverse waves can be avoided.
In an embodiment, in step S111, the polarization vector of the quasi-P wave may be obtained by solving a feature value of a Kelvin-christofel equation, and then the polarization vector of the quasi-P wave is normalized to obtain a normalized polarization vector of the quasi-P wave.
In an embodiment, the seismic mode may include a quasi-P wave, and the step S110 of obtaining the polarization vector of the seismic mode by solving the Kelvin-christofel equation may include: and solving a Kelvin-Christoffel equation of the three-dimensional anisotropic medium to obtain a normalized polarization vector of the quasi-P wave. And only solving the normalized polarization vector of the quasi-P wave by using a Kelvin-Christoffel equation, so that the singularity of the transverse wave can be avoided.
FIG. 3 is a flow chart illustrating a method for optimizing polarization vectors for seismic modes using simulated annealing in accordance with an embodiment of the present invention. As shown in fig. 3, the method for optimizing the polarization vector of the seismic mode by using the simulated annealing method in step S120 may include:
step S1211: optimizing the normalized polarization vector of the quasi-P wave by using a simulated annealing method;
step S1212: based on the orthogonal relation of the polarization vectors of the quasi-P wave, the SH wave and the quasi-SV wave, the polarization vector of the SH wave is obtained through calculation by utilizing the optimized normalized polarization vector of the quasi-P wave and the propagation direction of a seismic wave vector wave field, and the polarization vector of the quasi-SV wave is obtained through calculation by utilizing the optimized normalized polarization vector of the quasi-P wave and the optimized polarization vector of the SH wave, wherein the optimized seismic wave mode comprises the optimized normalized polarization vector of the quasi-P wave, the optimized polarization vector of the SH wave and the optimized polarization vector of the quasi-SV wave.
In this embodiment, only the normalized polarization vector of the quasi-P wave can be optimized, and then the polarization vectors of other wave modes can be obtained based on the optimized normalized polarization vector, so that the calculation amount of the optimization process can be reduced.
FIG. 4 is a schematic flow chart of a method for optimizing polarization vectors for seismic modes using simulated annealing in accordance with another embodiment of the present invention. As shown in fig. 4, in step S120, the method for optimizing the polarization vector of the seismic mode by using the simulated annealing method may include:
step S1221: establishing a target function based on the maximized norm, and setting an error limit in the maximum wave number range in the target function;
step S1222: searching the value of the optimized operator coefficient variable in the objective function by using a simulated annealing method so as to enable the objective function value to meet the error limit;
step S1223: constructing an optimization operator by using the value of the optimization operator coefficient variable obtained by searching;
step S1224: and multiplying the polarization vector of the seismic wave form by the constructed optimization operator to calculate and obtain the polarization vector of the optimized seismic wave form.
In this embodiment, an optimization operator can be constructed by searching for a value of an optimization operator coefficient variable that meets requirements, and a polarization vector is further optimized. Wavefield separation accuracy may be improved by reducing the error margin.
In an embodiment, a specific implementation for step S1211 described above may be similar to FIG. 4, and the polarization vector of the seismic waveform in step S1224 is replaced with the normalized polarization vector of the quasi-P wave.
In an embodiment, in step S1221, the objective function may be:
wherein k isxIn terms of the wave number, the number of waves,is the maximum wave number, N is the number of grid points, N is more than or equal to 1 and less than or equal to N/2, N is an integer, bnTo optimize operator coefficient variables, Δ x is the sampling interval and T is the error limit.
In an embodiment, in step S1222, the method for searching the value of the optimization operator coefficient variable in the objective function by using the simulated annealing method so that the objective function value satisfies the error limit may include: in terms of the absolute value of the coefficient amplitude of the optimization operator at [0,2]And under the condition that the interval and the amplitude of the optimization operator coefficient are damped and oscillated around the central position, searching the value of the optimization operator coefficient variable in the objective function by using a simulated annealing method so as to enable the objective function value to meet the error limit. In an embodiment, the operator coefficients b are optimizednShould be an oscillation attenuated around a central position 0, i.e. | bn|＞|bn+1I, and | bn||bn+1N/2, | < 0, N ═ 1, 2. In this embodiment, the optimization operator coefficient is searched by using the condition, so that the search range can be reduced, and the optimization efficiency can be improved.
FIG. 5 is a flow chart illustrating a method for elastic wave field separation of a seismic wave vector wavefield using polarization vectors of optimized seismic wave patterns in an embodiment of the present invention. As shown in fig. 5, in step S130, the method for performing elastic wave field separation on the seismic wave vector wave field by using the optimized polarization vector of the seismic wave pattern may include:
step S131: converting the polarization vector of the optimized seismic wave form from a wave number domain to a space domain;
step S132: and carrying out spatial filtering on the seismic wave vector wave field by using the polarization vector of the spatial domain so as to carry out elastic wave field separation.
An example of a wavefield separation method of an embodiment of the present invention is illustrated below, taking quasi-P waves in a three-dimensional non-uniform TTI medium as an example.
For a non-uniform medium, theoretically, anisotropic parameters of each spatial grid node need to be utilized, a separation operator is obtained for each node, and then the model is subjected to spatial filtering in a spatial domain to perform vector wave field separation:
qP＝LPx[Ux]+LPy[Uz]+LPz[Uy] (1)
where qP denotes the wave field of the quasi-P wave in the spatial domain, Ux、UyAnd UzRepresenting three directional components of the coupled vector wavefield, LPx、LPyAnd LPzThe quasi-differential operators respectively represent X, Y and Z directions; []Representing spatial convolution (filtering).
And in the space domain, performing space filtering on the vector wave field by using a quasi-differential operator to obtain a separated quasi-P wave field. In order to accurately separate the longitudinal and transverse wave fields, it is necessary to calculate the polarization vectors corresponding to the wave modes, and then project the vector wave field to the polarization vector direction to separate the wave field.
Under the three-dimensional condition, solving a Kelvin-Christoffel equation of the three-dimensional TTI medium can obtain a quadrature-P wave, a quadrature-SV wave and an SH wave polarization vector, wherein P is used as PP、pSVAnd pSHExpressed in normalized wavenumber vectorDenotes the propagation direction of the wave, where kx、kyAnd kzRepresenting the components of the wave number in the x, y and z directions, respectively, | k | represents the modulus of the wave number vector,representing the components of the normalized wave number in the x, y and z directions, respectively.
The wave field separation method in the three-dimensional TTI medium obtains the normalized polarization vector of the quasi-P wave by solving the Kelvin-Christoffel equationRespectively representing normalized polarization vectorsComponents in the x, y and z directions), the direction of propagation of the wave isThe polarization vectors of the quasi-SV and SH waves can be calculated from the normalized polarization vectors and propagation directions of the quasi-P waves.
In the embodiment, the normalized polarization vector of the quasi-P wave can be obtained by solving the Kelvin-Christoffel equation and is recorded asThe propagation direction of the wave isThe polarization vector p of the SH waveSHIt can be calculated from the normalized polarization vector and propagation direction of the quasi-P wave:
wherein p isSHx、pSHyAnd pSHzRespectively representing polarization vectors p of SH wavesSHThe components in the x, y and z directions.
In an embodiment, the polarization vector of the quasi-SV wave may be calculated from the normalized polarization vector of the quasi-P wave and the polarization vector of the SH wave:
the fixed propagation direction is a propagation direction in which S wave singularity exists, and assuming that the propagation direction is parallel to the TI medium symmetry axis, the polarization direction of the P wave is parallel to the propagation direction in the propagation direction, which is recorded as:
by substituting equation (4) into equations (2) and (3), the polarization vectors of the two S-waves in the propagation direction can be obtained:
pSV＝(0,0,0),pSH＝(0,0,0) (5)
it can be seen from the formula (5) that the amplitudes of the polarization vectors of the two S-waves are zero in the propagation direction in which the singularity exists, thereby avoiding the problem of singularity.
In the embodiment, solving the Kelvin-christofel equation to obtain the normalized polarization vector of the quasi-P wave requires format optimization to obtain higher precision, so that a global optimization operator is introduced to optimize a separation operator:
according to the sampling theory of discrete signals, a band-limited continuous signal f (x) can be sampled with a uniformly sampled signal fnAnd (3) interpolating and reconstructing through a sinc function:
where, Δ x is the sampling interval,for the cut-off wavenumber, x is the consecutive point, and n represents the nth sampling point.
If the first derivative is calculated for the left and right sides of equation (6), and x is taken to be 0, then it can be obtained:
and (3) a window function with the length of N +1 points exists, N is an even number, and the formula (7) is truncated to obtain a conventional finite difference operator.
Wherein,
since the singular point n is present as 0, in order to avoid singularity, equation (7) is expressed as:
wherein,fnand f-nRepresenting a uniformly sampled signal, the windowing function, after truncation, has:
wherein,bnrepresents the optimization operator coefficients, w (n) represents the truncated window function.
Fourier transform of equation (10) can yield:
the left side of equation (11) is the analytic solution, and the right side is the numerical solution.
In the embodiment, in order to meet the requirement of wide-band seismic simulation, the wave number coverage range of the difference operator can be widened. In some embodiments, the maximum absolute spectral error over a range of wavenumbers is controlled using a maximized norm, and the objective function is established as follows:
is the maximum wavenumber range that the optimization operator can cover, and T is the maximum allowable error limit. The upper error limit of the finite difference operator (separation operator) can be directly controlled by T. The error is quickly searched by using a quickly-converged global optimization algorithmAnd (4) limiting the global optimal optimization operator coefficient. By increasing continuouslyThe optimized staggered grid optimization operator coefficient with larger spectrum coverage range can be obtained. Therefore, the objective function established based on the maximized norm of the present embodiment is more flexible than the objective function established by the existing least squares method.
In the embodiment, in order to achieve the purpose of reducing the optimization cost, the inventor discovers, according to the sinc interpolation theory: (1) n/2 optimization operator coefficients are arranged in an optimized N-point grid finite operator (separation operator); (2) the absolute value of the amplitude of each optimization operator coefficient is 0,2]Within the interval; (3) the amplitude of the optimization operator coefficient should be an oscillation attenuated around the central position 0, i.e. | bn|＞|bn+1I, and | bn||bn+1N/2, | < 0, N ═ 1, 2. The optimization operator coefficients can be searched according to the above (1) to (3) principles. Thus, b can be determined by determining only1To bnAnd the whole operator is optimized.
For a high-order grid finite difference operator, for example, N is 16, 8 optimization operator coefficients need to be optimized, and the method belongs to the problem of extremum solving of a high-dimensional complex function. For such a complex objective function, the linear search method and the least square method cannot be solved flexibly. The embodiment of the invention directly searches the optimal optimization operator coefficient for the target problem by adopting a simulated annealing method. And the value range of each optimization operator coefficient can be set according to the conditions (2) and (3), and the solution result of the optimization operator coefficients is limited by the condition (2), so that the search range can be greatly reduced, and the simulated annealing method is more efficient.
In an embodiment, for the second-order central finite difference operator (separation operator), the Z-transform in the spatial difference format has:
wherein Z is a complex variable, F2(Z) is a Z-transform representation of a second-order-center finite difference operator, Z1And Z-1Indicating the index of the Z variable.
Transforming both sides of equation (13) to the wavenumber domain and performing euler expansion, we can get:
F2(k)＝-isin(k) (14)
wherein k represents a wave number, F2(k) Is a wavenumber domain representation of the second-order central finite difference operator.
The two sides of equation (14) are multiplied by i and divided by k to obtain the second-order optimization operator of the wavenumber domain:
wherein, W2(k) Representing a second order optimization operator with the wave number k as a variable.
Similar to the above method, optimization operators of fourth order, sixth order, etc. can be obtained. The optimization operator of any order can be:
wherein, W2n(k) And (4) an optimization operator (wave number domain) of 2n order with the wave number k as a variable. bnThe method is characterized in that the optimized operator coefficient obtained by calculation is searched by using a simulated annealing method.
In the embodiment of the invention, the global optimal algorithm and the singularity-avoiding three-dimensional wave field separation algorithm are combined, the global optimal solution is solved by using a simulated annealing method, the separation operator is optimized by using the optimal solution, and the inverse transformation is carried out back to the space domain to obtain the pseudo-differential operator. The precision of the separated operator obtained by optimization is high, the precision of the high-order operator can be achieved by the low-order operator, and the calculation amount is effectively saved. The polarization vector of the SH wave can be obtained by solving the normalized polarization vector of the quasi-P wave and knowing the propagation direction, and then the polarization vector of the quasi-SV wave is obtained by calculation through the normalized polarization vector of the quasi-P wave and the polarization vector of the SH wave. The problem that two transverse waves cannot be separated due to the singularity of the transverse waves in the specific direction of the three-dimensional TI medium can be solved.
In an embodiment, the elastic wave wavefield separation method may include two steps of (1) optimizing a separation operator using a global optimization method and (2) avoiding singularity of a three-dimensional wavefield separation algorithm.
In an embodiment, optimizing the separation operator using the global optimization method may include the steps of:
(1) setting an upper error limit T;
(2) wave number is withinAfter uniform dispersion in the rangePerforming the subsequent steps (3) to (4) on each wave number, and searching for the optimal optimization operator coefficient meeting T;
(3) and carrying out global search by using a simulated annealing algorithm, wherein key parameters needing to be set comprise: marklov chain length, start temperature, end temperature, and step size factor; in addition, the dimension M of the independent variable and the value range of each independent variable, that is, the number of the optimized operator coefficients to be optimized by the 2M order difference operator and the value range of each optimized operator coefficient are also provided.
(4) If the searched optimization operator coefficient enables the objective function value to meet the error limit, returning to the step (2), and if k is k +1, performing global optimization on the next wave number sampling point; and if not, stopping the process, and taking the optimization operator coefficient of the last wave number sampling point as the optimal solution to output.
(5) And optimizing the separating operator by using a 2M-order optimization difference operator.
In an embodiment, the flow of the three-dimensional wavefield separation algorithm for avoiding singularity may be as follows:
(1) solving a Kelvin-Christoffel equation to obtain a normalized polarization vector of the quasi-P wave;
(2) calculating the polarization vector of the SH wave according to the normalized polarization vector and the propagation direction of the Quasi-P wave;
(3) and calculating the polarization vector of the quasi-SV wave according to the normalized polarization vector of the quasi-P wave and the polarization vector of the SH wave.
In the embodiment, the normalized polarization vector obtained in the step (1) can be optimized by using the global optimization algorithm, and in the steps (2) and (3), the polarization vector of the SH wave and the polarization vector of the quasi-SV wave are solved.
In other embodiments, other separation operator optimization algorithms, such as window function, least squares, etc., may be selected as desired.
FIGS. 6-8 are wave field snapshots of the X, Y, and Z components, respectively, of an impulse response numerical simulation result in accordance with an embodiment of the present invention. FIGS. 9-11 are wavefield snapshots of the quasi-P, quasi-SV, and SH waves, respectively, after the wavefield separation shown in FIGS. 6-8. Fig. 9 to 11 show the results of the wave field separation in the three-dimensional uniform TTI anisotropic medium, and comparing fig. 6 to 8 with fig. 9 to 11, it can be seen that the quasi-P wave, the quasi-SV wave and the SH wave are all separated cleanly, without the interference of another wave, and the vector wave field in the three-dimensional TTI medium is well separated. Therefore, the separation strategy of the embodiment of the invention under the three-dimensional model is effective.
Firstly, the global optimization operator can optimize the quasi-differential operator, so that the quasi-differential operator has higher separation precision, and meanwhile, the calculation efficiency is greatly improved. Secondly, the algorithm for avoiding the singularity of the three-dimensional wave field can avoid the problem that the singularity of two shear waves can not be separated in a specific direction. Therefore, the method of the embodiment of the invention introduces the global optimization operator and the wave field separation algorithm for avoiding the singularity of the three-dimensional wave field, and can improve the precision and the efficiency of the three-dimensional vector wave field separation. The separation operator is optimized by the global optimization operator, and the separation operator with higher precision can be obtained. The wave field is separated by utilizing an algorithm for avoiding singularity, so that the problem that the two shear waves cannot be separated due to the singularity in a specific direction can be solved.
Based on the same inventive concept as the elastic wave field separation method shown in fig. 1, the embodiment of the present application further provides an elastic wave field separation device, as described in the following embodiments. Because the principle of solving the problems of the elastic wave field separation device is similar to that of the elastic wave field separation method, the implementation of the elastic wave field separation device can refer to the implementation of the elastic wave field separation method, and repeated parts are not described again.
Fig. 12 is a schematic structural view of an elastic wave field separating device according to an embodiment of the present invention. As shown in fig. 12, the elastic wave field separation device according to the present embodiment may include: a polarization vector generating unit 210, a polarization vector optimizing unit 220, and a vector wave field separating unit 230, which are connected in sequence.
A polarization vector generation unit 210 for: under the condition of avoiding transverse wave singularity, obtaining a polarization vector of a seismic wave type by solving a Kelvin-Christoffel equation;
a polarization vector optimization unit 220 for: optimizing the polarization vector of a seismic wave mode by using a simulated annealing method;
a vector wave field separating unit 230 for: and performing elastic wave field separation on the seismic wave vector wave field by using the optimized polarization vector of the seismic wave mode.
Fig. 13 is a schematic structural diagram of a polarization vector generation unit in an embodiment of the present invention. The seismic wave patterns include a quasi-P wave, a quasi-SV wave, and an SH wave, and as shown in fig. 13, the polarization vector generation unit 210 may include: a quasi-P wave polarization vector generation block 211 and an SH-wave and quasi-SV wave polarization vector generation block 212, which are connected to each other.
A quasi-P wave polarization vector generation module 211 for: solving a Kelvin-Christoffel equation of the three-dimensional anisotropic medium to obtain a normalized polarization vector of the quasi-P wave;
an SH wave and quasi-SV wave polarization vector generation module 212 to: based on the orthogonal relation of the polarization vectors of the quasi-P wave, the SH wave and the quasi-SV wave, the polarization vector of the SH wave is obtained by calculation according to the normalized polarization vector of the quasi-P wave and the propagation direction of the seismic wave vector wave field, and the polarization vector of the quasi-SV wave is obtained by calculation according to the normalized polarization vector of the quasi-P wave and the polarization vector of the SH wave.
In an embodiment, the seismic modes may include quasi-P waves, and the polarization vector generation unit 210 may include: a quasi-P wave polarization vector solving module to: and solving a Kelvin-Christoffel equation of the three-dimensional anisotropic medium to obtain a normalized polarization vector of the quasi-P wave.
Fig. 14 is a schematic structural diagram of a polarization vector optimization unit according to an embodiment of the present invention. As shown in fig. 14, the polarization vector optimization unit 220 may include: a quasi-P wave polarization vector optimization module 2211 and a quasi-SV wave polarization vector optimization module 2212, which are connected to each other.
A quasi-P wave polarization vector optimization module 2211 for: optimizing the normalized polarization vector of the quasi-P wave by using a simulated annealing method;
an SH wave and quasi-SV wave polarization vector optimization module 2212 to: based on the orthogonal relation of the polarization vectors of the quasi-P wave, the SH wave and the quasi-SV wave, the polarization vector of the SH wave is obtained through calculation by utilizing the optimized normalized polarization vector of the quasi-P wave and the propagation direction of a seismic wave vector wave field, and the polarization vector of the quasi-SV wave is obtained through calculation by utilizing the optimized normalized polarization vector of the quasi-P wave and the optimized polarization vector of the SH wave, wherein the optimized seismic wave mode comprises the optimized normalized polarization vector of the quasi-P wave, the optimized polarization vector of the SH wave and the optimized polarization vector of the quasi-SV wave.
Fig. 15 is a schematic structural diagram of a polarization vector optimization unit according to another embodiment of the present invention. As shown in fig. 15, the polarization vector optimization unit 220 may include: an objective function establishing module 2221, an optimization operator coefficient determining module 2222, an optimization operator establishing module 2223 and a vector optimization calculating module 2224, which are connected in sequence.
An objective function establishing module 2221 configured to: establishing a target function based on the maximized norm, and setting an error limit in the maximum wave number range in the target function;
an optimization operator coefficient determination module 2222 for: searching the value of the optimized operator coefficient variable in the objective function by using a simulated annealing method so as to enable the objective function value to meet the error limit;
an optimization operator construction module 2223 for: constructing an optimization operator by using the value of the optimization operator coefficient variable obtained by searching;
a vector optimization calculation module 2224 to: and multiplying the polarization vector of the seismic wave form by the constructed optimization operator to calculate and obtain the polarization vector of the optimized seismic wave form.
In an embodiment, the objective function establishing module 2221 is further configured to execute: the objective function is:
wherein k isxIn terms of the wave number, the number of waves,is the maximum wave number, N is the number of grid points, N is more than or equal to 1 and less than or equal to N/2, N is an integer, bnTo optimize operator coefficient variables, Δ x is the sampling interval and T is the error limit.
In an embodiment, the optimization operator coefficient determining module 2222 may include: a condition search module to: and searching the value of an optimization operator coefficient variable in the objective function by using a simulated annealing method according to the condition that the absolute value of the amplitude of the optimization operator coefficient is in the interval of [0,2] and the attenuation oscillation of the amplitude of the optimization operator coefficient around the central position so as to enable the objective function value to meet the error limit.
Figure 16 is a schematic diagram of the structure of a vector wave field separating element in an embodiment of the present invention. As shown in fig. 16, the vector wave field separating unit 230 may include: a domain conversion module 231 and a wave field separation module 232, which are connected to each other.
A domain conversion module 231 configured to: converting the polarization vector of the optimized seismic wave form from a wave number domain to a space domain;
a wave field separation module 232 to: and carrying out spatial filtering on the seismic wave vector wave field by using the polarization vector of the spatial domain so as to carry out elastic wave field separation.
Embodiments of the present invention further provide a computer-readable storage medium, on which a computer program is stored, where the computer program, when executed by a processor, implements the steps of the method described in the above embodiments.
The invention also provides computer equipment. As shown in fig. 17, the computer device 300 includes a memory 310, a processor 320, and a computer program stored on the memory 310 and executable on the processor 320, wherein the processor 320 executes the computer program to implement the steps of the method according to the above embodiments.
In summary, the elastic wave field separation method, the elastic wave field separation device, the elastic wave field separation storage medium and the computer equipment can combine the polarization vector solution for avoiding singularity and the polarization vector optimization under the condition of avoiding transverse wave singularity, can avoid the problem that the singularity of two transverse waves cannot be separated in a specific direction, and can successfully obtain the polarization vectors of various wave modes by obtaining the polarization vectors of the seismic wave modes by solving the Kelvin-christofel equation. The polarization vector of the seismic wave mode is optimized by using a simulated annealing method, so that the convergence can be fast and successful, the optimal polarization vector can be obtained, and the precision and the efficiency of elastic wave field separation can be further improved.
In the description herein, reference to the description of the terms "one embodiment," "a particular embodiment," "some embodiments," "for example," "an example," "a particular example," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. The sequence of steps involved in the various embodiments is provided to schematically illustrate the practice of the invention, and the sequence of steps is not limited and can be suitably adjusted as desired.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are only exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (9)
1. An elastic wave field separation method, comprising:
under the condition of avoiding transverse wave singularity, obtaining a polarization vector of a seismic wave type by solving a Kelvin-Christoffel equation;
optimizing the polarization vector of a seismic wave mode by using a simulated annealing method;
performing elastic wave field separation on the seismic wave vector wave field by using the optimized polarization vector of the seismic wave mode; the method comprises the following steps of obtaining a polarization vector of the seismic wave mode by solving a Kelvin-Christoffel equation under the condition of avoiding transverse wave singularity, wherein the seismic wave mode comprises a quasi-P wave, a quasi-SV wave and an SH wave, and the method comprises the following steps:
solving a Kelvin-Christoffel equation of the three-dimensional anisotropic medium to obtain a normalized polarization vector of the quasi-P wave;
based on the orthogonal relation of the polarization vectors of the quasi-P wave, the SH wave and the quasi-SV wave, the polarization vector of the SH wave is obtained by calculation according to the normalized polarization vector of the quasi-P wave and the propagation direction of the seismic wave vector wave field, and the polarization vector of the quasi-SV wave is obtained by calculation according to the normalized polarization vector of the quasi-P wave and the polarization vector of the SH wave.
2. The elastic wave field separation method of claim 1,
the seismic modes include quasi-P waves, and the polarization vectors of the seismic modes are obtained by solving a Kelvin-christoflel equation under the condition of avoiding the singularity of transverse waves, and the method comprises the following steps:
solving a Kelvin-Christoffel equation of the three-dimensional anisotropic medium to obtain a normalized polarization vector of the quasi-P wave;
optimizing polarization vectors of seismic modes using simulated annealing, comprising:
optimizing the normalized polarization vector of the quasi-P wave by using a simulated annealing method;
based on the orthogonal relation of the polarization vectors of the quasi-P wave, the SH wave and the quasi-SV wave, the polarization vector of the SH wave is obtained through calculation by utilizing the optimized normalized polarization vector of the quasi-P wave and the propagation direction of a seismic wave vector wave field, and the polarization vector of the quasi-SV wave is obtained through calculation by utilizing the optimized normalized polarization vector of the quasi-P wave and the optimized polarization vector of the SH wave, wherein the optimized seismic wave mode comprises the optimized normalized polarization vector of the quasi-P wave, the optimized polarization vector of the SH wave and the optimized polarization vector of the quasi-SV wave.
3. The method of elastic wave field separation of claim 1 wherein optimizing the polarization vectors of the seismic modes using simulated annealing comprises:
establishing a target function based on the maximized norm, and setting an error limit in the maximum wave number range in the target function;
searching the value of the optimized operator coefficient variable in the objective function by using a simulated annealing method so as to enable the objective function value to meet the spectral error limit;
constructing an optimization operator by using the value of the optimization operator coefficient variable obtained by searching;
and multiplying the polarization vector of the seismic wave form by the constructed optimization operator to calculate and obtain the polarization vector of the optimized seismic wave form.
4. The method of elastic wave field separation of claim 1 wherein elastic wave field separation of a seismic wave vector wavefield using polarization vectors of optimized seismic wave modes comprises:
converting the polarization vector of the optimized seismic wave form from a wave number domain to a space domain;
and carrying out spatial filtering on the seismic wave vector wave field by using the polarization vector of the spatial domain so as to carry out elastic wave field separation.
5. A method for separation of an elastic wave field according to claim 3, characterized in that the objective function is:
wherein k isxIn terms of the wave number, the number of waves,is the maximum wave number, N is the number of grid points, N is more than or equal to 1 and less than or equal to N/2, N is an integer, bnTo optimize operator coefficient variables, Δ x is the sampling interval and T is the error limit.
6. The method for separating an elastic wave field according to claim 3, wherein searching for the value of the optimization operator coefficient variable in the objective function using a simulated annealing method so that the objective function value satisfies the spectral error limit comprises:
and searching the value of an optimization operator coefficient variable in the objective function by using a simulated annealing method according to the condition that the absolute value of the amplitude of the optimization operator coefficient is in the interval of [0,2] and the attenuation oscillation of the amplitude of the optimization operator coefficient around the central position, so that the objective function value meets the spectrum error limit.
7. An elastic wave field separation device characterized by comprising:
a polarization vector generation unit for: under the condition of avoiding transverse wave singularity, obtaining a polarization vector of a seismic wave type by solving a Kelvin-Christoffel equation;
a polarization vector optimization unit to: optimizing the polarization vector of a seismic wave mode by using a simulated annealing method;
a vector wave field separating unit for: performing elastic wave field separation on the seismic wave vector wave field by using the optimized polarization vector of the seismic wave mode;
the method comprises the following steps of obtaining a polarization vector of the seismic wave mode by solving a Kelvin-Christoffel equation under the condition of avoiding transverse wave singularity, wherein the seismic wave mode comprises a quasi-P wave, a quasi-SV wave and an SH wave, and the method comprises the following steps:
solving a Kelvin-Christoffel equation of the three-dimensional anisotropic medium to obtain a normalized polarization vector of the quasi-P wave;
based on the orthogonal relation of the polarization vectors of the quasi-P wave, the SH wave and the quasi-SV wave, the polarization vector of the SH wave is obtained by calculation according to the normalized polarization vector of the quasi-P wave and the propagation direction of the seismic wave vector wave field, and the polarization vector of the quasi-SV wave is obtained by calculation according to the normalized polarization vector of the quasi-P wave and the polarization vector of the SH wave.
8. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the method of claims 1 to 6.
9. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the steps of the method of claims 1 to 6 are implemented when the processor executes the program.
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