CN111025386B - Vertical and horizontal wave separation method without separation false image - Google Patents

Vertical and horizontal wave separation method without separation false image Download PDF

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CN111025386B
CN111025386B CN201911279186.8A CN201911279186A CN111025386B CN 111025386 B CN111025386 B CN 111025386B CN 201911279186 A CN201911279186 A CN 201911279186A CN 111025386 B CN111025386 B CN 111025386B
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周熙焱
常旭
孟晓波
祖绍环
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Chengdu Univeristy of Technology
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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
    • G01V1/282—Application of seismic models, synthetic seismograms
    • 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
    • G01V1/30—Analysis
    • 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
    • G01V1/30—Analysis
    • G01V1/303—Analysis for determining velocity profiles or travel times

Abstract

The invention relates to a vertical and horizontal wave separation method without separation artifacts, belonging to the technical field of seismic wave information processing. The invention mainly overcomes the defects in the prior art, and provides a vertical and horizontal wave separation method without separation artifacts, which comprises the following specific steps: and performing forward modeling by using a first-order velocity-strain equation, and performing longitudinal and transverse wave decoupling based on the formula and a longitudinal and transverse wave decoupling equation to obtain a separated longitudinal and transverse wave velocity field. The invention can not only ensure that the phase and amplitude of the separation result are not changed, but also ensure that the separation result has no separation false image; the accurate longitudinal and transverse wave separation provides support for forward simulation and recognition of seismic wave propagation, elastic waves are relatively complex due to the fact that the elastic waves comprise the longitudinal and transverse waves, and inconvenience is brought to recognition of wave field propagation rules due to coupling of the longitudinal and transverse waves when wave fields of the elastic waves are forward; accurate longitudinal and transverse wave separation provides support for elastic wave imaging, surface data longitudinal and transverse wave separation, microseism positioning and the like which depend on elastic wave field continuation algorithms.

Description

Vertical and horizontal wave separation method without separation false image
Technical Field
The invention relates to a vertical and horizontal wave separation method without separation artifacts, belonging to the technical field of seismic wave information processing.
Background
In the past exploration, the earth medium is assumed to be a sound wave model, a single-component detector is adopted to acquire seismic signals, but as simple oil and gas reservoirs are discovered in succession, more complex oil and gas reservoirs have to be searched, so that a plurality of work areas begin to adopt multi-component data acquisition, the model based on the sound wave assumption is not applicable in partial areas, and the earth medium must be regarded as an elastic medium. Our land geophones also change from single to three-component, offshore from hydrophones monitoring water pressure to four-component submarine cables (Yu et al, 2013, Ikeda, 1986). For these data, we cannot simply treat the z-component as a P-wave, and the single component data is processed. Besides P wave information, the multi-component data also carry information of underground transverse waves, and if the information of the longitudinal waves and the transverse waves can be extracted, more information can be provided for geological interpretation of the user, so that the oil and gas reservoir can be better identified. The velocity of the transverse wave is smaller than that of the longitudinal wave, and the converted wave can carry information with larger offset distance relative to the P wave according to Snell law. In some special configurations, such as at the top of the cloud, the imaging results tend to be better for converted shear waves than for longitudinal waves (Granli et al, 1999). In addition, the addition of converted shear wave information reduces the multi-solution of interpretation and inversion problems (such as AVA, AVO, etc.) (Saha et al, 2014).
However, offset imaging is a very important step in order to image seismic data. The migration imaging can make the diffracted wave converge, make the geological structure return to the true position, the imaging result after the migration processing is closer to the true geological structure. The elastic wave reverse time migration inherits the advantages of common sound wave reverse time migration, and meanwhile, imaging can be carried out through transverse waves. The elastic wave reverse time migration adopts an elastic wave equation, is not based on sound wave hypothesis any more, and not only can obtain the imaging result of PP, but also can obtain the imaging result of PS, thereby obtaining more information of underground medium structures and being more beneficial to the explanation of underground target bodies. In the forward and backward wave fields of the elastic wave equation, both longitudinal and transverse waves exist in the wave field, and if the longitudinal and transverse waves are directly imaged without being separated, the longitudinal and transverse waves cannot be imaged due to crosstalk of the longitudinal and transverse waves, so that the longitudinal and transverse waves in the wave field must be separated before imaging (Yan and Sava, 2008). Therefore, it is necessary to propose a vertical and horizontal wave separation method that ensures separation of the wave field dynamics without separation artifacts.
There are also some methods like elastic wave reverse time migration, which also require longitudinal and transverse wave separation. For example, full waveform inversion, which is to invert the parameters of subsurface elastic waves by using the waveform information of seismic waves, is equivalent to reverse time migration of one elastic wave in each iteration process, and therefore, it is also necessary to separate longitudinal waves from transverse waves in the elastic wave field. And the least square reverse time migration inverses the reflectivity parameters of the underground medium, each iteration is also equivalent to one elastic wave reverse time migration, and the longitudinal wave and the transverse wave in the elastic wave field need to be separated. In addition, longitudinal and transverse wave separation is also needed in a seismic source reverse time positioning imaging method of micro seismic data, and seismic source positioning reverse time imaging is to reversely transmit seismic waveforms recorded on the earth surface and then image by methods of maximum amplitude, autocorrelation, cross correlation and the like to obtain the position of a seismic source, but longitudinal and transverse waves in a reversely transmitted elastic wave field also need to be separated in the process.
In addition, forward modeling is also a very important step in seismology, and forward modeling can enable people to more clearly recognize the propagation law of seismic waves and is also an important step for inverting the problem. For forward simulation of elastic waves, in order to more clearly understand propagation rules of elastic waves or when inverting specific elastic parameters, it is necessary to separate longitudinal waves and transverse waves of forward simulated wave fields. The mode separation of longitudinal and transverse waves is realized, the physical significance of the separated wave field is clearer and more definite, and the method plays a vital role in knowing the propagation characteristics of the waves and inverting the specific problems.
It can be seen that the separation of longitudinal and transverse waves of elastic waves is an important link in many technologies, and an accurate method for separating longitudinal and transverse waves must be provided in order to ensure the accuracy of methods such as elastic wave reverse time migration. At present, some longitudinal and transverse wave separation methods exist, such as longitudinal and transverse wave separation based on rotation divergence, longitudinal and transverse wave decoupling based on a first-order velocity-stress equation and the like, but the methods have the following defects; the physical meaning and the vector characteristic obtained by the method of longitudinal and transverse wave separation based on the rotation divergence are inconsistent with the original wave field; the method of longitudinal and transverse wave decoupling based on the first order velocity-stress equation presents separation artifacts.
Disclosure of Invention
The invention mainly overcomes the defects in the prior art, and provides a vertical and horizontal wave separation method without separation artifacts.
The technical scheme provided by the invention for solving the technical problems is as follows: a vertical and horizontal wave separation method without separation artifacts comprises the following specific steps: performing forward modeling by using a first-order velocity-strain equation, and performing longitudinal and transverse wave decoupling based on the formula and a longitudinal and transverse wave decoupling equation to obtain a separated longitudinal and transverse wave velocity field;
the first order velocity-strain equation is:
Figure BDA0002316265330000031
Figure BDA0002316265330000032
in the case of 2D:
Figure BDA0002316265330000033
Figure BDA0002316265330000034
Figure BDA0002316265330000035
Figure BDA0002316265330000036
Figure BDA0002316265330000037
in the 3D case:
Figure BDA0002316265330000038
Figure BDA0002316265330000041
Figure BDA0002316265330000042
Figure BDA0002316265330000043
Figure BDA0002316265330000044
Figure BDA0002316265330000045
Figure BDA0002316265330000046
Figure BDA0002316265330000047
Figure BDA0002316265330000048
in the formula: rho is density; lambda and mu are both Lame constants; v is a velocity field, a strain field and a Dirichlet function; is a first derivative of time; x, y and z are all spatial directions;
the longitudinal and transverse wave decoupling equation is as follows:
in the case of 2D:
Figure BDA0002316265330000049
Figure BDA00023162653300000410
Figure BDA00023162653300000411
Figure BDA00023162653300000412
in the 3D case:
Figure BDA00023162653300000413
Figure BDA00023162653300000414
Figure BDA0002316265330000051
Figure BDA0002316265330000052
Figure BDA0002316265330000053
Figure BDA0002316265330000054
in the formula: v. ofpx、vpy、vpzThe x, y and z components of the separated longitudinal wave velocity field are respectively; v. ofsx、vsy、vszThe x, y, and z components of the separated shear velocity field, respectively.
The further technical scheme is that the specific process of the longitudinal and transverse wave decoupling is as follows: and solving a longitudinal wave and transverse wave decoupling equation by adopting a staggered grid finite difference numerical value.
The further technical proposal is that v is in the 3D casexAndxxthe calculation formula of (a) is as follows:
Figure BDA0002316265330000055
Figure BDA0002316265330000056
Figure BDA0002316265330000057
Figure BDA0002316265330000058
Figure BDA0002316265330000059
in the formula: i. j and k are space coordinates respectively; c. ClIs a difference coefficient; n is a time coordinate; Δ t is the time sampling interval; Δ x, Δ y, Δ z are the spatial sampling intervals in the x, y, z directions, respectively; dx、Dy、DzDifference operators in x, y and z directions respectively; m is the difference order; l is the grid distance between the difference point and the calculation point; p is an intermediate variable.
The invention has the following beneficial effects:
(1) not only can the phase and amplitude of the separation result be ensured not to be changed, but also the separation result can be ensured not to have separation false images;
(2) the accurate longitudinal and transverse wave separation provides support for forward simulation and recognition of seismic wave propagation, elastic waves are relatively complex due to the fact that the elastic waves comprise the longitudinal and transverse waves, and inconvenience is brought to recognition of wave field propagation rules due to coupling of the longitudinal and transverse waves when wave fields of the elastic waves are forward;
(3) accurate longitudinal and transverse wave separation provides support for elastic wave imaging, surface data longitudinal and transverse wave separation, microseism positioning and the like which depend on elastic wave field continuation algorithms.
Elastic wave field continuation is needed in methods of elastic wave imaging, including elastic wave reverse time deviation, elastic wave least square deviation, elastic wave full waveform inversion and the like, longitudinal waves and transverse waves are often needed to be separated in the continuation process, and the separated wave fields are used for imaging or inversion. The accurate longitudinal and transverse wave separation method proposed by us is the guarantee of accurate imaging and inversion results.
And (3) separating longitudinal waves and transverse waves of the earth surface data, namely separating the longitudinal waves and the transverse waves in the seismic records received on the earth surface, and then respectively carrying out post-processing. The method is to extend the surface seismic record to an underground reference surface and then extend the surface seismic record to the surface in a reverse direction, and the wave field is separated into longitudinal and transverse waves in the extending process. Therefore, the accurate longitudinal and transverse separation method provides a theoretical basis for the separation method based on the extended surface seismic record.
And a theoretical basis is provided for the microseism data reverse-time imaging positioning method. The microseism is a signal generated by shale fracturing, and the signal can be received by a detector. The reverse-time imaging positioning method is to perform reverse continuation on received seismic signals and then perform imaging by adopting methods such as correlation or superposition and the like, and the maximum energy value in an imaging result can often reflect the position of a micro seismic source, so that positioning is performed. In the method, wave field continuation is needed, longitudinal and transverse waves are separated in the continuation process, and imaging is carried out under proper imaging conditions, so that an accurate longitudinal and transverse separation method is a guarantee for accurate positioning imaging.
Drawings
FIG. 1 is a three-level model diagram;
FIG. 2 is a graph of velocity and strain alignment in a cross-grid differential;
FIG. 3 is a total wave field diagram obtained by forward modeling based on a first order velocity-strain equation according to an embodiment;
FIG. 4 is a diagram of a separated longitudinal and transverse wave velocity field obtained by first order velocity-strain equation decoupling according to an embodiment;
fig. 5 is a waveform diagram at x-2 Km.
Detailed Description
The present invention will be further described with reference to the following examples and the accompanying drawings.
The invention relates to a vertical and horizontal wave separation method without separation false image, which comprises the following steps:
performing forward modeling by adopting a first-order velocity-strain equation, and performing longitudinal and transverse wave decoupling based on the formula and a longitudinal and transverse wave decoupling equation;
the first order velocity-strain equation is:
Figure BDA0002316265330000071
Figure BDA0002316265330000072
in the formula: rho is density; λ and μ are Lame constants;
in the case of 2D:
Figure BDA0002316265330000073
Figure BDA0002316265330000074
Figure BDA0002316265330000075
Figure BDA0002316265330000076
Figure BDA0002316265330000077
in the 3D case:
Figure BDA0002316265330000078
Figure BDA0002316265330000081
Figure BDA0002316265330000082
Figure BDA0002316265330000083
Figure BDA0002316265330000084
Figure BDA0002316265330000085
Figure BDA0002316265330000086
Figure BDA0002316265330000087
Figure BDA0002316265330000088
in the formula: rho is density; lambda and mu are both Lame constants; v is a velocity field, a strain field and a Dirichlet function; is a first derivative of time; x, y and z are all spatial directions;
the longitudinal and transverse wave decoupling equation is as follows:
in the case of 2D:
Figure BDA0002316265330000089
Figure BDA00023162653300000810
Figure BDA00023162653300000811
Figure BDA00023162653300000812
in the 3D case
Figure BDA00023162653300000813
Figure BDA00023162653300000814
Figure BDA0002316265330000091
Figure BDA0002316265330000092
Figure BDA0002316265330000093
Figure BDA0002316265330000094
In the formula: v. ofpx、vpy、vpzThe x, y and z components of the separated longitudinal wave velocity field are respectively; v. ofsx、vsy、vszThe x, y, and z components of the separated shear velocity field, respectively.
Solving a longitudinal and transverse wave decoupling equation by adopting a staggered grid finite difference numerical value to obtain a separated longitudinal and transverse wave velocity field; in the solving process, a staggered differential format is adopted, namely the staggered arrangement is carried out on time and space, 1/2 points are added in each integer grid point on the time and space, the arrangement mode of speed and stress on the space is given in figure 2, and the staggered differential format can better meet the stability on an interface and reduce frequency dispersion.
The longitudinal and transverse wave decoupling equation is an accurate longitudinal and transverse decoupling formula, and other items are not discarded in longitudinal and transverse decoupling, so that the separated longitudinal and transverse waves are longitudinal and transverse wave components in an original wave field, and the characteristics of phase protection, amplitude protection and no separation false image can be achieved.
V in the 3D casexAndxxthe calculation formula of (a) is as follows:
Figure BDA0002316265330000095
Figure BDA0002316265330000096
in which the spatial partial derivatives of velocity and stress are found by the following formula, D is given belowx xxAnd DxvxThe calculation formula of (2):
Figure BDA0002316265330000097
Figure BDA0002316265330000101
coefficient of difference clComprises the following steps:
Figure BDA0002316265330000102
in the formula: i. j and k are space coordinates respectively; c. ClIs a difference coefficient; n is a time coordinate; Δ t is the time sampling interval; Δ x, Δ y, Δ z are the spatial sampling intervals in the x, y, z directions, respectively; dx、Dy、DzDifference operators in x, y and z directions respectively; m is the difference order; l is the grid distance between the difference point and the calculation point; p is an intermediate variable.
When the separation wave field is calculated, the calculation can be directly carried out according to the longitudinal and transverse wave decoupling equation or according to vi＝vpi+vsiTwo of the two quantities are obtained, and the other quantity is obtained according to the relation between the total wave field and the longitudinal wave and the transverse wave; so that the amount of calculation can be reduced.
The invention can also be applied to other algorithms, such as elastic wave reverse time migration, microseism reverse time imaging positioning and the like based on the longitudinal and transverse wave separation in wave field continuation methods.
Examples
In the 2D case, taking the three-layer model of fig. 1 as an example, the total wave field obtained by forward modeling based on the first-order velocity-strain equation is shown in fig. 3, and then the longitudinal and transverse wave separation is performed by the above-mentioned longitudinal and transverse wave decoupling equation, and the vector P-wave and S-wave field obtained by separation is shown in fig. 4, where fig. 4(a) is the P-wave x-component obtained by separation, fig. 4(b) is the P-wave z-component obtained by separation, fig. 4(c) is the S-wave x-component obtained by separation, and fig. 4(D) is the S-wave z-component obtained by separation.
Meanwhile, a waveform diagram at x 2Km is extracted again, as shown in fig. 5, where fig. 5(a) shows a total wave field x component, a separated P-wave x component, and a separated S-wave x component, and fig. 5(b) shows a total wave field z component, a separated P-wave z component, and a separated S-wave z component.
It can be seen that the separate P-wave and S-wave waveforms are consistent with the corresponding wavefield waveforms in the total wavefield, whether the x-component or the z-component.
It can therefore be shown that the first order velocity-strain based compressional-shear decoupling equation can ensure that the phase and amplitude of the separation wavefield are unchanged, with separation results that are free of separation artifacts at the interface.
Although the present invention has been described with reference to the above embodiments, it should be understood that the present invention is not limited to the above embodiments, and those skilled in the art can make various changes and modifications without departing from the scope of the present invention.

Claims (3)

1. A method for separating longitudinal and transverse waves without separation artifacts is characterized by comprising the following specific steps:
performing forward modeling by using a first-order velocity-strain equation, and performing longitudinal and transverse wave decoupling based on the formula and a longitudinal and transverse wave decoupling equation to obtain a separated longitudinal and transverse wave velocity field;
the first order velocity-strain equation is:
in the case of 2D:
Figure FDA0002701477810000011
Figure FDA0002701477810000012
Figure FDA0002701477810000013
Figure FDA0002701477810000014
Figure FDA0002701477810000015
in the 3D case:
Figure FDA0002701477810000016
Figure FDA0002701477810000017
Figure FDA0002701477810000018
Figure FDA0002701477810000019
Figure FDA00027014778100000110
Figure FDA00027014778100000111
Figure FDA00027014778100000112
Figure FDA00027014778100000113
Figure FDA00027014778100000114
in the formula: rho is density; lambda and mu are both Lame constants; v is a velocity field, is a strain field,
Figure FDA00027014778100000211
is a time first derivative; x, y and z are all spatial directions;
the longitudinal and transverse wave decoupling equation is as follows:
in the case of 2D:
Figure FDA0002701477810000021
Figure FDA0002701477810000022
Figure FDA0002701477810000023
Figure FDA0002701477810000024
in the 3D case:
Figure FDA0002701477810000025
Figure FDA0002701477810000026
Figure FDA0002701477810000027
Figure FDA0002701477810000028
Figure FDA0002701477810000029
Figure FDA00027014778100000210
in the formula: v. ofpx、vpy、vpzThe x, y and z components of the separated longitudinal wave velocity field are respectively; v. ofsx、vsy、vszThe x, y, and z components of the separated shear velocity field, respectively.
2. The method for separating longitudinal and transverse waves without separation artifacts of claim 1, wherein the specific process of longitudinal and transverse wave decoupling is as follows: and solving a longitudinal wave and transverse wave decoupling equation by adopting a staggered grid finite difference numerical value.
3. A method of vertical and horizontal wave separation without separation artefacts as claimed in claim 2, wherein v is a 3D casexAndxxthe calculation formula of (a) is as follows:
Figure FDA0002701477810000031
Figure FDA0002701477810000032
Figure FDA0002701477810000033
Figure FDA0002701477810000034
Figure FDA0002701477810000035
in the formula: i. j and k are space coordinates respectively; c. ClIs a difference coefficient; n is a time coordinate; Δ t is the time sampling interval; Δ x is the spatial sampling interval in the x-direction; dx、Dy、DzDifference operators in x, y and z directions respectively; m is the difference order; l is the grid distance between the difference point and the calculation point; p is an intermediate variable.
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