CN104216011B - A kind of stable qP ripple reverse-time migration methods of TTI media - Google Patents
A kind of stable qP ripple reverse-time migration methods of TTI media Download PDFInfo
- Publication number
- CN104216011B CN104216011B CN201310220888.5A CN201310220888A CN104216011B CN 104216011 B CN104216011 B CN 104216011B CN 201310220888 A CN201310220888 A CN 201310220888A CN 104216011 B CN104216011 B CN 104216011B
- Authority
- CN
- China
- Prior art keywords
- wave
- equation
- equations
- regularization
- tti media
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
Abstract
A kind of stable qP ripple reverse-time migration methods of TTI media, it is related to seismic prospecting data processing technology field, and its content of the invention is：The qP wave equations with regularization term are exported on the basis of existing TTI media relatively stablize qP wave equations, adaptive regularization parameter selection is then carried out：Wherein, θ, φ are respectively the inclination angle and azimuth on stratum.It adds regularization term, in the case of excessive amount of calculation and storage capacity is not increased, the qP wave equations more stablized so that TTI media RTM is wider to the adaptability of model, adds the practicality of algorithm on the basis of existing stable qP propagation operators to qP wave equations；Using stratigraphic dip and azimuth information, the size of regularization coefficient is automatically determined, without artificial excessive intervention so that regularization equation is more sane when handling real data.
Description
Technical field：
The present invention relates to seismic prospecting data processing technology field, and in particular to a kind of TTI media stable qP ripple inverse times
Offset method.
Background technology：
In TTI media stable propagation qP ripples be TTI RTM currently can practical key, be also that study hotspot is asked
Topic.Stable qP ripples propagation operator research mainly has following two thinkings in current TTI media：(1) from equations for elastic waves.
Directly from anisotropic medium equations for elastic waves, do acoustic approximation and obtain onomatopoeia wave equation corresponding with equations for elastic waves,
The equation so obtained remains the most of feature of former equations for elastic waves system, such as is meeting the situation of certain boundary conditions
Under, the conservativeness of elastic potential energy and kinetic energy summation is kept, this can strengthen stability when equation solution.But simultaneously and elastic wave
Corresponding qP wave equations are still more complicated, solve that efficiency comparison is low, and the original intention of this and acoustic approximation is run counter to a bit.
On the basis of onomatopoeia wave equation corresponding with elastic wave, angular derivative can be ignored, approximate equation is obtained, but in the equation only
Include first order differential operator, it is impossible to solve the equation with common single order central difference schemes are stable, this comes for reverse-time migration
It is more unfavorable to say；(2) from dispersion relation.QP wave equations in TTI media can also be exported from the dispersion relation of coupling.But
It is that qP wave equations are excessive to the former equations for elastic waves system reform derived from dispersion relation, it is impossible to keep elastic wave system good
Feature.Such as due to intermediate variable chooses improper, even if boundary values in some equation communication processes as derived from dispersion relation
Condition is met, and can not also keep the potential energy and kinetic energy summation conservation of system, this can cause numerical solution extremely unstable.In order that
It is stable by dispersion relation derived equation numerical solution, some compromises can be done to acoustic approximation, that is, introduces limited shear wave velocity, obtains
To so-called limited shear wave equation.Limited shear wave equation solution is more stablized, but the problem of also have its own, such as it is remaining horizontal
Wave energy is stronger than acoustic approximation equation, solves amount of calculation also larger.In addition, limited shear wave equation can be strengthened solving stabilization
Property, but cannot guarantee that absolute.
The content of the invention：
It is an object of the invention to provide a kind of qP ripple reverse-time migration methods that TTI media are stable, it is passed in existing stable qP
Broadcast on the basis of operator, regularization term is added to qP wave equations, in the case of excessive amount of calculation and storage capacity is not increased, obtained more
Stable qP wave equations so that TTI media RTM is wider to the adaptability of model, adds the practicality of algorithm；Inclined using stratum
Angle and azimuth information, automatically determine the size of regularization coefficient, without artificial excessive intervention so that regularization equation is in processing
It is more sane during real data.
In order to solve the problems existing in background technology, the present invention uses following technical scheme：A, band regularization term TTI are situated between
QP wave equations in matter；
(a) qP wave equations are exported by equations for elastic waves
It is for doing the equations for elastic waves after acoustic approximation in TTI media：
The definition of wherein differential operator is：
C11, C13And C33For stiffness coefficient, θ,Respectively stratigraphic dip and azimuth, AndIt is inclined for direction
Derivative, vx, vy, vzFor velocity component, σ11, σ33For the components of stress.For the equation (1) after acoustic approximation in TTI media, in order to
Computational efficiency, ignores the derivative term wherein about angle, then (1) be changed into：
In density under 1 hypothesis, its corresponding second-order equation can be written as：
(b) qP wave equations are exported by dispersion relation；
Corresponding limited shear wave equation is exported using following dispersion relation：
Wherein, ω is circular frequency, vpx, vpzFor the qP wave velocities in qP ripple x and z directions, vpnFor qP ripple nmo speed.vszFor
The speed of qS ripples in a z-direction, k 'x, k 'yAnd k 'zWave number respectively on the direction of three, space.V is fast for the reference chosen
Degree.Introduce after appropriate middle wave field variable, its corresponding limited shear wave equation is：
Wherein,
(c) the qP wave equations of the stabilization with regularization term
In isotropism ACOUSTIC WAVE EQUATION solution procedure, a kind of optimization method of anti-frequency dispersion, by changing ACOUSTIC WAVE EQUATION pair
The dispersion relation answered, obtains anti-dispersion equation, and implementation step is as follows：
For ACOUSTIC WAVE EQUATION in isotropic medium：
Plane wave solution obtains form：
For ACOUSTIC WAVE EQUATION in band regularization term isotropic medium：
Its corresponding plane wave solution is：
Notice：
Then (10) can write：
In qP wave equations in solving TTI media, regularization term is introduced, to high wave number composition useless in unstable solution
Appropriate decay is done, the equation more stablized.
It is succinct in order to describe, (6) are rewritten as：
Add after regularization term, (13) can be changed into：
Wherein σ is regularization coefficient, can be verified, solves the labile element of (14) than solving high wave number in (13) wave field
Less, so as to cause TTI media RTM handle real data when applicability it is stronger.Can also be using addition for equation (4)
The thought of regularization term builds stable propagation equation.
B, adaptive regularization parameter selection：From (14) as can be seen that the selection of regularization parameter is to final wave field meter
Calculate result have a great impact, in order to cause algorithm handle real data when it is more sane, using such a way from
The calculating regularization coefficient of adaptation：
Wherein, θ,The respectively inclination angle and azimuth on stratum.
The invention has the advantages that：It is added just on the basis of existing stable qP propagation operators to qP wave equations
Then change item, in the case of excessive amount of calculation and storage capacity is not increased, the qP wave equations more stablized so that TTI media RTM
Adaptability to model is wider, adds the practicality of algorithm；Using stratigraphic dip and azimuth information, regularization is automatically determined
The size of coefficient, without artificial excessive intervention so that regularization equation is more sane when handling real data.
Brief description of the drawings：
Fig. 1 is single-shot TTI media qP ripple RTM calculation flow charts proposed by the present invention.
Embodiment：
Present embodiment takes following technical scheme：QP wave equations in A, band regularization term TTI media；
(a) qP wave equations are exported by equations for elastic waves
It is for doing the equations for elastic waves after acoustic approximation in TTI media：
The definition of wherein differential operator is：
C11, C13And C33For stiffness coefficient, θ,Respectively stratigraphic dip and azimuth, AndIt is inclined for direction
Derivative, vx, vy, vzFor velocity component, σ11, σ33For the components of stress.For the equation (1) after acoustic approximation in TTI media, in order to
Computational efficiency, ignores the derivative term wherein about angle, then (1) be changed into：
In density under 1 hypothesis, its corresponding second-order equation can be written as：
(b) qP wave equations are exported by dispersion relation；
Corresponding limited shear wave equation is exported using following dispersion relation：
Introduce after appropriate middle wave field variable, its corresponding limited shear wave equation is：
Wherein,
(c) the qP wave equations of the stabilization with regularization term
In isotropism ACOUSTIC WAVE EQUATION solution procedure, a kind of optimization method of anti-frequency dispersion, by changing ACOUSTIC WAVE EQUATION pair
The dispersion relation answered, obtains anti-dispersion equation, and implementation step is as follows：
For ACOUSTIC WAVE EQUATION in isotropic medium：
Plane wave solution obtains form：
For ACOUSTIC WAVE EQUATION in band regularization term isotropic medium：
Its corresponding plane wave solution is：
Notice：
Then (10) can write：
In qP wave equations in solving TTI media, regularization term is introduced, to high wave number composition useless in unstable solution
Appropriate decay is done, the equation more stablized.
It is succinct in order to describe, (6) are rewritten as：
Add after regularization term, (13) can be changed into：
Wherein σ is regularization coefficient, can be verified, solves the labile element of (14) than solving high wave number in (13) wave field
Less, so as to cause TTI media RTM handle real data when applicability it is stronger.Can also be using addition for equation (4)
The propagation equation of the thought construction of stable of regularization term.
B, adaptive regularization parameter selection：From (14) as can be seen that the selection of regularization parameter is to final wave field meter
Calculate result have a great impact, in order to cause algorithm handle real data when it is more sane, using such a way from
The calculating regularization coefficient of adaptation：
Wherein, θ,The respectively inclination angle and azimuth on stratum.
Present embodiment has the advantages that：It is on the basis of existing stable qP propagation operators, to qP ripple sides
Journey adds regularization term, in the case of excessive amount of calculation and storage capacity is not increased, the qP wave equations more stablized so that
TTI media RTM is wider to the adaptability of model, adds the practicality of algorithm；Using stratigraphic dip and azimuth information, automatically
The size of regularization coefficient is determined, without artificial excessive intervention so that regularization equation is more sane when handling real data.
Claims (1)
1. a kind of stable qP ripple reverse-time migration methods of TTI media, it is characterised in that its main implementation steps are：(A), export
QP wave equations in band regularization term TTI media；
(a) qP wave equations are exported by equations for elastic waves
It is for doing the equations for elastic waves after acoustic approximation in TTI media：
The definition of wherein differential operator is：
C11、C13And C33For stiffness coefficient, θ,Respectively stratigraphic dip and azimuth, AndFor Directional partial derivative,
vx、vy、vzFor velocity component, σ11、σ33For the components of stress；For the equation (1) after acoustic approximation in TTI media, in order to calculate
Efficiency, ignores the derivative term wherein about angle, then (1) be changed into：
In density under 1 hypothesis, its corresponding second-order equation can be written as：
(b) qP wave equations are exported by dispersion relation
Corresponding limited shear wave equation is exported using following dispersion relation：
Wherein ω is circular frequency, vpx、vpzRespectively the qP wave velocities in qP ripples x and z directions, vpnFor qP ripple nmo speed, vszFor
The speed of qS ripples in a z-direction, k 'x、k′yAnd k 'zWave number respectively on the direction of three, space；Wave field variable in the middle of introducing
Afterwards, corresponding limited shear wave equation is：
Wherein,
(c) the qP wave equations of the stabilization with regularization term
In isotropism ACOUSTIC WAVE EQUATION solution procedure, a kind of optimization method of anti-frequency dispersion is corresponding by changing ACOUSTIC WAVE EQUATION
Dispersion relation, obtains anti-dispersion equation, and implementation step is as follows：For ACOUSTIC WAVE EQUATION in isotropic medium：
Plane wave solution obtains form：
For ACOUSTIC WAVE EQUATION in band regularization term isotropic medium：
Its corresponding plane wave solution is：
Notice：
Then (10) can write：
In qP wave equations in solving TTI media, regularization term is introduced, suitable is done to high wave number composition useless in unstable solution
When decay, the equation more stablized；
It is succinct in order to describe, (6) are rewritten as：
Wherein：
Add after regularization term, (13) can be changed into：
Wherein σ is regularization parameter, can be verified, solves (14) than solving the labile element of high wave number in (13) wave field more
It is few, so as to cause TTI media RTM applicabilities when handling real data stronger；Also can be by adding just for equation (4)
Then change the propagation equation of item construction of stable；
(B) adaptive regularization parameter selection：From (14) as can be seen that the selection of regularization parameter calculates knot to final wave field
Fruit have a great impact, in order to cause algorithm handle real data when it is more sane, it is adaptive using such a way
Calculating regularization parameter：
Wherein, θ,The respectively inclination angle and azimuth on stratum.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201310220888.5A CN104216011B (en) | 2013-06-05 | 2013-06-05 | A kind of stable qP ripple reverse-time migration methods of TTI media |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201310220888.5A CN104216011B (en) | 2013-06-05 | 2013-06-05 | A kind of stable qP ripple reverse-time migration methods of TTI media |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN104216011A CN104216011A (en) | 2014-12-17 |
| CN104216011B true CN104216011B (en) | 2017-08-04 |
Family
ID=52097706
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201310220888.5A Expired - Fee Related CN104216011B (en) | 2013-06-05 | 2013-06-05 | A kind of stable qP ripple reverse-time migration methods of TTI media |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN104216011B (en) |
Families Citing this family (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104749625B (en) * | 2015-03-11 | 2016-10-05 | 中国科学院地质与地球物理研究所 | A kind of geological data inclination angle method of estimation based on Regularization Technique and device |
| CN105717539B (en) * | 2016-01-28 | 2018-01-30 | 中国地质大学（北京） | A kind of three-dimensional TTI media reverse-time migration imaging method calculated based on more GPU |
| CN108333628B (en) * | 2018-01-17 | 2019-09-03 | 中国石油大学(华东) | Elastic wave least square reverse-time migration method based on regularization constraint |
| CN109946742B (en) * | 2019-03-29 | 2020-09-11 | 中国石油大学(华东) | Pure qP wave seismic data simulation method in TTI medium |
Family Cites Families (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20100135115A1 (en) * | 2008-12-03 | 2010-06-03 | Chevron U.S.A. Inc. | Multiple anisotropic parameter inversion for a tti earth model |
| WO2011141440A1 (en) * | 2010-05-12 | 2011-11-17 | Shell Internationale Research Maatschappij B.V. | Seismic p-wave modelling in an inhomogeneous transversely isotropic medium with a tilted symmetry axis |
| CN102156299A (en) * | 2011-04-08 | 2011-08-17 | 中国石油化工股份有限公司 | Method for building anisotropic velocity model |
-
2013
- 2013-06-05 CN CN201310220888.5A patent/CN104216011B/en not_active Expired - Fee Related
Also Published As
| Publication number | Publication date |
|---|---|
| CN104216011A (en) | 2014-12-17 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Buckmaster et al. | Nonuniqueness of weak solutions to the SQG equation | |
| CN102854533B (en) | A kind of denoising method improving seismic data signal to noise ratio (S/N ratio) based on wave field separation principle | |
| CN104216011B (en) | A kind of stable qP ripple reverse-time migration methods of TTI media | |
| CN104133241B (en) | Wave field separation method and apparatus | |
| CN106646612B (en) | Reconstruction of seismic data method based on matrix contraction | |
| Zhao et al. | Generating facies maps by assimilating production data and seismic data with the ensemble Kalman filter | |
| CN106443768B (en) | A kind of prestack depth domain synthetic seismogram production method | |
| CN106772585B (en) | A kind of quasi- analysis method and device of the optimization decoupling equation based on elastic wave | |
| CN107479092A (en) | A kind of frequency domain high order ACOUSTIC WAVE EQUATION the Forward Modeling based on directional derivative | |
| CN103823239A (en) | Frequency domain optimization mixture staggered grid finite difference forward modeling method | |
| CN105717539A (en) | Multi GPU calculation based reverse time migration imaging method of 3D TTI medium | |
| CN107179550B (en) | A kind of seismic signal zero phase deconvolution method of data-driven | |
| Adjerid et al. | The discontinuous Galerkin method for two-dimensional hyperbolic problems. Part I: Superconvergence error analysis | |
| CN109188520A (en) | Thin reservoir thickness prediction method and device | |
| CN106896403A (en) | Elastic Gaussian beam offset imaging method and system | |
| CN108181653A (en) | For VTI medium reverse-time migrations method, equipment and medium | |
| CN107798156A (en) | A kind of frequency domain 2.5 ties up viscoelastic wave method for numerical simulation and device | |
| CN104297800A (en) | Self-phase-control prestack inversion method | |
| CN106569260B (en) | For high-dip structure area two-dimension earthquake speed change sky school drawing methods | |
| CN109946742A (en) | The pure rolling land qP shakes digital simulation method in a kind of TTI medium | |
| CN109655894B (en) | Construction method and system of carbonate rock ancient river channel seismic inversion low-frequency model | |
| CN108279437A (en) | Variable density ACOUSTIC WAVE EQUATION time higher order accuracy staggering mesh finite-difference method | |
| Zhai et al. | A new fractal interpolation algorithm and its applications to self-affine signal reconstruction | |
| Renzi et al. | The influence of landslide shape and continental shelf on landslide generated tsunamis along a plane beach | |
| Liu et al. | Recovery of high frequency wave fields from phase space–based measurements |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20170804 Termination date: 20210605 |