CN106338766B - Prestack time migration method based on split-step fast fourier transformation - Google Patents
Prestack time migration method based on split-step fast fourier transformation Download PDFInfo
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Abstract
The present invention provides a kind of prestack time migration method based on split-step fast fourier transformation, and this method includes：Input pretreated seismic data；Root mean sequare velocity is picked up by interactive mode；Ray propagation time of the calculating imaging point to focal point；The seismic data in time and space domain is transformed into frequency wave number；Obtain the continuation value of background wave field；Wave field after continuation is fourier transformed to frequency space domain, time shift operation is carried out by the step Fourier time-displacement operator of time-domain, realizes the continuation to disturbing wave field；And firing time image-forming condition is utilized, phase shift is made to frequency space domain seismic wave field and carries out the integral of effective frequency range, obtains the seismic imaging result of big gun record.The prestack time migration method based on split-step fast fourier transformation can apply root mean sequare velocity into line displacement, in the case where not increasing speed modeling difficulty, adaptability that pre-stack time migration vertically and horizontally changes speed is improved and to guarantor's width ability of migration imaging.
Description
Technical field
The present invention relates to the migration imaging fields in seism processing, especially relate to a kind of based on step Fourier
The prestack time migration method of algorithm.
Background technology
Seismic migration is a kind of complementary operation by earthquake information into rearrangement, to keep seismic wave energy playback empty to it
Between actual position, obtain underground real construction form.Wave equation prestack migration imaging be broadly divided into pre-stack time migration at
Two class of picture and pre-stack depth migration imaging.Pre-stack depth migration is adaptable to underground lateral variation in velocity, it is possible to provide Depth Domain
Photo-quality imaging as a result, but it is high and computationally intensive to the required precision of rate pattern, be a high investment high repayment therefore
Scheme.It is high that pre-stack time migration is imaged computational efficiency, while its requirement to rate pattern application conditions is low, construction it is complicated,
There is preferable imaging effect in the case that lateral variation in velocity is little.Therefore, pre-stack time migration is practical technique at this stage.
The principle that pre-stack time migration imaging is realized according to algorithm can be divided into two major classes：Offset method based on ray theory
With the offset method based on wave field extrapolation.Conventional ray method pre-stack time migration uses root mean sequare velocity, it can realize vertical
Lateral velocity variation, calculation amount is smaller, and calculates root mean sequare velocity and improve its precision and be easier, but its numerical value response characteristic
Not as good as wave field method.Nevertheless, pre-stack time migration (PSTM) is still only penetrated in the seismic data processing software of mainstream at present
Collimation method is without wave field method.This is because wave field method PSTM quotes interval velocity in recursive process, when calculating m- interval velocity model
With great difficulty.Therefore, in practice, if spending same cost if necessary, people would rather establish depth-interval velocity mould
Type and the higher pre-stack depth migration of choice accuracy, so, reference interval velocity model becomes the biggest obstacle of wave field method PSTM.
With the increase of oil-gas exploration difficulty, it is more and more important that seismic data protects width processing.Occurs plane in recent years
Wave, phase shift add the wave fields class prestack time migration technique such as interpolation and constant-velocity scan, but its all multi objective cannot be satisfied practicality and want
It asks.
In frequency wavenumber domain, Dubrulle (1983), Ekren and Ursin (1999) realize the plane to common offset
Wave field continuation.But theoretically common offset trace gather plane wave pre-stack time migration can only be handled with vertical velocity variation
Medium, and the holding of Seismic Wave Dynamics Characteristics is also needed to further increase.
Go out from the integral formula (Ehinger A., Lailly P., and Marfurt K.J.1996) of single track Green's function
Hair, Jianhua P. and Dan N. (2008) borrow phase shift method and obtain the Kirchhoff type prestacks with wave field method response characteristic
Time migration result.This mode can retain the major advantage of ray method, moreover it is possible to improve amplitude and waveform characteristic.But with
Road, which is unit progress wave field extrapolation, can lead to considerable calculation amount.
Wang Youxin (2008) adds the method for interpolation to realize the pre-stack time migration to single shot record by phase shift.This method at
Image angle degree is high, but computationally intensive, calculates wave field by linear interpolation, does not adapt to the large change of lateral velocity.
Sergey fomel (2013) propositions go to wave equation under cartesian coordinate system under imaging ray coordinate system
The method solved, the approximate solution that Green's function is calculated in being deviated The method avoids Conventional Time, when improving
Between calculations of offset precision, but its cross directional variations bad adaptability to speed.
Since wave field method has good numerical characteristic, so, wave field method pre-stack time migration has important practical valence
Value, many research work attempt to the estimated performance of wave field method, but are limited by reference root mean sequare velocity and become with speed-adaptive
Change two problems, it is difficult to meet real requirement.We have invented when a kind of new prestack based on split-step fast fourier transformation thus
Between offset method, solve the two technical problems.
Invention content
The object of the present invention is to provide it is a kind of can generate more true and reliable imaging results based on step Fourier
The prestack time migration method of algorithm.
The purpose of the present invention can be achieved by the following technical measures：Pre-stack time migration based on split-step fast fourier transformation
Method, being somebody's turn to do the prestack time migration method based on split-step fast fourier transformation includes：Step 1, pretreated seismic data is inputted
pu(t,x,y)；Step 2, pretreated seismic data p is utilizeduRoot mean sequare velocity spectrum is calculated in (t, x, y), by interaction side
Formula picks up root mean sequare velocity, and obtains mean-square-root velocity field v within the scope of work arearms(t,x,y)；Step 3, it is based on root mean sequare velocity
Field vrms(t, x, y), the ray propagation time τ of calculating imaging point to focal point；Step 4, using Fourier transformation, by when m- sky
Between domain seismic data pu(t, x, y) transforms to frequency wavenumber domain p* u(w,kx,ky), wherein p* u(w,kx,ky)=FFT (pu
(t,x,y))；Step 5, using step Fourier phase-shift operator by p* u(w,kx,ky) directly continuation to underground imaging point when
Between on τ, obtain the continuation value of background wave field；Step 6, the wave field after continuation is fourier transformed Frequency-Space Domain, passed through
The step Fourier time-displacement operator of time-domain carries out time shift operation, realizes the continuation to disturbing wave field；And step 7, according at
The ray propagation time τ of picture point to focal point makees phase using firing time image-forming condition to Frequency-Space Domain seismic wave field
The integral for moving and carrying out effective frequency range obtains the seismic imaging result of big gun record.
The purpose of the present invention can be also achieved by the following technical measures：
In step 1, total big gun collection p interval velocity model in depth domain forward modeling obtainedu(t, x, y) carries out denoising, static correction
These are routinely pre-processed.
In step 2, the root mean sequare velocity that seed point location is picked up by interactive mode, smoothly obtains by three-dimensional interpolation
The mean-square-root velocity field v of target arearms(t, x, y), the mean-square-root velocity field are used for the step Fourier prestack to seismic data
Time migration.
In step 2, pretreated seismic data p is utilizedu(t, x, y) calculates root mean sequare velocity spectrum, by interaction side
Formula, according to 100 meters at equal intervals pick up seed point location root mean sequare velocity, then by interpolation smoothing obtain between be divided into 10 meters
The time-domain mean-square-root velocity field v of modelrms(t, x, y), i.e. velocity field needed for pre-stack time migration.
In step 3, it is based on mean-square-root velocity field vrms(t, x, y) calculates imaging point to focal point using ray method
The ray propagation timeWherein, τ is the time of imaging point, and x is the position of imaging point, xsFor shake
The position of source point, vrmsFor root mean sequare velocity.
In steps of 5, it by the mean-square-root velocity field in application time domain, is obtained by single step continuation, on continuation time τ
For the mutually transposition of background velocity, the phase-shift operator expression formula is as follows：
Wherein, vrms0(τ) is the background root mean square field speed angle value at τ moment, srms0(τ) is the slowness of ambient field, and srms0
(τ)=1/vrms0(τ), w are frequency, kxFor the wave number in the directions x, kyFor the wave number in the directions y.
In step 6, the wave field that step 5 is calculated is transformed into Frequency-Space Domain through Fourier inversion, in this base
On plinth by the step Fourier time-displacement operator of time-domain be calculated for Perturbation when transplant, it is real using time-displacement operator
Now to the continuation of Perturbation, expression formula is：
Wherein, Δ srms(τ, x, y) is the slowness of Perturbation, so far, is completed to geophone station side earthquake record in imaging point
The wave field extrapolation at τ moment at position.
In step 7, Frequency-Space Domain seismic wave field continuation value step 6 obtained, according to firing time image-forming condition
Implementing phase is mobile and is integrated to effective frequency range, obtains final temporal-spatial field seismic wave field value, image-forming condition table
It is up to formula：
Wherein, I is the temporal-spatial field seismic wave field after phase shift, and w1 to w2 is the effective band range of seismic wave.
Step 7 further includes：The record-shifted imaging of big gun is converted into common imaging gather, merges identical geophone offset；To own
Single-shot imaging results are superimposed according to spatial position, or are directly superimposed to common imaging gather, and the prestack time of target area is obtained
Migration imaging result.
The present invention proposes that a kind of prestack time migration method based on split-step fast fourier transformation, key therein are according to
Root velocity interpolation wave field extrapolation.In general, ray method quotes root mean sequare velocity, wave field method quotes interval velocity, and establishes interval velocity
Model has great difficulty, so, pre-stack time migration mainly uses ray method.However, the numerical value of ray method pre-stack time migration
Response characteristic is not as good as wave field method and guarantor's width is poor, for this purpose, application root mean sequare velocity that can be simple and fast realizes that wave field method is inclined
Shifting is that pre-stack time migration needs the major issue solved.In wave field class algorithm, phase shift method, plane wave method, substep Fu
In leaf and screen algorithm gradually recursion can be become One-step Extrapolation, to quote root mean sequare velocity, wherein split-step fast fourier transformation letter
It is clean and have single order lateral velocity variation ability, meet the precondition of pre-stack time migration just.The present invention is based on step Fouriers
Algorithm realizes wave field method pre-stack time migration using root mean sequare velocity, is mainly characterized by：1. quoting root mean sequare velocity, lead to
It crosses single step wave field extrapolation and realizes that speed is longitudinally varying, avoid the error that interval velocity is introduced in successively downward recursion；2. passing through
The variation of lateral velocity single order is realized in relative time shift compensation；3. by the mixing of shot point ray method and geophone station wave field method, realization is penetrated
The mutual supplement with each other's advantages of collimation method high efficiency and wave field method high-fidelity.Either ray method or wave field method, both can be used in theory
Pre-stack time migration can be used for pre-stack depth migration.In practice, if it is known that interval velocity, pre-stack depth migration compare prestack
The imaging effect of time migration is good, still, more difficult than calculating root mean sequare velocity due to calculating accurate interval velocity, it uses
Mean-square-root velocity field realizes that wave field method pre-stack time migration be can yet be regarded as the high imaging method of a kind of efficient quick, fidelity.
The prestack time migration method based on split-step fast fourier transformation of the present invention, wave field method prestack time migration technique are answered
With preceding, the pretreatments such as conventional denoising, static correction are carried out to seismic data first, by analyzing seismic data, are obtained accurately
Root velocity field.Then, ray method, the raytime of calculating focal point to imaging point are utilized.At this point, seismic data is transformed into
Frequency wavenumber domain carries out a phase shift to the seismic data of frequency wavenumber domain using background root mean sequare velocity, realizes to background
The wave field extrapolation of field；Seismic data after continuation is transformed into Frequency-Space Domain, is carried out using disturbance mean-square-root velocity field primary
The wave field extrapolation to Perturbation is realized in time shift；According to the propagation time of focal point to imaging point, to the frequency-space after continuation
Domain wave field implementing phase movement；After wavefield phase moves, the integral of effective frequency range is carried out to seismic wavefield data, is obtained final
Seismic wave field continuation value；Finally, all single-shot imaging results are superimposed according to spatial position, or straight to common imaging gather
Superposition is connect, the pre-stack time migration imaging results of target area are obtained.
The prestack time migration method based on split-step fast fourier transformation is realized using the mean-square-root velocity field of low cost
Pre-stack time migration based on split-step fast fourier transformation avoids interval velocity in downward recursion by single step wave field extrapolation and repeats
Continuous positive inverse transformation improves offset accuracy while not increasing calculating cost and improves amplitude response.At the same time, pass through
The hybrid operation of ray method and wave field method had both embodied the good amplitude response of wave field method or had adopted ray method adaptation speed
The advantages of spending change in time and space, get the mastery complementary effect, and computational efficiency greatly improved.With conventional pre-stack time migration algorithm
It compares, the present invention can apply root mean sequare velocity into line displacement, in the case where not increasing speed modeling difficulty, when improving prestack
Between offset adaptability that speed is vertically and horizontally changed and to guarantor's width ability of migration imaging.
Description of the drawings
Fig. 1 is the flow of the specific embodiment of the prestack time migration method based on split-step fast fourier transformation of the present invention
Figure；
Fig. 2 is the corresponding depth of marmousi models-interval velocity schematic diagram in specific embodiments of the present invention；
Fig. 3 is m- root mean sequare velocity schematic diagram when marmousi models are corresponding in specific embodiments of the present invention；
Fig. 4 is the ray method pre-stack time migration result schematic diagram of marmousi models in specific embodiments of the present invention；
Fig. 5 is the wave field method prestack based on split-step fast fourier transformation of marmousi models in specific embodiments of the present invention
Time migration result schematic diagram；
Specific implementation mode
To enable the purpose, technical scheme and advantage of the embodiment of the present invention to be clearer and more comprehensible, below in conjunction with of the invention real
The attached drawing in example is applied, technical solution in the embodiment of the present invention carries out clear, complete description.
As shown in FIG. 1, FIG. 1 is the flow charts of the prestack time migration method based on split-step fast fourier transformation of the present invention.
In step 101, seismic data is inputted, which is by the pretreated big gun altogether such as conventional denoising, static correction
Point trace gather.In one embodiment, total big gun collection p marmousi interval velocity model in depth domain forward modelings as shown in Figure 2 obtainedu
(t, x, y) carries out the conventional pretreatment such as denoising, static correction.Flow enters step 102.
In step 102, root mean sequare velocity is picked up, root mean sequare velocity, which is calculated, using pretreated seismic data composes,
The root mean sequare velocity that seed point location is picked up by interactive mode, the root mean sequare velocity of target area is smoothly obtained by three-dimensional interpolation
, the mean-square-root velocity field is used for the step Fourier pre-stack time migration to seismic data.In one embodiment, using pre-
Treated seismic data pu(t, x, y) calculates root mean sequare velocity spectrum, by interactive mode, according to 100 meters of pickups kind at equal intervals
Then the root mean sequare velocity of son point position is divided into 10 meters of marmousi models by interpolation smoothing acquisition between as shown in Figure 3
Time-domain mean-square-root velocity field vrms(t, x, y), i.e. velocity field needed for pre-stack time migration.Flow enters step 103.
In step 103, computational methods and the use mean-square-root velocity field, calculate imaging point to shake when being travelled using ray
The ray propagation time of source point.In one embodiment, it is based on mean-square-root velocity field vrms(t, x, y), is calculated into using ray method
Ray propagation time of the picture point to focal pointWherein, τ is the time of imaging point, and x is imaging
The position of point, xsFor the position of focal point, vrmsFor root mean sequare velocity, flow enters step 104.
In step 104, using Fourier transformation, the common-shot-gather of temporal-spatial field is transformed into frequency wavenumber domain.
In one embodiment, changed by two-dimentional Fourier, frequency-wave will be changed by pretreated geophone station side seismic data
The p of number field* u(w,kx,ky), wherein p* u(w,kx,ky)=FFT (pu(t,x,y)).Flow enters step 105.
In step 105, using step Fourier phase-shift operator and using the mean-square-root velocity field to the common-source point road
Collect seismic data and carries out wave field extrapolation, the frequency wavenumber domain seismic wavefield data postponed outside.
To earthquake data application one by reference background slowness srms0The phase-shift operator that (τ) is obtained.In pre-stack depth migration
In, the step-length of phase shift continuation is a fixed depth value Δ z, needs the wave field extrapolation that imaging point position is obtained by Layer by layer recurrence
Value.In embodiments of the present invention, it by the mean-square-root velocity field in application time domain, is obtained by single step continuation, in continuation time τ
The upper mutually transposition for background velocity, the phase-shift operator expression formula are as follows：
Wherein, vrms0(τ) is the background root mean square field speed angle value at τ moment, srms0(τ) is the slowness of ambient field, and srms0
(τ)=1/vrms0(τ), w are frequency, kxFor the wave number in the directions x, kyFor the wave number in the directions y.
Using above-mentioned formula, so that it may with by upgoing wave p* u(w,kx,ky) directly time τ of the continuation to underground imaging point
On, obtain the continuation value of background wave field.Flow enters step 106.
In step 106, using Fourier inversion, the frequency wavenumber domain seismic wavefield data postponed outside is transformed into frequency
Rate-spatial domain, the Frequency-Space Domain seismic wavefield data after being converted.Using step Fourier time-displacement operator and use institute
It states mean-square-root velocity field and continuation processing is carried out to the Frequency-Space Domain seismic wavefield data after transformation, obtain the frequency of secondary continuation
Rate-spatial domain seismic wavefield data.
The wave field that step 105 is calculated is transformed into Frequency-Space Domain through Fourier inversion, is passed through on this basis
The step Fourier time-displacement operator of time-domain be calculated for Perturbation when transplant, using time-displacement operator, realize to disturbance
The continuation of field, expression formula are：
Wherein, Δ srms(τ, x, y) is the slowness of Perturbation.
So far, the wave field extrapolation to geophone station side earthquake record τ moment at imaging point position is completed.Flow enters
Step 107.
In step 107, according to the ray propagation time of the focal point to imaging point, using firing time image-forming condition,
Phase shift is made to Frequency-Space Domain seismic wave field and carries out the integral of effective frequency range, obtains the seismic imaging result of big gun record；
The record-shifted imaging of big gun is converted into common imaging gather, merges identical geophone offset, which can be used for later stage AVO
Analysis and lithological inversion；All single-shot imaging results are superimposed according to spatial position, or common imaging gather is directly superimposed,
Obtain the pre-stack time migration imaging results of target area.
In one embodiment, Frequency-Space Domain seismic wave field continuation value step 106 obtained, according to firing time at
Slice part implementing phase is mobile and is integrated to effective frequency range, obtains final temporal-spatial field seismic wave field value, is imaged
Conditional expression is：
Wherein, I is the temporal-spatial field seismic wave field after phase shift, and w1 to w2 is the effective band range of seismic wave.
According to the final temporal-spatial field seismic wave field at picture value, by its all single-shot imaging results according to space
Position is superimposed, or the record-shifted imaging of big gun is converted into common imaging gather, is directly superimposed to common imaging gather, energy
Obtain step Fourier pre-stack time migration imaging results as shown in Figure 5, with shown in Fig. 4 use ray method pre-stack time migration
Obtained marmousi migration results are compared, wave field abundant information in the migration result obtained using the method for the present invention, in stratum
The weak reflection in portion is clear, guarantor's width of wave field method migration before stack is embodied, while at the position shown in box, using the method for the present invention
Obtained fault imaging result improves a lot compared with ray method offset, and breakpoint is clear-cut, and resolution ratio is also higher.
Claims (8)
1. a kind of prestack time migration method based on split-step fast fourier transformation, which is characterized in that this method includes：
Step 1, pretreated big gun collection seismic data p altogether is inputtedu(t,x,y)；
Step 2, pretreated big gun collection seismic data p altogether is utilizeduRoot mean sequare velocity spectrum is calculated in (t, x, y), by interaction side
Formula picks up root mean sequare velocity, and obtains mean-square-root velocity field v within the scope of work arearms(t,x,y)；
Step 3, it is based on mean-square-root velocity field vrms(t, x, y), the ray propagation time t of calculating imaging point to focal points；
Step 4, using Fourier transformation, by the total big gun collection seismic data p of temporal-spatial fieldu(t, x, y) transforms to frequency-wavenumber
Domain p* u(w,kx,ky), wherein p* u(w,kx,ky)=FFT (pu(t,x,y))；
Step 5, using step Fourier phase-shift operator by p* u(w,kx,ky) directly continuation on time τ, obtained at subsurface imaging point
To the continuation value of background wave field；
Step 6, the wave field after continuation is fourier transformed Frequency-Space Domain, passes through the step Fourier time shift of time-domain
Operator carries out time shift operation, realizes the continuation to disturbing wave field；
Step 7, according to the ray propagation time t of imaging point to focal points, using firing time image-forming condition, to frequency-space
Domain seismic wave field makees phase shift and carries out the integral of effective frequency range, obtains the seismic imaging result of total big gun collection seismic data；
In step 2, pretreated big gun collection seismic data p altogether is utilizedu(t, x, y) calculates root mean sequare velocity spectrum, by interaction side
Formula picks up the root mean sequare velocity of seed point location according to 100 meters at equal intervals, then by being divided into 10 meters between interpolation, smooth acquisition
Time-domain mean-square-root velocity field vrms(t, x, y), i.e. velocity field needed for pre-stack time migration.
2. a kind of prestack time migration method based on split-step fast fourier transformation according to claim 1, which is characterized in that
In step 1, total big gun collection seismic data p interval velocity model in depth domain forward modeling obtainedu(t, x, y) carries out denoising, static correction
Conventional pretreatment.
3. a kind of prestack time migration method based on split-step fast fourier transformation according to claim 1, which is characterized in that
In step 2, the root mean sequare velocity that seed point location is picked up by interactive mode, by three-dimensional interpolation, smoothly obtains target area
Mean-square-root velocity field vrms(t,x,y)。
4. a kind of prestack time migration method based on split-step fast fourier transformation according to claim 1, which is characterized in that
In step 3, it is based on mean-square-root velocity field vrms(t, x, y), the ray for calculating imaging point to focal point using ray method are propagated
TimeWherein, τ is time, x at subsurface imaging pointmFor the position of imaging point, xsFor focal point
Position, vrmsFor root mean sequare velocity.
5. a kind of prestack time migration method based on split-step fast fourier transformation according to claim 1, which is characterized in that
In steps of 5, the step Fourier phase-shift operator expression formula is as follows：
Wherein, srms0(τ) is the slowness of ambient field, and srms0(τ)=1/vrms0(τ), vrms0(τ) is the background root mean square at τ moment
Field speed angle value, w are frequency, kxFor the space wave number in the directions x, kyFor the space wave number in the directions y.
6. a kind of prestack time migration method based on split-step fast fourier transformation according to claim 1, which is characterized in that
In step 6, the wave field that step 5 is calculated is transformed into Frequency-Space Domain through Fourier inversion, passed through on this basis
The step Fourier time-displacement operator of time-domain be calculated for Perturbation when transplant, using step Fourier time-displacement operator,
Realize that the continuation to Perturbation, expression formula are：
Wherein, Δ srms(τ, x, y) is the slowness of Perturbation.
7. a kind of prestack time migration method based on split-step fast fourier transformation according to claim 1, which is characterized in that
In step 7, Frequency-Space Domain seismic wave field continuation value step 6 obtained, according to firing time image-forming condition implementing phase
Movement simultaneously integrates effective frequency range, obtains final temporal-spatial field seismic wave field value, image-forming condition expression formula is：
Wherein, I (x, y, ts) be phase shift after temporal-spatial field seismic wave field, w1 to w2 be seismic wave effective band model
It encloses.
8. a kind of prestack time migration method based on split-step fast fourier transformation according to claim 1, which is characterized in that
Step 7 further includes：The imaging of total big gun collection earthquake data offset is converted into common imaging gather, merge same offset away from；To own
Big gun collection seismic data imaging results are superimposed according to spatial position altogether, or are directly superimposed to common imaging gather, and target area is obtained
Pre-stack time migration imaging results.
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