CN109557581A - Reconstruction of seismic data method and system based on Fourier transformation - Google Patents
Reconstruction of seismic data method and system based on Fourier transformation Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
- G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
- G01V1/36—Effecting static or dynamic corrections on records, e.g. correcting spread; Correlating seismic signals; Eliminating effects of unwanted energy
- G01V1/362—Effecting static or dynamic corrections; Stacking
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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
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V2210/00—Details of seismic processing or analysis
- G01V2210/70—Other details related to processing
Abstract
Disclose a kind of Reconstruction of seismic data method and system based on Fourier transformation.This method may include:, by multistep autoregression method, to be established Fourier based on primary earthquake data and rebuild linear equation；Linear equation is rebuild based on Fourier, and objective function is established by Least squares inversion；Based on objective function, sparse solution is obtained, and then rebuilds seismic data.The present invention combines least square Fourier method for reconstructing with multistep autoregression method, complicated seismic data can accurately be rebuild achieves good application effect, has very important effect to precision, improvement Overlay, the quality for promoting migration before stack etc. that improve subsequent velocity analysis.
Description
Technical field
The present invention relates to oil gas technical field of physical geography, more particularly, to a kind of earthquake based on Fourier transformation
Data re-establishing method and system.
Background technique
It is well known that the acquisition of seismic data seriously affects the final imaging results of seismic data, and earthquake data acquisition
In a very common problem be exactly seismic data along direction in space be irregular sampling or dilution sampling.Ideal
In the case of, the sampling to seismic wave field should be rule and densification.Currently, carrying out space densification to seismic wave field with wave detector
Sampling technically be feasible in calculating, but be economically unaffordable.Therefore seismic data is in space side
The reason of upward sparse sampling, sparse sampling was relatively cheap, but means to collect mainly due to the considerations of economic angle
Less data, and will lead to and contain space aliasing in seismic data, especially in 3-d seismic exploration.Cause earthquake number
Mainly have the reason of irregular sampling according on direction in space: the presence (building, road, bridge etc.) of surface obstructions object or ground
Factor (prohibiting exploiting field and mountain area, forest, River Network etc.), the instrument hardware (geophone, air cannon, cable etc.) of shape condition
Acquire bad track caused by problem, when acquisition of marine seismic data the pinniform of cable drift about etc..The irregular sampling of seismic data
Or sparse sampling is to the filtering of the domain DMO, FK, velocity analysis, multiple attenuation, the methods of Power estimation and wave equation migration
Processing result brings serious influence.Therefore the reconstruction of research irregular sampling seismic data is to the subsequent velocity analysis of raising
Precision, improvement Overlay, the quality for promoting migration before stack etc. have very important effect.By to original seismic data
Rebuild, make it includes geophysical information more really reflect the geophysical characters of underground geologic bodies so that after
Continuous seismic data process can better meet the requirement that meticulous depiction is carried out to complex geological structure, provide more for oil-gas exploration
Effective instruction and help etc. have important practical significance.
Reconstruction of seismic data method based on Fourier transformation does not need geology or geophysics it is assumed that only requiring earthquake number
According to being space finite bandwidth, and computational efficiency is high.It is two-dimensional non-that Fourier's method for reconstructing has been successfully applied to a peacekeeping
The reconstruction of rule sampling data, Fourier's method for reconstructing are using the Fourier of Least squares inversion estimation irregular sampling data
How number, preferably estimate that Fourier coefficient is the core of this method.Once Fourier coefficient is correctly estimated, data can
To be reconstructed on any sampling grid.Fourier's method for reconstructing is applied to irregular sampling earthquake number by Duijndam etc. (1999)
According to regularization on, and successfully solve a series of problems, such as parameter selection.Liu and Sachhi (2001,2003,2004) is proposed
Fourier's method for reconstructing of minimum weight norm interpolation (MWNI), the reconstruction with limit seismic data are expressed as minimum norm
Least square problem.This constrains the solution of inversion equation with freight weight limit construction method using the regularization term of Adaptive spectra weighted norm,
Using the bandwidth of data and the shape of frequency spectrum as the prior information with limit Reconstruction of seismic data problem, therefore obtain than traditional
The anti-alias method that band limit data Fourier method for reconstructing is preferably solved, but do not provided.Zwartjes (2005) with
Zwartjes and Sachhi (2007) proposes sparse constraint Fourier's method for reconstructing using non-quadratic form regularization term, to change
Reconstruction effect when kind seismic data is containing wider airway, and preferably resolve the reconstruction of the seismic data containing space aliasing
Problem.Fourier's method for reconstructing can not only rebuild the seismic data of rule sampling, can equally rebuild irregular and adopt at random
The seismic data of sample, but the seismic data containing space aliasing cannot be rebuild well.It is based on therefore, it is necessary to develop one kind
The Reconstruction of seismic data method and system of Fourier transformation.
The information for being disclosed in background of invention part is merely intended to deepen the reason to general background technique of the invention
Solution, and it is known to those skilled in the art existing to be not construed as recognizing or imply that the information is constituted in any form
Technology.
Summary of the invention
The Reconstruction of seismic data method and system based on Fourier transformation that the invention proposes a kind of, can be by minimum two
Multiply Fourier's method for reconstructing to combine with multistep autoregression method, can accurately rebuild achieving very well for complicated seismic data
Application effect, have very to improving the precision of subsequent velocity analysis, improving Overlay, the quality for promoting migration before stack etc.
Important role.
According to an aspect of the invention, it is proposed that a kind of Reconstruction of seismic data method based on Fourier transformation.The side
Method may include:, by multistep autoregression method, to be established Fourier based on primary earthquake data and rebuild linear equation；Based on institute
It states Fourier's reconstruction linear equation and objective function is established by Least squares inversion；Based on the objective function, obtain sparse
Solution, and then rebuild seismic data.
Preferably, the multistep autoregression method includes: and obtains the primary earthquake data conversion to frequency domain approximate
Linear lineups seismic data；Harmonic function superposition is obtained by autoregression model based on the lineups seismic data
Seismic data；Based on the seismic data that the lineups seismic data is superimposed with the harmonic function, seismic data probability is obtained,
And then it establishes the Fourier and rebuilds linear equation.
Preferably, the lineups seismic data are as follows:
Wherein, (m Δ x, n Δ f) indicates that lineups seismic data, Δ x representation space domain sampling interval, Δ f indicate frequency to S
Domain sampling interval, pjIndicate the slope of j-th of linear event, AjIndicate that amplitude, m indicate that the road number of seismic data, n indicate every
The sampling number of road seismic data.
Preferably, the seismic data of the harmonic function superposition are as follows:
Wherein, L indicates the quantity of harmonic function, and (j, n Δ f) indicate prediction filtering factor to P.
Preferably, the seismic data probability are as follows:
P ' (j, n Δ f/ α)=P (j, n Δ f) j=1,2 ..., L (3)
Wherein, P ' (j, n Δ f/ α) indicates seismic data probability.
Preferably, the objective function are as follows:
Wherein, J indicates that objective function, d indicate that the vector of data space, m indicate the vector of the model space, and matrix A indicates
Fourier inversion operation,Indicate the covariance matrix of noise,Indicate the covariance matrix of prior model, m0It indicates first
Test the initial solution of model.
Preferably, the sparse solution are as follows:
Wherein,W is the diagonal matrix of weight coefficient composition.
It, can be with according to another aspect of the invention, it is proposed that a kind of Reconstruction of seismic data system based on Fourier transformation
Include: memory, is stored with computer executable instructions；Processor, the processor run the computer in the memory
Executable instruction executes following steps: being based on primary earthquake data, by multistep autoregression method, establishes Fourier and rebuild line
Property equation；Linear equation is rebuild based on the Fourier, and objective function is established by Least squares inversion；Based on the target
Function obtains sparse solution, and then rebuilds seismic data.
Preferably, the multistep autoregression method includes: and obtains the primary earthquake data conversion to frequency domain approximate
Linear lineups seismic data；Harmonic function superposition is obtained by autoregression model based on the lineups seismic data
Seismic data；Based on the seismic data that the lineups seismic data is superimposed with the harmonic function, seismic data probability is obtained,
And then it establishes the Fourier and rebuilds linear equation.
Preferably, the objective function are as follows:
Wherein, J indicates that objective function, d indicate that the vector of data space, m indicate the vector of the model space, and matrix A indicates
Fourier inversion operation,Indicate the covariance matrix of noise,Indicate the covariance matrix of prior model, m0It indicates first
Test the initial solution of model.
Methods and apparatus of the present invention has other characteristics and advantages, these characteristics and advantages are attached from what is be incorporated herein
It will be apparent in figure and subsequent specific embodiment, or will be in the attached drawing being incorporated herein and subsequent specific reality
It applies in mode and is stated in detail, the drawings and the detailed description together serve to explain specific principles of the invention.
Detailed description of the invention
Exemplary embodiment of the present is described in more detail in conjunction with the accompanying drawings, of the invention is above-mentioned and other
Purpose, feature and advantage will be apparent, wherein in exemplary embodiments of the present invention, identical reference label is usual
Represent same parts.
Fig. 1 shows the flow chart of the step of Reconstruction of seismic data method according to the present invention based on Fourier transformation.
Fig. 2 a and Fig. 2 b respectively illustrate the trace gather data and reconstruction according to an embodiment of the invention containing airway
The schematic diagram of seismic data.
Fig. 3 a, Fig. 3 b, Fig. 3 c and Fig. 3 d respectively illustrate actual seismic data according to an embodiment of the invention,
It shakes track data, seismic data, the schematic diagram according to the present invention for rebuilding seismic data is rebuild according to sparse inversion method.
Fig. 4 a, Fig. 4 b, Fig. 4 c and Fig. 4 d respectively illustrate according to an embodiment of the invention according to sparse inversion side
The differential section of the reconstruction seismic data of method, the differential section according to the present invention for rebuilding seismic data, Fig. 3 c boxed area, figure
The schematic diagram of 3d boxed area.
Specific embodiment
The present invention will be described in more detail below with reference to accompanying drawings.Although showing the preferred embodiment of the present invention in attached drawing,
However, it is to be appreciated that may be realized in various forms the present invention and should not be limited by the embodiments set forth herein.On the contrary, providing
These embodiments are of the invention more thorough and complete in order to make, and can will fully convey the scope of the invention to ability
The technical staff in domain.
Fig. 1 shows the flow chart of the step of Reconstruction of seismic data method according to the present invention based on Fourier transformation.
In this embodiment, the Reconstruction of seismic data method according to the present invention based on Fourier transformation may include:
Step 101, primary earthquake data are based on, by multistep autoregression method, Fourier is established and rebuilds linear equation；?
In one example, multistep autoregression method includes: that primary earthquake data conversion to frequency domain is obtained the lineups of approximately linear
Seismic data；The seismic data of harmonic function superposition is obtained by autoregression model based on lineups seismic data；Based on same
The seismic data that phase axis seismic data is superimposed with harmonic function obtains seismic data probability, and then establishes Fourier and rebuild linearly
Equation.
In one example, lineups seismic data are as follows:
Wherein, (m Δ x, n Δ f) indicates that lineups seismic data, Δ x representation space domain sampling interval, Δ f indicate frequency to S
Domain sampling interval, pjIndicate the slope of j-th of linear event, AjIndicate that amplitude, m indicate that the road number of seismic data, n indicate every
The sampling number of road seismic data.
In one example, the seismic data of harmonic function superposition are as follows:
Wherein, L indicates the quantity of harmonic function, and (j, n Δ f) indicate prediction filtering factor to P.
In one example, seismic data probability are as follows:
P ' (j, n Δ f/ α)=P (j, n Δ f) j=1,2 ..., L (3)
Wherein, P ' (j, n Δ f/ α) indicates seismic data probability.
It specifically,, can by selecting suitable penalty function when seismic data is when Fourier meets sparsity and assumes
To obtain preferable reconstruction effect.But with the increase of seismic data complexity, the hypothesis of sparsity not satisfaction when
It waits, rebuilds effect and set with regard to different, need the data by predicting multistep autoregression method as prior information, obtain
Better reconstructed results.
Assuming that earthquake data packet contains limited linear event, it is made of N number of equidistant seismic channel, part seismic channel is
Missing.Seismic data is transformed into frequency domain from time-domain first, in the domain f-x, seismic data can be indicated with vector x (f),
xT(f)=[x1(f),x2(f),x3(f),…,xN(f)], in N track data, only M track data is known, uses n={ n respectively
(1), (2) n, n (3) ..., n (M) } and m=m (1), m (2), m (3) ..., m (N-M) } indicate given data and unknown data
The subscript in (i.e. missing road).
The seismic data being made of the lineups of L approximately linear is represented by formula (1) in the domain f-x, for each frequency
Rate ingredient f, formula (1) show to be indicated with multiple harmonic function in each linear event in the domain f-x.Consider when Δ x '=
When α Δ x, Δ f '=Δ f/ α, formula (4) are obtained:
In addition, L harmonic function superposition is expressed as formula (2), likewise, right by way of autoregression model
In Δ x ' and Δ f ', formula (5) are obtained:
According to formula (2), formula (4) and formula (5), can obtain seismic data probability is formula (3), the formula be multistep from
The basis of homing method.It shows that on the frequency axis, each ingredient for predictive filter is predictable.This is just meaned
, if it is known that the predictive filter of certain frequencies, can predict to obtain the predictive filter of other frequencies.That is, can
To extract the predictive filter of radio-frequency component from the predictive filter for rebuilding the obtained low-frequency component without space aliasing, in turn
It rebuilds and obtains the radio-frequency component of missing seismic channel.
Step 102, linear equation is rebuild based on Fourier and objective function is established by Least squares inversion.
In one example, objective function are as follows:
Wherein, J indicates that objective function, d indicate that the vector of data space, m indicate the vector of the model space, and matrix A indicates
Fourier inversion operation,Indicate the covariance matrix of noise,Indicate the covariance matrix of prior model, m0It indicates first
Test the initial solution of model.
Step 103, it is based on objective function, obtains sparse solution, and then rebuild seismic data.
In one example, sparse solution are as follows:
Wherein,W is the diagonal of weight coefficient composition
Battle array, i.e. W=diag (Δ xi)。
The trace gather data containing airway that Fig. 2 a and Fig. 2 b show according to an embodiment of the invention and reconstruction earthquake
The schematic diagram of data.
Specifically, Fourier's method for reconstructing can use a linear system representation:
D=Am (8),
When the linear equation to be solved is morbid state or is ill posed, pass through the objective function of Least squares inversion foundation
In will include a model compensation item, establish objective function be formula (6), whereinIt contains any about prior model
Information.Objective function is minimized, i.e., derivation is carried out about m to formula (6), and make derivative zero, then can be obtained:
Due to lacking prior information, m can be taken0=0, can obtain least-norm solution in this way is formula (10):
Wherein, λ is damping factor.In actual seismic data reconstruction processes, A is generally takenHThe main diagonal element of A matrix
1%.By the penalty function ρ (m) of the non-quadratic form form of selection appropriate, can obtain ideal sparse solution is formula (7), into
And seismic data is rebuild, as shown in Figure 2 b.
This method combines least square Fourier method for reconstructing with multistep autoregression method, can accurately rebuild multiple
Miscellaneous seismic data achieves good application effect, to the precision of the subsequent velocity analysis of raising, improvement Overlay, is promoted and is folded
The quality etc. of preceding offset has very important effect.
Using example
A concrete application example is given below in the scheme and its effect of the embodiment of the present invention for ease of understanding.This field
It should be understood to the one skilled in the art that the example is only for the purposes of understanding the present invention, any detail is not intended to be limited in any way
The system present invention.
Fig. 3 a, Fig. 3 b, Fig. 3 c and Fig. 3 d respectively illustrate actual seismic data according to an embodiment of the invention,
It shakes track data, seismic data, the schematic diagram according to the present invention for rebuilding seismic data is rebuild according to sparse inversion method.
Principle and implementation method according to the present invention, to the more complicated practical common offset earthquake number in one, certain area
According to being rebuild, as shown in Figure 3a.The data a total of 500, road spacing are 15m, time sampling interval 2ms, and the time adopts
Number of samples is 1751.It pumps 131 track data therein at random to be rebuild, as shown in Figure 3b.Assuming that earthquake data packet is containing limited
A linear event is made of N number of equidistant seismic channel, and part seismic channel is missing from.First by seismic data from the time
Domain transforms to frequency domain, and in the domain f-x, seismic data can be indicated with vector x (f), xT(f)=[x1(f),x2(f),x3
(f),…,xN(f)], in N track data, only M track data is known, uses n={ n (1), n (2), n (3) ..., n respectively
(M) } and m=m (1), m (2), m (3) ..., m (N-M) } indicate the subscript in given data and unknown data (i.e. missing road).
The seismic data being made of the lineups of L approximately linear is represented by formula (1) in the domain f-x, for each frequency
Rate ingredient f, formula (1) show to be indicated with multiple harmonic function in each linear event in the domain f-x.Consider when Δ x '=
When α Δ x, Δ f '=Δ f/ α, formula is obtained, in addition, by way of autoregression model, expression that L harmonic function is superimposed
For formula (2), likewise, obtain formula (5) for Δ x ' and Δ f ', according to formula (2), formula (4) and formula (5), can obtain
Seismic data probability is formula (3), which is the basis of multistep autoregression method.It shows on the frequency axis, for prediction
Each ingredient of filter is predictable.It means that if it is known that the predictive filter of certain frequencies, can predict
Obtain the predictive filter of other frequencies.That is, can be from the prediction for rebuilding the obtained low-frequency component without space aliasing
The predictive filter of radio-frequency component is extracted in filter, and then is rebuild and obtained the radio-frequency component of missing seismic channel.
Fourier's method for reconstructing can be formula (8) with a linear system representation, when the linear equation to be solved
When being morbid state or is ill posed, by include a model compensation item in the objective function of Least squares inversion foundation, it build
Vertical objective function is formula (6), whereinContain any information about prior model.Pair objective function is minimized, i.e.,
Formula (6) carries out derivation about m, and makes derivative zero, then formula (9) can be obtained, and due to lacking prior information, can take m0=
0, can obtain least-norm solution in this way is formula (10), by the penalty function ρ (m) of the non-quadratic form form of selection appropriate,
It is formula (7) that ideal sparse solution, which can be obtained, and then rebuilds seismic data, as shown in Figure 3d.
Fig. 4 a, Fig. 4 b, Fig. 4 c and Fig. 4 d respectively illustrate according to an embodiment of the invention according to sparse inversion side
The differential section of the reconstruction seismic data of method, the differential section according to the present invention for rebuilding seismic data, Fig. 3 c boxed area, figure
The schematic diagram of 3d boxed area.From differential section and enlarged local section comparison as can be seen that by making in Least squares inversion
The prior information generated with multistep autoregression method, can obtain relatively good reconstructed results.
In conclusion the present invention combines least square Fourier method for reconstructing with multistep autoregression method, Neng Goujing
That really rebuilds complicated seismic data achieves good application effect, is superimposed to improving the precision of subsequent velocity analysis, improving
Effect, the quality for promoting migration before stack etc. have very important effect.
It will be understood by those skilled in the art that above to the purpose of the description of the embodiment of the present invention only for illustratively saying
The beneficial effect of bright the embodiment of the present invention is not intended to limit embodiments of the invention to given any example.
According to an embodiment of the invention, providing a kind of Reconstruction of seismic data system based on Fourier transformation, can wrap
Include: memory is stored with computer executable instructions；Processor, the computer executable instructions in processor run memory,
It executes following steps: being based on primary earthquake data, by multistep autoregression method, establish Fourier and rebuild linear equation；It is based on
Fourier rebuilds linear equation and establishes objective function by Least squares inversion；Based on objective function, sparse solution is obtained, in turn
Rebuild seismic data.
In one example, multistep autoregression method includes: that primary earthquake data conversion to frequency domain is obtained approximate line
The lineups seismic data of property；The earthquake number of harmonic function superposition is obtained by autoregression model based on lineups seismic data
According to；Based on the seismic data that lineups seismic data is superimposed with harmonic function, seismic data probability is obtained, and then establishes Fourier
Rebuild linear equation.
In one example, objective function are as follows:
Wherein, J indicates objective function,Indicate the covariance matrix of noise,Indicate the covariance square of prior model
Battle array.
The present invention combines least square Fourier method for reconstructing with multistep autoregression method, can accurately rebuild multiple
Miscellaneous seismic data achieves good application effect, to the precision of the subsequent velocity analysis of raising, improvement Overlay, is promoted and is folded
The quality etc. of preceding offset has very important effect.
It will be understood by those skilled in the art that above to the purpose of the description of the embodiment of the present invention only for illustratively saying
The beneficial effect of bright the embodiment of the present invention is not intended to limit embodiments of the invention to given any example.
Various embodiments of the present invention are described above, above description is exemplary, and non-exclusive, and
It is not limited to disclosed each embodiment.Without departing from the scope and spirit of illustrated each embodiment, for this skill
Many modifications and changes are obvious for the those of ordinary skill in art field.
Claims (10)
1. a kind of Reconstruction of seismic data method based on Fourier transformation, comprising:
It establishes Fourier by multistep autoregression method based on primary earthquake data and rebuilds linear equation；
Linear equation is rebuild based on the Fourier, and objective function is established by Least squares inversion；
Based on the objective function, sparse solution is obtained, and then rebuilds seismic data.
2. the Reconstruction of seismic data method according to claim 1 based on Fourier transformation, wherein the multistep autoregression
Method includes:
By the primary earthquake data conversion to frequency domain, the lineups seismic data of approximately linear is obtained；
The seismic data of harmonic function superposition is obtained by autoregression model based on the lineups seismic data；
Based on the seismic data that the lineups seismic data is superimposed with the harmonic function, seismic data probability is obtained, in turn
It establishes the Fourier and rebuilds linear equation.
3. the Reconstruction of seismic data method according to claim 2 based on Fourier transformation, wherein the lineups earthquake
Data are as follows:
Wherein, (m Δ x, n Δ f) indicates that lineups seismic data, Δ x representation space domain sampling interval, Δ f indicate that frequency domain is adopted to S
Sample interval, pjIndicate the slope of j-th of linear event, AjIndicate that amplitude, m indicate that the road number of seismic data, n are indicated per genuine
Shake the sampling number of data.
4. the Reconstruction of seismic data method according to claim 3 based on Fourier transformation, wherein the harmonic function is folded
The seismic data added are as follows:
Wherein, L indicates the quantity of harmonic function, and (j, n Δ f) indicate prediction filtering factor to P.
5. the Reconstruction of seismic data method according to claim 4 based on Fourier transformation, wherein the seismic data is general
Rate are as follows:
P ' (j, n Δ f/ α)=P (j, n Δ f) j=1,2 ..., L (3)
Wherein, P ' (j, n Δ f/ α) indicates seismic data probability.
6. the Reconstruction of seismic data method according to claim 1 based on Fourier transformation, wherein the objective function
Are as follows:
Wherein, J indicates that objective function, d indicate that the vector of data space, m indicate the vector of the model space, and matrix A indicates in Fu
Leaf inverse transformation operation,Indicate the covariance matrix of noise,Indicate the covariance matrix of prior model, m0Indicate priori mould
The initial solution of type.
7. the Reconstruction of seismic data method according to claim 1 based on Fourier transformation, wherein the sparse solution are as follows:
Wherein,W is the diagonal matrix of weight coefficient composition.
8. a kind of Reconstruction of seismic data system based on Fourier transformation, which is characterized in that the system includes:
Memory is stored with computer executable instructions；
Processor, the processor run the computer executable instructions in the memory, execute following steps:
It establishes Fourier by multistep autoregression method based on primary earthquake data and rebuilds linear equation；
Linear equation is rebuild based on the Fourier, and objective function is established by Least squares inversion；
Based on the objective function, sparse solution is obtained, and then rebuilds seismic data.
9. the Reconstruction of seismic data system according to claim 8 based on Fourier transformation, wherein the multistep autoregression
Method includes:
By the primary earthquake data conversion to frequency domain, the lineups seismic data of approximately linear is obtained；
The seismic data of harmonic function superposition is obtained by autoregression model based on the lineups seismic data；
Based on the seismic data that the lineups seismic data is superimposed with the harmonic function, seismic data probability is obtained, in turn
It establishes the Fourier and rebuilds linear equation.
10. the Reconstruction of seismic data system according to claim 8 based on Fourier transformation, wherein the objective function
Are as follows:
Wherein, J indicates that objective function, d indicate that the vector of data space, m indicate the vector of the model space, and matrix A indicates in Fu
Leaf inverse transformation operation,Indicate the covariance matrix of noise,Indicate the covariance matrix of prior model, m0Indicate priori mould
The initial solution of type.
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| CN112649848A (en) * | 2019-10-12 | 2021-04-13 | 中国石油化工股份有限公司 | Method and apparatus for solving seismic wave impedance using wave equation |
| CN112649848B (en) * | 2019-10-12 | 2024-01-23 | 中国石油化工股份有限公司 | Method and device for solving earthquake wave impedance by utilizing wave equation |
| CN111551988A (en) * | 2020-04-23 | 2020-08-18 | 中国地质大学（武汉） | Seismic data anti-alias interpolation method combining deep learning and prediction filtering |
| CN111551988B (en) * | 2020-04-23 | 2021-06-25 | 中国地质大学（武汉） | Seismic data anti-alias interpolation method combining deep learning and prediction filtering |
| CN112698403A (en) * | 2020-12-04 | 2021-04-23 | 中国石油天然气股份有限公司 | Variable density seismic section display method and device |
| CN112698403B (en) * | 2020-12-04 | 2023-08-22 | 中国石油天然气股份有限公司 | Variable density seismic section display method and device |
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