CN107356971A - Geological data rule method and device - Google Patents
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Abstract
The invention provides a kind of geological data rule method and device, this method to include：Obtain the Gaussian wave group matrix expression of seismic target earthquakes data；Target sparse decomposition model based on L1 norms is established based on Gaussian wave group matrix expression；Using can be micro- convex function to L1 norms carry out approximation process, obtain object function；Object function is solved by projection gradient method, obtains the coefficient vector in feasible zone；According to the coefficient vector in feasible zone and Gaussian wave group matrix expression reconstruct seismic target earthquakes data.In the geological data rule method of the present invention, the influence of random noise can be eliminated by expressing seismic target earthquakes data by Gaussian wave group matrix expression, so that the effect of data reconstruction is more preferable, and, coefficient vector in feasible zone is calculated by projection gradient method, accelerates calculating speed, computational efficiency is high, alleviating geological data rule method of the prior art is influenceed the technical problem serious, data reconstruction is ineffective and computational efficiency is poor by noise.
Description
Technical field
The present invention relates to the technical field of seismic data process, more particularly, to a kind of geological data rule method and dress
Put.
Background technology
In seismic prospecting, earthquake data acquisition is the discrete sampling to continuous wave field caused by focus.In order to standard
True recovery seismic wave field, it is desirable to which sampling process meets Nyquist/aromatic sampling thheorem, i.e. sample frequency is at least original letter
Two times of number peak frequency.However, in the sampling process of reality, due to the limitation of the factors such as landform, bad track, noise, expense,
The geological data of acquisition is generally unsatisfactory for sampling thheorem, i.e. data are imperfect.The imperfection of sampled data causes data in frequency
Rate domain produces alias, to subsequent processes (such as：AVO analyses, migration imaging etc.) cause many difficulties.
In order to eliminate the influence of lack sampling data, complete geological data, the skill method of generally use data normalization are reconstructed.
Data normalization method of the prior art is based on various conversion (such as Fourier transform, Radon conversion, Curvelet conversion)
And the demosaicing of geological data is realized using compressive sensing theory.
These methods employ the knowledge of multi-scale geometric analysis, and missing data weight is realized using the geometric properties of image
Structure, but these methods are influenceed serious during data reconstruction by noise, data reconstruction is ineffective and computational efficiency
It is poor.
The content of the invention
In view of this, it is existing to alleviate it is an object of the invention to provide a kind of geological data rule method and device
Geological data rule method in technology is influenceed the skill serious, data reconstruction is ineffective and computational efficiency is poor by noise
Art problem.
In a first aspect, the embodiments of the invention provide a kind of geological data rule method, methods described includes：
The Gaussian wave group matrix expression of seismic target earthquakes data is obtained, wherein, wrapped in the Gaussian wave group matrix expression
The Discrete Operator of coefficient vector and Gaussian wave group is included, the seismic target earthquakes data are to meet the data of seismic wave sampling thheorem；
Target sparse decomposition model based on L1 norms is established based on the Gaussian wave group matrix expression；
Using can be micro- convex function to the L1 norms carry out approximation process, obtain object function, wherein, the target letter
Number is the function on the coefficient vector；
The object function is solved by projection gradient method, obtains the coefficient vector in feasible zone；
The seismic target earthquakes number is reconstructed according to the coefficient vector in the feasible zone and the Gaussian wave group matrix expression
According to.
With reference in a first aspect, the embodiments of the invention provide the possible embodiment of the first of first aspect, wherein, obtain
The Gaussian wave group matrix expression of seismic target earthquakes data is taken, including：
Gaussian wave group expression formula is obtained, wherein, the Gaussian wave group expression formula is used to represent seismic wave field；
The superposition expression formula of the seismic target earthquakes data is built based on the Gaussian wave group expression formula；
The superposition expression formula of the seismic target earthquakes data is converted into the Gaussian wave group matrix expression.
With reference in a first aspect, the embodiments of the invention provide the possible embodiment of second of first aspect, wherein, base
The target sparse decomposition model based on L1 norms is established in the Gaussian wave group matrix expression, including：
Establish the mathematical modeling of earthquake data acquisition；
The mathematical modeling is entered by line translation based on the Gaussian wave group matrix expression, obtains equation group to be solved；
Constraints based on the Its Sparse Decomposition model of the equation group structure based on L1 norms to be solved；
Pass through formula c1→ min structures Its Sparse Decomposition the model based on L1 norms, wherein, c is expressed as coefficient vector；
Mould is decomposed based on target sparse described in the constraints and the Its Sparse Decomposition model construction based on L1 norms
Type.
With reference in a first aspect, the embodiments of the invention provide the possible embodiment of the third of first aspect, wherein, adopt
Approximation process is carried out to the L1 norms with convex function that can be micro-, obtains object function, including：
Convex function that can be micro- described in acquisition；
Equilibrium relationships between convex function that can be micro- described in foundation and the L1 norms；
The object function is established based on the target sparse decomposition model and the equilibrium relationships.
With reference in a first aspect, the embodiments of the invention provide the possible embodiment of the 4th of first aspect kind, wherein, lead to
Cross projection gradient method and solve the object function, obtain the coefficient vector in feasible zone, including：
The iterative formula of gradient descent algorithm is obtained, wherein, the iterative formula includes iteration step length and the target
The iterative gradient of function；
The iteration step length in the iterative formula is determined based on step-length selection formula；
Set the initial solution of the coefficient vector；
The solving result of the coefficient vector is determined based on the initial solution, the iteration step length and the iterative formula；
The solving result of the coefficient vector is projected in feasible zone based on projection formula, obtained in the feasible zone
Coefficient vector.
Second aspect, the embodiment of the present invention additionally provide a kind of geological data regularization device, and the device includes：
Acquisition module, for obtaining the Gaussian wave group matrix expression of seismic target earthquakes data, wherein, the Gaussian wave group square
Battle array expression formula includes the Discrete Operator of coefficient vector and Gaussian wave group, and the seismic target earthquakes data are fixed to meet seismic wave sampling
The data of reason；
Module is established, mould is decomposed for establishing the target sparse based on L1 norms based on the Gaussian wave group matrix expression
Type；
Approximation process module, for using convex function that can be micro- to carry out approximation process to the L1 norms, obtain target letter
Number, wherein, the object function is the function on the coefficient vector；
Module is solved, for solving the object function by projection gradient method, obtains the coefficient vector in feasible zone；
Reconstructed module, for reconstructing institute according to the coefficient vector in the feasible zone and the Gaussian wave group matrix expression
State seismic target earthquakes data.
With reference to second aspect, the embodiments of the invention provide the possible embodiment of the first of second aspect, wherein, institute
Stating acquisition module includes：
First acquisition unit, for obtaining Gaussian wave group expression formula, wherein, the Gaussian wave group expression formula is used to represent ground
Seismic wave field；
First construction unit, for building the superposition expression of the seismic target earthquakes data based on the Gaussian wave group expression formula
Formula；
Converting unit, for the superposition expression formula of the seismic target earthquakes data to be converted into the Gaussian wave group expression matrix
Formula.
With reference to second aspect, the embodiments of the invention provide the possible embodiment of second of second aspect, wherein, institute
State and establish module and include：
First establishes unit, for establishing the mathematical modeling of earthquake data acquisition；
Converter unit, for the mathematical modeling to be entered into line translation based on the Gaussian wave group matrix expression, treated
Solve equation group；
Second construction unit, for the pact based on the Its Sparse Decomposition model of the equation group structure based on L1 norms to be solved
Beam condition；
3rd construction unit, for passing through formula c1→ min structures Its Sparse Decomposition the model based on L1 norms, its
In, c is expressed as coefficient vector；
4th construction unit, for based on the constraints and the Its Sparse Decomposition model construction institute based on L1 norms
State target sparse decomposition model.
With reference to second aspect, the embodiments of the invention provide the possible embodiment of the third of second aspect, wherein, institute
Stating approximation process module includes：
Second acquisition unit, for obtaining the convex function that can be micro-；
Second establishes unit, for establishing the equilibrium relationships between the convex function that can be micro- and the L1 norms；
3rd establishes unit, for establishing the target letter based on the target sparse decomposition model and the equilibrium relationships
Number.
With reference to second aspect, the embodiments of the invention provide the possible embodiment of the 4th of second aspect kind, wherein, institute
Stating solution module includes：
3rd acquiring unit, for obtaining the iterative formula of gradient descent algorithm, wherein, the iterative formula is included repeatedly
Length of riding instead of walk and the iterative gradient of the object function；
First determining unit, for determining the iteration step length in the iterative formula based on step-length selection formula；
Setup unit, for setting the initial solution of the coefficient vector；
Second determining unit, for determining the system based on the initial solution, the iteration step length and the iterative formula
The solving result of number vector；
Projecting cell, for being projected to the solving result of the coefficient vector in feasible zone based on projection formula, obtain
Coefficient vector in the feasible zone.
The embodiment of the present invention brings following beneficial effect：The embodiments of the invention provide a kind of geological data regularization side
Method, the geological data rule method include：The Gaussian wave group matrix expression of seismic target earthquakes data is obtained, wherein, high bass wave
Bag matrix expression includes the Discrete Operator of coefficient vector and Gaussian wave group, and seismic target earthquakes data are fixed to meet seismic wave sampling
The data of reason；Target sparse decomposition model based on L1 norms is established based on Gaussian wave group matrix expression；Using can be micro- it is convex
Function pair L1 norms carry out approximation process, obtain object function, wherein, object function is the function on coefficient vector；Pass through
Projection gradient method solves object function, obtains the coefficient vector in feasible zone；According to the coefficient vector and high bass wave in feasible zone
Bag matrix expression reconstructs seismic target earthquakes data.
In existing data normalization method, typically by it is various conversion (such as Fourier transform, Radon convert,
Curvelet conversion etc.) and realize using compressive sensing theory the demosaicing of geological data.With existing data normalization side
Method is compared, and in the geological data rule method of the embodiment of the present invention, passes through the discrete calculation with coefficient vector and Gaussian wave group
The Gaussian wave group matrix expression of son shows seismic target earthquakes data, and when solving coefficient vector, be converted to based on
The target sparse decomposition model of L1 norms is solved, and uses convex function that can be micro- to approach L1 norms in solution procedure,
Object function is obtained, and then object function is solved by projection gradient method, the coefficient vector in feasible zone is obtained, finally, passes through
Coefficient vector and Gaussian wave group matrix expression in feasible zone are completed to seismic target earthquakes data reconstruction.The ground of the embodiment of the present invention
Shake in data normalization method, the shadow of random noise can be eliminated by expressing seismic target earthquakes data by Gaussian wave group matrix expression
Ring so that the effect of data reconstruction is more preferable, also, calculates the coefficient vector in feasible zone by projection gradient method, accelerates meter
Speed is calculated, computational efficiency is high, and alleviating geological data rule method of the prior art is influenceed serious, data weight by noise
The technical problem that structure is ineffective and computational efficiency is poor.
Other features and advantages of the present invention will illustrate in the following description, also, partly become from specification
Obtain it is clear that or being understood by implementing the present invention.The purpose of the present invention and other advantages are in specification, claims
And specifically noted structure is realized and obtained in accompanying drawing.
To enable the above objects, features and advantages of the present invention to become apparent, preferred embodiment cited below particularly, and coordinate
Appended accompanying drawing, is described in detail below.
Brief description of the drawings
, below will be to specific in order to illustrate more clearly of the specific embodiment of the invention or technical scheme of the prior art
The required accompanying drawing used is briefly described in embodiment or description of the prior art, it should be apparent that, in describing below
Accompanying drawing is some embodiments of the present invention, for those of ordinary skill in the art, before creative work is not paid
Put, other accompanying drawings can also be obtained according to these accompanying drawings.
Fig. 1 is a kind of flow chart of geological data rule method provided in an embodiment of the present invention；
Fig. 2 is the method flow of the Gaussian wave group matrix expression of acquisition seismic target earthquakes data provided in an embodiment of the present invention
Figure；
Fig. 3 establishes the target sparse based on L1 norms to be provided in an embodiment of the present invention based on Gaussian wave group matrix expression
The flow chart of decomposition model；
Fig. 4 obtains the method flow diagram of object function to be provided in an embodiment of the present invention；
Fig. 5 be it is provided in an embodiment of the present invention can micro- convex function approach the coordinate diagrams of L1 norms；
Fig. 6 solves object function to be provided in an embodiment of the present invention by projection gradient method, obtains the coefficient in feasible zone
The flow chart of vector；
Fig. 7 is a kind of structural representation of geological data regularization device provided in an embodiment of the present invention.
Icon：
11- acquisition modules；12- establishes module；13- approximation process modules；14- solves module；15- reconstructed modules.
Embodiment
To make the purpose, technical scheme and advantage of the embodiment of the present invention clearer, below in conjunction with accompanying drawing to the present invention
Technical scheme be clearly and completely described, it is clear that described embodiment is part of the embodiment of the present invention, rather than
Whole embodiments.Based on the embodiment in the present invention, those of ordinary skill in the art are not making creative work premise
Lower obtained every other embodiment, belongs to the scope of protection of the invention.
For ease of understanding the present embodiment, first to a kind of geological data regularization disclosed in the embodiment of the present invention
Method describes in detail.
Embodiment one：
A kind of geological data rule method, with reference to figure 1, the geological data rule method includes：
S101, the Gaussian wave group matrix expression for obtaining seismic target earthquakes data, wherein, wrapped in Gaussian wave group matrix expression
The Discrete Operator of coefficient vector and Gaussian wave group is included, seismic target earthquakes data are to meet the data of seismic wave sampling thheorem；
One important step of geological data regularization is converted (such as using some：Radon is converted, Curvelet conversion
Deng) appropriate expression wave field, that is, pass through suitable basic function and represent geological data.Under the assumed condition of far field, seismic wave field can
To be considered by part plan wave component, therefore it can be superimposed by Gaussian wave group and represent seismic wave field.
Gaussian wave group matrix expression is employed in the embodiment of the present invention to represent seismic target earthquakes data, in Gaussian wave group square
In battle array expression formula, include the Discrete Operator of coefficient vector and Gaussian wave group.
S102, based on Gaussian wave group matrix expression establish the target sparse decomposition model based on L1 norms；
In order to solve the coefficient vector in Gaussian wave group matrix expression, it is dilute that inventor establishes the target based on L1 norms
Decomposition model is dredged, should the specifically L1 least norm moulds with Prescribed Properties of the target sparse decomposition model based on L1 norms
Type, it is specifically introduced again in content below.
S103, using can be micro- convex function to L1 norms carry out approximation process, obtain object function, wherein, object function
For the function on coefficient vector；
After establishing based on the target sparse decomposition model of L1 norms, using can be micro- convex function L1 norms are forced
Nearby manage, obtain object function, so, the solution to the target sparse decomposition model based on L1 norms has been converted to target
The solution of function, the object function are specially minimization object function under equality constraint, are hereinafter specifically described again.
S104, by projection gradient method solve object function, obtain the coefficient vector in feasible zone；
Solution to object function is a convex optimization problem, generally use interior point method, projection gradient method and homotopy calculation
Method etc..Comparatively, interior point method is very accurate, but speed is slower, and Projected rule has preferable arithmetic speed, and same
Human relations method is practical to small scale problem.
In embodiments of the present invention, object function is solved using projection gradient method, can so accelerates the speed calculated
Degree.
S105, seismic target earthquakes data are reconstructed according to the coefficient vector in feasible zone and Gaussian wave group matrix expression.
After the coefficient vector in feasible zone is obtained, because the Discrete Operator of Gaussian wave group is known, then just can
Seismic target earthquakes data are represented by Gaussian wave group matrix expression, it is, the reconstruct of seismic target earthquakes data can be completed.
In existing data normalization method, typically by it is various conversion (such as Fourier transform, Radon convert,
Curvelet conversion etc.) and realize using compressive sensing theory the demosaicing of geological data.With existing data normalization side
Method is compared, and in the geological data rule method of the embodiment of the present invention, passes through the discrete calculation with coefficient vector and Gaussian wave group
The Gaussian wave group matrix expression of son shows seismic target earthquakes data, and when solving coefficient vector, be converted to based on
The target sparse decomposition model of L1 norms is solved, and uses convex function that can be micro- to approach L1 norms in solution procedure,
Object function is obtained, and then object function is solved by projection gradient method, the coefficient vector in feasible zone is obtained, finally, passes through
Coefficient vector and Gaussian wave group matrix expression in feasible zone are completed to seismic target earthquakes data reconstruction.The ground of the embodiment of the present invention
Shake in data normalization method, the shadow of random noise can be eliminated by expressing seismic target earthquakes data by Gaussian wave group matrix expression
Ring so that the effect of data reconstruction is more preferable, also, calculates the coefficient vector in feasible zone by projection gradient method, accelerates meter
Speed is calculated, computational efficiency is high, and alleviating geological data rule method of the prior art is influenceed serious, data weight by noise
The technical problem that structure is ineffective and computational efficiency is poor.
The above has carried out simple introduction to earthquake data normalization method, and content therein is specifically retouched below
State.
Further, with reference to figure 2, the Gaussian wave group matrix expression of seismic target earthquakes data is obtained, including：
S201, Gaussian wave group expression formula is obtained, wherein, Gaussian wave group expression formula is used to represent seismic wave field；
Specifically, under two-dimensional case, the Gaussian wave group of a practical parametrization can be expressed as：
Wherein, x=(x1,x2)T, k=(k1,k2)TFor wave number, xcIt is the position at Bo Bao centers, RθIt is to be defined by angle, θ
Spin matrix：
γ=(xc, k, α, β, θ) and it is a parameter sets, Λ (α, β, k) is a diagonal matrix, is defined as：
Wherein, parameter alpha defines the number of concussion in a Gaussian wave group half-breadth, and β defines vertical and along concussion direction
The ratio of Gaussian wave group width.
S202, the superposition expression formula based on Gaussian wave group expression formula structure seismic target earthquakes data；
Assuming that seismic target earthquakes data are f (x), therefore can obtain the Gaussian wave group expression formula of seismic target earthquakes data,
F (x)=∑γcγψγ(x) (4)
Wherein, cγIt is unknown coefficient sets, by solving coefficient cγRealize that the Gaussian wave group of geological data decomposes.It is above-mentioned
Formula (4) is the superposition expression formula of seismic target earthquakes data.
S203, the superposition expression formula of seismic target earthquakes data is converted into Gaussian wave group matrix expression.
After the superposition expression formula of seismic target earthquakes data is obtained, formula (4) can be expressed as matrix form by we：
F=Ψ c (5)
Wherein, f is column vector geological data, and Ψ is ripple bag ψγ(x) Discrete Operator formed, c be the coefficient to be solved to
Amount, and with openness, c is specially column vector.Formula (5) is Gaussian wave group matrix expression.
Further, with reference to figure 3, the target sparse based on L1 norms is established based on Gaussian wave group matrix expression and decomposes mould
Type, including：
S301, the mathematical modeling for establishing earthquake data acquisition；
Specifically, the mathematical modeling that earthquake data acquisition can be expressed as,
D=Φ f (6)
Wherein, f is original wavefield data, and Φ is observing matrix, and d is the geological data of collection.Formula (6) is earthquake number
According to the mathematical modeling of collection.
Due to the imperfection of gathered data, Φ is a deficient set matrix, and it is one to reconstruct original wave field by deficiency of data
It is individual to owe fixed indirect problem, there is infinite multiresolution.
S302, mathematical modeling entered by line translation based on Gaussian wave group matrix expression, obtain equation group to be solved；
Formula (5) is substituted into formula (6), and remembers A=Φ Ψ, equation group to be solved can be obtained,
Ac=d (7)
Formula (7) is equation group to be solved.
Although it is also an indirect problem for owing fixed to recover original wave field c from deficiency of data d, due to c be it is sparse, then
Vectorial c can be solved by solving following Lp-Lq regularization models under certain condition,
Wherein, p >=0,0≤q≤1, α>0, c0It is a priori value, D is a scalar operator.
S303, the constraints based on Its Sparse Decomposition model of the equation group to be solved structure based on L1 norms；
After equation group to be solved is obtained, the constraint using equation group to be solved as the Its Sparse Decomposition model based on L1 norms
Condition.
S304, pass through formula | | c | |1→ min builds the Its Sparse Decomposition model based on L1 norms, wherein, c is expressed as coefficient
Vector；
S305, the Its Sparse Decomposition model construction target sparse decomposition model based on constraints and based on L1 norms.
In the present invention, following L1 least norms model is used (to be decomposed namely based on the target sparse of L1 norms
Model) solution that vectorial c is uniquely determined is solved,
||c||1→ min, s.t.Ac=d (9)
Wherein, L1 norms | | | |1It is defined as,
||c||1=∑i|ci| (10)
Wherein, ciFor vectorial c component.
Formula (9) is target sparse decomposition model, it is necessary to which explanation, formula (9) L1 least norms model is Lp-
A kind of form of Lq regularization models.
Further, with reference to figure 4, using can be micro- convex function approximation process is carried out to L1 norms, obtain object function, wrap
Include：
S401, acquisition can be micro- convex function；
Specifically, formula (9) is a convex optimization problem, the methods of can passing through interior point method, solves, and is calculated to improve
Efficiency, the present invention using can micro- convex function approach L1 norms (L1 norms non-differentiability).
As parameter σ ＞ ＞ 1, can micro- convex function be：
This can be micro- the gradient of convex function be：
S402, foundation can be micro- convex function and L1 norms between equilibrium relationships；
This can micro- convex function approach L1 norms (with reference to figure 5).
Construct a convex function that can be micro- to approach L1 norms, i.e.,
||t||1≈fσ(t) (13)
S403, object function established based on target sparse decomposition model and equilibrium relationships.
And then formula (9) can using approximate representation as：
Wherein, N be vectorial c length, ciIt is vectorial c i-th of element.Formula (14) is object function.
Further, with reference to figure 6, object function is solved by projection gradient method, obtains the coefficient vector in feasible zone, is wrapped
Include：
S601, the iterative formula for obtaining gradient descent algorithm, wherein, iterative formula includes iteration step length and object function
Iterative gradient；
Specifically, formula (14) is expressed as the minimization object function J under equality constraintσ(c) Projected can, be passed through
Method solves to it.
The iterative formula of gradient descent algorithm is expressed as：
Wherein, μkIt is along the direction of searchStep-size in search, namely iteration step length,JσRepresent changing for object function
For gradient.
S602, formula is chosen based on step-length determine iteration step length in iterative formula；
When solving extensive problem with gradient descent algorithm, sixty-four dollar question is that great iteration step length can obtain
Go out most fast convergence rate, therefore, find suitable iteration step length μkIt is very important.
Here iteration step length μkSelection be based on two formula,
Wherein,sk-1=ck-ck-1, the iteration step length of selection is,
It can accelerate convergence rate using alternate iteration step length.
S603, the initial solution for setting coefficient vector；
Make initial solution c0=AT(AAT)-1d；
In addition, choosing greatest iteration step number J, parameter σ ＞ ＞ 1 are (such as：σ=1000).
S604, the solving result for determining based on initial solution, iteration step length and iterative formula coefficient vector；
Specifically, it is iterated circulation：J=1,2 ..., J
Order
The solving result of coefficient vector is obtained according to the iterative formula of gradient descent algorithm：(step size mu is by formula by c=c- μ g
(16-17) is calculated)；
S605, based on projection formula the solving result of coefficient vector is projected in feasible zone, obtain be in feasible zone
Number vector.
In order to ensure solving result is in feasible zone ScIn={ c Ac=d }, following projection formula has been used,
Wherein,It is defined as x:=x-AT(AAT)-1(Ax-d)。
It is, c is projected in feasible set, c=c-A is obtainedT(AAT)-1(Ac-d)；
Obtain the solution of the coefficient vector in feasible zone：
Finally, the coefficient vector in feasible zone obtains
Embodiment two：
The embodiment of the present invention additionally provides a kind of geological data regularization device, with reference to figure 7, geological data rule makeup
Put including：
Acquisition module 11, for obtaining the Gaussian wave group matrix expression of seismic target earthquakes data, wherein, Gaussian wave group matrix
Expression formula includes the Discrete Operator of coefficient vector and Gaussian wave group, and seismic target earthquakes data are to meet the number of seismic wave sampling thheorem
According to；
Module 12 is established, mould is decomposed for establishing the target sparse based on L1 norms based on Gaussian wave group matrix expression
Type；
Approximation process module 13, for using convex function that can be micro- to carry out approximation process to L1 norms, object function is obtained,
Wherein, object function is the function on coefficient vector；
Module 14 is solved, for solving object function by projection gradient method, obtains the coefficient vector in feasible zone；
Reconstructed module 15, for reconstructing seismic target earthquakes according to the coefficient vector in feasible zone and Gaussian wave group matrix expression
Data.
Further, acquisition module 11 includes：
First acquisition unit, for obtaining Gaussian wave group expression formula, wherein, Gaussian wave group expression formula is used to represent seismic wave
；
First construction unit, for the superposition expression formula based on Gaussian wave group expression formula structure seismic target earthquakes data；
Converting unit, for the superposition expression formula of seismic target earthquakes data to be converted into Gaussian wave group matrix expression.
Further, establishing module 12 includes：
First establishes unit, for establishing the mathematical modeling of earthquake data acquisition；
Converter unit, for mathematical modeling to be entered into line translation based on Gaussian wave group matrix expression, obtain equation to be solved
Group；
Second construction unit, for the constraint bar based on Its Sparse Decomposition model of the equation group to be solved structure based on L1 norms
Part；
3rd construction unit, for passing through formula c1→ min builds the Its Sparse Decomposition model based on L1 norms, wherein, c tables
It is shown as coefficient vector；
4th construction unit, for the Its Sparse Decomposition model construction target sparse point based on constraints and based on L1 norms
Solve model.
Further, approximation process module 13 includes：
Second acquisition unit, for obtain can be micro- convex function；
Second establishes unit, for establish can be micro- convex function and L1 norms between equilibrium relationships；
3rd establishes unit, for establishing object function based on target sparse decomposition model and equilibrium relationships.
Further, solving module 14 includes：
3rd acquiring unit, for obtaining the iterative formula of gradient descent algorithm, wherein, iterative formula includes iteration step
Long and object function iterative gradient；
First determining unit, for determining the iteration step length in iterative formula based on step-length selection formula；
Setup unit, for setting the initial solution of coefficient vector；
Second determining unit, for determining the solving result of coefficient vector based on initial solution, iteration step length and iterative formula；
Projecting cell, for being projected to the solving result of coefficient vector in feasible zone based on projection formula, obtain feasible
Coefficient vector in domain.
Specific work process in device, the corresponding process in preceding method embodiment is may be referred to, will not be repeated here.
The computer program product for the geological data rule method that the embodiment of the present invention is provided, including store program
The computer-readable recording medium of code, the instruction that described program code includes can be used for performing described in previous methods embodiment
Method, specific implementation can be found in embodiment of the method, will not be repeated here.
It is apparent to those skilled in the art that for convenience and simplicity of description, the device of foregoing description
Specific work process, may be referred to the corresponding process in preceding method embodiment, will not be repeated here.
In addition, in the description of the embodiment of the present invention, unless otherwise clearly defined and limited, term " installation ", " phase
Even ", " connection " should be interpreted broadly, for example, it may be being fixedly connected or being detachably connected, or be integrally connected；Can
To be mechanical connection or electrical connection；Can be joined directly together, can also be indirectly connected by intermediary, Ke Yishi
The connection of two element internals.For the ordinary skill in the art, with concrete condition above-mentioned term can be understood at this
Concrete meaning in invention.
If the function is realized in the form of SFU software functional unit and is used as independent production marketing or in use, can be with
It is stored in a computer read/write memory medium.Based on such understanding, technical scheme is substantially in other words
The part to be contributed to prior art or the part of the technical scheme can be embodied in the form of software product, the meter
Calculation machine software product is stored in a storage medium, including some instructions are causing a computer equipment (can be
People's computer, server, or network equipment etc.) perform all or part of step of each embodiment methods described of the present invention.
And foregoing storage medium includes：USB flash disk, mobile hard disk, read-only storage (ROM, Read-Only Memory), arbitrary access are deposited
Reservoir (RAM, Random Access Memory), magnetic disc or CD etc. are various can be with the medium of store program codes.
In the description of the invention, it is necessary to explanation, term " " center ", " on ", " under ", "left", "right", " vertical ",
The orientation or position relationship of the instruction such as " level ", " interior ", " outer " be based on orientation shown in the drawings or position relationship, merely to
Be easy to the description present invention and simplify description, rather than instruction or imply signified device or element must have specific orientation,
With specific azimuth configuration and operation, therefore it is not considered as limiting the invention.In addition, term " first ", " second ",
" the 3rd " is only used for describing purpose, and it is not intended that instruction or hint relative importance.
Finally it should be noted that：Embodiment described above, it is only the embodiment of the present invention, to illustrate the present invention
Technical scheme, rather than its limitations, protection scope of the present invention is not limited thereto, although with reference to the foregoing embodiments to this hair
It is bright to be described in detail, it will be understood by those within the art that：Any one skilled in the art
The invention discloses technical scope in, it can still modify to the technical scheme described in previous embodiment or can be light
Change is readily conceivable that, or equivalent substitution is carried out to which part technical characteristic；And these modifications, change or replacement, do not make
The essence of appropriate technical solution departs from the spirit and scope of technical scheme of the embodiment of the present invention, should all cover the protection in the present invention
Within the scope of.Therefore, protection scope of the present invention described should be defined by scope of the claims.
Claims (10)
- A kind of 1. geological data rule method, it is characterised in that including：Obtain seismic target earthquakes data Gaussian wave group matrix expression, wherein, the Gaussian wave group matrix expression include be The Discrete Operator of number vector and Gaussian wave group, the seismic target earthquakes data are to meet the data of seismic wave sampling thheorem；Target sparse decomposition model based on L1 norms is established based on the Gaussian wave group matrix expression；Using can be micro- convex function to the L1 norms carry out approximation process, obtain object function, wherein, the object function is Function on the coefficient vector；The object function is solved by projection gradient method, obtains the coefficient vector in feasible zone；The seismic target earthquakes data are reconstructed according to the coefficient vector in the feasible zone and the Gaussian wave group matrix expression.
- 2. according to the method for claim 1, it is characterised in that obtain the Gaussian wave group expression matrix of seismic target earthquakes data Formula, including：Gaussian wave group expression formula is obtained, wherein, the Gaussian wave group expression formula is used to represent seismic wave field；The superposition expression formula of the seismic target earthquakes data is built based on the Gaussian wave group expression formula；The superposition expression formula of the seismic target earthquakes data is converted into the Gaussian wave group matrix expression.
- 3. according to the method for claim 1, it is characterised in that established based on the Gaussian wave group matrix expression and be based on L1 The target sparse decomposition model of norm, including：Establish the mathematical modeling of earthquake data acquisition；The mathematical modeling is entered by line translation based on the Gaussian wave group matrix expression, obtains equation group to be solved；Constraints based on the Its Sparse Decomposition model of the equation group structure based on L1 norms to be solved；Pass through formula | | c | |1→ min structures Its Sparse Decomposition the model based on L1 norms, wherein, c is expressed as coefficient vector；Based on target sparse decomposition model described in the constraints and the Its Sparse Decomposition model construction based on L1 norms.
- 4. according to the method for claim 1, it is characterised in that use convex function that can be micro- to approach the L1 norms Processing, obtains object function, including：Convex function that can be micro- described in acquisition；Equilibrium relationships between convex function that can be micro- described in foundation and the L1 norms；The object function is established based on the target sparse decomposition model and the equilibrium relationships.
- 5. according to the method for claim 1, it is characterised in that the object function is solved by projection gradient method, obtained Coefficient vector in feasible zone, including：The iterative formula of gradient descent algorithm is obtained, wherein, the iterative formula includes iteration step length and the object function Iterative gradient；The iteration step length in the iterative formula is determined based on step-length selection formula；Set the initial solution of the coefficient vector；The solving result of the coefficient vector is determined based on the initial solution, the iteration step length and the iterative formula；The solving result of the coefficient vector is projected in feasible zone based on projection formula, obtains the coefficient in the feasible zone Vector.
- 6. a kind of geological data regularization device, it is characterised in that described device includes：Acquisition module, for obtaining the Gaussian wave group matrix expression of seismic target earthquakes data, wherein, the Gaussian wave group matrix table Include the Discrete Operator of coefficient vector and Gaussian wave group up to formula, the seismic target earthquakes data are to meet seismic wave sampling thheorem Data；Module is established, for establishing the target sparse decomposition model based on L1 norms based on the Gaussian wave group matrix expression；Approximation process module, for using convex function that can be micro- to carry out approximation process to the L1 norms, object function is obtained, its In, the object function is the function on the coefficient vector；Module is solved, for solving the object function by projection gradient method, obtains the coefficient vector in feasible zone；Reconstructed module, for reconstructing the mesh according to the coefficient vector in the feasible zone and the Gaussian wave group matrix expression Mark geological data.
- 7. device according to claim 6, it is characterised in that the acquisition module includes：First acquisition unit, for obtaining Gaussian wave group expression formula, wherein, the Gaussian wave group expression formula is used to represent seismic wave ；First construction unit, for building the superposition expression formula of the seismic target earthquakes data based on the Gaussian wave group expression formula；Converting unit, for the superposition expression formula of the seismic target earthquakes data to be converted into the Gaussian wave group matrix expression.
- 8. device according to claim 6, it is characterised in that the module of establishing includes：First establishes unit, for establishing the mathematical modeling of earthquake data acquisition；Converter unit, for the mathematical modeling to be entered into line translation based on the Gaussian wave group matrix expression, obtain to be solved Equation group；Second construction unit, for the constraint bar based on the Its Sparse Decomposition model of the equation group structure based on L1 norms to be solved Part；3rd construction unit, for passing through formula | | c | |1→ min structures Its Sparse Decomposition the model based on L1 norms, wherein, C is expressed as coefficient vector；4th construction unit, for based on mesh described in the constraints and the Its Sparse Decomposition model construction based on L1 norms Mark Its Sparse Decomposition model.
- 9. device according to claim 6, it is characterised in that the approximation process module includes：Second acquisition unit, for obtaining the convex function that can be micro-；Second establishes unit, for establishing the equilibrium relationships between the convex function that can be micro- and the L1 norms；3rd establishes unit, for establishing the object function based on the target sparse decomposition model and the equilibrium relationships.
- 10. device according to claim 6, it is characterised in that the solution module includes：3rd acquiring unit, for obtaining the iterative formula of gradient descent algorithm, wherein, the iterative formula includes iteration step Long and the object function iterative gradient；First determining unit, for determining the iteration step length in the iterative formula based on step-length selection formula；Setup unit, for setting the initial solution of the coefficient vector；Second determining unit, for based on the initial solution, the iteration step length and the iterative formula determine the coefficient to The solving result of amount；Projecting cell, for being projected to the solving result of the coefficient vector in feasible zone based on projection formula, obtain described Coefficient vector in feasible zone.
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