CN109991657A - High resolution seismic data processing method based on inverse two points of recursion singular value decompositions - Google Patents
High resolution seismic data processing method based on inverse two points of recursion singular value decompositions Download PDFInfo
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Abstract
The invention discloses the High resolution seismic data processing methods based on inverse two points of recursion singular value decompositions, which comprises the following steps: step 1: obtaining single-channel seismic signal；Step 2: seismic signal being decomposed using MRSVD algorithm, then obtains new detail signal and approximate signal using the obtained layer-by-layer backward induction method of details singular value；Step 3: new detail signal being gradually added in original signal, the high frequency section of seismic signal is compensated, to obtain high-resolution seismic signal.
Description
Technical field
The present invention relates to field of seismic exploration, and in particular to the seismic data high score based on inverse two points of recursion singular value decompositions
Resolution processing method.
Background technique
In seismic prospecting, the resolution ratio for improving seismic signal is problem particularly significant in data acquisition and procession.Cause
It is that the key factor of stratum detailed information is obtained in seismic survey work for seismic signal resolution ratio, to research thin layer or small ground
Plastid has a very important significance, and many Geophysicist propose and developed at a few class High resolution seismic datas thus
The method of reason: (1) spectral whitening, it is one that it, which improves signal resolution by broadening amplitude spectrum, and does not change the phase spectrum of wavelet
The filtering of kind " net amplitude "；(2) inverse Q filtering, a technique for compensation attenuation by earth absorption effect, it can not only be compensated
Amplitude decaying and frequency loss, but also the phase characteristic of record can be improved, so as to improve the continuity of lineups, improve weak
The energy of back wave and signal-to-noise ratio, the resolution ratio of seismic data；(3) multiple dimensioned conjoint analysis method, this method usually utilize survey
The geophysical techniques such as well data, crosshole seismic, VSP over the ground under same target geological body carry out the reflection of different scale property,
Seismic data resolution is improved by the synergy between them；
(4) deconvolution, by assuming that seismic wavelet is minimum phase, reflection coefficient is the distribution of Gauss white noise, using earthquake
The auto-correlation of record replaces the auto-correlation of wavelet, and uses the Wiener filtering based on second-order statistic on this basis to realize son
Wave estimation and deconvolution.
The above method has a good effect to seismic data resolution is improved, however these methods or is difficult to keep earthquake
Data amplitudes relativeness or height rely on Q value and seek or need data in special well, can only be respective
Preferable compensation result is obtained in the scope of application.
SVD decomposition is using this biggish feature of correlation between seismic signal, according to Energy distribution relationship, by stretching
A kind of method that seismic data is decomposed in contracting rotation.Signal decomposition can be that a series of reflection signal thin portions are special by SVD method
The combination of the approximate signal of the detail signal and reflection signal main body framework of sign.Multiresolution singular value decomposition algorithm (Multi-
Resolution singular value decomposition, MRSVD) it is by two points of recursion structural principles of matrix and the side SVD
Method combines, and gradually carries out the adaptive Time-Frequency Analysis Method of one kind of multi-scale refinement to signal by Telescopic rotating.This method
There is no the problems for determining row matrix, columns, and the structure of matrix is simple, but in the way of recursive decomposition and this simple two
Sub-matrix structure combines, and the multi-level decomposition that a kind of pair of signal is gradually removed but is able to achieve, well faint in signal
Detail signal and main running signal embody at many levels, to be conducive to extract wherein implicit signal characteristic.At present at
Function be applied to signal identification, signal restores and the fields such as de-noising, mechanical fault diagnosis.
In order to make it easy to understand, being illustrated to MRSVD algorithm principle.
MRSVD decomposable process: for discrete seismic signal X=(x1,x2,x3,…,xN), a line number is constructed with this signal
For 2 Hankel matrix,
SVD processing is carried out to this matrix, is obtained
H=uSVT (2)
Orthogonal matrix u=(u in formula1,u2), u ∈ R2×2, orthogonal matrix V=(υ1,υ2,…,υ(N-1)), V ∈ R(N-1)×(N-1),
Diagonal matrix S=(diag (σa,σd), O), S ∈ R2×(N-1),σa< < σd.Formula (2) is rewritten into column vector uiAnd υiIndicate shape
Formula:
In formula, ui∈R2×1, υi∈R(N-1)×1, i=1,2.It enablesThen Ha∈R2×(N-1), it is corresponding to be
Big singular value reflects the body feature of signal, is called approximate matrix；Hd∈R2×(N-1), it is small that it is corresponding
Singular value reflects the minutia of signal, is called detail matrices.
The approximate signal A that first time SVD is obtained1With detail signal D1Respectively from matrix Ha、HdIt obtains.With detail signal D1=
(d1,d2,…,dN) seek for come illustrate its obtain process, detail matrices HdIt is the vector of two rows
Wherein, u2,1, u2,2For column vector u2The the 1st, 2 coordinate.
Such as (5) formula, if Ld1And Ld2It is detail matrices HdThe subvector of two row vectors, and respectively represent in respective row vector
D2,d3..., dN-1, but Ld1≠Ld2.Such as d2In Ld1In value be σd1u2,1υ2,2, and in Ld2In value be σd1u2,2υ2,1, this
Two values are obviously unequal.So in order to obtain the complete approximate signal of information, by Ld1And Ld2It is averaging, recycles this flat
Mean value is as detail signal D1In corresponding data.Therefore, D1Finally it is represented by following form:
D=(d1, (Ld1+Ld2)/2,dN) (6)
Similarly, approximate signal A can be obtained1.Thus the result D of the 1st decomposition has been obtained using MRSVD method1And A1,
Detail signal D1Corresponding is small singular value σd1, reflection be signal minutia.Approximate signal A1Corresponding is big unusual
Value σa1, reflection be signal body feature.Followed by A1Matrix shown in (1) formula of construction, and similarly handled, it can
Obtain two component signal D2And A2, so successively decomposed, original signal be finally decomposed into a series of detail signal and approximation
Signal.
As shown in Fig. 2, inventor studies the amplitude spectrum of approximate signal obtained in MRSVD decomposable process, discovery
It is constantly increasing with number is decomposed, the high frequency section of original signal constantly is decomposed out in the form of detail signal, MRSVD
Substantially constantly decomposite the high fdrequency component of signal.
Therefore, the restructuring procedure that inventor studies discovery MRSVD is exactly that detail signal and approximate signal are successively superimposed
Process, i.e., by M layers of detail signal DMWith approximate signal AMThe approximate signal A of superposition building (M-1) layerM-1, then approximate
Signal AM-1Again with detail signal DM-1The approximate signal A of superposition building (M-2) layerM-2, so successively carry out, former letter can be obtained
The reconstruction formula of number X are as follows:
In formula, M indicates total Decomposition order.
Summary of the invention
Present invention aims at establishing, a kind of seismic data based on inverse two points of recursion singular value decompositions (IMRSVD) is adaptive
High resolution data processing methods are answered, the missing high frequency section backstepping for the seismic signal that can be will test comes out, to be superimposed acquisition
High-resolution seismic signal.
In order to realize above-mentioned technical effect, the invention adopts the following technical scheme:
High resolution seismic data processing method based on inverse two points of recursion singular value decompositions, comprising the following steps:
Step 1: obtaining single-channel seismic signal X；
Step 2: seismic signal being decomposed using MRSVD algorithm, is then successively inversely passed using obtained details singular value
It pushes away and obtains new detail signal and approximate signal；
Step 3: new detail signal is gradually added in original signal, the high frequency section of seismic signal is compensated, thus
Obtain high-resolution seismic signal, the formula of use are as follows:
In formula, X indicates original signal, A 'iIndicate i-th high frequency compensation as a result, G indicates total backward induction method number, D 'i
For detail signal.
As a kind of optimal technical scheme, total backward induction method number is controlled by revising plan mould, amendment side
Differential mode calculation formula are as follows:
Wherein, A 'i(t) indicate i-th high frequency compensation as a result, t be the time, N be signal length, a is constant.To every
The signal A' of secondary high frequency compensation1, A'2,...,A'(G-1),A'GCalculating its revising plan mould is V1,V2,...,V(G-1),VGIf
V(G-6)≈V(G-3)≈VG, i.e. revising plan mould restrains and reaches maximum value, and at this moment total backward induction method number G is determined, and
A'GFor finally obtained high-resolution seismic exploration signal.
As a kind of optimal technical scheme, the details singular value σ that is decomposed in above-mentioned steps 2 using MRSVDd1,
σd2,…,σdM, new details singular value σ ' is gone out by fitting function backward induction methoddi(i=1,2 ...), then pass through details singular value
Obtain corresponding detail signal D 'i, fit indices function are as follows:
Wherein, j indicates the decomposition number of MRSVD；anRepresent polynomial coefficient；K is a positive number, usually less than 3；N
It is polynomial order, so that F (j) is approached known details singular value under least squares sense, acquire k and polynomial system
Number.
As a kind of optimal technical scheme, MRSVD forward direction decomposed class is obtained by following formula:
Ej=∑ | Aj-1-Aj|2/∑|Aj-1|2, (j=1 ..., M)
J indicates that MRSVD forward direction decomposes jth layer, works as Ej≤10-6When, Cycle-decomposition terminates, and M is that MRSVD forward direction decomposes total layer
Number；Aj-1And AjRespectively -1 layer of approximate signal decomposed with jth layer of jth.
As a kind of optimal technical scheme, new details singular value details of construction matrix is utilizedTo
Obtain corresponding detail signal.
The beneficial effects of the present invention are:
Inverse two points are established by the high frequency section of backward induction method seismic signal the present invention is based on the feature of original signal to pass
It pushes away singular value decomposition (IMRSVD), the main thought of the algorithm: the height in order to restore the missing of seismic signal caused by earth filtering
Frequently, we are by the 1st detail signal of feature backward induction method of the obtained detail signal of MRSVD, i.e., the 1st time extrapolation original signal
High frequency section, detail signal is added to obtained on original signal the 1st high frequency compensation as a result, then backward induction method the 2nd is thin
Signal is saved, i.e., detail signal is added on original signal and obtains the 2nd high frequency compensation by the high frequency section of the 2nd time extrapolation original signal
As a result, such gradually backward induction method carries out, constantly compensate seismic signal high frequency section, expand seismic signal bandwidth, thus real
The high resolution processing of existing seismic data.
Detailed description of the invention
Fig. 1 is IMRSVD decomposition diagram proposed by the present invention.
Fig. 2 is the amplitude spectrogram of approximate signal obtained in MRSVD decomposable process, and wherein lines divide from top to bottom in Fig. 2
Original, the 10th~50 decomposition is not represented.
Fig. 3 is two-dimensional theoretical model forward modeling seismic cross-section.
Fig. 4 is the theoretical model seismic cross-section after IMRSVD high resolution processing.
Fig. 5 is two-dimentional actual seismic sectional view.
Fig. 6 is the two-dimentional actual seismic sectional view after IMRSVD high resolution processing.
Fig. 7 is the amplitude spectrum comparison diagram of the 134th track data before and after IMRSVD high resolution processing.
Specific embodiment
The technical scheme in the embodiments of the invention will be clearly and completely described below, it is clear that described implementation
Example is only a part of the embodiment of the present invention, instead of all the embodiments.The detailed description of embodiment of the invention below is simultaneously
It is not intended to be limiting the range of claimed invention, but is merely representative of selected embodiment of the invention.Based on of the invention
Embodiment, those skilled in the art's every other embodiment obtained without making creative work, all belongs to
In the scope of protection of the invention.
Embodiment
Based on MRSVD technology, the present invention provides IMRSVD algorithms, for so that seismic signal high-resolution
Place, the high frequency of the missing of seismic signal caused by the core of the method is to restore earth filtering, by MRSVD forward direction point
All details singular values that solution obtains are fitted extrapolation, obtain the 1st new detail signal, i.e., the 1st time original signal of extrapolating
High frequency section D '1, by detail signal D '1It is added on original signal X and obtains the result X ' of the 1st high frequency compensation1, then inversely pass
Push away the 2nd detail signal D '2, i.e., the high frequency section D ' of the 2nd time extrapolation original signal2, by detail signal D '2Be added to original signal X '1
On obtain the result X ' of the 2nd high frequency compensation2, so gradually backward induction method, continuous compensation seismic signal high frequency section expand ground
Signal bandwidth is shaken, to realize the high resolution processing of seismic data.
Therefore, in the present invention, the High-resolution Processing method includes following procedure:
High resolution seismic data processing method based on inverse two points of recursion singular value decompositions, comprising the following steps:
Step 1: obtaining single-channel seismic signal X；
Step 2: seismic signal being decomposed using MRSVD algorithm, is then successively inversely passed using obtained details singular value
It pushes away and obtains new detail signal and approximate signal；
Specifically, MRSVD forward direction decomposed class is obtained by following formula:
Ej=∑ | Aj-1-Aj|2/∑|Aj-1|2, (j=1 ..., M)
J indicates that MRSVD forward direction decomposes jth layer, works as Ej≤10-6When, Cycle-decomposition terminates, and M is that MRSVD forward direction decomposes total layer
Number；Aj-1And AjRespectively -1 layer of approximate signal decomposed with jth layer of jth.
The details singular value σ decomposed using MRSVDd1,σd2,…,σdM, these details surprise is fitted by fitting function
Different value, so that backward induction method goes out new details singular value σ 'di(i=1,2 ...), then obtained by details singular value corresponding thin
Save signal D 'i, fitting function are as follows:
Wherein, j indicates the decomposition number of MRSVD；anRepresent polynomial coefficient；K is a positive number, usually less than 3；N
It is polynomial order, so that F (j) is approached known details singular value under least squares sense, acquire k and polynomial system
Number.
Using new details singular value details of construction matrix, it isTo obtain corresponding details letter
Number.
Step 3: new detail signal is gradually added in original signal, the high frequency section of seismic signal is compensated, thus
Obtain high-resolution seismic signal, the formula of use are as follows:
In formula, X indicates original signal, A 'iIndicate i-th high frequency compensation as a result, G indicates total backward induction method number, D 'i
For detail signal.
Total backward induction method number is controlled by revising plan mould, revising plan mould are as follows:
Wherein, A 'i(t) indicate i-th high frequency compensation as a result,tFor the time,NFor the length of signal, a is constant.To every
The signal A' of secondary high frequency compensation1,A'2,...,A'(G-1),A'GCalculating its revising plan mould is V1,V2,...,V(G-1),VGIf
V(G-6)≈V(G-3)≈VG, i.e. revising plan mould restrains and reaches maximum value, and at this moment total backward induction method number G is determined, and
A'GFor finally obtained high-resolution seismic exploration signal.
In the present invention, Fig. 3 is the original graph of theoretical model data, and Fig. 4 is that treated by the method for the invention
Theoretical model high-resolution is as a result, comparison diagram 4, Fig. 3 can see, and the thin layer of the second layer from top to bottom in Fig. 3 cannot be distinguished, the
Three layers of discrimination are bad, and wedge model can be differentiated to the 23rd, after IMRSVD is handled, as shown in figure 4, from upper
The second layer can have a degree of differentiation down, and third layer can be distinguished completely, and wedge model also by that can only divide originally
Distinguish that the 23rd has been increased to and can differentiate to the 18th.
Fig. 5, Fig. 6 are respectively the actual seismic data of IMRSVD before and after the processing, and comparison diagram 5, Fig. 6 can see, and are passed through
After IMRSVD processing, seismic resolution is significantly increased, the continuity enhancing of seismic event, especially in 1.0 seconds or so masters
Want target zone effect particularly evident, we have extracted the 134th track data of IMRSVD before and after the processing and have carried out Analyzing the amplitude spectrum, such as
Shown in Fig. 7, it can be seen that after the processing of IMRSVD method, low frequency part can be positively maintained, and high frequency section is had
Effect is promoted, and is had great significance to earthquake increase resolution.
According to above-described embodiment, the present invention can be realized well.It is worth noting that before based on said structure design
It puts, to solve same technical problem, even if that makes in the present invention is some without substantive change or polishing, is used
Technical solution essence still as the present invention, therefore it should also be as within the scope of the present invention.
Claims (5)
1. the High resolution seismic data processing method based on inverse two points of recursion singular value decompositions, which is characterized in that including following
Step:
Step 1: obtaining single-channel seismic signal X；
Step 2: seismic signal is decomposed using singular value decomposition algorithms of differentiating more, it is then layer-by-layer using obtained details singular value
Backward induction method obtains new detail signal and approximate signal；
Step 3: new detail signal being gradually added in original signal, the high frequency section of seismic signal is compensated, to obtain
High-resolution seismic signal, the formula of use are as follows:
In formula, X indicates original signal, A 'iIndicate i-th high frequency compensation as a result, G indicates total backward induction method number, D 'iIt is thin
Save signal.
2. the High resolution seismic data processing method according to claim 1 based on inverse two points of recursion singular value decompositions,
It is characterized in that, being controlled by revising plan mould total backward induction method number, revising plan mould are as follows:
Wherein, A 'i(t) indicate i-th high frequency compensation as a result, t be the time, N be signal length, a is constant, to each height
The signal A' of frequency compensation1,A'2,...,A'(G-1),A'GCalculating its revising plan mould is V1,V2,...,V(G-1),VGIf V(G-6)
≈V(G-3)≈VG, i.e. revising plan mould restrains and reaches maximum value, and at this moment total backward induction method number G is determined, and A'GFor
Finally obtained high-resolution seismic exploration signal.
3. the High resolution seismic data processing method according to claim 1 based on inverse two points of recursion singular value decompositions,
It is characterized in that, the details singular value σ decomposed in above-mentioned steps 2 using MRSVDd1,σd2,…,σdM, pass through fitting function
It is fitted details singular value, so that backward induction method goes out new details singular value σ 'di(i=1,2 ...), then obtained by details singular value
To corresponding detail signal D'i, fit indices function are as follows:
Wherein, j indicates the decomposition number of MRSVD；anRepresent polynomial coefficient；K is a positive number, usually less than 3；N is multinomial
The order of formula makes F (j) approach known details singular value under least squares sense, acquires k and polynomial coefficient.
4. the High resolution seismic data processing method according to claim 3 based on inverse two points of recursion singular value decompositions,
It is characterized in that, MRSVD forward direction decomposed class is obtained by following formula:
Ej=∑ | Aj-1-Aj|2/∑|Aj-1|2, (j=1 ..., M)
Wherein, j indicates that MRSVD forward direction decomposes jth layer, works as Ej≤10-6When, Cycle-decomposition terminates, and M is that MRSVD forward direction is decomposed always
The number of plies；Aj-1And AjRespectively -1 layer of approximate signal decomposed with jth layer of jth.
5. the High resolution seismic data processing method according to claim 3 based on inverse two points of recursion singular value decompositions,
It is characterized in that, being using new details singular value details of construction matrixTo obtain corresponding details
Signal.
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