CN102193107B - Method for separating and denoising seismic wave field - Google Patents

Abstract

The invention discloses a method for separating and denoising a seismic wave field, comprising the following steps of: 1, reading seismic data, including m channels with each having n sampling points, into a two-dimensional array F1; 2, subjecting original seismic data F1 to linear correction to obtain L1; 3, subjecting the linearly-corrected seismic signal L1 to singular value decomposition; 4, processing a singular value series sigma1, and extracting a singular value sigma 2 reconstruction signal of a target signal to obtain L2; 5, subjecting the reconstructed signal L2 to linear inverse moveout correction in accordance with the time-distance rule of seismic wave velocity and seismic signals to obtain F2, and returning to an input data field; and 6, outputting the data F2 subjected to linear inverse correction in a seismic data format during input, thus separating and denoising seismic wave field are completed by combining linear correction with singular value decomposition. The method has the characteristic of thorough wave field separation.

Description

A kind of seismic wave field separates and denoising method

Technical field

The invention belongs to the Seismic wave processing technical field, particularly a kind of based on linearity correction (LineNormal Move Out, abbreviation LNMO) unite seismic wave field separation and the denoising method of realization with svd (Singular ValueDecomposition is called for short SVD).

Technical background

Seismic wave field is very complicated, in the open air during earthquake data acquisition, and the propagation property of the impact of extraneous various disturbing factors and seismic event self, the undesired signal that can bring many regular and irregulars into; In addition, some of indoor processing processed measure also can introduce a large amount of noises, as deconvolution, skew etc., has had a strong impact on the extraction of geological information.Seismic wave field separates with denoising extremely important, and it is prerequisite and the guarantee that improves seismic data signal to noise ratio (S/N ratio) and resolution, therefore, in geological data is processed, will do unremitting struggle with undesired signal all the time.SVD filtering is to optimize to extract relevant information from multitrace seismogram, to utilize singular value to strengthen coherent energy as orthogonal basis in the feature of signal space Orthogonal Decomposition, the compacting noise, be that it is to utilize coherence's difference of seismic event to reach the purpose of wave field separation and denoising, if come reconstruction signal just to realize elimination to weak signal and random noise with larger singular value; In order to eliminate specific lineups, also can cast out larger singular value and come reconstruction signal.Existing method is nearly all just come seismic wave field separation and denoising with SVD single method technology, and the application space is limited, and useful signal easily is damaged, and has affected the extraction of effective information.

Summary of the invention

In order to overcome above-mentioned the deficiencies in the prior art, the object of the invention is to propose a kind of seismic wave field separates and denoising method, realize that with the means of SVD Combined Treatment seismic wave field separates and denoising by LNMO, directly carry out SVD wave field separation and denoising for interested seismic signal composition, avoided the conventional art application space narrow, the defective that the useful signal loss is serious has wave field separation characteristics thoroughly.

To achieve these goals, the technical solution used in the present invention is: a kind of seismic wave field separates the method with denoising, comprises the steps:

The first step: will contain the m road, per pass has the geological data of n sampled point to read two-dimensional array F ₁In;

Second step: with original earthquake data F ₁Carry out linearity correction, obtain L ₁:

Carry out linearity correction for linear pattern signal (as: direct wave, refraction wave) lineups, its implementation is the apparent velocity value of given linear lineups, relation by apparent velocity and offset distance, for each seismic trace is determined the linearity correction time difference, then each data of each seismic trace are carried out time shift; During linearity correction, method for determining difference is:

$\mathrm{\ΔT}=\frac{x}{V_T}$

Wherein: Δ T is the linearity correction time difference, V _TBe the lineups apparent velocity that needs are proofreaied and correct, x is offset distance;

Carry out linearity correction for non-conversion reflection wave (as: reflected P-P ripple, S-S ripple) lineups, its implementation is at that time on the basis of rule, for each seismic trace is determined the linearity correction time difference, then each data of each seismic trace are carried out time shift; During linearity correction, method for determining difference is:

$\mathrm{\&Delta;t}=t-{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0=\sqrt{{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0^2+\frac{x^2}{v^2}}-{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0$

Wherein: Δ t is the non-conversion reflection wave linearity correction time difference, and x is offset distance, and t is that offset distance is the whilst on tour of x, t ₀Be the whilst on tour in the zero shot-geophone distance situation, v is stack velocity;

Carry out linearity correction for conversion reflection wave (as: reflected P-S ripple) lineups, be when transformed wave on the basis of rule, for each seismic trace is determined the linearity correction time difference, then each data of each seismic trace are carried out time shift; During linearity correction, method for determining difference is:

$\mathrm{\&Delta;}{t}_{\mathrm{PS}}=t_{\mathrm{PS}}-{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_{0\mathrm{PS}}=\frac{1}{v_P}(\sqrt{x_{\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="HSA00000048453700032.png"\; state="\{\{state\}\}">P</figure-callout>}}^2+z^2}-z)+\frac{1}{v_S}(\sqrt{x_{\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HSA00000048453700032.png"\; state="\{\{state\}\}">S</figure-callout>}}^2+z^2}-z)$

Wherein: Δ t _PSBe the conversion reflection wave linearity correction time difference, x _PBe the distance of focus to transfer point, x _SBe the distance of transfer point to acceptance point, t _PSThat offset distance is (x _P+ x _S) whilst on tour, t _0PSBe the whilst on tour in the zero shot-geophone distance situation, v _PBe p wave interval velocity, v _SBe the S wave velocity, z is the reflecting interface degree of depth;

The 3rd step: to the seismic signal L after the process linearity correction ₁Carry out svd:

L ₁＝U∑ ₁V ^T

Wherein: upper angle T represents transposition, and U is by L ₁L ₁ ^TFeature value vector consist of, V is by L ₁ ^TL ₁Feature value vector consist of, ∑ ₁Be made of singular value, singular value is descending to be arranged on the principal diagonal of matrix:

${\mathrm{\&Sigma;}}_1=\left[\begin{array}{cccc}{\mathrm{\&sigma;}}_1& & & 0\\ & {\mathrm{\&sigma;}}_2& & \\ & & \mathrm{<figure-callout\; id="0"\; label="O"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">O</figure-callout>}& \\ 0& & & {\mathrm{\&sigma;}}_m\end{array}\right]$

Wherein: σ ₁, σ ₂Λ σ _mBe L ₁Singular value;

The 4th step: to ∑ ₁Process, extract the singular value ∑ of echo signal ₂Reconstruction signal obtains L ₂Signal can be divided into two classes and be reconstructed, specific as follows:

(1) svd low-pass filtering, extract linear wave field:

$L_{\mathrm{Lp}}=\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_j{u}_j{v}_j^T$

Wherein: upper angle T represents transposition, L _LpBe the signal of reconstruct after the SVD low-pass filtering, j is the singular value sequence number, and p is L ₁Order, and 1≤p≤m, σ _jBe L ₁J singular value, u _jBe L ₁L ₁ ^TJ proper vector, v _jBe L ₁ ^TL ₁J proper vector;

(2) svd high-pass filtering, isolate other seismic signal:

$L_{\mathrm{Hp}}=\underset{j=q}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_j{u}_j{v}_j^T$

Wherein: upper angle T represents transposition, L _HpBe the signal of reconstruct after the svd high-pass filtering, j is the singular value sequence number, and q is L ₁Order, and 1≤q≤m, m are earthquake total road number, σ _jBe L ₁J singular value, u _jBe L ₁L ₁ ^TJ proper vector, v _jBe L ₁ ^TL ₁J proper vector;

The relative size of singular value is depended in the selection of p and q, and specific practice is by singular value σ _jThe function curve of subscript j determine;

According to actual filtering situation, L ₂Be L _Lp, L _HPOne of;

The 5th the step: according to seimic wave velocity and seismic signal the time apart from rule, with the signal L after reconstruct ₂Carry out anti-correction of the linearity time difference, obtain F ₂, get back in the data field of input:

Carry out the anti-correction of linearity for linear pattern signal (as: direct wave, refraction wave) lineups, on the basis of linearity correction apparent velocity value, the relation of Negotiation speed and offset distance is determined linear anti-the correction time difference for each seismic trace, then each data of each seismic trace is carried out time shift:

$\mathrm{\&Delta;T}=\frac{x}{V_T}$

Wherein: Δ T is the linear anti-time difference, the V of proofreading and correct _TBe the lineups apparent velocity that needs are proofreaied and correct, x is offset distance;

Carry out the anti-correction of linearity for non-conversion reflection wave (as: reflected P-P ripple, S-S ripple) lineups, at that time on the basis of rule and linearity correction apparent velocity value, determine anti-the correction time difference for each seismic trace, then each data of each seismic trace carried out time shift:

$\mathrm{\&Delta;t}=t-{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0=\sqrt{{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0^2+\frac{x^2}{v^2}}-{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0$

Wherein: Δ t is anti-the correction time difference, and x is offset distance, and t is that offset distance is the whilst on tour of x, t ₀Be the whilst on tour in the zero shot-geophone distance situation, v is stack velocity;

Carry out the anti-correction of linearity for conversion reflection wave (as: reflected P-S ripple) lineups, conversion during reflection wave on the basis of rule and linearity correction apparent velocity value, determine linear anti-the correction time difference for each seismic trace, then each data of each seismic trace carried out time shift:

$\mathrm{\&Delta;}{t}_{\mathrm{PS}}=t_{\mathrm{PS}}-{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_{0\mathrm{PS}}=\frac{1}{v_P}(\sqrt{x_{\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="HSA00000048453700032.png"\; state="\{\{state\}\}">P</figure-callout>}}^2+z^2}-z)+\frac{1}{v_S}(\sqrt{x_{\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HSA00000048453700032.png"\; state="\{\{state\}\}">S</figure-callout>}}^2+z^2}-z)$

Wherein: Δ t _PSBe the linear anti-time difference, the x of proofreading and correct of conversion reflection wave _PBe the distance of focus to transfer point, x _SBe the distance of transfer point to acceptance point, t _PSThat offset distance is (x _P+ x _S) whilst on tour, t _0PSBe the whilst on tour in the zero shot-geophone distance situation, v _PBe p wave interval velocity, v _SBe the S wave velocity, z is the reflecting interface degree of depth;

The 6th step: with the data F after the anti-correction of linearity ₂By the geological data formatted output in when input, just completed linearity correction and united with svd and realize that seismic wave field separates and denoising.

Because adopting LNMO with the means of SVD Combined Treatment, seismic wave field to be separated with denoising, the present invention processes, the result of doing like this is that purpose is stronger, directly carry out SVD wave field separation and denoising for interested seismic signal composition, avoided simultaneously the application space of conventional art narrow, the defectives such as the useful signal loss is serious have wave field separation characteristics thoroughly.

Description of drawings

Fig. 1 is that example of the present invention one seismic wave field separates and denoising figure as a result, and wherein (a) be ray tracing list big gun seismologic record, and model records and contains direct wave and three reflection line-ups, and has added strong random noise figure; (b) for model seismogram is carried out figure after LNMO (simultaneously downwards time shift 100ms) processes by direct wave; (c) be singular value spectrogram after original seismic data LNMO; (d) for extracting the figure as a result of the 1st σ reconstruction signal; (e) for the result of figure c being carried out the anti-figure as a result that proofreaies and correct of linearity; (f) be singular value spectrogram after LNMO, extract 2～60 σ reconstruction signals; (g) for extracting the figure as a result of 2～60 σ reconstruction signals; (h) for the result of figure g being carried out the anti-figure as a result that proofreaies and correct of linearity.

Fig. 2 is example two wave field separations of the present invention and denoising figure as a result, and wherein (a) is original single big gun seismogram, contains direct wave, ground roll, refraction wave and random noise; (b) process rear figure as a result for the non-conversion reflection wave being carried out LNMO; (c) be singular value spectrogram after original seismic data LNMO, extract the result of 1～5 σ reconstruct seismic signal; (d) the reflection seismic waves field pattern for extracting; (e) be singular value spectrogram after original seismic data LNMO, extract 6～228 σ reconstruct seismic signals; (f) the interference noise figure for extracting; (g) for the isolated effective reflection of SVD being carried out the anti-figure as a result that proofreaies and correct of linearity; (h) for the isolated interference noise of SVD being carried out the anti-figure as a result that proofreaies and correct of linearity.

Fig. 3 is the t of real data LNMO ₀Time and corresponding stack velocity Parameter Map.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in further detail.

Referring to Fig. 1, Fig. 2, Fig. 3, a kind of seismic wave field separates and denoising method, comprises the steps:

The first step: will contain the m road, per pass has the geological data of n sampled point to read two-dimensional array F ₁In;

Second step: with original earthquake data F ₁Carry out linearity correction, obtain L ₁:

Carry out linearity correction for linear pattern signal (as: direct wave, refraction wave) lineups, its implementation is the apparent velocity value of given linear lineups, relation by apparent velocity and offset distance, for each seismic trace is determined the linearity correction time difference, then each data of each seismic trace are carried out time shift; During linearity correction, method for determining difference is:

$\mathrm{\&Delta;T}=\frac{x}{V_T}$

Wherein: Δ T is the linearity correction time difference, V _TBe the lineups apparent velocity that needs are proofreaied and correct, x is offset distance;

Carry out linearity correction for non-conversion reflection wave (as: reflected P-P ripple, S-S ripple) lineups, its implementation is at that time on the basis of rule, for each seismic trace is determined the linearity correction time difference, then each data of each seismic trace are carried out time shift; During linearity correction, method for determining difference is:

$\mathrm{\&Delta;t}=t-{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0=\sqrt{{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0^2+\frac{x^2}{v^2}}-{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0$

Wherein: Δ t is the non-conversion reflection wave linearity correction time difference, and x is offset distance, and t is that offset distance is the whilst on tour of x, t ₀Be the whilst on tour in the zero shot-geophone distance situation, v is stack velocity;

Carry out linearity correction for conversion reflection wave (as: reflected P-S ripple) lineups, be when transformed wave on the basis of rule, for each seismic trace is determined the linearity correction time difference, then each data of each seismic trace are carried out time shift; During linearity correction, method for determining difference is:

$\mathrm{\&Delta;}{t}_{\mathrm{PS}}=t_{\mathrm{PS}}-{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_{0\mathrm{PS}}=\frac{1}{v_P}(\sqrt{x_{\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="HSA00000048453700032.png"\; state="\{\{state\}\}">P</figure-callout>}}^2+z^2}-z)+\frac{1}{v_S}(\sqrt{x_{\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HSA00000048453700032.png"\; state="\{\{state\}\}">S</figure-callout>}}^2+z^2}-z)$

Wherein: Δ t _PSBe the conversion reflection wave linearity correction time difference, x _PBe the distance of focus to transfer point, x _SBe the distance of transfer point to acceptance point, t _PSThat offset distance is (x _P+ x _S) whilst on tour, t _0PSBe the whilst on tour in the zero shot-geophone distance situation, v _PBe p wave interval velocity, v _SBe the S wave velocity, z is the reflecting interface degree of depth;

The 3rd step: to the seismic signal L after the process linearity correction ₁Carry out svd:

L ₁＝U∑ ₁V ^T

Wherein: upper angle T represents transposition, and U is by L ₁L ₁ ^TFeature value vector consist of, V is by L ₁ ^TL ₁Feature value vector consist of, ∑ ₁Be made of singular value, singular value is descending to be arranged on the principal diagonal of matrix:

${\mathrm{\&Sigma;}}_1=\left[\begin{array}{cccc}{\mathrm{\&sigma;}}_1& & & 0\\ & {\mathrm{\&sigma;}}_2& & \\ & & \mathrm{<figure-callout\; id="0"\; label="O"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">O</figure-callout>}& \\ 0& & & {\mathrm{\&sigma;}}_m\end{array}\right]$

Wherein: σ ₁, σ ₂Λ σ _mBe L ₁Singular value;

The 4th step: to ∑ ₁Process, extract the singular value ∑ of echo signal ₂Reconstruction signal obtains L ₂Signal can be divided into two classes and be reconstructed, specific as follows:

(1) svd low-pass filtering, extract linear wave field:

$L_{\mathrm{Lp}}=\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_j{u}_j{v}_j^T$

Wherein: upper angle T represents transposition, L _LpBe the signal of reconstruct after the svd low-pass filtering, j is the singular value sequence number, and p is L ₁Order, and 1≤p≤m, σ _jBe L ₁J singular value, u _jBe L ₁L ₁ ^TJ proper vector, v _jBe L ₁ ^TL ₁J proper vector;

(2) svd high-pass filtering, isolate other seismic signal:

$L_{\mathrm{Hp}}=\underset{j=q}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_j{u}_j{v}_j^T$

Wherein: upper angle T represents transposition, L _HpBe the signal of reconstruct after the svd high-pass filtering, j is the singular value sequence number, and q is L ₁Order, and 1≤q≤m, m are earthquake total road number, σ _jBe L ₁J singular value, u _jBe L ₁L ₁ ^TJ proper vector, v _jBe L ₁ ^TL ₁J proper vector;

The relative size of singular value is depended in the selection of p and q, and specific practice is by singular value σ _jThe function curve of subscript j determine;

According to actual filtering situation, L ₂Be L _Lp, L _HPOne of;

The 5th the step: according to seimic wave velocity and seismic signal the time apart from rule, with the signal L after reconstruct ₂Carry out anti-correction of the linearity time difference, obtain F ₂, get back in the data field of input:

Carry out the anti-correction of linearity for linear pattern signal (as: direct wave, refraction wave) lineups, on the basis of linearity correction apparent velocity value, the relation of Negotiation speed and offset distance is determined linear anti-the correction time difference for each seismic trace, then each data of each seismic trace is carried out time shift:

$\mathrm{\&Delta;T}=\frac{x}{V_T}$

Wherein: Δ T is the linear anti-time difference, the V of proofreading and correct _TBe the lineups apparent velocity that needs are proofreaied and correct, x is offset distance;

Carry out the anti-correction of linearity for non-conversion reflection wave (as: reflected P-P ripple, S-S ripple) lineups, at that time on the basis of rule and linearity correction apparent velocity value, determine anti-the correction time difference for each seismic trace, then each data of each seismic trace carried out time shift:

$\mathrm{\&Delta;t}=t-{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0=\sqrt{{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0^2+\frac{x^2}{v^2}}-{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0$

Wherein: Δ t is anti-the correction time difference, and x is offset distance, and t is that offset distance is the whilst on tour of x, t ₀Be the whilst on tour in the zero shot-geophone distance situation, v is stack velocity;

Carry out the anti-correction of linearity for conversion reflection wave (as: reflected P-S ripple) lineups, conversion during reflection wave on the basis of rule and linearity correction apparent velocity value, determine linear anti-the correction time difference for each seismic trace, then each data of each seismic trace carried out time shift:

$\mathrm{\&Delta;}{t}_{\mathrm{PS}}=t_{\mathrm{PS}}-{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_{0\mathrm{PS}}=\frac{1}{v_P}(\sqrt{{\mathrm{<figure-callout\; id="2"\; label="x\; P"\; filenames="HSA00000048453700032.png"\; state="\{\{state\}\}">x</figure-callout>}}_P^{}+z^2}-z)+\frac{1}{v_S}(\sqrt{{\mathrm{<figure-callout\; id="2"\; label="x\; S"\; filenames="HSA00000048453700032.png"\; state="\{\{state\}\}">x</figure-callout>}}_S^{}+z^2}-z)$

Wherein: Δ t _PSBe the linear anti-time difference, the x of proofreading and correct of conversion reflection wave _PBe the distance of focus to transfer point, x _SBe the distance of transfer point to acceptance point, t _PSThat offset distance is (x _P+ x _S) whilst on tour, t _0PSBe the whilst on tour in the zero shot-geophone distance situation, v _PBe p wave interval velocity, v _SBe the S wave velocity, z is the reflecting interface degree of depth;

The 6th step: with the data F after the anti-correction of linearity ₂By the geological data formatted output in when input, just completed linearity correction and united with svd and realize that seismic wave field separates and denoising.

Embodiment one:

Take a ray tracing model, the implementation step of this example is described as example:

The first step: will contain 60 roads, per pass has the geological data of 600 sampled points to read two-dimensional array F ₁In;

Second step: with original earthquake data F ₁Carry out linearity correction, obtain L ₁:

Carry out linearity correction for the direct wave lineups, given direct wave apparent velocity value 1400m/s, the relation of Negotiation speed and offset distance for each seismic trace is determined linear normal moveout, is then carried out time shift to each data of each seismic trace; During linearity correction, method for determining difference is:

$\mathrm{\&Delta;T}=\frac{x}{V_T}$

Wherein: Δ T is the linearity correction time difference, V _TBe the lineups apparent velocity that needs are proofreaied and correct, x is offset distance;

Carry out linearity correction for non-conversion reflection wave (as: reflected P-P ripple, S-S ripple) lineups, its implementation is at that time on the basis of rule, for each seismic trace is determined the linearity correction time difference, then each data of each seismic trace are carried out time shift; During linearity correction, method for determining difference is:

$\mathrm{\&Delta;t}=t-{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0=\sqrt{{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0^2+\frac{x^2}{v^2}}-{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0$

Wherein: Δ t is the non-conversion reflection wave linearity correction time difference, and x is offset distance, and t is that offset distance is the whilst on tour of x, t ₀Be the whilst on tour in the zero shot-geophone distance situation, v is stack velocity;

Carry out linearity correction for conversion reflection wave (as: reflected P-S ripple) lineups, be when transformed wave on the basis of rule, for each seismic trace is determined the linearity correction time difference, then each data of each seismic trace are carried out time shift; During linearity correction, method for determining difference is:

$\mathrm{\&Delta;}{t}_{\mathrm{PS}}=t_{\mathrm{PS}}-{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_{0\mathrm{PS}}=\frac{1}{v_P}(\sqrt{{\mathrm{<figure-callout\; id="2"\; label="x\; P"\; filenames="HSA00000048453700032.png"\; state="\{\{state\}\}">x</figure-callout>}}_P^{}+z^2}-z)+\frac{1}{v_S}(\sqrt{{\mathrm{<figure-callout\; id="2"\; label="x\; S"\; filenames="HSA00000048453700032.png"\; state="\{\{state\}\}">x</figure-callout>}}_S^{}+z^2}-z)$

Wherein: Δ t _PSBe the conversion reflection wave linearity correction time difference, x _PBe the distance of focus to transfer point, x _SBe the distance of transfer point to acceptance point, t _PSThat offset distance is (x _P+ x _S) whilst on tour, t _0PSBe the whilst on tour in the zero shot-geophone distance situation, v _PBe p wave interval velocity, v _SBe the S wave velocity, z is the reflecting interface degree of depth;

The 3rd step: to the seismic signal L after the process linearity correction ₁Carry out svd:

L ₁＝U∑ ₁V ^T

Wherein: upper angle T represents transposition, and U is by L ₁L ₁ ^TFeature value vector consist of, V is by L ₁ ^TL ₁Feature value vector consist of, ∑ ₁Be made of singular value, singular value is descending to be arranged on the principal diagonal of matrix:

${\mathrm{\&Sigma;}}_1=\left[\begin{array}{cccc}{\mathrm{\&sigma;}}_1& & & 0\\ & {\mathrm{\&sigma;}}_2& & \\ & & \mathrm{<figure-callout\; id="0"\; label="O"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">O</figure-callout>}& \\ 0& & & {\mathrm{\&sigma;}}_m\end{array}\right]$

Wherein: σ ₁, σ ₂Λ σ _mBe L ₁Singular value;

The 4th step: to singular value series ∑ ₁Process, extract the singular value ∑ of echo signal ₂Reconstruction signal obtains L ₂Signal can be divided into two classes and be reconstructed, specific as follows:

(1) svd low-pass filtering is got the 1st singular value reconstruction signal, extracts through wave field:

$L_{\mathrm{Lp}}=\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_j{u}_j{v}_j^T$

Wherein: upper angle T represents transposition, L _LpBe the signal of reconstruct after the svd low-pass filtering, j is the singular value sequence number, and p is L ₁Order, and p=1, σ _jBe L ₁J singular value, u _jBe L ₁L ₁ ^TJ proper vector, v _jBe L ₁ ^TL ₁J proper vector;

(2) the 2nd～60 singular value reconstruction signal got in svd high-pass filtering, isolates other signal:

$L_{\mathrm{Hp}}=\underset{j=q}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_j{u}_j{v}_j^T$

Wherein: upper angle T represents transposition, L _HpBe the signal of reconstruct after the svd high-pass filtering, j is the singular value sequence number, and q is L ₁Order, and q=2, m are earthquake total road number, and m=60, σ _jBe L ₁J singular value, u _jBe L ₁L ₁ ^TJ proper vector, v _jBe L ₁ ^TL ₁J proper vector;

The relative size of singular value is depended in the selection of p and q, and specific practice is by singular value σ _jThe function curve of subscript j determine;

According to actual filtering situation, L ₂Be L _Lp, L _HPOne of;

The 5th the step: during according to direct wave apparent velocity 1400m/s and direct wave apart from rule, with the signal L after reconstruct ₂Carry out anti-correction of the linearity time difference, obtain F ₂, get back in the data field of input:

Carry out the anti-correction of linearity for linear pattern signal (as: direct wave, refraction wave) lineups, on the basis of linearity correction apparent velocity value, the relation of Negotiation speed and offset distance is determined linear anti-the correction time difference for each seismic trace, then each data of each seismic trace is carried out time shift:

$\mathrm{\&Delta;T}=\frac{x}{V_T}$

Wherein: Δ T is the linear anti-time difference, the V of proofreading and correct _TBe the lineups apparent velocity that needs are proofreaied and correct, x is offset distance;

Carry out the anti-correction of linearity for non-conversion reflection wave (as: reflected P-P ripple, S-S ripple) lineups, at that time on the basis of rule and linearity correction apparent velocity value, determine anti-the correction time difference for each seismic trace, then each data of each seismic trace carried out time shift:

$\mathrm{\&Delta;t}=t-{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0=\sqrt{{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0^2+\frac{x^2}{v^2}}-{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0$

Wherein: Δ t is anti-the correction time difference, and x is offset distance, and t is that offset distance is the whilst on tour of x, t ₀Be the whilst on tour in the zero shot-geophone distance situation, v is stack velocity;

Carry out the anti-correction of linearity for conversion reflection wave (as: reflected P-S ripple) lineups, conversion during reflection wave on the basis of rule and linearity correction apparent velocity value, determine linear anti-the correction time difference for each seismic trace, then each data of each seismic trace carried out time shift:

$\mathrm{\&Delta;}{t}_{\mathrm{PS}}=t_{\mathrm{PS}}-{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_{0\mathrm{PS}}=\frac{1}{v_P}(\sqrt{{\mathrm{<figure-callout\; id="2"\; label="x\; P"\; filenames="HSA00000048453700032.png"\; state="\{\{state\}\}">x</figure-callout>}}_P^{}+z^2}-z)+\frac{1}{v_S}(\sqrt{{\mathrm{<figure-callout\; id="2"\; label="x\; S"\; filenames="HSA00000048453700032.png"\; state="\{\{state\}\}">x</figure-callout>}}_S^{}+z^2}-z)$

Wherein: Δ t _PSBe the linear anti-time difference, the x of proofreading and correct of conversion reflection wave _PBe the distance of focus to transfer point, x _SBe the distance of transfer point to acceptance point, t _PSThat offset distance is (x _P+ x _S) whilst on tour, t _0PSBe the whilst on tour in the zero shot-geophone distance situation, v _PBe p wave interval velocity, v _SBe the S wave velocity, z is the reflecting interface degree of depth;

The 6th step: with the data F after the anti-correction of linearity ₂By the geological data formatted output in when input, just completed linearity correction and united with svd and realize that seismic wave field separates and denoising.

Embodiment two

Take an actual seismic data, the implementation step of this example is described as example:

The first step: will contain 228 roads, per pass has the geological data of 2112 sampled points to read two-dimensional array F ₁In;

Second step: with original earthquake data F ₁Carry out linearity correction, obtain L ₁:

Carry out linearity correction for reflected P-P ripple lineups, its implementation is at that time on the basis of rule, for each seismic trace is determined the linearity correction time difference, then each data of each seismic trace is carried out time shift; During linearity correction, method for determining difference is:

$\mathrm{\&Delta;T}=\frac{x}{V_T}$

Wherein: Δ T is the linearity correction time difference, V _TBe the lineups apparent velocity that needs are proofreaied and correct, x is offset distance;

Carry out linearity correction for non-conversion reflection wave (as: reflected P-P ripple, S-S ripple) lineups, its implementation is at that time on the basis of rule, for each seismic trace is determined the linearity correction time difference, then each data of each seismic trace are carried out time shift.During linearity correction, method for determining difference is:

$\mathrm{\&Delta;t}=t-{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0=\sqrt{{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0^2+\frac{x^2}{v^2}}-{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0$

Wherein: Δ t is the non-conversion reflection wave linearity correction time difference, and x is offset distance, and t is that offset distance is the whilst on tour of x, t ₀Be the whilst on tour in the zero shot-geophone distance situation, v is stack velocity;

Carry out linearity correction for conversion reflection wave (as: reflected P-S ripple) lineups, be when transformed wave on the basis of rule, for each seismic trace is determined the linearity correction time difference, then each data of each seismic trace are carried out time shift; During linearity correction, method for determining difference is:

$\mathrm{\&Delta;}{t}_{\mathrm{PS}}=t_{\mathrm{PS}}-{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_{0\mathrm{PS}}=\frac{1}{v_P}(\sqrt{{\mathrm{<figure-callout\; id="2"\; label="x\; P"\; filenames="HSA00000048453700032.png"\; state="\{\{state\}\}">x</figure-callout>}}_P^{}+z^2}-z)+\frac{1}{v_S}(\sqrt{{\mathrm{<figure-callout\; id="2"\; label="x\; S"\; filenames="HSA00000048453700032.png"\; state="\{\{state\}\}">x</figure-callout>}}_S^{}+z^2}-z)$

Wherein: Δ t _PSBe the conversion reflection wave linearity correction time difference, x _PBe the distance of focus to transfer point, x _SBe the distance of transfer point to acceptance point, t _PSThat offset distance is (x _P+ x _S) whilst on tour, T _0PSBe the whilst on tour in the zero shot-geophone distance situation, v _PBe p wave interval velocity, v _SBe the S wave velocity, z is the reflecting interface degree of depth;

The 3rd step: to the seismic signal L after the process linearity correction ₁Carry out svd:

L ₁＝U∑ ₁V ^T

Wherein: upper angle T represents transposition, and U is by L ₁L ₁ ^TFeature value vector consist of, V is by L ₁ ^TL ₁Feature value vector consist of, ∑ ₁Be made of singular value, singular value is descending to be arranged on the principal diagonal of matrix:

${\mathrm{\&Sigma;}}_1=\left[\begin{array}{cccc}{\mathrm{\&sigma;}}_1& & & 0\\ & {\mathrm{\&sigma;}}_2& & \\ & & \mathrm{<figure-callout\; id="0"\; label="O"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">O</figure-callout>}& \\ 0& & & {\mathrm{\&sigma;}}_m\end{array}\right]$

Wherein: σ ₁, σ ₂Λ σ _mBe L ₁Singular value;

The 4th step: to singular value sequence ∑ ₁Process, extract the singular value ∑ of echo signal ₂Reconstruction signal obtains L ₂Signal can be divided into two classes and be reconstructed, specific as follows:

(1) svd low-pass filtering is extracted the 1st～5 singular value reconstruction signal, extracts reflection wave:

$L_{\mathrm{Lp}}=\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_j{u}_j{v}_j^T$

Wherein: upper angle T represents transposition, L _LpBe the signal of reconstruct after the svd low-pass filtering, j is the singular value sequence number, and p is L ₁Order, and p=5, σ _jBe L ₁J singular value, u _jBe L ₁L ₁ ^TJ proper vector, v _jBe L ₁ ^TL ₁J proper vector;

(2) svd high-pass filtering, extract the 6th～228 singular value reconstruction signal, burbling noise:

$L_{\mathrm{Hp}}=\underset{j=q}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_j{u}_j{v}_j^T$

Wherein: upper angle T represents transposition, L _HpBe the signal of reconstruct after the svd high-pass filtering, j is the singular value sequence number, and q is L ₁Order, and q=6, m are earthquake total road number, and m=228, σ _jBe L ₁J singular value, u _jBe L ₁L ₁ ^TJ proper vector, v _jBe L ₁ ^TL ₁J proper vector;

The relative size of singular value is depended in the selection of p and q, and specific practice is by singular value σ _jThe function curve of subscript j determine;

According to actual filtering situation, L ₂Be L _Lp, L _HPOne of;

The 5th the step: according to earthquake overlap wave velocity and reflected P-P ripple the time apart from rule, with the signal L after reconstruct ₂Carry out anti-correction of the linearity time difference, obtain F ₂, get back in the data field of input:

Carry out the anti-correction of linearity for linear pattern signal (as: direct wave, refraction wave) lineups, on the basis of linearity correction apparent velocity value, the relation of Negotiation speed and offset distance is determined linear anti-the correction time difference for each seismic trace, then each data of each seismic trace is carried out time shift:

$\mathrm{\&Delta;T}=\frac{x}{V_T}$

Wherein: Δ T is the linear anti-time difference, the V of proofreading and correct _TBe the lineups apparent velocity that needs are proofreaied and correct, x is offset distance;

Carry out the anti-correction of linearity for non-conversion reflection wave (as: reflected P-P ripple, S-S ripple) lineups, at that time on the basis of rule and linearity correction apparent velocity value, determine anti-the correction time difference for each seismic trace, then each data of each seismic trace carried out time shift:

$\mathrm{\&Delta;t}=t-{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0=\sqrt{{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0^2+\frac{x^2}{v^2}}-{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_0$

Wherein: Δ t is anti-the correction time difference, and x is offset distance, and t is that offset distance is the whilst on tour of x, t ₀Be the whilst on tour in the zero shot-geophone distance situation, v is stack velocity;

Carry out the anti-correction of linearity for conversion reflection wave (as: reflected P-S ripple) lineups, conversion during reflection wave on the basis of rule and linearity correction apparent velocity value, determine linear anti-the correction time difference for each seismic trace, then each data of each seismic trace carried out time shift:

$\mathrm{\&Delta;}{t}_{\mathrm{PS}}=t_{\mathrm{PS}}-{\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="HSA00000048453700011.png,HSA00000048453700031.png"\; state="\{\{state\}\}">t</figure-callout>}}_{0\mathrm{PS}}=\frac{1}{v_P}(\sqrt{{\mathrm{<figure-callout\; id="2"\; label="x\; P"\; filenames="HSA00000048453700032.png"\; state="\{\{state\}\}">x</figure-callout>}}_P^{}+z^2}-z)+\frac{1}{v_S}(\sqrt{{\mathrm{<figure-callout\; id="2"\; label="x\; S"\; filenames="HSA00000048453700032.png"\; state="\{\{state\}\}">x</figure-callout>}}_S^{}+z^2}-z)$

Wherein: Δ t _PSBe the linear anti-time difference, the x of proofreading and correct of conversion reflection wave _PBe the distance of focus to transfer point, x _SBe the distance of transfer point to acceptance point, t _PSThat offset distance is (x _P+ x _S) whilst on tour, t _0PSBe the whilst on tour in the zero shot-geophone distance situation, v _PBe p wave interval velocity, v _SBe the S wave velocity, z is the reflecting interface degree of depth;

The 6th step: with the data F after the anti-correction of linearity ₂By the geological data formatted output in when input, just completed linearity correction and united with svd and realize that seismic wave field separates and denoising.

Claims (1)

1. a seismic wave field separates the method with denoising, it is characterized in that, comprises the steps:

The first step: will contain the m road, per pass has the geological data of n sampled point to read two-dimensional array F ₁In;

Second step: original earthquake data F1 is carried out linearity correction, obtain L ₁:

Carry out linearity correction for linear pattern signal lineups, its implementation is the apparent velocity value of given linear lineups, by the relation of apparent velocity and offset distance, for each seismic trace is determined the linearity correction time difference, then each data of each seismic trace are carried out time shift; During linearity correction, method for determining difference is:

$\mathrm{\&Delta;T}=\frac{x}{V_T}$

Wherein: Δ T is the linearity correction time difference, V _TBe the lineups apparent velocity that needs are proofreaied and correct, x is offset distance;

Carry out linearity correction for the non-conversion reflection line-ups, its implementation is at that time on the basis of rule, for each seismic trace is determined the linearity correction time difference, then each data of each seismic trace is carried out time shift; During linearity correction, method for determining difference is:

$\mathrm{\&Delta;t}=t-t_0=\sqrt{t_0^2+\frac{x^2}{v^2}}-t_0$

Wherein: Δ t is the non-conversion reflection wave linearity correction time difference, and x is offset distance, and t is that offset distance is the whilst on tour of x, t ₀Be the whilst on tour in the zero shot-geophone distance situation, v is stack velocity;

For the conversion reflection line-ups carry out linearity correction, be when transformed wave on the basis of rule, for each seismic trace is determined the linearity correction time difference, then each data of each seismic trace are carried out time shift; During linearity correction, method for determining difference is:

${\mathrm{\&Delta;t}}_{\mathrm{PS}}=t_{\mathrm{PS}}-t_{0\mathrm{PS}}=\frac{1}{v_P}(\sqrt{x_P^2+z^2}-z)+\frac{1}{v_s}(\sqrt{x_S^2+z^2}-z)$

Wherein: Δ t _PSBe the conversion reflection wave linearity correction time difference, x _PBe the distance of focus to transfer point, x _SBe the distance of transfer point to acceptance point, t _PSThat offset distance is x _P+ x _SWhilst on tour, t _0PSBe the whilst on tour in the zero shot-geophone distance situation, v _PBe p wave interval velocity, v _SBe the S wave velocity, z is the reflecting interface degree of depth;

The 3rd step: to the seismic signal L after the process linearity correction ₁Carry out svd:

L ₁=U∑ ₁V ^T

Wherein: upper angle T represents transposition, U by $L_1{L}_1^T$ Feature value vector consist of, V by $L_1^T{L}_1$ Feature value vector consist of, ∑ ₁Be made of singular value, singular value is descending to be arranged on the principal diagonal of matrix:

Wherein: σ ₁, σ ₂σ _mBe L ₁Singular value;

The 4th step: to ∑ ₁Process, extract the singular value ∑ of echo signal ₂Reconstruction signal obtains L ₂Signal can be divided into two classes and be reconstructed, specific as follows:

(1) svd low-pass filtering, extract linear wave field:

$L_{\mathrm{Lp}}=\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_j{u}_j{v}_j^T$

Wherein: upper angle T represents transposition, L _LpBe the signal of reconstruct after the SVD low-pass filtering, j is the singular value sequence number, and p is L ₁Order, and 1≤p≤m, σ _jBe L ₁J singular value, u _jFor $L_1{L}_1^T$ J proper vector, v _jFor $L_1^T{L}_1$ J proper vector;

(2) svd high-pass filtering, isolate other seismic signal:

$L_{\mathrm{Hp}}=\underset{j=q}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_j{u}_j{v}_j^T$

Wherein: upper angle T represents transposition, L _HpBe the signal of reconstruct after the svd high-pass filtering, j is the singular value sequence number, and q is L ₁Order, and 1≤q≤m, m are earthquake total road number, σ _jBe L ₁J singular value, u _jFor $L_1{L}_1^T$ J proper vector, v _jFor $L_1^T{L}_1$ J proper vector;

The relative size of singular value is depended in the selection of p and q, and specific practice is by singular value σ _jThe function curve of subscript j determine;

According to actual filtering situation, L ₂Be L _Lp, L _HPOne of;

The 5th the step: according to seimic wave velocity and seismic signal the time apart from rule, with the signal L after reconstruct ₂Carry out anti-correction of the linearity time difference, obtain F ₂, get back in the data field of input:

Carry out the anti-correction of linearity for linear pattern signal lineups, on the basis of linearity correction apparent velocity value, the relation of Negotiation speed and offset distance is that each seismic trace is determined linear anti-the correction time difference, then each data of each seismic trace is carried out time shift:

$\mathrm{\&Delta;T}=\frac{x}{V_T}$

Wherein: Δ T is the linear anti-time difference, the V of proofreading and correct _TBe the lineups apparent velocity that needs are proofreaied and correct, x is offset distance;

Carrying out for the non-conversion reflection line-ups that linearity is anti-proofreaies and correct, at that time on the basis of rule and linearity correction apparent velocity value, is that each seismic trace is determined anti-the correction time difference, then each data of each seismic trace is carried out time shift:

$\mathrm{\&Delta;t}=t-t_0=\sqrt{t_0^2+\frac{x^2}{v^2}}-t_0$

Wherein: Δ t is anti-the correction time difference, and x is offset distance, and t is that offset distance is the whilst on tour of x, t ₀Be the whilst on tour in the zero shot-geophone distance situation, v is stack velocity;

Carrying out the anti-correction of linearity for the conversion reflection line-ups, on the basis of rule and linearity correction apparent velocity value, is that each seismic trace is determined the linear anti-correction time difference when the conversion reflection wave, then each data of each seismic trace is carried out time shift:

$\mathrm{\&Delta;}{t}_{\mathrm{PS}}=t_{\mathrm{PS}}-t_{0\mathrm{PS}}=\frac{1}{v_P}(\sqrt{x_P^2+z^2}-z)+\frac{1}{v_S}(\sqrt{x_S^2+z^2}-z)$

Wherein: Δ t _PSBe the linear anti-time difference, the x of proofreading and correct of conversion reflection wave _PBe the distance of focus to transfer point, x _SBe the distance of transfer point to acceptance point, t _PSThat offset distance is x _P+ x _SWhilst on tour, t _0PSBe the whilst on tour in the zero shot-geophone distance situation, v _PBe p wave interval velocity, v _SBe the S wave velocity, z is the reflecting interface degree of depth;

The 6th step: with the data F after the anti-correction of linearity ₂By the geological data formatted output in when input, just completed linearity correction and united with svd and realize that seismic wave field separates and denoising.

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