High-resolution processing method for seismic data based on inverse multi-resolution singular value decomposition

Abstract

A high-resolution processing method for seismic data based on inverse multi-resolution singular value decomposition includes the steps of: step 1: obtaining a single-trace seismic signal X as a raw signal; step 2: decomposing the seismic signal by using MRSVD algorithm to obtain a series of detailed singular values and inversely recursing the detailed singular values layer by layer to obtain a new detailed signal and an approximate signal; and step 3: sequentially superimposing the new detailed signal on the raw signal, layer by layer, to compensate the high-frequency component of the seismic signal so as to obtain a high-resolution seismic signal.

Claims

1. A high-resolution processing method for seismic data based on inverse multi-resolution singular value decomposition (MRSVD), which comprises the steps of: step 1: obtaining a single-trace seismic signal X as a raw signal; step 2: decomposing the seismic signal by using MRSVD algorithm to obtain a detailed singular value, and inversely recursing the detailed singular value layer by layer to obtain a new detailed signal and an approximate signal; and step 3: sequentially superimposing new detailed signals on the raw signal, layer by layer, to compensate a high-frequency portion of the seismic signal so as to obtain a high-resolution seismic signal by an equation as: $A_i^{\prime }=X+\underset{i=1}{\overset{G}{.Math.}}{D}_i^{\prime },\left(i=1,2,\mathrm{.Math.},G\right)$ wherein X represents the raw signal, A.sub.i′ represents a result of i.sup.th high-frequency compensation, G represents a total number of inverse recursion, and D.sub.i′ is detailed signals.

2. The high-resolution processing method, as recited in claim 1, wherein a number of inverse recursion is controlled by modifying a variance mode, wherein an equation of the modified variance mode is shown as: $V_i=\underset{t=1}{\overset{N}{.Math.}}{\left[1-\exp \left(-\frac{A_i^{\mathrm{\prime 2}}\left(t\right)}{a^2}\right)\right]}^2/{\left\{\underset{t=1}{\overset{N}{.Math.}}\left[1-\exp \left(-\frac{A_i^{\mathrm{\prime 2}}\left(t\right)}{a^2}\right)\right]\right\}}^2$ wherein A.sub.i′ (t) represents the result of the i.sup.th high-frequency compensation, t is a time, N is a length of the signal, a is a constant, wherein for each high-frequency compensated signal A′.sub.1, A′.sub.2, . . . , A′.sub.(G-1), A′.sub.G, the corresponding modified variance mode is calculated as V.sub.1, V.sub.2, . . . , V.sub.(G-1), V.sub.G, wherein if V.sub.(G-6)≈V.sub.(G-3)≈V.sub.G, the modified variance mode is converged and reached its maximum value, wherein the total number of inverse recursion G is determined and the high-resolution seismic signal A.sub.G′ is finally obtained.

3. The high-resolution processing method, as recited in claim 1, wherein, in the step 2, the detail singular values σ.sub.d1, σ.sub.d2, . . . σ.sub.dM are obtained by using MRSVD decomposition, wherein the detail singular values are fitted by fitting function and inversely recursed to obtain the new detailed singular value σ′.sub.di (i=1,2, . . . ), wherein the corresponding detailed signal D.sub.i′ is obtained through the detail singular value, wherein the fitting function is shown as follows: $F\left(j\right)={\left(j\right)}^k\exp \left(\underset{n=0}{\overset{N}{.Math.}}{a}_n{j}^n\right),k\ge 0$ wherein j represents a number of decomposition of MRSVD, a.sub.n represents a of polynomial coefficient, k is a positive number which is normally less than 3, N is a polynomial order, wherein at a condition of least square, F(j) is approximated close to the known detailed singular value, and the value k and the polynomial coefficient are obtained.

4. The high-resolution processing method, as recited in claim 1, wherein a series of MRSVD forward decomposition is obtained by an equation of:
E.sub.j=Σ|A.sub.j-1−A.sub.j|.sup.2/Σ|A.sub.j-1|.sup.2,(j=1, . . . ,M) wherein j represents the j.sup.th layer of MRSVD forward decomposition, wherein when E.sub.j≤10.sup.−6, a decomposition cycle is ended, wherein M represents a total number of the layers of MRSVD forward decomposition, A.sub.j-1 and A.sub.j are approximate signals obtained from the (j-1).sup.th and j.sup.th layer respectively.

5. The high-resolution processing method, as recited in claim 1, wherein a detail matrix is built with the new detail singular values, which is $H_d=\left[\begin{array}{c}{\sigma }_d{u}_{2,1}{v}_2^T\\ {\sigma }_d{u}_{2,2}{v}_2^T\end{array}\right],$ such that the corresponding detailed signals are obtained.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is an exploded schematic diagram of IMRSVD according to a preferred embodiment of the present invention.

(2) FIG. 2 is a diagram illustrating the amplitude spectrum of the approximate signal obtained during the MRSVD decomposition process according to the above preferred embodiment of the present invention, wherein the lines in FIG. 2 represent the original and 10th to 50th decompositions from top to bottom, respectively.

(3) FIG. 3 is a seismic sectional view of a forward problem of a two-dimensional theoretical model.

(4) FIG. 4 is a seismic sectional view of a theoretical model after IMRSVD high-resolution processing according to the above preferred embodiment of the present invention.

(5) FIG. 5 is a sectional view of a two-dimensional actual seismic profile.

(6) FIG. 6 is a sectional view of a two-dimensional actual seismic profile after IMRSVD high-resolution processing according to the above preferred embodiment of the present invention.

(7) FIG. 7 is a comparison of the amplitude spectrum of the 134th trace data before and after IMRSVD high-resolution processing according to the above preferred embodiment of the present invention.

(8) FIG. 8 is an illustration of the detail matrix H.sub.d.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

(9) In the following description, for purpose of explanation, numerous specific details are set forth in order to provide a thorough understanding of some example embodiments. It will be evident, however, to one of ordinary skill in the art that embodiments of the present invention may be practiced without these specific details.

(10) The present invention provides an IMRSVD (Inverse Multi-Resolution Singular Value Decomposition) algorithm for restoring high resolution seismic signals based on MRSVD (Multi-Resolution Singular Value Decomposition) technology. The core of the method of the present invention is to recover the high frequency of the seismic signal loss caused by the earth filtering, wherein through the MRSVD forward decomposition, all the singular values are obtained and processed by fitting and extrapolating so as to obtain a first new detailed signal. In other words, the a high-frequency portion D.sub.1′ of a raw (original) signal X is extrapolated for the first time, wherein the detailed signal D.sub.1′ is superimposed on the raw signal X to obtain a result X.sub.1′ of first high frequency compensation and then to recursively reverse the second detailed signal D.sub.2′. In other words, the high frequency portion D.sub.2′ of the raw signal X is extrapolated for the second time, wherein the detailed signal D.sub.2′ is superimposed on the signal X.sub.1′ to obtain a result X.sub.2′ of second high frequency compensation. Therefore, through successively reverse recurrence to continuously compensate the high frequency component, seismic signal bandwidth is expanded to achieve high-resolution processing of seismic data.

(11) Therefore, according to the present invention, the high-resolution processing method comprises the following processes:

(12) The high-resolution processing method based on Inverse Multi-Resolution Singular Value Decomposition comprises the following steps.

(13) Step 1: Obtain a single-trace seismic signal X as a raw signal.

(14) Step 2: Decompose the seismic signal by using MRSVD algorithm to obtain a detailed singular value, and inversely recurse the detailed singular value layer by layer to obtain a new detailed signal and an approximate signal.

(15) Specifically, a series of the MRSVD forward decomposition is obtained by the following equation:
E.sub.j=Σ|A.sub.j-1−A.sub.j|.sup.2/Σ|A.sub.j-1|.sup.2,(j=1, . . . .

(16) wherein j represents the j.sup.th layer of MRSVD forward decomposition. When E.sub.j≤10.sup.−6, a decomposition cycle is ended. M represents a total number of the layer of MRSVD forward decomposition. A.sub.j-1 and A.sub.j are the approximate signals obtained from the (j−1).sup.th and j.sup.th layer respectively.

(17) The detail singular values σ.sub.d1, σ.sub.d2, . . . are obtained by using MRSVD decomposition, wherein the detail singular values are fitted by fitting function and inversely recursed to obtain the new detailed singular value σ.sub.d1′ (i=1, 2, . . . . Then the corresponding detailed signal D.sub.i′ is obtained through the detail singular value, wherein the fitting function is shown as follows:

(18) $F\left(j\right)={\left(j\right)}^k\exp \left(\underset{n=0}{\overset{N}{.Math.}}{a}_n{j}^n\right),k\ge 0$

(19) wherein j represents the number of decomposition of MRSVD, a.sub.n represents a of polynomial coefficient, k is a positive number which is normally less than 3, N is a polynomial order, wherein at the condition of least square, F(j) is approximated close to the known detailed singular value, and the value k and the polynomial coefficient are obtained.

(20) A detail matrix is built with the new detail singular values, which is

(21) $H_d=\left[\begin{array}{c}{\sigma }_d{u}_{2,1}{v}_2^T\\ {\sigma }_d{u}_{2,2}{v}_2^T\end{array}\right],$
such that the corresponding detailed signals are obtained.

(22) Step 3: Sequentially superimpose the new detailed signals on the raw signal, layer by layer, to compensate the high-frequency portion of the seismic signal so as to obtain a high-resolution seismic signal by an equation as:

(23) 0$A_i^{\prime }=X+\underset{i=1}{\overset{G}{.Math.}}{D}_i^{\prime },\left(i=1,2,\mathrm{.Math.},G\right)$

(24) wherein X represents the raw signal, A.sub.i′ represents the result of the i.sup.th high-frequency compensation, G represents the total number of inverse recursion, and D.sub.i′ is the detailed signals.

(25) The number of inverse recursion is controlled by modifying the variance mode, wherein an equation of the modified variance mode is shown as follows:

(26) $V_i=\underset{t=1}{\overset{N}{.Math.}}{\left[1-\exp \left(-\frac{A_i^{{\prime }_2}\left(t\right)}{a^2}\right)\right]}^2/{\left\{\underset{t=1}{\overset{N}{.Math.}}\left[1-\exp \left(-\frac{A_i^{{\prime }_2}\left(t\right)}{a^2}\right)\right]\right\}}^2$

(27) wherein A.sub.i′(t) represents the result of the i.sup.th high-frequency compensation, t is the time, N is the length of the signal, a is a constant. For each high-frequency compensated signal A.sub.1′, A.sub.2′, . . . , A.sub.(G-1)′, A.sub.G′ the corresponding modified variance mode is calculated as V.sub.1, V.sub.2, . . . , V.sub.(G-1), V.sub.G. If V.sub.(G-6)≈V.sub.(G-3)≈V.sub.G, the modified variance mode is converged and reached its maximum value. Therefore, the total number of inverse recursion G is determined and the high-resolution seismic signal A.sub.G′ is finally obtained.

(28) According to the present invention, FIG. 3 is a conventional theoretical model and FIG. 4 is a theoretical model after IMRSVD high-resolution processing according to the present invention, wherein the FIG. 3 and the FIG. 4 are compared to show the differences therebetween. In FIG. 3, from top to bottom, the second thin layer cannot be distinguished, the third layer cannot well distinguished, and the wedge-shaped model can only be distinguished to the 23rd trace. After IMRSVD high-resolution processing as shown in FIG. 4, from top to bottom, the second layer can be distinguished in certain degree, the third layer is completely distinguishable, and the wedge-shaped model is significantly improved from being able to distinguish only the 23rd trace to being able to distinguish the 18th trace.

(29) FIGS. 5 and 6 illustrate the actual seismic data before and after IMRSVD processing respectively. Comparing FIG. 5 with FIG. 6, it can be seen that after the IMRSVD processing, the seismic resolution is significantly increased, and the continuity of the seismic phase axis is enhanced, especially it is significant to show the effect of the main target layer at about 1.0 second. Accordingly, the data at 134th trace is extracted before and after IMRSVD processing for amplitude spectrum analysis. As shown in FIG. 7, it can be seen that after the IMRSVD is processed, the low frequency portion can be effectively maintained and the high frequency portion is effectively improved, to greatly improve the seismic resolution.

(30) The above description is only the preferred embodiment of the present invention, and is not intended to be limiting. The present invention should include all modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention.