WO2016044538A1

WO2016044538A1 - Bandwidth extension beyond the vibrator sweep signal via a constrained simultaneous multiple vibrator inversion

Info

Publication number: WO2016044538A1
Application number: PCT/US2015/050607
Authority: WO
Inventors: Stephen K. Chiu
Original assignee: Conocophillips Company
Priority date: 2014-09-19
Filing date: 2015-09-17
Publication date: 2016-03-24

Abstract

Method for processing seismic data includes: dividing an inversion into at least three frequency regions, region 1, region 2, and region 3; computing, via a computing processor, an inversion of source separation in region 2 using M=(G^HG)^-1G^H D= VS^-1 U^HD, wherein, M is reflectivity of the data, G is the vibrator- sweep matrix, D is the input data matrix, U is a matrix of eigenvectors that span the data space, V is a matrix of eigenvectors that span the model space, S is a diagonal eigenvalue matrix whose diagonal elements are called singular values, and H is a conjugate transpose operator; selecting a stable solution within region 2 at a reference frequency (f_RL), wherein f_RL = f₃ + δf, wherein δf is between 0 to 10 Hz, and wherein the solution at the frequency of f_RL is chosen as a referenced solution; replacing singular values, S, within low-frequency range (f₁ to f₂) with S'=S+δS, where δs represents a fraction of singular value of the referenced solution and the fraction typically ranges between 1 to 30 percent; computing a generalized least-squares solution for the low-frequency range (f₁ to f₂) as M = V S'^-1U^HD; selecting a stable solution within region 2 as a reference frequency (f_RH), wherein f_RH = f₄ - δf, wherein δf is between 0 to 10 Hz and wherein the solution at the frequency of f_RH is chosen as a referenced solution; replacing singular values, S, within high-frequency range (f₅ to f₆) with S'=S+δS, where δS represents a fraction of singular value of the referenced solution and the fraction typically ranges between 1 to 30 percent; and computing a generalized least-squares solution as, M = VS'^-1 U^HD.

Description

BANDWIDTH EXTENSION BEYOND THE VIBRATOR SWEEP SIGNAL VIA A CONSTRAINED SIMULTANEOUS MULTIPLE VIBRATOR INVERSION

FIELD OF THE INVENTION

[0001] The present invention relates generally to seismic data acquisition. More particularly, but not by way of limitation, embodiments of the present invention include tools and methods for recovering data bandwidth using a constrained simultaneous multiple vibrator inversion.

BACKGROUND OF THE INVENTION

[0002] During seismic data acquisition, seismic signals generated by seismic sources are directed into the subsurface of the earth. The seismic signals interact (e.g., reflect, refract, etc.) with certain subsurface features, which can affect measured parameters such as travel time and seismic velocity. Reflected seismic signals can be captured at the surface by geophones and subsequently analyzed to gain an understanding of subsurface geology. A broad and full spectrum of seismic energy is generally desirable for the seismic signals since various layers and interfaces of the subsurface respond differently to different wavelength of seismic energy. High frequency energy can provide higher resolution of the geological structures while lower frequency energy can provide information useful for analyzing geological properties (e.g., nature and composition of the various layers).

[0003] Recently, a technique using point source and point receiver acquisition combined with simultaneous multiple sourcing (SMS) has been successfully employed to acquire high-fold 3D land seismic data. Popular SMS technologies used in land acquisitions include high-fidelity simultaneous vibratory seismic (Sallas, et al, 1998) and high-fidelity vibroseis seismic acquisition such as ZenSeis™ (Eick, et al, 2009). Krohn and Johnson (2006) describe some concepts of high-fidelity vibratory seismic (HFVS) technology that can be used to increase production rates, reduce acquisition costs, increase spatial sampling, and improve data quality. Important to SMS technology is a process of separating multiple sweeps and multi-vibrator gathers into a single source gather through a matrix inversion. This matrix inversion usually involves solving a system of equations using direct-equation solvers. [0004] Fast direct-equation solvers such as Lower Upper (LU) decomposition can be used to handle large volumes of 3D prestack data. Unfortunately, some fast direct- equation solvers are not able to accurately determine the uniqueness of the system of equations to be solved. The direct-equation solver can have difficulty producing a satisfactory solution if the matrix is ill-conditioned. In linear algebra terms, the condition number of a matrix is a measure of stability or sensitivity of a matrix to small changes in input data. Matrices with condition numbers near 1 are said to be well-conditioned. Matrices with condition numbers much greater than one (such as around 10⁶) are said to be ill-conditioned. If a matrix has a large condition number, the solutions are unstable with respect to small changes in data. In this case, the solutions from an ill-conditioned matrix are unreliable.

[0005] Use of singular value decomposition can be a better way to examine the uniqueness of the system of the equations to be solved. The singular value decomposition decomposes the matrix into eigenvector matrices and a diagonal eigenvalue matrix whose diagonal elements are called singular values. The condition number of a matrix is the ratio of its largest singular value to its smallest singular value and the determinant of a matrix is a product of singular values.

[0006] If some of the singular values are close to zero, the condition number of the matrix will be extremely large, indicating that the matrix is ill-conditioned, and the determinant of the matrix derived from product of the singular values is also very small or close to zero. Thus the solutions for this system of equations are questionable. Traditional approaches for handling ill-conditioned matrix include excluding unreliable solutions or applying global damping factors to stabilize the solutions. These approaches reduce unstable solutions to negligibly small or zero.

[0007] There can be challenges and limitations for ranges of frequencies that may be delivered and recorded by SMS technology. Physical limitations of hydraulic sweep-type vibrator and typical recording geophone often limit bandwidth of recorded data between 5 to 90 Hz. For typical SMS source separations, solutions are relatively stable within bandwidth of vibrator sweep signal. Outside the bandwidth of the vibrator sweep signal, the matrix becomes ill-conditioned. BRIEF SUMMARY OF THE DISCLOSURE

[0008] The present invention relates generally to seismic data acquisition. More particularly, but not by way of limitation, embodiments of the present invention include tools and methods for recovering data bandwidth using a constrained simultaneous multiple vibrator inversion.

[0009] One method for processing data of a constrained simultaneous multiple vibrator inversion includes: a) dividing an inversion into at least three frequency regions, region 1, region 2, and region 3, wherein region 1 corresponds to a low- frequency range (fi to f₂) outside a vibrator sweep band, wherein region 2 corresponds to a frequency range (f₃ to f₄) within the vibrator sweep band, and wherein region 3 corresponds to a high-frequency range (f₅ to f₆) outside the vibrator sweep band; b) computing, via a computing processor, an inversion of source separation in region 2 using M=(G^HG) ¹ G^H D= VS ¹ U^HD , wherein, M is reflectivity of the data, G is the vibrator- sweep matrix, D is the input data matrix, U is a matrix of eigenvectors that span the data space, V is a matrix of eigenvectors that span the model space, S is a diagonal eigenvalue matrix whose diagonal elements are called singular values, and H is a conjugate transpose operator; c) selecting a stable solution within region 2 at a reference frequency (fRL), wherein f^ = f_{3 +} δί, wherein 5f is between 0 to 10 Hz, and wherein the solution at the frequency of f_RL is chosen as a referenced solution; d) replacing singular values, S, within low-frequency range (fi to f₂) with S'=S+5S, where 5S represents a fraction of singular value of the referenced solution and the fraction typically ranges between 1 to 30 percent; f) computing a generalized least-squares solution for the low-frequency range (fi to f₂) as M = VS' ¹ U^HD ; g) selecting a stable solution within region 2 as a reference frequency

(fim), wherein f_RH = f₄ - 6f, wherein 5f is between 0 to 10 Hz and wherein the solution at the frequency of fRH is chosen as a referenced solution; h) replacing singular values, S, within high-frequency range (f₅ to f₆) with S'=S+5S, where 5S represents a fraction of singular value of the referenced solution and the fraction typically ranges between 1 to 30 percent; and f) computing a generalized least-squares solution as, M = V S'^-1 U^HD . BRIEF DESCRIPTION OF THE DRAWINGS

[0010] A more complete understanding of the present invention and benefits thereof may be acquired by referring to the follow description taken in conjunction with the accompanying drawings in which:

[0011] FIG. 1 illustrates regions of Zenseis™ inversion within vibrator sweep band and outside vibrator sweep band.

[0012] FIG. 2a-2b illustrate a source-record example of traditional Zenseis™ inversion by excluding unreliable solutions from 0 to 3 Hz, which cause rapid decay of signal amplitudes between 0 to 3 Hz: (a) inverted data and (b) power spectrum showing frequency range between 0 and 40 Hz.

[0013] FIG. 3a-3b illustrate a source-record example of traditional Zenseis™ inversion including solutions between 0 to 3Hz without matrix regularization: (a) inverted data and (b) power spectrum showing frequency range between 0 and 40 Hz.

[0014] FIG. 4a-4b illustrate source-record example of new constrained Zenseis™ inversion according to one or more embodiments: (a) inverted data and (b) power spectrum showing frequency range between 0 and 40 Hz.

[0015] FIG. 5a-5b illustrate a source-record example of traditional Zenseis™ inversion: (a) inverted data and (b) power spectrum of a windowed data highlighted by a box showing frequency range of 0-40 Hz.

[0016] FIG. 6a-6a illustrate a source-record example of new constrained Zenseis™ inversion according to one or more embodiments: (a) inverted data and (b) power spectrum of a windowed data highlighted by a box showing frequency range of 0-40 Hz.

DETAILED DESCRIPTION

[0017] Reference will now be made in detail to embodiments of the invention, one or more examples of which are illustrated in the accompanying drawings. Each example is provided by way of explanation of the invention, not as a limitation of the invention. It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the scope or spirit of the invention. For instance, features illustrated or described as part of one embodiment can be used on another embodiment to yield a still further embodiment. Thus, it is intended that the present invention cover such modifications and variations that come within the scope of the invention.

[0018] The present invention provides tools and methods for extending data bandwidth of matrix inversions during seismic data acquisition and processing. A bandwidth extension that extends beyond the vibrator sweep signal is crucial to subsequent processing steps in order to produce high-resolution images of a reservoir. The methods described herein may be particularly useful for low frequency components used in seismic-attribute inversion and Zenseis/HFVS inversions. A recovered spectrum that is outside the vibrator-sweep bandwidth can be either a low-frequency spectrum or a high-frequency spectrum.

[0019] To recover a spectrum beyond the vibrator sweep bandwidth, a stable solution is needed to constrain a simultaneous multiple vibrator inversion. The stable solution is chosen to be a solution inside the vibrator sweep bandwidth but should as close as possible to the recovered spectrum. A percentage of the singular value of chosen solution ("referenced" solution) is added to the singular values of the solution matrix for the recovered spectrum. Typical percentages can range from about 1% to about 30%. The use of "referenced" singular value to stabilize the solutions outside the vibrator sweep bandwidth does not typically produce phase distortion of the inverted data. This damping factor is local and limits the inversion from creating excessive noise. The damping factor should also small enough to provide a reasonable solution. The constrained inversion only modifies the solutions outside the vibrator sweep bandwidth and does not alter the solutions within the vibrator sweep bandwidth.

[0020] High-fidelity simultaneous vibratory seismic systems such as Zenseis/HFVS technology require separating multiple sweeps and multi-vibrator gathers into a single source gather through a matrix inversion that involves solving a system of equations. The use of singular value decomposition (SVD) can generate the most robust least- squares solution and provide diagnostic tools to analyze the uniqueness of the system of equations to be solved. A description of SVD can be found in Chiu et al. (2005). Chiu et al. describes applying SVD to obtain a more robust least-squares solution and to produce a better source separation when the vibrator sweep matrix is ill-conditioned. [0021] A multi-vibrator gather is assumed to be a convolution model: vibrator sweeps that have unique phase rotations convolve with reflectivity series (Chiu, 2005). The data trace di(t) for sweep i is

d_i(t) = g_ij(t) ® m_j(t) (1) for i = 1 .... number of sweeps; j = 1, ... number of vibrators

g_j is the sweep i from vibrator j, and m . , the reflectivity model of vibrator j.

[0022] In the frequency domain, equation 1 in matrix notation becomes

D(f) = G(f) M(f) (2)

[0023] The least-squares solution of equation 4 is

G^HGM=G^HD (3)

[0024] Using the singular value decomposition (Aki and Richard, 1980 and Golub and Van Loan, 1996), G becomes

G=USV^H (4) where U is a matrix of eigenvectors that span the data space, V is a matrix of eigenvectors that span the model space, S is a diagonal eigenvalue matrix whose diagonal elements are called singular values, and H is a conjugate transpose operator.

[0025] The generalized least-squares solution of M is

M=(G^HG) ¹ G^H D= VS ¹ U^HD (5)

[0026] The damped least-squares solution is

(G^HG + ²I) M = G^HD (6) where β²Ι is a global damping factor added to the matrix G^HG to make the inversion stable, β² is a constant, and I is an identity matrix.

[0027] For typical SMS source separations, the inversion produces stable solutions within the vibrator-sweep bandwidth. Outside the vibrator-sweep band, it requires regularization of the matrix, but the regularization of the matrix basically reduces the unstable solution to be negligibly small or zero. If regularization is not applied to constrain the solution, the solution becomes unreliable, leading to an incorrect solution. [0028] To recover the signal outside the vibrator-sweep band, in some embodiments, the present invention employs the following steps in order to constrain the simultaneous multiple vibrator inversion:

1) The inversion is divided into three frequency regions as in FIG. 1, where region 1 corresponds to the low-frequency range (fl to f2) outside the vibrator-sweep band, region 2 corresponds to the frequency range (O to f4) within the vibrator-sweep band, and region 3 corresponds to the high-frequency range (f5 to f6) outside the vibrator- sweep band.

2) The inversion of the source separation in region 2 is computed via equation 5.

3) The inversion of the source separation in region 1 requires choosing a stable solution within region 2 and in the vicinity of frequency f3 (a referenced frequency fit) to constrain the ill-conditioned matrix. The referenced frequency is typically chosen as f_R ⁼f₃+6f where 5f typically ranges between 0 to 10 Hz. This stable solution at this particular frequency is referred as "referenced" solution.

4) The singular values, S, in equation 5 within low- frequency range (fl to f2) are replaced by S' = S + 5S, where 5S represents a fraction of singular value of the referenced solution and the fraction typically ranges between 1 to 30 percent. This regularization factor is local and effective to prevent the inversion becoming unstable, but it is small enough in constraining the ill-conditioned matrix to provide a realistic solution.

5) The generalized least-squares solution of equation 5 is computed using S' instead of S.

6) The inversion of the source separation in region 3 operates the same way as in region 1, but the referenced solution is chosen in the vicinity of frequency f4.

[0029] The present invention only modifies the solutions outside the vibrator-sweep band and does not alter the solutions within the vibrator-sweep bandwidth. Outside the vibrator-sweep band, this invention recovers the weak signal using the "referenced" singular value to stabilize the solutions. In addition, this method does not produce phase distortion of the inverted data outside the vibrator-sweep band. If the multiple sources are reduced to a single source, this invention is also applicable to a single source.

[0030] In some embodiments, the present invention includes: 1) dividing an inversion into at least three frequency regions, region 1, region 2, and region 3, wherein region 1 corresponds to a low-frequency range (fi to f₂) outside a vibrator sweep band, wherein region 2 corresponds to a frequency range (f₃ to f₄) within the vibrator sweep band, and wherein region 3 corresponds to a high-frequency range (f₅ to f₆) outside the vibrator sweep band;

2) computing, via a computing processor, an inversion of source separation in region 2 using M=(G^HG) ¹ G^H D= VS^"1 U^HD , wherein, M is reflectivity of the data, G is the vibrator-sweep matrix, D is the input data matrix, U is a matrix of eigenvectors that span the data space, V is a matrix of eigenvectors that span the model space, S is a diagonal eigenvalue matrix whose diagonal elements are called singular values, and H is a conjugate transpose operator.

3) selecting a stable solution within region 2 at a reference frequency (fRL), wherein f^ = f_{3 +} δί, wherein 5f is between 0 to 10 Hz, and wherein the solution at the frequency of f^ is chosen as a referenced solution;

4) replacing singular values, S, within low-frequency range (fi to f₂) with S'=S+5S, where 5S represents a fraction of singular value of the referenced solution and the fraction typically ranges between 1 to 30 percent;

5) computing a generalized least-squares solution for the low-frequency range (fi to f₂) as M = VS' ¹ U^HD .

6) selecting a stable solution within region 2 as a reference frequency (fim), wherein fRH = f₄ - 5f, wherein 5f is between 0 to 10 Hz and wherein the solution at the frequency of fRH is chosen as a referenced solution;

7) replacing singular values, S, within high-frequency range (f₅ to f₆) with S'=S+5S, where 5S represents a fraction of singular value of the referenced solution and the fraction typically ranges between 1 to 30 percent; and

8) computing a generalized least-squares solution as, M = V S' ¹ U^HD .

[0031] The low-frequency range of region 1 can overlap with frequency band of region 2. Likewise, the high-frequency range of region 3 can overlap with frequency band of region 2. In some embodiments, 5f is greater than 10 Hz. The fraction of singular value ranges between 1 to 30 percent of the referenced solution. In other embodiments, the fraction of singular value is greater than 30 percent of the referenced solution. The singular value decomposition can be used to decompose M=(G^HG) ¹ G^H D = VS ¹ U^HD . The constrained simultaneous multiple vibrator inversion can be applied only to a particular region, for example, region 1 or region 3. Moreover, the constrained simultaneous multiple vibrator inversion may be applied to one or more simultaneous sources.

EXAMPLE

[0032] This example illustrates recovery of a low-frequency spectrum. High- frequency spectrum recovery can work using similar or analogous steps.

[0033] A real data example was acquired with 4 simultaneous vibratory sources with 4 repeated sweeps at the same source locations. The vibrator sweep bandwidth was between 3-88 Hz. The output data from the traditional Zenseis™ inversion typically has a frequency bandwidth between 3-88 Hz. A method of the present invention was used to recover a low-frequency spectrum between 0-3Hz. Because of initial tapering of the vibration sweep, a referenced solution at 5Hz is chosen to be used in constraining the solutions between 0-3Hz and the fraction of the singular value of the referenced solution is 3 percent.

[0034] FIG. 1 illustrates concepts of a traditional Zenseis™ inversion. Region 1, low-frequency spectrum, ranges from frequency fl to £2. Region 2, vibrator sweep band, ranges from frequency f3 to f4. Region 3, high-frequency spectrum, ranges from frequency £5 to f6. As shown in FIG. 2b, there can be a rapid decay of amplitude from 3 to 0 Hz when unreliable solutions are excluded. FIG. 2a illustrates the inverted data corresponding to FIG. 2b. However, if matrix regularization is not applied to constrain the solution, the unconstrained traditional Zenseis boosts up the low-frequency solutions excessively between 0 to 3 Hz (FIGS. 3a-3b). FIGS. 4a-4b show the inversion result using a method of the present invention. The method produces stable solutions between 0 to 3 Hz and recovers the low-frequency signal outside the vibrator-sweep band. The low-frequency bandwidth is improved without excessively boosting up the noise. Another way to examine the improvement of this invention is to perform spectral analysis on a windowed data that have good signal-to-noise ratio between the traditional Zenseis™ and the present invention. The analysis window is highlighted by a box in FIGS. 5 and 6. The present invention (FIG. 6) recovers the low-frequency data considerably between 0-5 Hz. The recovered low-frequency data consist of mostly signal instead of noise. Thus, the invention is successful to recover low-frequency data that are outside the vibrator sweep signal, without boosting up the noise.

[0035] Although the systems and processes described herein have been described in detail, it should be understood that various changes, substitutions, and alterations can be made without departing from the spirit and scope of the invention as defined by the following claims. Those skilled in the art may be able to study the preferred embodiments and identify other ways to practice the invention that are not exactly as described herein. It is the intent of the inventors that variations and equivalents of the invention are within the scope of the claims while the description, abstract and drawings are not to be used to limit the scope of the invention. The invention is specifically intended to be as broad as the claims below and their equivalents.

REFERENCES

[0036] All of the references cited herein are expressly incorporated by reference. The discussion of any reference is not an admission that it is prior art to the present invention, especially any reference that may have a publication data after the priority date of this application. Incorporated references are listed again here for convenience:

1. Aki, K., and Richard, P., 1980, Quantitative seismology - theory and methods, volume 2, W.H. Freeman, San Franciso, 659-689.

2. Baeten, G, Egreteau, A., Gibson, J., Lin, F., Maxwell, P., and Sallas, J., 2010, Low-frequency generation using seismic vibrators, 72th EAGE, Annual meeting, B015.

3. Chiu, S. K., Emmons, C. W., and Eick P. P., 2005, High Fidelity Vibratory Seismic (HFVS): robust inversion using generalized inverse: 75th Annual Internat. Mtg. Soc. Expl. Geophys. Expanded Abstracts, 1650-1653.

4. Golub, G.H. and Van Loan, C.F., 1996, Matrix computations, Johns Hopkins university press, Baltimore and London.

5. Krohn, C, 2006, Shaped high frequency vibratory source, U.S. Patent 7,436,734.

6. Sallas, J., Corrigan, D., and Allen, K.P., 1998, High fidelity vibratory source seismic method with source separation, U.S. Patent 5,721,710.

Claims

1. A method for processing data of a constrained simultaneous multiple vibrator inversion, the method comprising:

a) dividing an inversion into at least three frequency regions, region 1, region 2, and region 3, wherein region 1 corresponds to a low-frequency range (fi to f₂) outside a vibrator sweep band, wherein region 2 corresponds to a frequency range (f₃ to f₄) within the vibrator sweep band, and wherein region 3 corresponds to a high-frequency range (f₅ to f₆) outside the vibrator sweep band;

b) computing, via a computing processor, an inversion of source separation in region 2 using M=(G^HG) ¹ G^H D = VS^"1 U^HD , wherein, M is reflectivity of the data, G is the vibrator-sweep matrix, D is the input data matrix, U is a matrix of eigenvectors that span the data space, V is a matrix of eigenvectors that span the model space, S is a diagonal eigenvalue matrix whose diagonal elements are called singular values, and H is a conjugate transpose operator;

c) selecting a stable solution within region 2 at a reference frequency (fRL), wherein f^ = f_{3 +} δί, wherein 5f is between 0 to 10 Hz, and wherein the solution at the frequency of f^ is chosen as a referenced solution;

d) replacing singular values, S, within low-frequency range (fi to f₂) with S'=S+5S, where 5S represents a fraction of singular value of the referenced solution and the fraction typically ranges between 1 to 30 percent;

f) computing a generalized least-squares solution for the low-frequency range (fi to f₂) as M = VS' ¹ U^HD ;

g) selecting a stable solution within region 2 as a reference frequency (fim), wherein fRH = f₄ - 5f, wherein 5f is between 0 to 10 Hz and wherein the solution at the frequency of fRH is chosen as a referenced solution;

h) replacing singular values, S, within high-frequency range (f₅ to f₆) with S'=S+5S, where 5S represents a fraction of singular value of the referenced solution and the fraction typically ranges between 1 to 30 percent; and

f) computing a generalized least-squares solution as, M = VS' ¹ U^HD .

2. The method of claim 1 , wherein the low- frequency range of region 1 overlaps with frequency band of region 2.

3. The method of claim 1 , wherein the high-frequency range of region 3 overlaps with frequency band of region 2.

4. The method of claim 1 , wherein 5f is greater than 10 Hz.

5. The method of claim 1 , wherein the fraction of singular value ranges between 1 to 30 percent of the referenced solution.

6. The method of claim 1 , wherein the fraction of singular value is greater than 30 percent of the referenced solution.

7. The method of claim 1 , wherein singular value decomposition is used to decompose M =(G^HG) ¹ G^H D= VS ¹ U^HD .

8. The method of claim 1 , wherein the constrained simultaneous multiple vibrator inversion is applied only to region 1.

9. The method of claim 1 , wherein the constrained simultaneous multiple vibrator inversion is applied only to region 3.

10. The method of claim 1 , wherein the constrained simultaneous multiple vibrator inversion is applied to one or more simultaneous sources.