A time-frequency analysis method for gas reservoir characterization with sparse generalized w transform

Abstract

The application discloses a kind of sparse generalized W transform gas reservoir characterization time-frequency analysis method, for the first time L1 norm is introduced to the mathematical relationship between generalized W transform and seismic signal for sparse constraint, and is solved using Bregman iteration algorithm, to obtain a kind of analysis result with higher time-frequency resolution.The method absorbs the advantage that generalized W transform highlights low-frequency information of seismic signal, avoids the problem of main frequency splitting, and provides a more sparse time-frequency representation for non-stationary seismic signals. When applied to the time-frequency analysis of actual seismic data, it can provide a high-precision seismic spectral decomposition result for gas reservoirs, thereby more accurately delineating the low-frequency abnormal area of gas reservoir.

Description

Technical Field

[0001] This invention belongs to the field of signal processing and proposes a time-frequency analysis method for characterizing gas-bearing reservoirs using sparse generalized W transform. Background Technology

[0002] In seismic exploration, the signals used are typically non-stationary. Traditional Fourier transforms cannot effectively characterize the local frequency features of such signals, while time-frequency analysis can map one-dimensional time signals to the two-dimensional time-frequency domain. Through spectral decomposition, it reveals the geological structure and reservoir information hidden in seismic data, thus becoming an important tool for processing non-stationary seismic signals.

[0003] Traditional time-frequency analysis methods include short-time Fourier transform, wavelet transform, and S-transform. The S-transform, due to its Gaussian window's adaptive frequency response, has been widely used in seismic signal processing and analysis. However, the S-transform's window size varies with frequency in a pre-defined and fixed manner, failing to provide a sufficiently flexible and reliable time-frequency representation of seismic signals. Therefore, various generalized S-transforms have emerged to adjust for this variation, but unfortunately, they still haven't solved the problem of the dominant frequency shifting to higher frequencies in the S-transform.

[0004] In recent years, the W-transform, by constructing a Gaussian window with a dominant frequency weight, has effectively highlighted the low-frequency information of seismic signals by aligning the centroid of the spectral energy with the dominant frequency of the waveform, and has successfully solved the dominant frequency offset problem in the S-transform and its generalized transformations. However, the Gaussian window of the W-transform includes the absolute value of the dominant frequency, which leads to the splitting of the time-frequency amplitude peak at the dominant frequency location. To solve this problem, the generalized W-transform parameterizes the window function, achieving significant results. However, its time-frequency resolution is still fundamentally limited by the Heisenberg uncertainty principle, making it difficult to simultaneously obtain high time resolution and high frequency resolution in the time-frequency domain. This is especially true for complex seismic signals, whose frequency components span multiple scales. The generalized W-transform may exhibit ambiguity or distortion when capturing these components, limiting the accurate analysis of local details.

[0005] With the continuous advancement of seismic exploration technology, the requirements for the accuracy of seismic data interpretation are increasing, and high resolution has become an indispensable key factor. Currently, existing time-frequency analysis techniques are insufficient to meet these more stringent resolution requirements. Therefore, developing more effective time-frequency analysis tools to accurately extract key information from seismic data has become an urgent and important task. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention proposes a sparse generalized W-transform-based time-frequency analysis method for characterizing gas-bearing reservoirs, which significantly improves energy concentration and enhances the accuracy of oil and gas reservoir characterization. Based on sparse representation theory, this method treats the time-frequency transformation process of a signal as a linear inversion problem under sparse constraints, using the Bregman iterative algorithm to solve it, ultimately obtaining a time-frequency spectrum with high resolution. Compared to existing methods, the sparse generalized W-transform highlights the low-frequency information of the signal, better characterizes its time-frequency characteristics, and significantly improves the time-frequency resolution and energy concentration of the time-frequency spectrum.

[0007] To achieve the above objectives, the present invention employs the following technical solution: a time-frequency analysis method for characterizing gas-bearing reservoirs using sparse generalized W-transform, comprising the following steps:

[0008] S1. Input the original two-dimensional seismic profile x(s,t) to be analyzed, where s is the number of traces and t is the time. Analyze each trace of seismic signal x(t) one by one.

[0009] S2. Perform a generalized W transform on the signal to obtain the time-domain and frequency-domain expressions of the generalized W transform, respectively:

[0010]

[0011] Where τ and f represent time and frequency respectively, f0(τ) is the time-varying dominant frequency of the signal and Δf(τ) = f - f0(τ), k represents the scaling factor, p is the trend factor, and Z(α) is the Fourier transform of x(t);

[0012] S3. Based on sparsity theory, a new sparse generalized W-transform time-spectrum decomposition model is constructed using the L1 norm.

[0013] S4. Use the Bregman iterative algorithm to accelerate the solution and obtain the sparse generalized W transform time-frequency results of the signal;

[0014] S5. Take the modulus of the time-frequency transformation result to obtain the energy at each time-frequency point, thereby obtaining the time spectrum of the sparse generalized W transform;

[0015] S6. The average spectrum of the original seismic data is calculated using Fourier transform. Two frequency values ​​are considered as upper and lower band limits. Two high- and low-frequency attribute profiles within the range are extracted from the time spectrum obtained in S5. The energy attenuation of the seismic signal in these two profiles is used to characterize the gas-bearing reservoir.

[0016] Preferably, after obtaining the frequency domain representation of the signal in step S2, step S3 involves constructing the spectral decomposition model of the signal's sparse generalized W transform as follows:

[0017] a. Using the frequency domain expression of the generalized W transform, its discrete form is obtained as follows:

[0018]

[0019] Where n and l represent discrete time and frequency, respectively, and N represents the number of sampling points;

[0020] b. Rewrite formula (2) in matrix form as follows:

[0021] W = AX = AFx (3)

[0022] in, It is a column vector composed of the discrete form of the generalized W transform of the signal, GWT[n,l]. The matrix is ​​generated by the window function, X∈C N×1 Let F be a column vector generated by X(α), and F∈C. N×N It is the Fourier transform matrix, and x is the input signal;

[0023] c. Based on formula (3), the new spectral decomposition model for the sparse generalized W transform of the signal is:

[0024]

[0025] Where G is the window function matrix of the generalized W transform. and Fourier transform matrix F∈C N×N The pseudo-inverse of the product, λ≥0 is the equilibrium parameter.

[0026] Preferably, the Bregman iterative algorithm is used to solve the problem in step S4 as follows:

[0027]

[0028] Where i is the iteration number.

[0029] The present invention has the following beneficial effects:

[0030] This invention proposes a time-frequency analysis method for characterizing gas-bearing reservoirs using the sparse generalized W-transform. For the first time, the L1 norm is introduced into the mathematical relationship between the generalized W-transform and seismic signals to impose sparse constraints, and the Bregman iterative algorithm is used for solving, resulting in an analysis result with higher time-frequency resolution. This method combines the advantages of the generalized W-transform in highlighting low-frequency information of seismic signals and avoiding the problem of dominant frequency splitting, and provides a more sparse time-frequency representation for non-stationary seismic signals.

[0031] This invention proposes a time-frequency analysis method for characterizing gas-bearing reservoirs using sparse generalized W-transform. Synthetic signals show that, compared to generalized S-transform, W-transform, and their generalized transformations, the sparse generalized W-transform, through sparsity constraints, achieves a higher time-frequency resolution analysis result that highlights low-frequency information and avoids dominant frequency splitting. Analysis of two high- and low-frequency attribute profiles extracted after applying the sparse generalized W-transform to a 2D seismic profile demonstrates that the sparse generalized W-transform can effectively characterize gas-bearing reservoirs and more clearly delineate their location and boundaries. Attached Figure Description

[0032] Figure 1 (a) is the synthesized signal;

[0033] Figure 1 (b) is the time-varying dominant frequency of the synthesized signal;

[0034] Figure 1 (c) is the result of the generalized S-transform of the synthesized signal;

[0035] Figure 1 (d) shows the W-transform result of the synthesized signal;

[0036] Figure 1 (e) represents the generalized W transform result of the synthesized signal;

[0037] Figure 1 (f) represents the sparse generalized W transform result of the synthesized signal;

[0038] Figure 2 This is a profile of 1079 seismic data channels for a certain oil and gas field.

[0039] Figure 3 (a) and (b) are the low-frequency profile (28Hz) and high-frequency profile (42Hz) extracted by the generalized S-transform, respectively;

[0040] Figure 3 (c) and (d) are the low-frequency profile (28Hz) and high-frequency profile (42Hz) extracted by W transform, respectively;

[0041] Figure 3 (e) and (f) are the low-frequency profile (28Hz) and high-frequency profile (42Hz) extracted by the generalized W transform, respectively;

[0042] Figure 3 (g) and (h) are the low-frequency profile (28Hz) and high-frequency profile (42Hz) extracted by the sparse generalized W transform, respectively. Detailed Implementation

[0043] The following will describe in detail a time-frequency analysis method for characterizing gas-bearing reservoirs using sparse generalized W transform, with reference to the accompanying drawings.

[0044] Example 1

[0045] The sparse generalized W transform proposed in this invention includes the following steps:

[0046] S1. Input the original two-dimensional seismic profile x(s,t) to be analyzed, where s is the number of traces and t is the time. Analyze each trace of seismic signal x(t) one by one.

[0047] S2. Select appropriate parameters k and p to perform a generalized W transform on the signal, and obtain the time-domain and frequency-domain expressions of the generalized W transform as follows:

[0048]

[0049] Where τ and f represent time and frequency respectively, f0(τ) is the time-varying dominant frequency of the signal and Δf(τ) = f - f0(τ), k represents the scaling factor, p is the trend factor, and X(α) is the Fourier transform of x(t);

[0050] S3. Based on the frequency domain expression of the generalized W transform, its discrete form is obtained as follows:

[0051]

[0052] Where n and l represent discrete time and frequency, respectively, and N represents the total length of the signal;

[0053] S4. Rewrite the discrete form of the generalized W transform as a matrix expression as follows:

[0054] W = AX = AFx (3)

[0055] in, It is a column vector composed of the discrete form of the generalized W transform of the signal, GWT[n,l]. The matrix is ​​generated by the window function, X∈C N×1 Let F be a column vector generated by X(α), and F∈C. N×N It is the Fourier transform matrix, and x is the input signal;

[0056] S5. Introducing the L1 norm and selecting an appropriate parameter λ, a new sparse generalized W-transform time-spectral decomposition model is constructed as follows:

[0057]

[0058] Where G is the window function matrix of the generalized W transform. and Fourier transform matrix F∈C N×N The pseudo-inverse of the product, where λ≥0 is the equilibrium parameter;

[0059] S6. Use the Bregman iterative algorithm to accelerate the solution. The solution process is as follows:

[0060]

[0061] Where i is the iteration number.

[0062] S7. Obtain the time-frequency result of the sparse generalized W transform of the signal through step S6, and take the modulus of the result to obtain the time spectrum of the sparse generalized W transform.

[0063] The performance of this method in synthesized signals is as follows: Figure 1 As shown. Figure 1 (a) is the synthesized signal, which is formed by the convolution of Ricker wavelets with reflection coefficients and dominant frequencies of 50Hz, 40Hz, 30Hz, and 20Hz, respectively. Figure 1 (b) shows the time-varying dominant frequency obtained through the Hilbert transform. Figure 1 (c)-(f) correspond to the time-frequency analysis results of the generalized S-transform, W-transform, generalized W-transform, and sparse generalized W-transform, respectively, with the dashed line representing the time-varying dominant frequency. It can be seen that the generalized S-transform provides a coarse time-frequency representation of the signal, but its time resolution is low in the low-frequency region, failing to highlight the low-frequency characteristics of the signal. The W-transform, by introducing a time-varying dominant frequency, significantly improves the time resolution in the low-frequency region, but a splitting phenomenon exists at the dominant frequency. The generalized W-transform improves the dominant frequency splitting problem of the W-transform by parameterizing the time-varying dominant frequency function. However, limited by the uncertainty principle, all of the above methods exhibit significant energy diffusion, resulting in severe interference between seismic signals. In contrast, the sparse generalized W-transform has a high time resolution in the low-frequency region, significantly reducing seismic signal interference and highlighting low-frequency information.

[0064] Example 2

[0065] The sparse generalized W transform proposed in this invention is applied to the characterization of gas-bearing reservoirs in a gas field in western Sichuan. The specific steps are as follows:

[0066] S1-S7 are the same as in Example 1;

[0067] S8. The average spectrum of the original seismic data is calculated using Fourier transform. Considering two frequency values ​​as upper and lower band limits, two high (42Hz) and low (28Hz) frequency attribute profiles are extracted from the time spectrum obtained in S7. The energy attenuation of the seismic signal in these two profiles is used to characterize the gas-bearing reservoir.

[0068] Figure 2 This is a 2D seismic profile of a gas field in western Sichuan. The profile contains 1079 traces, each with 251 sampling points and a sampling interval of 2 ms. The two vertical lines A and B represent two gas wells, and the box represents the gas reservoir development area. The low-frequency and high-frequency profiles corresponding to the generalized S-transform, W-transform, generalized W-transform, and sparse generalized W-transform are shown below. Figure 3As shown in (a) and (b), (c) and (d), (e) and (f), (g) and (h), the generalized S-transform cannot accurately represent the low-frequency information of well A. The energy in the study area shown by the other three methods is stronger in the low-frequency range and weaker in the high-frequency range, effectively describing the anomalous energy attenuation caused by the gas-bearing reservoir at wells A and B. However, the sparse generalized W-transform can more clearly characterize the reservoir boundary and further achieve high-precision delineation of the anomalous attenuation region of the gas-bearing reservoir. Compared with the generalized S-transform, W-transform, and generalized W-transform, the sparse generalized W-transform significantly improves the time-frequency energy concentration and describes the reservoir characteristics more accurately.

[0069] The above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art can still make modifications or equivalent substitutions to the specific implementation schemes of the present invention, and these modifications or equivalent substitutions do not depart from the spirit and scope of the present invention, and are all within the protection scope of the claims of the present invention.

Claims

1. A time-frequency analysis method for characterizing gas-bearing reservoirs using sparse generalized W-transform, characterized in that, Includes the following steps: S1. Input the original two-dimensional seismic profile to be analyzed. , For the Tao, For the time period, each seismic signal was analyzed one by one. ; S2. Perform a generalized W transform on the signal to obtain the time-frequency domain expression of the generalized W transform: ； ； in, and Representing time and frequency respectively, The time-varying dominant frequency of the signal and , Indicates the scale factor. As a trend factor, for Fourier transform, Represents the frequency variable in the Fourier transform domain; S3. Based on sparsity theory, a new sparse generalized W-transform time-frequency decomposition model is constructed using the L1 norm. The process is as follows: a. Using the frequency domain expression of the generalized W-transform, its discrete form is obtained as follows: ； in, and Representing discrete time and frequency respectively, Indicates the number of sampling points; i is the imaginary unit; b. Rewrite formula (2) in matrix form as follows: ； in, It is the discrete form G of the generalized W transform of the signal. The column vectors arranged in order, It is a matrix generated by a window function. yes The generated column vector, It is the Fourier transform matrix, where x is the input signal; c. Based on formula (3), the new spectral decomposition model for sparse signals is: ； Where G is the window function matrix of the generalized W transform. and Fourier transform matrix The pseudo-inverse of the product, where λ≥0 is the equilibrium parameter; S4. Use the Bregman iterative algorithm to accelerate the solution and obtain the sparse generalized W transform time-frequency results of the signal; S5. Take the modulus of the time-frequency transformation result to obtain the energy at each time-frequency point, thereby obtaining the time spectrum of the sparse generalized W transform; S6. The average spectrum of the original seismic data is calculated using Fourier transform. Two frequency values ​​are considered as upper and lower band limits. Two high- and low-frequency attribute profiles within the range are extracted from the time spectrum obtained in S5. The energy attenuation of the seismic signal in these two profiles is used to characterize the gas-bearing reservoir.

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