A method for gas-bearing reservoir identification using a local frequency constrained normalized w transform

Abstract

The application discloses a normalized W transform method based on local frequency constraint and used for gas reservoir identification. The method firstly inputs a seismic signal, adopts total variation regularization combined with Bregman iteration to solve local frequency, and improves stability and noise resistance of frequency estimation; on the basis, a standard deviation function fusing local frequency constraint, frequency deviation suppression and amplitude adaptive adjustment is constructed, adaptive regulation and control of a W transform analysis window are realized, a time-varying main frequency normalization mechanism is introduced, and a high-resolution time-frequency spectrum is obtained; finally, at least two characteristic frequency points are selected based on energy accumulation distribution of the time-frequency spectrum, linear fitting is performed on the characteristic frequency points, a frequency attenuation gradient attribute is calculated, and the frequency attenuation gradient attribute is used for representing distribution characteristics of the gas reservoir.

Description

Technical Field

[0001] This invention belongs to the field of oil and gas exploration technology, specifically relating to a method for identifying gas-bearing reservoirs using a normalized W-transform with local frequency constraints. Background Technology

[0002] Accurate identification and prediction of oil and gas reservoirs are of great significance for oil and gas exploration and development. When seismic waves propagate in fluid-bearing reservoirs, the energy of the high-frequency amplitude spectrum attenuates significantly due to absorption and scattering by the medium, thus exhibiting anomalous response characteristics in seismic records. By analyzing this frequency-related energy attenuation law, the spatial distribution and fluid distribution characteristics of reservoirs can be effectively characterized.

[0003] To extract frequency variation information from seismic signals, commonly used analysis methods include Short-Time Fourier Transform (STFT), Continuous Wavelet Transform (CWT), and S-Transform (ST). ST combines the advantages of STFT and CWT, preserving the phase information of STFT while possessing multi-resolution analysis capabilities, thus it is widely used in time-frequency analysis of seismic signals and reservoir characteristic description. However, the fixed functional relationship between the window function and frequency in the S-Transform leads to poor adaptability when processing complex non-stationary signals. To improve this, researchers have proposed various generalized S-Transform methods, optimizing the window function by introducing adjustable parameters to improve time-frequency resolution. Although these methods improve the focusing of the time spectrum to some extent, the narrowing of the Gaussian window width with increasing frequency still causes a shift in spectral energy towards higher frequencies, thereby reducing the time resolution in the low-frequency band and limiting its application in gas-bearing reservoir prediction. To further improve the accuracy of time-frequency analysis, researchers have proposed the W-Transform method. This method effectively eliminates the inherent frequency shift problem in the S-Transform by introducing a time-varying dominant frequency, enabling good time resolution in both high and low frequency components. However, because the Gaussian window of the W-transform contains the absolute value of the dominant frequency, the peak time-frequency amplitude at the dominant frequency is prone to splitting, affecting the concentration of the dominant frequency energy. To address this issue, the normalized W-transform introduces a normalization coefficient along the dominant frequency direction to correct the time-frequency spectrum of the W-transform, thereby improving the energy concentration effect. However, this method is still limited by the accuracy of dominant frequency extraction, making it difficult to achieve fine characterization of complex seismic signals.

[0004] With the increasing demands for exploration precision and reservoir characterization, existing time-frequency analysis techniques are no longer sufficient to meet the requirements of high-resolution seismic interpretation in terms of time-frequency resolution and spectral energy concentration. Therefore, there is an urgent need to develop a time-frequency analysis method with higher time-frequency resolution, stronger spectral characterization capabilities, and better noise resistance to achieve accurate identification and prediction of oil and gas reservoirs. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of the prior art by providing a method for identifying gas-bearing reservoirs using a normalized W-transform with local frequency constraints. This invention can significantly improve time-frequency energy focusing and effectively characterize the spatial distribution of oil and gas reservoirs.

[0006] To achieve the aforementioned technical objective, the present invention employs the following technical solution:

[0007] Step 1: Input the raw seismic signal to be analyzed ,in Representing time, constructing its analytic signal for:

[0008]

[0009] in The original seismic signal The result of the Hilbert transform is expressed as:

[0010]

[0011] It is the imaginary unit. Instantaneous amplitude; For instantaneous phase, This indicates that the integral takes the value according to the definition of Cauchy's principal value. For the introduced time integration variable;

[0012] Step 2: Calculate the instantaneous phase using the analytic signal obtained in Step 1. The original instantaneous frequency is obtained by differentiating the instantaneous phase. An optimization model with total variational regularization as a constraint term is constructed, and the original instantaneous frequency is subjected to constraint optimization to obtain the local frequency. By introducing total variational regularization constraints into the optimization model, noise fluctuations in the original instantaneous frequency are effectively suppressed, maintaining the continuity of frequency changes, thereby improving the stability and accuracy of local frequency estimation. The calculation process of the original instantaneous frequency includes the following steps:

[0013] (1) Based on analytic signals Calculate its instantaneous phase And by differentiating the instantaneous phase with respect to time, the original instantaneous frequency is obtained:

[0014]

[0015] (2) The original instantaneous frequency is further expanded into an equivalent form based on the real and imaginary parts of the analytic signal:

[0016]

[0017] in, Indicates the instantaneous amplitude of the signal. and They represent signals respectively. and its Hilbert transform The first derivative;

[0018] Step 3: Solve the optimization model using the Bregman iterative algorithm to obtain the local frequency distribution results. The Bregman iterative algorithm introduces auxiliary variables and splits the original optimization problem, transforming it into multiple sub-problems that are solved alternately. This improves computational efficiency while ensuring solution accuracy and accelerates the model's convergence speed.

[0019] Step 4: Based on the local frequency results Preset standard deviation function ,in Representing frequency; based on the standard deviation function, the seismic signal... Perform W-transform calculations to obtain the time-frequency representation of the signal. The standard deviation function adaptively changes with local frequency, enabling the time-frequency analysis window to dynamically change according to different frequency components, thereby improving the concentration and resolution of time-frequency energy.

[0020] Step 5: Use the standard deviation function set in Step 4 The W-transform result is normalized along the local frequency direction to obtain the normalized W-transform with local frequency constraints. The normalization process is used to compensate for the scale differences corresponding to different frequency components, making the time-frequency energy more concentrated near the local frequency.

[0021] Step 6: Use the local frequency constraint normalized W transform obtained in Step 5 to perform time-frequency analysis on the input seismic signal to obtain the corresponding time-frequency energy spectrum; select at least two characteristic frequency points based on the energy accumulation distribution of the time-frequency spectrum, and perform linear fitting on the characteristic frequency points to calculate the frequency attenuation gradient attribute. The frequency attenuation gradient attribute is used to characterize the distribution characteristics of gas-bearing reservoirs and improve the characterization accuracy of gas-bearing reservoirs.

[0022] Preferably, the optimization function of the optimization model constructed in step 2 with total variational regularization as a constraint can be defined as:

[0023]

[0024] Among them, local frequency By solving the optimization model, we obtain that D is a diagonal matrix with diagonal elements as follows: , It is a column vector. R is a first-order difference operator. The weights are for total variational regularization. This optimization model achieves smooth constraints on instantaneous frequencies and preservation of details by balancing data fidelity terms with total variational regularization terms.

[0025] Preferably, the Bregman iterative algorithm described in step 3 can be defined as:

[0026]

[0027] in, For penalty parameters, For splitting variables, For Bregman iteration parameters, Indicates the number of iterations. This indicates selecting the value that minimizes the objective function within the parentheses. This represents the square of the L2 norm.

[0028] Preferably, the seismic signal analyzed in step 4 W transformation The definition is as follows:

[0029]

[0030] in, Representing the imaginary unit, the W transform significantly improves the clarity and resolution of time-frequency representations by introducing local frequencies.

[0031] Preferably, the step 4 described It can be defined as:

[0032]

[0033]

[0034] in, Indicates the scale factor. Indicates the instantaneous amplitude of the signal. Indicates instantaneous amplitude The amplitude modulation function obtained after normalization and bias processing is used to adjust the time-frequency resolution in different energy regions. The modulation index is used to control the local frequency constraint strength and the attenuation rate of the frequency deviation. This represents the bias constant, used to avoid excessively small normalized amplitude. Compared to traditional fixed or single-scale functions, the standard deviation function simultaneously introduces local frequency constraints, frequency deviation suppression, and adaptive amplitude adjustment mechanisms, enabling dynamic adjustment of the time-frequency analysis window driven by multi-parameter coupling.

[0035] Preferably, the seismic signal analyzed in step 5 Normalized W-transform with local frequency constraints The definition is as follows:

[0036]

[0037] The present invention provides a method for identifying gas-bearing reservoirs using a normalized W-transform with local frequency constraints, which has the following advantages:

[0038] The local frequency-constrained normalized W-transform proposed in this invention first uses a total variational regularization method to calculate the local frequency of the signal, thereby obtaining a more stable and robust dominant frequency. Then, the W-transform result is multiplied by a standard deviation function normalized along the time-varying dominant frequency to form a local frequency-constrained normalized W-transform, effectively suppressing the splitting phenomenon that may occur in the traditional W-transform. Compared with the traditional W-transform, this method exhibits superior performance in time-frequency characterization and can significantly improve time resolution. By performing a local frequency-constrained normalized W-transform on the seismic signal, a high-precision time-frequency spectrum can be obtained. Key frequencies are extracted based on the cumulative energy distribution characteristics of the time-frequency energy spectrum, and linear fitting is performed on these key frequencies to calculate the frequency attenuation gradient attribute. This frequency attenuation gradient attribute is used to characterize the distribution characteristics of gas-bearing reservoirs. Attached Figure Description

[0039] Figure 1 This is a schematic flowchart of the method of the present invention;

[0040] Figure 2 This is a seismic profile of a region in China.

[0041] Figure 3 Comparison of attenuation gradient properties obtained after processing seismic signals through (a) W transform, (b) three-parameter W transform, (c) normalized W transform, and (d) normalized W transform with local frequency constraints. Detailed Implementation

[0042] The invention will now be further described with reference to the accompanying drawings.

[0043] See Figure 1 A method for identifying gas-bearing reservoirs using a local frequency-constrained normalized W-transform includes the following steps:

[0044] Step 1: Input the raw seismic signal to be analyzed ,in For time, its corresponding analytical signal for:

[0045]

[0046] in The original real signal, Indicates signal The Hilbert transform result, It is the imaginary unit. Instantaneous amplitude; It is the instantaneous phase;

[0047] First, define the expression for the Hilbert transform as:

[0048]

[0049] in, This indicates that the integral takes the value according to the definition of Cauchy's principal value. This is the time integration variable introduced.

[0050] Step 2: Use the analytical signal obtained in Step 1 Calculate its instantaneous phase The original instantaneous frequency is obtained by differentiating the instantaneous phase, and an optimization model with total variational regularization as a constraint is established for the input signal. The original instantaneous frequency is processed to obtain its local frequency. ;

[0051] First, define the expression for the original instantaneous frequency as follows:

[0052]

[0053] The original instantaneous frequency is further expanded into an equivalent form based on the real and imaginary parts of the analytic signal:

[0054]

[0055] in, Indicates the instantaneous amplitude of the signal. and They represent signals respectively. and its Hilbert transform The first derivative;

[0056] Solving for local frequencies using a total variational regularized optimization function:

[0057]

[0058] in, Let D be the local frequency to be solved, and let D be a diagonal matrix with diagonal elements as follows: , It is a column vector. R is a first-order difference operator. For total variational regularization weights;

[0059] Step 3: To improve the solution efficiency and convergence stability, the Bregman iterative algorithm is used to accelerate the solution of the optimization model, thereby obtaining high-resolution local frequency distribution results;

[0060] Optimization using the Bregman iterative algorithm:

[0061]

[0062] in, For penalty parameters, For splitting variables, For Bregman iteration parameters, Indicates the number of iterations. This indicates selecting the value that minimizes the objective function within the parentheses. Represents the square of the L2 norm;

[0063] Step 4: To improve the clarity and resolution of the time-frequency representation, the W-transform is applied to the analyzed seismic signal by introducing local frequencies. The definition is as follows:

[0064]

[0065] in, Represents the imaginary unit;

[0066] Standard deviation function for:

[0067]

[0068]

[0069] in, Let a(t) represent the scaling factor, and a(t) represent the instantaneous amplitude of the signal. Indicates instantaneous amplitude The amplitude modulation function obtained after normalization and bias processing is used to adjust the time-frequency resolution in different energy regions. The modulation index is used to control the local frequency constraint strength and the attenuation rate of the frequency deviation. This represents the bias constant, used to avoid the normalized amplitude being too small;

[0070] Step 5: Use the standard deviation function set in Step 4 The W-transform result is normalized along the local frequency direction to obtain the normalized W-transform with local frequency constraints. This achieves an improvement in time resolution, and its expression is as follows:

[0071]

[0072] Step 6: Perform time-frequency analysis on the input seismic signal using the local frequency-constrained normalized W transform obtained in Step 5 to obtain the corresponding time-frequency energy spectrum; select characteristic frequency points based on the cumulative energy distribution of the time-frequency spectrum. Specifically, select the frequency points corresponding to when the cumulative energy reaches 65% and 85% respectively, and perform linear fitting on the two frequency points to calculate the frequency attenuation gradient attribute. The frequency attenuation gradient attribute is used to characterize the distribution characteristics of the gas-bearing reservoir.

[0073] See Figures 1 to 3 This invention uses actual earthquake data from a certain region in China as an example for illustration. Figure 2 The seismic profile connecting wells A and B in the study area is shown. The sampling interval for this seismic data is 2 ms, with a total of 251 sampling points and 678 seismic traces. The dashed lines at points A and B in the figure correspond to the locations of the seismic traces connecting wells A and B, respectively. Figure 3 As shown, the seismic signal was processed by (a) W transform, (b) three-parameter W transform, (c) normalized W transform, and (d) normalized W transform with local frequency constraints, respectively, to obtain the corresponding attenuation gradient attribute map. The horizontal axis in the figure represents time, in seconds (s). From... Figure 3 (a) to Figure 3 The results in (d) show that the attenuation gradient attributes extracted using the W transform exhibit significant energy attenuation characteristics in the gas-bearing area. However, the range of this attenuation anomaly significantly exceeds the well logging interpretation interval, resulting in insufficient precision in reservoir boundary characterization and thus limiting the accurate delineation of favorable reservoir boundaries. The three-parameter W transform, by introducing an adaptive Gaussian window function, alleviates the energy splitting problem in the traditional W transform to some extent, making the attenuation anomaly in the gas-bearing area more concentrated. However, due to its limited time resolution, it is difficult to meticulously characterize the boundaries of gas-bearing reservoirs. Both the normalized W transform and the local frequency-constrained normalized W transform effectively improve the time resolution by standardizing the W transform results along the frequency trajectory. However, the performance of the normalized W transform depends on the accuracy of the dominant frequency estimation. When there is a deviation in the dominant frequency estimation, the continuity and resolution of its attenuation attribute map will be affected. In contrast, the local frequency-constrained normalized W transform proposed in this invention introduces a local frequency as a time-varying dominant frequency during the normalization process, making the transformation results more stable and accurate. This method significantly improves the ability to depict temporal continuity and details, and demonstrates better resolution in the identification of decay features, enabling it to more accurately reveal the spatial distribution characteristics of gas-bearing reservoirs.

[0074] Although specific embodiments of the invention have been described in detail with reference to the accompanying drawings, this should not be construed as limiting the scope of protection of this patent. Various modifications and variations that can be made by a person skilled in the art without inventive effort within the scope described in the claims still fall within the scope of protection of this patent.

Claims

1. A method for identifying gas-bearing reservoirs based on normalized W-transform with local frequency constraints, characterized in that, Includes the following steps: Step 1: Input the raw seismic signal to be analyzed ,in Representing time, its corresponding analytic signal for: ； in The original seismic signal The result of the Hilbert transform is expressed as: ； It is the imaginary unit. Instantaneous amplitude; For instantaneous phase, This indicates that the integral takes the value according to the definition of Cauchy's principal value. For the introduced time integration variable; Step 2: Use the analytical signal obtained in Step 1 Calculate its instantaneous phase The original instantaneous frequency is obtained by differentiating the instantaneous phase. An optimization model with total variational regularization as a constraint term is constructed, and the original instantaneous frequency is subjected to constraint optimization to obtain the local frequency. ; The calculation process for the original instantaneous frequency includes the following steps: (1) Based on analytic signals Calculate its instantaneous phase And by differentiating the instantaneous phase with respect to time, the original instantaneous frequency is obtained: ； (2) The original instantaneous frequency is further expanded into an equivalent form based on the real and imaginary parts of the analytic signal: ； in, Indicates the instantaneous amplitude of the signal. and They represent signals respectively. and its Hilbert transform The first derivative; Step 3: To improve the solution efficiency and convergence stability, the Bregman iterative algorithm is used to accelerate the solution of the optimization model; Step 4: Based on the local frequency results Preset standard deviation function ,in Indicates frequency; for seismic signals Perform W-transform calculations to obtain the time-frequency representation of the signal. ; Step 5: Use the standard deviation function set in Step 4 The W-transform result is normalized along the local frequency direction to obtain the normalized W-transform with local frequency constraints. ; Step 6: Use the local frequency constraint normalized W transform obtained in Step 5 to perform time-frequency analysis on the input seismic signal to obtain the corresponding time-frequency energy spectrum; select at least two characteristic frequency points based on the energy accumulation distribution of the time-frequency spectrum, and perform linear fitting on the characteristic frequency points to calculate the frequency attenuation gradient attribute, which is used to characterize the distribution characteristics of gas-bearing reservoirs.

2. The gas-bearing reservoir identification method based on normalized W-transform with local frequency constraints according to claim 1, characterized in that, In step 2, an optimization model is constructed with total variational regularization as a constraint term. Its optimization function can be defined as: ； Among them, local frequency By solving the optimization model, we obtain that D is a diagonal matrix with diagonal elements as follows: , It is a column vector. R is a first-order difference operator. For total variational regularization weights.

3. The gas-bearing reservoir identification method based on normalized W-transform with local frequency constraints according to claim 1, characterized in that, The Bregman iterative algorithm in step 3 can be defined as follows: ； in, For penalty parameters, For splitting variables, For Bregman iteration parameters, Indicates the number of iterations. This indicates selecting the value that minimizes the objective function within the parentheses. This represents the square of the L2 norm.

4. The gas-bearing reservoir identification method based on normalized W-transform with local frequency constraints according to claim 1, characterized in that, In step 4, the seismic signal to be analyzed W transformation The definition is as follows: ； ； ； in, Represents the imaginary unit. Indicates the scale factor. Indicates the instantaneous amplitude of the signal. Indicates instantaneous amplitude The amplitude modulation function obtained after normalization and bias processing is used to adjust the time-frequency resolution in different energy regions. The modulation index is used to control the local frequency constraint strength and the attenuation rate of the frequency deviation. This represents the bias constant, used to avoid the normalized amplitude being too small.

5. The gas-bearing reservoir identification method based on normalized W-transform with local frequency constraints according to claim 1, characterized in that, The seismic signal analyzed in step 5 Normalized W-transform with local frequency constraints The definition is as follows: 。

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