A characterization method for complex superimposed tight sandstone reservoirs in the statistical synchronous compression transform domain

Abstract

The present invention discloses a method for characterizing complex superimposed tight sandstone reservoirs in a statistical synchronous extrusion transform domain, comprising the following steps: S1, inputting a seismic signal x(t) to be analyzed, where t is time; S2, presetting a window function g(t) and an order K, and calculating the window function g(t) with different window functions t k g(t) and its derivative g′(t) under the short-time Fourier transform #imgabs0# and #imgabs1##imgabs2# where ω is the frequency; S3. Select an appropriate frequency filter h(ω) and calculate the inner products #imgabs3# and #imgabs4# between the above transformations. S4. Calculate the instantaneous frequency estimate of the signal in the short-time Fourier transform domain based on the above inner products #imgabs5# S5. According to the squeezing principle, use the fixed point iteration algorithm to obtain the statistical synchronous squeezing transform T x,K (t,ω); S6, analyze the frequency change in the synchronous compression transform domain to characterize the thickness variation characteristics of the complex superimposed tight sandstone reservoir. In addition, use T x,K (t,ω) can also reconstruct the original signal. The present invention can provide a highly robust and focused time-frequency distribution to finely characterize the characteristics of complex superimposed tight sandstone reservoirs.

Description

Technical Field

[0001] The present invention belongs to the field of seismic signal processing, and in particular relates to a method for characterizing complex superimposed tight sandstone reservoirs in a statistical synchronous compression transform domain. Background Art

[0002] Time-frequency analysis, a powerful tool for processing nonstationary signals, maps one-dimensional time series into two-dimensional distribution functions related to time and frequency, thereby providing information about the signal's time-varying spectrum. Common time-frequency analysis methods include the short-time Fourier transform (STFT), wavelet transform (WT), S transform (ST), and generalized S transform (GST). These methods all estimate the signal's frequency components within a window function (a continuously refined window function) so that its time-frequency energy is always distributed within a range centered on the signal's true instantaneous frequency. Therefore, limited by the Heisenberg uncertainty principle, the energy of the time-frequency distribution they represent is not sufficiently focused, and their time and frequency resolution cannot be optimized simultaneously. In seismic signal analysis, high-precision time-frequency analysis methods will help better detect the frequency variation characteristics caused by thickness variations in complex, stacked tight sandstone reservoirs, thereby facilitating the characterization of these reservoirs.

[0003] The synchronized squeezed wavelet transform (SSWT) is a new time-frequency post-processing method proposed by Daubechies et al. based on the WT. It effectively improves the time-frequency resolution of the WT by focusing the spectral energy onto the estimated instantaneous frequency curve. It was subsequently extended to the framework of the STFT. However, they require the signal to have weak amplitude and frequency modulation characteristics. Therefore, many studies have approximated the signal amplitude and phase to high-order Taylor expansions and derived various high-order instantaneous frequency estimation operators for use in the squeezing process to achieve a more focused time-frequency representation. These high-order methods have similar instantaneous frequency estimation processes: based on the original instantaneous frequency estimation results, they first discuss the error terms caused by high-order amplitude and phase characteristics. Then, they capture these error terms through the high-order partial derivative characteristics of the original time-frequency representation results to correct their instantaneous frequency estimates.

[0004] Although these high-order methods effectively improve the energy focusing of time-frequency representation and provide a clearer time-frequency description result, they rely on the high-order partial derivative characteristics of the original time-frequency representation results, which will cause large deviations in instantaneous frequency estimation under the influence of noise. Their time-frequency distribution focusing performance is not very robust. In addition, the seismic signals of complex superimposed tight sandstone reservoirs themselves have strong nonlinear time-frequency characteristics. Therefore, there is an urgent need to study a time-frequency representation method with strong robustness and high energy focusing. Summary of the Invention

[0005] To address the above-mentioned deficiencies in the prior art, the present invention provides a method for characterizing complex stacked tight sandstone reservoirs in the statistical synchronous squeezing transform domain. Within the STFT framework, the present invention derives a new instantaneous frequency estimator that can capture the high-order characteristics of frequency-amplitude-modulated signals, similar to high-order methods. A sliding frequency filter is constructed, which is convolved with the time-frequency coefficients to separate multi-component signals. This convolution relationship is then used to construct the inner product between a series of short-time Fourier transforms to derive a new instantaneous frequency estimator with local statistical properties. This estimator, when used in the synchronous squeezing process, can provide a robust, highly energy-focused time-frequency distribution for multi-component frequency-amplitude-modulated signals, thereby improving the accuracy of seismic signal processing for complex stacked tight sandstone reservoirs.

[0006] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is: a method for characterizing complex superimposed tight sandstone reservoirs in a statistical synchronous extrusion transform domain, comprising the following steps:

[0007] S1. Input the seismic signal x(t) to be analyzed, where t is time;

[0008] S2, preset window function g(t) and order K, calculate different window functions t k Short-time Fourier transform under g(t) and its derivative function g′(t) and

[0009]

[0010]

[0011] Where ω represents frequency, u is time, is the unit of the imaginary part of the complex number, and Indicates t k The complex conjugates of g(t) and g′(t);

[0012] S3. Select a suitable frequency filter h(ω) and calculate the inner product between the above short-time Fourier transforms and

[0013] S4, constructing a K-order matrix function A according to the inner product in step S3. K (t, ω), B K (t, ω) and D K (t, ω), based on which the instantaneous frequency estimate of the signal in the short-time Fourier transform domain is calculated

[0014] S5, using the instantaneous frequency estimation in step S4 The fixed point iteration algorithm is used to further accurately approximate the instantaneous frequency, and a robust statistical synchronous squeezing transform T with high focus of time-frequency distribution is obtained according to the squeezing principle. x，K (t,ω);

[0015] S6, according to the statistical synchronous extrusion transformation T in step S5 x，K (t, ω), the frequency change in the synchronous compression transform domain is analyzed to characterize the thickness variation characteristics of the complex superimposed tight sandstone reservoir, that is, the thinning of a layer is accompanied by an increase in the tuning frequency characteristic or the thickening of a layer is accompanied by a decrease in the tuning frequency characteristic. In addition, T x，K (t, ω) can also reconstruct the original signal.

[0016] Preferably, the frequency filter h(ω) in step S3 is selected according to the window function g(t). If the window function g(t) is selected as a Gaussian function, then h(ω) is also a Gaussian function associated therewith, and its specific mathematical expression is:

[0017]

[0018]

[0019] Where σ is a Gaussian parameter related to the window length of the window function. Using this filter h(ω), the following inner product can be calculated. The specific mathematical expression is defined as:

[0020]

[0021]

[0022]

[0023] Where * represents a convolution operator with respect to frequency ω.

[0024] As an advantage, the K-order matrix function A in step S4 K (t, ω), B K (t, ω) and D K (t, ω) is expressed as:

[0025]

[0026]

[0027]

[0028] Then the instantaneous frequency estimator of the signal in the time-frequency domain is It can be calculated by the following formula:

[0029]

[0030] Where, Indicates taking the real part of a complex number, |A K (t,ω)|、|B K (t,ω)| and |D K (t, ω)|represents the calculation of K-order matrix function A K (t, ω), B K (t, ω) and D K The determinant of (t, ω).

[0031] Preferably, the fixed point iteration algorithm in step S5 is described as follows:

[0032]

[0033] Where n represents the number of iterations. According to the extrusion principle, the statistical synchronous extrusion transformation T in step S5 is x，K (t, ω) is defined as:

[0034]

[0035] Where δ represents the Dirichlet function, is the statistical synchronous squeezing operator.

[0036] Preferably, the inverse transformation formula of the statistical synchronous squeezing transformation in step S6 is expressed as:

[0037]

[0038] The idea of ​​the present invention is:

[0039] First, input the seismic signal to be analyzed x(t), where t is time;

[0040] Second, preset the window function g(t) and order K, and calculate different window functions t k Short-time Fourier transform under g(t) and its derivative function g′(t) and Where ω is the frequency;

[0041] Third, select a suitable frequency filter h(ω) and calculate the inner product between the above short-time Fourier transforms and

[0042] Fourth, calculate the instantaneous frequency estimate of the signal in the short-time Fourier transform domain based on the inner product calculated above

[0043] Fifth, based on the instantaneous frequency estimator The fixed point iteration algorithm is used to further accurately approximate the instantaneous frequency, and a robust time-frequency distribution with high focus statistical synchronous squeezing transform T is obtained according to the squeezing principle. x，K (t,ω);

[0044] Sixth, the frequency variation in the synchronous compression transform domain is analyzed to characterize the thickness variation characteristics of the complex superimposed tight sandstone reservoir, that is, the thinning of a layer is accompanied by an increase in the tuning frequency characteristic or the thickening of a layer is accompanied by a decrease in the tuning frequency characteristic. In addition, T x，K (t, ω) can also reconstruct the original signal.

[0045] The working principle of the present invention is as follows: input the seismic signal x(t) to be analyzed, where t is time; preset the window function g(t) and the order K, and calculate the different window functions t k Short-time Fourier transform under g(t) and its derivative function g′(t) and Where ω is the frequency; select a suitable frequency filter h(ω), calculate the inner product between the above transformations and use it to calculate the instantaneous frequency estimate of the signal in the short-time Fourier transform domain According to the synchronous squeezing principle, the fixed point iteration algorithm is used to obtain the statistical synchronous squeezing transformation T x，K (t, ω); by observing the frequency change in the statistical synchronous compression transform domain, the thickness variation characteristics of the complex superimposed tight sandstone reservoir can be analyzed. In addition, the T x，K The invention can provide a highly robust energy-focused time-frequency distribution to improve the characterization accuracy of complex superimposed tight sandstone reservoirs.

[0046] To address the problems of high-order synchronous squeezing transforms (SSTs) causing large deviations in instantaneous frequency estimation under the influence of noise and lacking robust time-frequency focusing, the present invention proposes a method for characterizing complex stacked tight sandstone reservoirs in the SST domain. First, the seismic signal to be analyzed is input and its short-time Fourier transform (STFT) result is calculated. An appropriate frequency filter is then selected and an instantaneous frequency estimator with statistical effectiveness is constructed through inner product. Finally, based on the SST principle, a fixed-point iteration algorithm is used to squeeze the STFT result onto the estimated instantaneous frequency curve to obtain the SST. The thickness variation characteristics of complex stacked tight sandstone reservoirs are analyzed by observing frequency variations in the SST domain. Furthermore, the original signal can be reconstructed through inverse transformation. The present invention demonstrates excellent results in both time-frequency characterization and reconstruction capabilities, significantly improving the energy focusing of the time-frequency distribution, obtaining a highly robust time-frequency distribution, and improving the accuracy of seismic signal processing for complex stacked tight sandstone reservoirs. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1Flowchart of the present invention;

[0048] Figure 2 is a seismic profile, and the input seismic signal is the seismic signal corresponding to the through-well seismic trace in the figure;

[0049] Figure 3 The time-frequency characterization results obtained by different methods are: (a) short-time Fourier transform, (b) synchronous squeezing transform, (c) second-order synchronous squeezing transform, (d) fourth-order synchronous squeezing transform, (e) second-order multiple synchronous squeezing transform, and (f) the proposed statistical synchronous squeezing transform. DETAILED DESCRIPTION

[0050] The present invention will be further described below with reference to the accompanying drawings.

[0051] Example 1: See Figure 1 A method for characterizing complex superimposed tight sandstone reservoirs in a statistical synchronous compression transform domain includes the following steps:

[0052] S1. Input the seismic signal x(t) to be analyzed, where t is time;

[0053] S2, preset window function g(t) and order K, calculate different window functions t k Short-time Fourier transform under g(t) and its derivative function g′(t) and

[0054]

[0055]

[0056] Where ω represents frequency, u is time, is the unit of the imaginary part of the complex number, and Indicates t k The complex conjugates of g(t) and g′(t);

[0057] S3. Select a suitable frequency filter h(ω) and calculate the inner product between the above short-time Fourier transforms and

[0058] S4, constructing a K-order matrix function A according to the inner product in step S3. K (t, ω), B K (t, ω) and D K (t, ω), based on which the instantaneous frequency estimate of the signal in the short-time Fourier transform domain is calculated

[0059] S5, using the instantaneous frequency estimation in step S4 The fixed point iteration algorithm is used to further accurately approximate the instantaneous frequency, and a robust statistical synchronous squeezing transform T with high focus of time-frequency distribution is obtained according to the squeezing principle. x，K (t,ω);

[0060] S6, according to the statistical synchronous extrusion transformation T in step S5 x，K (t, ω), the frequency change in the synchronous compression transform domain is analyzed to characterize the thickness variation characteristics of the complex superimposed tight sandstone reservoir, that is, the thinning of a layer is accompanied by an increase in the tuning frequency characteristic or the thickening of a layer is accompanied by a decrease in the tuning frequency characteristic. In addition, T x，K (t, ω) can also reconstruct the original signal.

[0061] Preferably, the frequency filter h(ω) in step S3 is selected according to the window function g(t). If the window function g(t) is selected as a Gaussian function, then h(ω) is also a Gaussian function associated therewith, and its specific mathematical expression is:

[0062]

[0063]

[0064] Where σ is a Gaussian parameter related to the window length of the window function. Using this filter h(ω), the following inner product can be calculated. The specific mathematical expression is defined as:

[0065]

[0066]

[0067]

[0068] Where * represents a convolution operator with respect to frequency ω.

[0069] As an advantage, the K-order matrix function A in step S4 K (t, ω), B K (t, ω) and D K (t, ω) is expressed as:

[0070]

[0071]

[0072]

[0073] Then the instantaneous frequency estimator of the signal in the time-frequency domain is It can be calculated by the following formula:

[0074]

[0075] Where, Indicates taking the real part of a complex number, |A K (t,ω)|、|B K (t,ω)| and |D K (t, ω)|represents the calculation of K-order matrix function A K (t, ω), B K (t, ω) and D K The determinant of (t, ω).

[0076] Preferably, the fixed point iteration algorithm in step S5 is described as follows:

[0077]

[0078] Where n represents the number of iterations. According to the extrusion principle, the statistical synchronous extrusion transformation T in step S5 is x，K (t, ω) is defined as:

[0079]

[0080] Where δ represents the Dirichlet function, is the statistical synchronous squeezing operator.

[0081] Preferably, the inverse transformation formula of the statistical synchronous squeezing transformation in step S6 is expressed as:

[0082]

[0083] See also Figures 1 to 3 , we take the seismic signal of a complex superimposed tight sandstone reservoir as an example, Figure 2 The seismic profile is shown. The input seismic signal is the through-well seismic trace in the figure. The dotted box marks the position of the thin interbed. The horizontal axis represents time in seconds, and the vertical axis represents amplitude. Figure 3 The time-frequency spectra are respectively processed by short-time Fourier transform, synchronous squeezing transform, second-order synchronous squeezing transform, fourth-order synchronous squeezing transform, second-order multiple synchronous squeezing transform and the method of the present invention. The horizontal axis represents time in seconds, and the vertical axis represents frequency in Hertz. The embodiment proves that the result obtained after processing by the method of the present invention has a highly stable time-frequency distribution with highly focused energy. The time-frequency ridges described are also relatively clear, which can significantly improve the accuracy of seismic signal processing. In addition Figure 3 The time-frequency representation results in the dotted box in (f) clearly indicate the frequency variation pattern of the seismic signal: the frequency first increases and then decreases with time, which means that the thickness of the thin interlayer at this location first becomes thinner and then thicker.

[0084] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for characterizing complex superimposed tight sandstone reservoirs in a statistical synchronous compression transform domain, characterized in that: The following steps are involved: S1. Input the seismic signal x(t) to be analyzed, where t is time; S2, preset window function g(t) and order K, calculate different window functions t k Short-time Fourier transform under g(t) and its derivative function g′(t) and Where ω represents frequency, u is time, is the unit of the imaginary part of the complex number, and Indicates t k The complex conjugates of g(t) and g′(t); S3. Select a suitable frequency filter h(ω) and calculate the inner product between the above short-time Fourier transforms and S4, constructing a K-order matrix function A according to the inner product in step S3. K (t,ω),B K (t,ω) and D K (t,ω), based on which the instantaneous frequency estimate of the signal in the short-time Fourier transform domain is calculated S5, using the instantaneous frequency estimation in step S4 The fixed point iteration algorithm is used to further accurately approximate the instantaneous frequency, and a robust statistical synchronous squeezing transform T with high focus of time-frequency distribution is obtained according to the squeezing principle. x,K (t,ω); S6, according to the statistical synchronous extrusion transformation T in step S5 x,K (t,ω), analyze the frequency change in the synchronous compression transform domain to judge the thickness change characteristics of the complex superimposed tight sandstone reservoir, that is, the thinning of a layer is accompanied by an increase in the tuning frequency characteristic or the thickening of a layer is accompanied by a decrease in the tuning frequency characteristic. In addition, T x,K (t,ω) can also reconstruct the original signal.

2. The method for characterizing complex superimposed tight sandstone reservoirs in a statistical synchronous compression transform domain according to claim 1, characterized in that: The frequency filter h(ω) in step S3 is selected according to the window function g(t). If the window function g(t) is selected as a Gaussian function, then h(ω) is also a Gaussian function associated with it. Its specific mathematical expression is: Where σ is a Gaussian parameter related to the window length of the window function. Using this filter h(ω), the following inner product can be calculated. The specific mathematical expression is defined as: Where * represents a convolution operator with respect to frequency ω.

3. The method for characterizing complex superimposed tight sandstone reservoirs in a statistical synchronous extrusion transform domain according to claim 1, characterized in that: The K-order matrix function A in step S4 K (t,ω),B K (t,ω) and D K (t,ω) is expressed as: Then the instantaneous frequency estimator of the signal in the time-frequency domain is It can be calculated by the following formula: Where, Indicates taking the real part of a complex number, |A K (t,ω)|、|B K (t,ω)| and |D K (t,ω)|represents the calculation of K-order matrix function A K (t,ω),B K (t,ω) and D K The determinant of (t,ω).

4. The method for characterizing complex superimposed tight sandstone reservoirs in a statistical synchronous compression transform domain according to claim 1, characterized in that: The fixed point iteration algorithm in step S5 is described as follows: Where n represents the number of iterations. According to the extrusion principle, the statistical synchronous extrusion transformation T in step S5 is x,K (t,ω) is defined as: Where δ represents the Dirichlet function, is the statistical synchronous squeezing operator.

5. The method for characterizing complex superimposed tight sandstone reservoirs in a statistical synchronous compression transform domain according to claim 1, characterized in that: The inverse transformation formula of the statistical synchronous squeezing transformation in step S6 is expressed as: 。

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