Stratum thin interbed thickness analysis method of adaptive redistribution domain
By building an adaptive window in time-frequency analysis and redistributing time-frequency energy, the problem of insufficient resolution in thin interlayer formation signals is solved, and the time-frequency characterization and energy focus are achieved with higher accuracy , significantly improves the characterization of thin interlayer thickness changes.
Patent Information
- Application Number
- CN202411195595.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-08-29
- Publication Date
- 2024-12-24
AI Technical Summary
Traditional time-frequency analysis methods cannot achieve the optimal resolution in the time domain and the frequency domain at the same time, resulting in low characterization accuracy of thin interlayer formation signals, and post-processing technology has problems such as energy divergence and limited time-frequency energy focus.
By defining local signals in fixed neighborhoods at different times, analyzing the STFT time spectrum energy distribution and window function standard deviation of local signals, building an adaptive window and reassigning the time-frequency energy to the instantaneous frequency trajectory according to the principle of local maximum value, and proposing adaptive Redistribute transform ART(t,ω) to improve time-frequency resolution.
It significantly improves the energy focus of the time frequency distribution of the formation signal, enhances the accuracy of characterizing the change trend of thin interlayer thickness, and provides clearer time frequency readability.
Smart Images
Figure CN119179832A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to a signal processing method, and in particular relates to a method for analyzing the thickness of thin interlayers in a self-adaptive redistribution domain. Background Art
[0002] Thin interbedded strata are an important type of strata, and the study of this type of strata is of great research significance. However, the thickness of a single layer of thin interbedded strata ranges from several meters to more than ten meters, which brings challenges to the characterization of this type of strata. The stratum signal from the thin interbedded strata is a non-stationary signal with rapid changes in frequency and amplitude. Time-frequency analysis, as a powerful tool for studying non-stationary signals, has been widely used in the processing and interpretation of stratum signals. However, limited by the Heisenberg uncertainty principle, traditional time-frequency analysis methods such as short-time Fourier transform (STFT), wavelet transform, and S transform cannot achieve optimal resolution in both the time domain and the frequency domain, resulting in low characterization accuracy of thin interbedded stratum signals.
[0003] In order to improve the time-frequency readability of traditional time-frequency analysis methods, many post-processing techniques have emerged, including the redistribution method (RM), synchronous compression transform (SST) and synchronous extraction transform (SET). Among them, RM redistributes the time-frequency energy along the time and frequency directions, greatly improving the time-frequency energy focusing. However, RM cannot reconstruct the original signal. Unlike RM, SST only squeezes the time-frequency coefficients onto the instantaneous frequency trajectory along the frequency direction. It effectively improves the time-frequency resolution of traditional time-frequency analysis methods. And it effectively avoids the limitation that RM cannot reconstruct signals. Limited by weak frequency modulation and amplitude modulation, SST will have energy divergence when processing strong frequency signals. In addition, SET only extracts the time-frequency coefficients at the frequency fixed point of the instantaneous frequency estimator in SST, further improving the time-frequency resolution of the formation signal. The above post-processing methods can improve the characterization accuracy of non-stationary signals, but they all have the disadvantages of inaccurate estimation of the instantaneous frequency of the formation signal, global selection of the standard deviation of the window function, limited time-frequency energy focusing, and unclear characterization of thin interlayers. Therefore, it is urgent to study a time-frequency characterization method with high accuracy. Summary of the invention
[0004] In view of the shortcomings of the above-mentioned technologies, the present invention provides a method for analyzing the thickness of thin interlayers in strata in an adaptive redistribution domain. The present invention defines local signals of fixed neighborhoods at different times, analyzes the energy distribution of the STFT time-frequency spectrum of the local signal and the influence of the standard deviation of the window function on the time-frequency resolution, constructs an adaptive window, and redistributes the time-frequency energy to the instantaneous frequency trajectory according to the principle of local maximum. The present invention can provide a satisfactory time-frequency distribution for the signal of thin interlayers in strata, and can better analyze the thickness change trend of thin interlayers.
[0005] In order to achieve the above object, the technical solution adopted by the present invention is: a method for analyzing the thickness of thin interlayers in a stratum in an adaptive redistribution domain, comprising the following steps:
[0006] S1. Input the formation signal x(t) to be analyzed, where t is time;
[0007] S2, preset window function And set its standard deviation range [σ min ,σ max ], where σ(t) is the standard deviation, σ min With σ max are the minimum and maximum values of the standard deviation respectively, and the short-time Fourier transform G of the formation signal at different times u in the time interval [u-Δt,u+Δt] is calculated. e (t,ω), where Δt is the neighborhood size and ω represents the frequency;
[0008] S3. Give the criterion for judging the local maximum value and construct the rearrangement operator RO(t,ω) to extract G e The time-frequency coefficient at the instantaneous frequency (t, ω) is obtained to obtain the rearranged transformation value RT(t, ω);
[0009] S4. Define the information entropy C that reflects the degree of time-frequency energy focusing of formation signals σ,Δt (u), according to the information entropy, the standard deviation σ of the optimal window function corresponding to each moment u is obtained opt (u), propose adaptive redistribution transformation ART(t,ω);
[0010] S5. According to the adaptive redistribution transformation ART(t,ω) in step S4, the frequency change in the adaptive redistribution domain is analyzed to characterize the thickness change trend of the thin interlayers in the strata.
[0011] Preferably, the short-time Fourier transform G in step S2 e The explicit expression for (t,ω) is:
[0012]
[0013] Where s(u) is the signal of x(u) at the local time [u-Δt,u+Δt], Is an imaginary unit.
[0014] Preferably, the specific expression of the judgment criterion of the local maximum value in step S3 is:
[0015]
[0016] Among them, |G e (t,ω)| is G e The modulus of (t,ω);
[0017] The rearrangement operator RO(t,ω) constructed by the local maximum judgment criterion is:
[0018]
[0019] G is extracted by constructing the rearrangement operator RO(t,ω) e The time-frequency coefficient at the instantaneous frequency (t, ω) is obtained by rearranging the transformed value RT(t, ω) as follows:
[0020] RT(t,ω)=G e (t,ω)·RO(t,ω) (4) Preferably, the information entropy C in step S4 σ,Δt (u) The specific expression is:
[0021]
[0022] Where α is the order of information entropy;
[0023] Through information entropy C σ,Δt (u) Get the optimal window function standard deviation σ corresponding to each moment u opt The specific expression of (u) is:
[0024]
[0025] Where min(·) is the minimum function, and the range of σ is [σ min ,σ max ];
[0026] After selecting the optimal window function standard deviation σ opt The specific expression of the adaptive redistribution transform ART(t,ω) of (u) is:
[0027] ART(t,ω)=G opt (t,ω)·ARO(t,ω) (7)
[0028] Among them, G opt (t,ω) is the short-time Fourier transform result of x(u) under the standard deviation of the optimal window function, and ARO(t,ω) is the adaptive redistribution operator. Their expressions are as follows:
[0029]
[0030] in, is the Gaussian window function with the optimal standard deviation, and the specific expression is:
[0031]
[0032] Preferably, the order α of the information entropy is 3.
[0033] The idea of the present invention is:
[0034] First, input the formation signal x(t) to be analyzed, where t is time;
[0035] Second, preset window function And set its standard deviation range [σ min ,σ max ], where σ(t) is the standard deviation, σ min With σ max are the minimum and maximum values of the standard deviation respectively, and the short-time Fourier transform G of the formation signal at different times u in the time interval [u-Δt,u+Δt] is calculated. e (t,ω), where Δt is the neighborhood size and ω represents the frequency;
[0036] Third, the judgment criteria of the local maximum are given, and the rearrangement operator RO(t,ω) is constructed to extract G e The time-frequency coefficient at the instantaneous frequency (t, ω) is obtained to obtain the rearranged transformation value RT(t, ω);
[0037] Fourth, define the information entropy C that reflects the degree of time-frequency energy focusing of the formation signal σ,Δt (u), according to the information entropy, the standard deviation σ of the optimal window function corresponding to each moment u is obtained opt (u), propose adaptive redistribution transformation ART(t,ω);
[0038] Fifth, according to the adaptive redistribution transformation ART(t,ω) in step S4, the frequency change in the adaptive redistribution domain is analyzed to characterize the thickness change trend of the thin interlayers in the strata.
[0039] The working principle of the present invention is as follows: input the formation signal x(t) to be analyzed, where t is time; preset the window function And set its standard deviation range [σ min ,σ max ], where σ(t) is the standard deviation, σ min With σ max are the minimum and maximum values of the standard deviation respectively, and the short-time Fourier transform G of the formation signal at different times u in the time interval [u-Δt,u+Δt] is calculated. e (t,ω), where Δt is the neighborhood size and ω represents the frequency; the criterion for judging the local maximum is given, and the rearrangement operator RO(t,ω) is constructed to extract G e The time-frequency coefficient at the instantaneous frequency (t, ω) is obtained to obtain the rearrangement transformation value RT(t, ω); the information entropy G reflecting the degree of time-frequency energy focusing of the formation signal is defined σ,Δt(u), according to the information entropy, the standard deviation σ of the optimal window function corresponding to each moment u is obtained opt (u), an adaptive redistribution transformation ART(t,ω) is proposed; according to the adaptive redistribution transformation ART(t,ω) in step S4, the purpose of effectively analyzing the thickness of thin interlayers in the strata is achieved.
[0040] The present invention proposes a method for analyzing the thickness of thin interlayers in a formation in an adaptive redistribution domain. First, the formation signal to be analyzed is input and the short-time Fourier transform results of the local signal at different times are calculated. Then, the judgment criterion of the local maximum value is defined, and the standard deviation of the optimal window function at each moment is calculated by an information entropy function that reflects the degree of time-frequency energy focusing of the formation signal. Finally, according to the calculated optimal window function, the time-frequency coefficients are redistributed to the corresponding instantaneous frequency trajectory, and an adaptive redistribution transformation is proposed. The present invention can significantly improve the energy focusing of the time-frequency distribution of the formation signal and improve the characterization accuracy of the thin interlayer signal. BRIEF DESCRIPTION OF THE DRAWINGS
[0041] Figure 1 It is a flow chart of the present invention;
[0042] Figure 2 is the formation signal to be analyzed;
[0043] Figure 3 The time-frequency spectra are processed by (a) short-time Fourier transform, (b) synchronous squeezing transform, (c) synchronous extraction transform and (d) the method of the present invention. DETAILED DESCRIPTION
[0044] The present invention will be further described below in conjunction with the accompanying drawings.
[0045] Example 1: See Figure 1 , a method for analyzing the thickness of thin interbeds in a stratum with an adaptive redistribution domain, comprising the following steps:
[0046] S1. Input the formation signal x(t) to be analyzed, where t is time;
[0047] S2, preset window function And set its standard deviation range [σ min ,σ max ], where σ(t) is the standard deviation, σ min With σ max are the minimum and maximum values of the standard deviation respectively, and the short-time Fourier transform G of the formation signal at different times u in the time interval [u-Δt,u+Δt] is calculated. e (t,ω), where Δt is the neighborhood size and ω represents the frequency;
[0048] S3. Give the criterion for judging the local maximum value and construct the rearrangement operator RO(t,ω) to extract G e The time-frequency coefficient at the instantaneous frequency (t, ω) is obtained to obtain the rearranged transformation value RT(t, ω);
[0049] S4. Define the information entropy C that reflects the degree of time-frequency energy focusing of formation signals σ,Δt (u), according to the information entropy, the standard deviation σ of the optimal window function corresponding to each moment u is obtained opt (u), propose adaptive redistribution transformation ART(t,ω);
[0050] S5. According to the adaptive redistribution transformation ART(t,ω) in step S4, the frequency change in the adaptive redistribution domain is analyzed to characterize the thickness change trend of the thin interlayers in the strata.
[0051] Preferably, the short-time Fourier transform G in step S2 e The explicit expression for (t,ω) is:
[0052]
[0053] Where s(u) is the signal of x(u) at the local time [u-Δt,u+Δt], Is an imaginary unit.
[0054] Preferably, the specific expression of the judgment criterion of the local maximum value in step S3 is:
[0055]
[0056] Among them, |G e (t,ω)| is G e The modulus of (t,ω);
[0057] The rearrangement operator RO(t,ω) constructed by the local maximum judgment criterion is:
[0058]
[0059] G is extracted by constructing the rearrangement operator RO(t,ω) e The time-frequency coefficient at the instantaneous frequency (t, ω) is obtained by rearranging the transformed value RT(t, ω) as follows:
[0060] RT(t,ω)=G e (t,ω)·RO(t,ω) (4)
[0061] Preferably, the information entropy C in step S4 σ,Δt (u) The specific expression is:
[0062]
[0063] Where α is the order of information entropy;
[0064] Through information entropy C σ,Δt (u) Get the optimal window function standard deviation σ corresponding to each moment u opt The specific expression of (u) is:
[0065]
[0066] Where min(·) is the minimum function, and the range of σ is [σ min ,σ max ];
[0067] After selecting the optimal window function standard deviation σ opt The specific expression of the adaptive redistribution transform ART(t,ω) of (u) is:
[0068] ART(t,ω)=G opt (t,ω)·ARO(t,ω) (7)
[0069] Among them, G opt (t,ω) is the short-time Fourier transform result of x(u) under the standard deviation of the optimal window function, and ARO(t,ω) is the adaptive redistribution operator. Their expressions are as follows:
[0070]
[0071] in, is the Gaussian window function with the optimal standard deviation, and the specific expression is:
[0072]
[0073] Preferably, the order α of the information entropy is 3.
[0074] See also Figures 1 to 3 , let's take a tight sandstone formation signal as an example, Figure 2 The input formation signal is displayed, the horizontal axis represents time in milliseconds, and the vertical axis represents amplitude. The sampling frequency of the formation signal is 1000Hz. Figure 3They are (a) short-time Fourier transform, (b) synchronous extrusion transform, (c) synchronous extraction transform and (d) time-frequency spectrum processed by the method of the present invention. The horizontal axis represents time in milliseconds, and the vertical axis represents frequency in Hertz. It can be seen that the short-time Fourier transform result has low time-frequency resolution, fuzzy time-frequency energy, and cannot obtain effective information on the change of thin interlayer thickness. Compared with STFT, the time-frequency readability of SST is greatly improved, but due to inaccurate instantaneous frequency estimation, energy diverges at the instantaneous frequency trajectory. SET only extracts the time-frequency coefficients at the fixed frequency point of the SST instantaneous frequency estimator, which greatly improves the energy focusing degree of the formation signal, but because SET only selects a fixed global window function standard deviation, its time-frequency readability is limited. The result obtained after processing by the method of the present invention has a time-frequency distribution with highly focused energy. Compared with the other three methods, the instantaneous frequency trajectory described is also clearer. A decrease in frequency means that the thickness of the thin interlayer becomes thicker, and an increase in frequency means that the thickness of the thin interlayer becomes thinner, which can better characterize the change trend of the thickness of the thin interlayer.
[0075] 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 protection scope of the present invention.
Claims
1. A method for analyzing the thickness of thin interbeds in a self-adaptive redistribution domain, characterized in that: The following steps are involved: S1. Input the formation signal x(t) to be analyzed, where t is time; S2, preset window function And set its standard deviation range [σ min ,σ max ], where σ(t) is the standard deviation, σ min With σ max are the minimum and maximum values of the standard deviation respectively, and the short-time Fourier transform G of the formation signal at different times u in the time interval [u-Δt,u+Δt] is calculated. e (t,ω), where Δt is the neighborhood size and ω represents the frequency; S3. Give the criterion for judging the local maximum value and construct the rearrangement operator RO(t,ω) to extract G e The time-frequency coefficient at the instantaneous frequency (t, ω) is obtained to obtain the rearranged transformation value RT(t, ω); S4. Define the information entropy C that reflects the degree of time-frequency energy focusing of formation signals σ,Δt (u), according to the information entropy, the standard deviation σ of the optimal window function corresponding to each moment u is obtained oot (u), propose adaptive redistribution transformation ART(t,ω); S5. According to the adaptive redistribution transformation ART(t,ω) in step S4, the frequency change in the adaptive redistribution domain is analyzed to characterize the thickness change trend of the thin interlayers in the strata.
2. The method for analyzing the thickness of thin interlayers in a stratum according to claim 1, characterized in that: The short-time Fourier transform G in step S2 e The explicit expression for (t,ω) is: Where s(u) is the signal of x(u) at the local time [u-Δt,u+Δt], Is an imaginary unit.
3. The method for analyzing the thickness of thin interlayers in a stratum according to claim 1, characterized in that: The specific expression of the judgment criterion of the local maximum value in step S3 is: Among them, |G e (t,ω)| is G e The modulus of (t,ω); The rearrangement operator RO(t,ω) constructed by the local maximum judgment criterion is: G is extracted by constructing the rearrangement operator RO(t,ω) e The time-frequency coefficient at the instantaneous frequency (t, ω) is obtained by rearranging the transformed value RT(t, ω) as follows: RT(t,ω)=G e (t,ω)·RO(t,ω) (4).
4. The method for analyzing the thickness of thin interlayers in a stratum according to claim 3, characterized in that: The information entropy C in step S4 σ,Δt (u) The specific expression is: Where α is the order of information entropy; Through information entropy C σ,Δt (u) Get the optimal window function standard deviation σ corresponding to each moment u opt The specific expression of (u) is: Where min(·) is the minimum function, and the range of σ is [σ min ,σ max ]; After selecting the optimal window function standard deviation σ opt The specific expression of the adaptive redistribution transform ART(t,ω) of (u) is: ART(t,ω)=G opt (t,ω)·ARO(t,ω) (7) Among them, G opt (t,ω) is the short-time Fourier transform result of x(u) under the standard deviation of the optimal window function, and ARO(t,ω) is the adaptive redistribution operator. Their expressions are as follows: in, is the Gaussian window function with the optimal standard deviation, and the specific expression is:
5. The method for analyzing the thickness of thin interlayers in a stratum according to claim 4, characterized in that: The order α of the information entropy is 3.