Synchronous compression matching pursuit time-frequency characterization method

Abstract

The invention provides a synchronous compression matching pursuit time-frequency characterization method. The characterization method comprises the following steps: constructing a two-dimensional Gaussian function taking the center time and frequency of a time-frequency atom as a center; the time-frequency energy of the matched atoms is focused at the real center time and frequency position, and time-frequency domain reflection information can be displayed. And the time-frequency resolution of a spectral decomposition result is improved.

Description

Technical Field

[0001] The present invention relates to the field of oil and gas exploration and development, and in particular to a synchronous compression matching pursuit time-frequency characterization method. Background Art

[0002] Time-frequency analysis method is an important tool for reservoir exploration and reservoir description. It can convert signals from one-dimensional time domain to two-dimensional time-frequency domain, providing more valuable information for the study of underground geological bodies. Time-frequency spectrum is of great significance for the processing and interpretation of non-stationary signals. Methods such as short-time Fourier transform (STFT), continuous wavelet transform (CWT), S transform (ST) and Wigner-Ville distribution (WVD) are widely used in time-frequency analysis of signals. However, the time-frequency resolution of the above conventional methods is not enough to accurately describe the time-frequency variation characteristics of non-stationary signals.

[0003] The traditional matching pursuit Wigner-Ville time-frequency characterization method has a large distribution range of time-frequency energy groups, and the focus position of the energy group is fuzzy, making it difficult to accurately extract the time-frequency change characteristics of the signal. In order to solve these problems, this case proposes a synchronous compression matching pursuit time-frequency characterization method. By constructing a two-dimensional Gaussian function centered on the central time and frequency of the time-frequency atom, the time-frequency energy of the matching atom is focused on the real central time and frequency position, which manifests as higher time-frequency energy focusing and can display more time-frequency domain reflection information. The feasibility of the synchronous compression matching pursuit time-frequency characterization method is verified through model data and actual data. Summary of the invention

[0004] In view of the above problems, the present invention is proposed to provide a synchronous compressed matching pursuit time-frequency characterization method that overcomes the above problems or at least partially solves the above problems.

[0005] According to one aspect of the present invention, a synchronous compression matching pursuit time-frequency characterization method is provided, the characterization method comprising:

[0006] Construct a two-dimensional Gaussian function centered at the central time and frequency of the time-frequency atom;

[0007] Focusing the time-frequency energy of the matching atoms at the true central time and frequency position can display the reflection information in the time-frequency domain.

[0008] Optionally, constructing a two-dimensional Gaussian function centered on the central time and frequency of the time-frequency atom specifically includes:

[0009] Get the signal S to be decomposed, and the overcomplete atom library D includes k atoms composition, γ represents the control parameter of the atom;

[0010] Signal S is the matching atom found in the first iteration search. The projection component and the residual signal R1S obtained in the first iteration are composed of two parts, namely:

[0011]

[0012] Matching atoms satisfy the following formula:

[0013]

[0014] Where i is the index of the atom, k is the number of atoms in the atom library, is the inner product operator, is the absolute value symbol, and sup represents the supremum.

[0015] Optionally, the matching pursuit algorithm specifically includes:

[0016] Decompose the signal into a series of matching atoms;

[0017] The time-frequency energy distribution of the original signal is characterized by summing up the Wigner-Ville distribution of each matching atom. The time-frequency amplitude spectrum A(t,f) of the signal is expressed as:

[0018]

[0019] in, Represents matching atoms Wigner-Ville distribution, t represents the time domain, f represents the frequency domain, γ represents the control parameter of the atom, i is the index number of the atom, M is the number of matching atoms, and a i represents the amplitude of the matching atoms.

[0020] Optionally, the iterative process specifically includes:

[0021] The residual signal R1S after the first iteration is used as a new signal;

[0022] Re-search the atom library to find the best matching atom, continuously update the residual signal, and repeat this process;

[0023] If at the n+1th iteration, the matching atom found is The residual signal R n S is represented by the following formula:

[0024]

[0025] Where R n+1 S is the residual signal generated by the n+1th iteration;

[0026] If after m steps of iterative decomposition, the number of matches reaches the preset number or the signal residual energy is less than the energy threshold, the matching decomposition process of the signal is completed;

[0027] Finally, the linear combination of m matching atoms and the residual signal R obtained at the mth iteration are used m S represents the signal:

[0028]

[0029] Where R0S=S.

[0030] Optionally, the entire matching decomposition process in the iterative process complies with the law of conservation of energy. If the number of iterations or the energy threshold is not set, the best time-frequency atomic energy obtained by matching can be infinitely close to the original signal.

[0031] Optionally, focusing the time-frequency energy of the matching atoms at the real central time and frequency position specifically includes:

[0032] The energy distribution of the time-frequency atom has the characteristic of limited support. The time domain waveform of the time-frequency atom is expanded in the frequency direction according to the amplitude spectrum size. The time-frequency distribution of the time-frequency atom tfr g (t,f) is expressed as:

[0033]

[0034] in, For atom g γ (t), t represents the time domain and f represents the frequency domain.

[0035] Optionally, after expanding the time domain waveform of the time-frequency atom in the frequency direction according to the amplitude spectrum, the step further includes:

[0036] Considering that the waveform of the Ricker wavelet is closer to the actual seismic wavelet, we choose to build a Ricker wavelet library to decompose the signal. It is known that the time domain expression of the Ricker wavelet ψ is:

[0037]

[0038] And the frequency domain expression of the Ricker wavelet is:

[0039]

[0040] Where ξ is the peak frequency of the Ricker wavelet. Substituting equations 7 and 8 into equation 6, we get the time-frequency distribution tfr of the Ricker wavelet: ψ (t,f) is:

[0041]

[0042] As can be seen from the above formula, the waveform and amplitude spectrum of each time-frequency atom respectively control the energy distribution range in the time domain and frequency domain in the time-frequency distribution.

[0043] Optionally, the method for constructing the two-dimensional Gaussian function specifically includes:

[0044] The central time and frequency parameters of the best matching atom obtained in a certain iterative search are represented by u and ζ respectively, and the corresponding two-dimensional Gaussian function is expressed as:

[0045]

[0046] Among them, Δt and Δf are time and frequency intervals, respectively, and the time-frequency representation SSTtfr of the atoms is matched after compression. ψ (t,f) is expressed as:

[0047]

[0048] Optionally, the characterization method further includes: verifying the feasibility of the synchronous compression matching pursuit time-frequency characterization method.

[0049] Optionally, the feasibility of verifying the synchronous compression matching pursuit time-frequency characterization method specifically includes:

[0050] Obtain model data and actual information;

[0051] Based on the model data and the actual data, the feasibility of the synchronous compression matching pursuit time-frequency characterization method is verified.

[0052] The present invention provides a synchronous compression matching pursuit time-frequency characterization method, which includes: constructing a two-dimensional Gaussian function centered on the central time and frequency of the time-frequency atom; focusing the time-frequency energy of the matching atom on the real central time and frequency position, and being able to display the time-frequency domain reflection information. Improving the time-frequency resolution of the spectrum decomposition result.

[0053] The above description is only an overview of the technical solution of the present invention. In order to more clearly understand the technical means of the present invention, it can be implemented according to the contents of the specification. In order to make the above and other purposes, features and advantages of the present invention more obvious and easy to understand, the specific implementation methods of the present invention are listed below. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0055] Figure 1 A flowchart of a synchronous compression matching pursuit time-frequency characterization method provided by an embodiment of the present invention;

[0056] Figure 2 A signal waveform diagram provided by an embodiment of the present invention;

[0057] Figure 3 A diagram of the time-frequency distribution results of the matching pursuit Wigner-Ville provided in an embodiment of the present invention;

[0058] Figure 4 A schematic diagram of a synchronous compressed matching pursuit time-frequency spectrum provided by an embodiment of the present invention;

[0059] Figure 5 A schematic diagram of an actual earthquake signal provided by an embodiment of the present invention, with a signal duration of 0.24 seconds;

[0060] Figure 6 The matching pursuit Wigner-Ville time-frequency spectrum and synchronous compression matching pursuit time-frequency spectrum provided by the embodiment of the present invention;

[0061] Figure 7 The synchronous compression matching pursuit time-frequency spectrum provided by the embodiment of the present invention can distinguish more time-frequency energy cluster graphs;

[0062] Figure 8 The seismic profile provided for the embodiment of the present invention has a time length of 144 milliseconds and is composed of 380 seismic traces;

[0063] Fig. 9 A schematic diagram of a matching pursuit Wigner-Ville time-frequency spectrum result provided by an embodiment of the present invention;

[0064] Fig.10 A diagram of the vicinity of the stratigraphic layer where the time-frequency energy of the time-frequency spectrum result provided in the embodiment of the present invention is concentrated. DETAILED DESCRIPTION

[0065] The exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.

[0066] The terms "comprises" and "having" and any variations thereof in the description embodiments, claims and drawings of the present invention are intended to cover non-exclusive inclusions, for example, including a series of steps or units.

[0067] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0068] The matching pursuit method accurately decomposes and reconstructs the signal according to its structural characteristics. The time-frequency energy distribution of the signal can be obtained by summing up the Wigner-Ville distribution (WVD) of the matching atoms obtained by decomposition. Inspired by the SST strategy, this paper proposes a synchronous compression matching pursuit time-frequency characterization method, which constructs a two-dimensional Gaussian function to redistribute and compress the time-frequency energy cluster to improve the time-frequency resolution of the spectral decomposition result.

[0069] The matching pursuit algorithm decomposes the signal into a series of matching atoms. The time-frequency energy distribution of the original signal can be characterized by summing the Wigner-Ville distribution of each matching atom. The time-frequency amplitude spectrum A(t,f) of the signal is expressed as:

[0070]

[0071] In the above formula Represents matching atoms Wigner-Ville distribution, t represents the time domain, f represents the frequency domain, γ represents the control parameter of the atom, i is the index number of the atom, M is the number of matching atoms, and a i Representing the amplitude of the matching atom, the above formula is used to characterize the signal in time and frequency, which not only has the high-precision resolution of the Wigner-Ville distribution, but also avoids the interference of cross terms, so that the matching pursuit of the Wigner-Ville time-frequency spectrum can obtain a higher quality time-frequency representation of the signal.

[0072] like Figure 1 As shown in the first step, assume that the signal to be decomposed is S, and the overcomplete atom library D consists of k atoms , γ represents the control parameter of the atom. The signal S is composed of the matching atoms obtained by the first iteration search The projection component and the residual signal R1S obtained in the first iteration are composed of two parts, namely:

[0073]

[0074] Matching atoms satisfy the following formula:

[0075]

[0076] Where i is the index of the atom, k is the number of atoms in the atom library, is the inner product operator, is the absolute value symbol, and sup represents the supremum.

[0077] The residual signal R1S after the first iteration is used as a new signal, and the atom library is searched again to find the best matching atom, and the residual signal is continuously updated, and the iteration continues. If the matching atom found at the n+1th iteration is The residual signal R n S can be expressed by the following formula:

[0078]

[0079] Where R n+1 S is the residual signal generated by the n+1th iteration. If after m steps of iterative decomposition, the number of matches reaches the preset number or the signal residual energy is less than the energy threshold, the matching decomposition process of the signal is completed, and finally the linear combination of m matching atoms and the residual signal R obtained by the mth iteration can be used. m S represents the signal:

[0080]

[0081] Where R0S = S. The entire matching decomposition process complies with the law of energy conservation. If the number of iterations or energy threshold is not set, the best time-frequency atom obtained by matching can be infinitely close to the original signal.

[0082] Step 2: The energy distribution of the time-frequency atom has the characteristic of limited support. Therefore, the time domain waveform of the time-frequency atom is expanded in the frequency direction according to the amplitude spectrum size. The time-frequency distribution tfr of the time-frequency atom g (t,f) can be expressed as:

[0083]

[0084] in For atom g γ (t), t represents the time domain and f represents the frequency domain.

[0085] Considering that the waveform of the Ricker wavelet is closer to the actual seismic wavelet, we choose to build a Ricker wavelet library to decompose the signal. It is known that the time domain expression of the Ricker wavelet ψ is:

[0086]

[0087] And the frequency domain expression of the Ricker wavelet is:

[0088]

[0089] Where ξ is the peak frequency of the Ricker wavelet. Substituting equations 7 and 8 into equation 6, we can get the time-frequency distribution tfr of the Ricker wavelet: ψ (t,f) is:

[0090]

[0091] It can be seen from the above formula that the waveform and amplitude spectrum of each time-frequency atom respectively control its energy distribution range in the time domain and frequency domain in the time-frequency distribution, thereby having higher energy focusing and time-frequency resolution.

[0092] Step 3: Assuming that the central time and frequency parameters of the best matching atom obtained in a certain iterative search are represented by u and ζ respectively, the corresponding two-dimensional Gaussian function can be expressed as:

[0093]

[0094] Where Δt and Δf are time and frequency intervals, respectively, so the time-frequency representation of the matching atom after compression is SSTtfr ψ (t,f) can be expressed as:

[0095]

[0096] Step 4: In order to verify the feasibility of the synchronous compression matching pursuit time-frequency characterization method proposed in the present invention, firstly construct model data for testing. Figure 2 The signal shown is composed of 8 Ricker wavelets of different frequencies, namely 20 Hz, 40 Hz, and 50 Hz. The signal duration is 3.6 seconds. It can be seen that the time positions of the two wavelets at around 0.4 seconds are relatively close. Figure 3 The matching pursuit Wigner-Ville time-frequency distribution results are shown. Figure 4 The figure shows the time-frequency spectrum of the synchronous compression matching pursuit proposed by the present invention. By comparison, it can be seen that Figure 3 The time-frequency energy cluster is relatively fuzzy, especially at high-frequency positions, it is difficult to determine the center frequency of the time-frequency component. Figure 4 In the time-frequency spectrum shown, the time-frequency energy of each atom is compressed to the central time and frequency position of the matching atom, and adjacent atoms can be clearly separated, especially the two sub-waves around 0.4s.

[0097] Figure 5 This is an actual earthquake signal with a signal duration of 0.24 seconds. Figure 6 and 7 The matching pursuit Wigner-Ville time-frequency spectrum and the synchronous compressed matching pursuit time-frequency spectrum are shown respectively. Figure 6 The time-frequency resolution shown is relatively low. Multiple time-frequency atoms are fused together and cannot accurately describe the time-frequency variation characteristics of the signal. Figure 7 The synchronous compressed matching pursuit time-frequency spectrum shown can distinguish more time-frequency energy clusters and show higher time-frequency focusing. The results show that the time-frequency spectrum obtained by the invention has higher identifiability.

[0098] The feasibility of the present invention is further verified by using two-dimensional actual seismic data. Figure 8 The seismic profile shown has a time length of 144 milliseconds and consists of 380 seismic traces. The three curves are P-wave impedance logging curves. The logging interpretation of the black seismic phase axis around 60 milliseconds and 100 milliseconds is oil layer, and Fig. 9 and 10 The 30Hz spectrum decomposition results show strong amplitude energy at this position. Fig. 9 The time-frequency energy distribution of the matching pursuit Wigner-Ville time-frequency spectrum result shown is relatively fuzzy, and it is difficult to accurately reflect the time-frequency response characteristics of the thin layer. Fig.10 The time-frequency energy of the time-frequency spectrum results shown is concentrated near the stratigraphic layer, showing higher time-frequency resolution and lateral continuity, which is helpful to describe the local time-frequency characteristics of the reservoir.

[0099] The synchronous compression matching pursuit time-frequency characterization method proposed in the present invention exhibits higher time-frequency resolution and time-frequency energy focusing than the matching pursuit Wigner-Ville time-frequency characterization method, which proves the feasibility of the method proposed in this case.

[0100] Beneficial effect: The time-frequency spectrum decomposed by the method proposed in the present invention exhibits higher time-frequency resolution and time-frequency focusing, and can be better applied to the time-frequency analysis of actual seismic signals.

[0101] The above specific implementation methods further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above are only specific implementation methods of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. 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 synchronous compression matching pursuit time-frequency characterization method, characterized in that: The characterization method comprises: Construct a two-dimensional Gaussian function centered at the central time and frequency of the time-frequency atom; Focusing the time-frequency energy of the matching atoms at the true central time and frequency position can display the reflection information in the time-frequency domain.

2. According to the synchronous compression matching pursuit time-frequency characterization method of claim 1, it is characterized in that: The construction of a two-dimensional Gaussian function centered on the central time and frequency of the time-frequency atom specifically includes: Get the signal S to be decomposed, and the overcomplete atom library D includes k atoms composition, γ represents the control parameter of the atom; The signal S is the matching atom g obtained by the first iteration search. γ1 The projection component and the residual signal R1S obtained in the first iteration are composed of two parts, namely: Matching atoms satisfy the following formula: Where i is the index of the atom, k is the number of atoms in the atom library, <> is the inner product operator, || is the absolute value symbol, and sup represents the supremum.

3. According to the synchronous compression matching pursuit time-frequency characterization method of claim 1, it is characterized in that: The matching pursuit algorithm specifically includes: Decompose the signal into a series of matching atoms; The time-frequency energy distribution of the original signal is characterized by summing up the Wigner-Ville distribution of each matching atom. The time-frequency amplitude spectrum A(t,f) of the signal is expressed as: in, Represents matching atoms Wigner-Ville distribution, t represents the time domain, f represents the frequency domain, γ represents the control parameter of the atom, i is the index number of the atom, M is the number of matching atoms, and a i represents the amplitude of the matching atoms.

4. The synchronous compression matching pursuit time-frequency characterization method according to claim 2, characterized in that: The iterative process specifically includes: The residual signal R1S after the first iteration is used as a new signal; Re-search the atom library to find the best matching atom, continuously update the residual signal, and repeat this process iteratively; If at the n+1th iteration, the matching atom found is The residual signal R n S is represented by the following formula: Where R n+1 S is the residual signal generated by the n+1th iteration; If after m steps of iterative decomposition, the number of matches reaches the preset number or the signal residual energy is less than the energy threshold, the matching decomposition process of the signal is completed; Finally, the linear combination of m matching atoms and the residual signal R obtained at the mth iteration are used m S represents the signal: Where R0S=S.

5. The synchronous compression matching pursuit time-frequency characterization method according to claim 1, characterized in that: The entire matching decomposition process in the iterative process complies with the law of conservation of energy. If the number of iterations or the energy threshold is not set, the best time-frequency atomic energy obtained by matching is infinitely close to the original signal.

6. The synchronous compression matching pursuit time-frequency characterization method according to claim 1, characterized in that: The step of focusing the time-frequency energy of the matching atoms at the real central time and frequency position specifically includes: The energy distribution of the time-frequency atom has the characteristic of limited support. The time domain waveform of the time-frequency atom is expanded in the frequency direction according to the amplitude spectrum size. The time-frequency distribution of the time-frequency atom tfr g (t,f) is expressed as: in, For atom g γ (t), t represents the time domain and f represents the frequency domain.

7. The synchronous compression matching pursuit time-frequency characterization method according to claim 6, characterized in that: After the time domain waveform of the time-frequency atom is expanded in the frequency direction according to the amplitude spectrum, the following further comprises: Considering that the waveform of the Ricker wavelet is closer to the actual seismic wavelet, we choose to build a Ricker wavelet library to decompose the signal. It is known that the time domain expression of the Ricker wavelet ψ is: And the frequency domain expression of the Ricker wavelet is: Where ξ is the peak frequency of the Ricker wavelet. Substituting equations 7 and 8 into equation 6, we get the time-frequency distribution tfr of the Ricker wavelet: ψ (t,f) is: As can be seen from the above formula, the waveform and amplitude spectrum of each time-frequency atom respectively control the energy distribution range in the time domain and frequency domain in the time-frequency distribution.

8. The synchronous compression matching pursuit time-frequency characterization method according to claim 1, characterized in that: The method for constructing the two-dimensional Gaussian function specifically includes: The central time and frequency parameters of the best matching atom obtained in a certain iterative search are represented by u and ζ respectively, and the corresponding two-dimensional Gaussian function is expressed as: Among them, Δt and Δf are time and frequency intervals, respectively, and the time-frequency representation SSTtfr of the atoms is matched after compression. ψ (t,f) is expressed as:

9. The synchronous compression matching pursuit time-frequency characterization method according to claim 1, characterized in that: The characterization method also includes: verifying the feasibility of the synchronous compression matching pursuit time-frequency characterization method.

10. The synchronous compression matching pursuit time-frequency characterization method according to claim 9, characterized in that: The feasibility of verifying the synchronous compression matching pursuit time-frequency characterization method specifically includes: Obtain model data and actual information; Based on the model data and the actual data, the feasibility of the synchronous compression matching pursuit time-frequency characterization method is verified.

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