A time-domain compressed seismic spectral decomposition method based on matching pursuit

Abstract

This invention relates to the field of oil and gas geophysical exploration technology, and more specifically, to a time-domain compressed seismic spectral decomposition method based on matching pursuit. This method involves sparse decomposition of the seismic signal, specifically searching for the optimal matching wavelet, further deriving the reflection wavelet, and then performing Fourier transform and time-compression transform on the reflection wavelet to obtain its time-domain compressed spectrum. Finally, the time-domain compressed spectra of the reflection wavelet are superimposed and summed to improve the temporal resolution of the seismic record's time spectrum, avoid spurious spectral anomalies, and ensure the accuracy of the output results. Utilizing time-domain compression methods to improve the time-frequency resolution of data can highlight subtle features in the signal and their time-varying characteristics, improving the accuracy and reliability of signal processing. Applying this method to fields beyond seismic exploration can enhance signal feature recognition and improve signal detection capabilities.

Description

Technical Field

[0001] This invention relates to the field of oil and gas geophysical exploration technology, and more specifically, to a time-domain compressed seismic spectrum decomposition method based on matching pursuit. Background Technology

[0002] Seismic spectral decomposition is an important seismic data processing and interpretation technique that has been widely applied in various fields such as seismic facies description, formation absorption compensation, hydrocarbon detection, noise suppression, and thin-layer identification. Applying spectral decomposition to pre-stack seismic data and combining it with AVO (Amplitude Variation with Migration) technology for frequency-varying AVO dispersion parameter inversion can enable hydrocarbon detection.

[0003] Traditional spectral decomposition methods, such as Fourier transform or wavelet transform, may suffer from insufficient resolution when processing complex signals. The Wigner-Ville distribution (WVD), a commonly used time-frequency analysis method, offers high time-frequency resolution, but it suffers from cross-term interference in multi-component signal analysis. Matching pursuit, as an adaptive signal decomposition method, can effectively represent signals sparsely, improving their time-frequency resolution. However, the matching pursuit algorithm needs to be combined with other time-frequency analysis methods to calculate the signal's time spectrum. The matching pursuit-based WVD spectral decomposition method aims to solve the cross-term interference problem in multi-component signal analysis while improving the signal's time-frequency resolution. However, matching pursuit-based WVD is an energy spectrum, prone to producing spurious spectral anomalies, affecting hydrocarbon detection. Instantaneous spectrum calculations based on matching pursuit, using the decomposed wavelet amplitude envelope to calculate the wavelet time spectrum, result in seismic record time spectrums with low time resolution. Summary of the Invention

[0004] To overcome the shortcomings of the prior art, which uses the wavelet amplitude envelope to calculate the wavelet time spectrum based on matching pursuit to obtain the seismic record time spectrum with low time resolution, this invention provides a time-domain compressed seismic spectrum decomposition method based on matching pursuit, thereby improving the time resolution of the seismic record time spectrum.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a time-domain compressed seismic spectral decomposition method based on matching pursuit, comprising the following steps:

[0006] Step 1: Input the seismic signal and select a suitable wavelet atom library;

[0007] Step 2: Based on the matching pursuit algorithm, the seismic signal is sparsely decomposed to search for the optimal matching wavelet, and the corresponding wavelet coefficients are calculated to obtain a series of reflection wavelets;

[0008] Step 3: Given a time compression factor, perform Fourier transform and time compression transform on each matched wavelet obtained from the decomposition, and calculate the time-domain compressed time spectrum of the reflected wavelet.

[0009] Step 4: Compose and sum the time-domain compressed time-spectrum values ​​of the reflected wavelet to obtain the time-spectrum decomposition result of the entire original seismic signal.

[0010] Preferably, in step two, the seismic signal is used as the residual signal, the number of iterations is set, the best matching wavelet with the largest correlation coefficient with the current residual signal is searched within the number of iterations, the wavelet coefficient corresponding to the best matching wavelet is calculated, the residual signal is updated using the wavelet coefficient, and the iteration is stopped when the number of iterations or the residual signal energy is lower than a given threshold, resulting in a series of reflection wavelets.

[0011] Preferably, in step two, for the k-th iteration, the following formula is used to search for the best matching wavelet with the largest correlation coefficient to the current residual signal:

[0012]

[0013] Where s(t) represents the seismic signal, r 0 (t) represents the residual signal, w(t) represents the wavelet atom, and r k-1 (t),w(t)> represents the inner product of the residual signal and the wavelet atom. It is the normalization operator of the wavelet atom, and k represents the kth iteration.

[0014] Preferably, in step two, the formula for calculating the wavelet coefficients corresponding to the best-matched wavelet is:

[0015] C k Represents the wavelet coefficients in the k-th iteration;

[0016] The formula for updating the residual signal is: r k (t)=r k-1 (t)-C k w k (t).

[0017] Preferably, in step two, a series of reflected wavelets are obtained using the following formula:

[0018] Among them, C k w k (t) represents the reflected wavelet.

[0019] Preferably, in step three, the formula for performing Fourier transform on each matched wavelet is: Where f represents the frequency; each matched wavelet is compressed in the time direction, as shown by the formula: w k (t)→wk (at); where a is the time compression factor.

[0020] Preferably, in step three, the formula for calculating the time-domain compressed spectrum of each reflected wavelet is:

[0021] S k (t,f)=C k ·W k (f)env[w k (at)];

[0022] Among them, env[w k [(at)] represents the amplitude envelope of the time-domain compressed wavelet. By compressing the wavelet in the time direction, the wavelet duration is reduced, thereby improving the wavelet resolution.

[0023] Preferably, in step four, the formula for the summation of the time-domain compressed spectrum of the reflected wavelet is:

[0024]

[0025] Here, S(t,f) is the time spectrum of the entire original seismic signal. This time spectrum has a higher time resolution than the conventional time spectrum, and can more clearly describe the change of signal spectral energy over time.

[0026] Preferably, in step one, the input seismic signal is a post-stack seismic signal that has undergone a series of data processing steps, including trace gathering, dynamic correction, migration, and stacking.

[0027] Preferably, in step one, the wavelet atom library contains a series of Ricker wavelets w(τ) with different dominant frequencies, and its calculation formula is as follows:

[0028] w(τ)={1-2[πf d τ] 2}exp{-[πf d τ] 2};

[0029] Among them, f d The dominant frequency of the Ricker wavelet is 5Hz to 50Hz, and τ is the sampling time. The Ricker wavelet can accurately describe the propagation and reflection characteristics of seismic waves.

[0030] Compared with existing technologies, the advantages of this invention are as follows: By sparsely decomposing the seismic signal (i.e., searching for the optimal matching wavelet), and further deriving the reflection wavelet, the time-domain compressed spectrum of the reflection wavelet is obtained by performing Fourier transform and time compression transform on the reflection wavelet. Furthermore, the time-domain compressed spectra of the reflection wavelet are superimposed and summed, thereby improving the time resolution of the seismic record's time spectrum, avoiding false spectral anomalies, and ensuring the accuracy of the output results. Using time-domain compression methods to improve the time-frequency resolution of data can highlight subtle features in the signal and their time-varying characteristics, improving the accuracy and reliability of signal processing. Applying this method to fields beyond seismic exploration can enhance signal feature recognition and improve signal detection capabilities. Attached Figure Description

[0031] Figure 1 This is a flowchart illustrating a time-domain compressed seismic spectral decomposition method based on matching pursuit according to the present invention.

[0032] Figure 2 This is a schematic diagram of a seismic signal based on a time-domain compressed seismic spectral decomposition method according to the present invention;

[0033] Figure 3 This is a schematic diagram of the time-spectrum decomposition results of a time-domain compressed seismic spectrum decomposition method based on matching pursuit according to the present invention;

[0034] Figure 4 This is a comparison diagram of the time-spectrum decomposition results of a time-domain compressed seismic spectrum decomposition method based on matching pursuit according to the present invention. Detailed Implementation

[0035] The accompanying drawings are for illustrative purposes only and should not be construed as limiting this patent. To better illustrate this embodiment, some components in the drawings may be omitted, enlarged, or reduced, and do not represent the actual dimensions of the product. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings. The positional relationships described in the drawings are for illustrative purposes only and should not be construed as limiting this patent.

[0036] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "long," and "short" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present patent. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0037] The technical solution of the present invention will be further described in detail below through specific embodiments and in conjunction with the accompanying drawings:

[0038] Example 1

[0039] like Figure 1 As shown, a time-domain compressed seismic spectral decomposition method based on matching pursuit includes the following steps:

[0040] Step 1: Input the seismic signal and select a suitable wavelet atom library;

[0041] Step 2: Based on the matching pursuit algorithm, the seismic signal is sparsely decomposed to search for the optimal matching wavelet, and the corresponding wavelet coefficients are calculated to obtain a series of reflection wavelets;

[0042] Step 3: Given a time compression factor, perform Fourier transform and time compression transform on each matched wavelet obtained from the decomposition, and calculate the time-domain compressed time spectrum of the reflected wavelet.

[0043] Step 4: Compose and sum the time-domain compressed time-spectrum values ​​of the reflected wavelet to obtain the time-spectrum decomposition result of the entire original seismic signal.

[0044] The beneficial effects of this embodiment are as follows: By sparsely decomposing the seismic signal (i.e., searching for the optimal matching wavelet), and further deriving the reflection wavelet, the time-domain compressed spectrum of the reflection wavelet is obtained by performing Fourier transform and time compression transform on the reflection wavelet. Furthermore, the time-domain compressed spectra of the reflection wavelet are superimposed and summed, thereby improving the time resolution of the seismic record's time spectrum, avoiding false spectral anomalies, and ensuring the accuracy of the output results. Using time-domain compression methods to improve the time-frequency resolution of data can highlight subtle features in the signal and their time-varying characteristics, improving the accuracy and reliability of signal processing. Applying this method to fields beyond seismic exploration can enhance signal feature recognition and improve signal detection capabilities.

[0045] Example 2

[0046] The difference between Example 1 and Example 2 is as follows:

[0047] Furthermore, in step two, the seismic signal is used as the residual signal, the number of iterations is set, and the best matching wavelet with the largest correlation coefficient with the current residual signal is searched within the number of iterations. The wavelet coefficients corresponding to the best matching wavelet are calculated, and the residual signal is updated using the wavelet coefficients. When the number of iterations or the residual signal energy is lower than a given threshold, the iteration is stopped, and a series of reflection wavelets are obtained.

[0048] For the k-th iteration, the following formula is used to search for the best matching wavelet with the largest correlation coefficient to the current residual signal:

[0049]

[0050] Where s(t) represents the seismic signal, r 0 (t) represents the residual signal, w(t) represents the wavelet atom, and r k-1 (t),w(t)> represents the inner product of the residual signal and the wavelet atom. It is the normalization operator of the wavelet atom, and k represents the kth iteration.

[0051] The formula for calculating the wavelet coefficients corresponding to the best-matched wavelet is:

[0052] C k Represents the wavelet coefficients in the k-th iteration;

[0053] The formula for updating the residual signal is: r k (t)=r k-1 (t)-C k w k (t).

[0054] A series of reflected wavelets can be obtained through the following formula:

[0055] Among them, C k w k (t) represents the reflected wavelet.

[0056] The remaining features and working principles of this embodiment are the same as those of Embodiment 1.

[0057] Example 3

[0058] Based on Example 1 or Example 2, Example 1 or Example 2 are further defined, with the following differences:

[0059] Furthermore, in step three, the formula for performing the Fourier transform on each matched wavelet is as follows: Where f represents the frequency; each matched wavelet is compressed in the time direction, as shown by the formula: w k (t)→w k (at); where a is the time compression factor.

[0060] The time-domain compressed spectrum calculation formula for each reflected wavelet is as follows:

[0061] S k (t,f)=C k ·W k (f)env[w k (at)];

[0062] Among them, env[w k[(at)] represents the amplitude envelope of the time-domain compressed wavelet. By compressing the wavelet in the time direction, the wavelet duration is reduced, thereby improving the wavelet resolution.

[0063] Furthermore, in step four, the formula for the summation of the time-domain compressed spectrum of the reflected wavelet is:

[0064]

[0065] Here, S(t,f) is the time spectrum of the entire original seismic signal. This time spectrum has a higher time resolution than the conventional time spectrum, and can more clearly describe the change of signal spectral energy over time.

[0066] Furthermore, in step one, such as Figure 2 As shown, the input seismic signal is a post-stack seismic signal after a series of data processing steps, including trace gathering, dynamic correction, migration, and stacking.

[0067] Furthermore, in step one, the wavelet atom library contains a series of Ricker wavelets w(τ) with different dominant frequencies, and its calculation formula is as follows:

[0068] w(τ)={1-2[πf d τ] 2}exp{-[πf d τ] 2};

[0069] Among them, f d The dominant frequency of the Ricker wavelet is 5Hz to 50Hz, and τ is the sampling time. The Ricker wavelet can accurately describe the propagation and reflection characteristics of seismic waves.

[0070] Example 4

[0071] In this embodiment, given a time compression factor a = 2, spectral decomposition is performed through the following steps:

[0072] Step 1: As Figure 2 As shown, the input seismic signal undergoes a series of data processing steps, including gather extraction, dynamic correction, migration, and stacking. A suitable wavelet atom library is selected, containing a series of Ricker wavelets w(τ) with different dominant frequencies. The calculation formula is as follows:

[0073] w(τ)={1-2[πf d τ] 2}exp{-[πf d τ] 2};

[0074] Among them, f d τ is the dominant frequency of the Rick wavelet, with a frequency range of 5Hz to 50Hz, and τ is the sampling time.

[0075] Step 2: Based on the matching pursuit algorithm, the seismic signal is sparsely decomposed, the best matching wavelet is searched for, the corresponding wavelet coefficients are calculated, and a series of reflection wavelets are obtained.

[0076] The input seismic signal s(t) is treated as the residual signal r. 0 (t):

[0077] r 0 (t)=s(t)

[0078] Where t represents time.

[0079] For the k-th iteration, search for the best matching wavelet that has the largest correlation coefficient with the current residual signal.

[0080]

[0081] Where w(t) represents the wavelet atom, <r k-1 (t),w(t)> represents the inner product of the residual signal and the wavelet atom. It is the normalization operator for wavelet atoms.

[0082] Calculate the wavelet coefficients corresponding to the best-matched wavelet:

[0083]

[0084] Update the residual signal.

[0085] r k (t)=r k-1 (t)-C k w k (t)

[0086] Iteration stops when the number of iterations k or the residual signal energy falls below a given threshold. Seismic signals are represented by a series of reflected wavelets:

[0087]

[0088] Step 3: Perform Fourier transform and time-compression transform on each matched wavelet, and calculate the time-domain compressed spectrum of the reflected wavelet;

[0089] For each matched subwavelet w k (t) Perform Fourier transform:

[0090]

[0091] Where f represents frequency.

[0092] Given a time compression factor, compress each matched wavelet in the time direction:

[0093] w k (t)→w k (at)

[0094] The time-domain compressed time spectrum of each reflected wavelet is as follows:

[0095] S k (t,f)=C k ·W k (f)env[w k (at)]

[0096] Among them, env[w k [(at)] represents the amplitude envelope of the time-domain squeezed wavelet.

[0097] Step 4: Superimpose and sum the time-domain compressed time-spectrum values ​​of the reflected wavelet to obtain the time-spectrum decomposition results of the entire original seismic signal:

[0098]

[0099] Where S(t,f) is the time spectrum of the entire original seismic signal.

[0100] Get as Figure 3 The time-spectrum decomposition results shown are as follows: Figure 4 The time-spectrum decomposition results obtained by the conventional method are compared to the time-spectrum decomposition results calculated in this application, which have higher resolution.

[0101] The remaining working principles and processes of this embodiment are the same as those of Embodiment 1 or Embodiment 2.

[0102] In the specific implementation of the above embodiments, the technical features can be combined in any non-contradictory way. For the sake of brevity, not all possible combinations of the above technical features are described. However, as long as the combination of these technical features is not contradictory, it should be considered to be within the scope of this specification.

[0103] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A time-domain compressive seismic spectral decomposition method based on matching pursuit, characterized in that, Includes the following steps: Step 1: Input the seismic signal after a series of data processing steps including gather extraction, dynamic correction, migration, and stacking, and select a suitable wavelet atom library; Step 2: Based on the matching pursuit algorithm, the seismic signal is sparsely decomposed. The seismic signal is used as the residual signal. The number of iterations is set. Within the number of iterations, the best matching wavelet with the largest correlation coefficient with the current residual signal is searched. The wavelet coefficients corresponding to the best matching wavelet are calculated. The residual signal is updated using the wavelet coefficients. When the residual signal energy is lower than a given threshold, the iteration is stopped, and a series of reflection wavelets are obtained. Step 3: Given a time compression factor, perform Fourier transform and time compression transform on each matched wavelet obtained from the decomposition, and calculate the time-domain compressed time spectrum of the reflected wavelet. Step 4: Superimpose and sum the time-domain compressed time-spectrum values ​​of the reflected wavelet to obtain the time-spectrum decomposition results of the entire original seismic signal; In step three, the formula for Fourier transforming each matched wavelet is: where, represents frequency, represents a wavelet atom, i.e., the th iteration; Each matched wavelet is compressed in the time direction, as shown in the formula: ;in, It is a time compression factor; The formula for calculating the time-domain compressed spectrum of each reflected wavelet is as follows: ;in, This represents the amplitude envelope of the time-domain squeezed wavelet. Representing the Wavelet coefficients in the next iteration.

2. The time-domain compressed seismic spectral decomposition method based on matching pursuit according to claim 1, characterized in that: In step two, for the first In the next iteration, the following formula is used to search for the best matching wavelet with the highest correlation coefficient to the current residual signal: ， ； in, Indicates earthquake signal, Represents the residual signal. This represents the inner product of the residual signal and the wavelet atom. It is the normalization operator for wavelet atoms.

3. The time-domain compressed seismic spectral decomposition method based on matching pursuit according to claim 2, characterized in that: In step two, the formula for calculating the wavelet coefficients corresponding to the best-matched wavelet is: ； The formula for updating the residual signal is: .

4. The time-domain compressed seismic spectral decomposition method based on matching pursuit according to claim 3, characterized in that: In step two, a series of reflected wavelets are obtained using the following formula: ;in, This represents the reflected wavelet.

5. The time-domain compressed seismic spectral decomposition method based on matching pursuit according to claim 1, characterized in that: In step four, the formula for the superposition and summation of the time-domain compressed spectrum of the reflected wavelet is: ； in, It is the time spectrum of the entire original seismic signal.

6. The time-domain compressed seismic spectral decomposition method based on matching pursuit according to claim 1, characterized in that: In step one, the wavelet atom library contains a series of Ricker wavelets with different dominant frequencies. The calculation formula is as follows: ； in, The main frequency of the Ricker wavelet is set at 5Hz to 50Hz. Sampling time.

Images