Time-frequency spectrum decomposition method and device based on empirical matching pursuit and storage medium

Abstract

The invention belongs to the technical field of time-frequency spectrum decomposition, and discloses a time-frequency spectrum decomposition method and device based on empirical matching pursuit and a storage medium, the time-frequency spectrum decomposition method comprises the following steps: constructing an empirical mode decomposition (EMD) dictionary suitable for time-frequency analysis according to input seismic data; performing matching pursuit on a seismic signal to be decomposed by using the EMD dictionary to obtain a time-frequency atom combination of the seismic signal; and performing multiple synchronous compression transformation on the time-frequency atoms of the seismic signal to obtain the time-frequency distribution of the seismic signal. According to the method, a new time-frequency characterization method is deduced, a time-frequency spectrum decomposition strategy based on empirical matching pursuit is designed, and the time-frequency resolution of seismic signals is improved by introducing multiple synchronous compression transformation.

Description

Technical Field

[0001] This invention belongs to the field of time-spectrum decomposition technology, and discloses a time-spectrum decomposition method, device and storage medium based on empirical matching and tracking. Background Technology

[0002] In the field of signal processing, the analysis of non-steady-state signals is a significant challenge. Seismic signals are typical non-steady-state signals. Time-frequency analysis techniques can transform seismic signals from the time domain to the frequency domain, revealing the frequency variation over time. By observing these frequency variations, anomalies can be identified, often reflecting underlying geological structures and oil and gas reservoirs. Currently, time-frequency analysis techniques are widely used in seismic exploration.

[0003] Multi-volume data processing and interpretation technology based on geological targets is a new approach to improving the comprehensive application of seismic data. Its core is to generate multiple seismic data processing results tailored to different geological characteristics, with each set of seismic data having an interpretation result that can accurately describe certain geological details. Therefore, improving the time-frequency resolution of seismic signals and achieving precise exploration paths are essential to meeting the geological needs of oil and gas exploration and development in various fields. Summary of the Invention

[0004] To address this issue, this invention proposes a time-frequency decomposition method based on empirical matching pursuit, aiming to improve time-frequency resolution and enhance the reliability of oil and gas prediction.

[0005] The technical solution of this invention is as follows:

[0006] A temporal spectrum decomposition method based on empirical matching pursuit includes:

[0007] Construct an Empirical Mode Decomposition (EMD) dictionary suitable for time-frequency analysis based on the input seismic data;

[0008] The seismic signal to be decomposed is matched and tracked using the EMD dictionary to obtain the time-frequency atom combination of the seismic signal;

[0009] Multiple synchronous compression transformations are performed on the time-frequency atoms of the seismic signal to obtain the time-frequency distribution of the seismic signal.

[0010] Furthermore, the construction of an adaptive Empirical Mode Decomposition (EMD) dictionary based on the input seismic data includes:

[0011] The input seismic signal set is subjected to EMD decomposition to obtain a set of intrinsic mode functions (IMFs) containing time-frequency characteristics;

[0012] The expression for each IMF function is:

[0013]

[0014] Among them, D imf (t) is the IMF function after EMD decomposition, a(t) is the instantaneous amplitude, and t is time. For the instantaneous phase, the derivative of the instantaneous phase. Indicates instantaneous frequency;

[0015] instantaneous phase The subspace formed by the defined harmonic column vectors is expressed as follows:

[0016]

[0017] in, For phase, parameter k is used to adjust the phase amplitude, parameter λ is used to adjust the smoothness of the IMF function, and span{} is the spatial function;

[0018] The range of adjacent phase changes is obtained using a floor function:

[0019]

[0020] The IMF function D imf (t) is used as an atom of an overcomplete dictionary. An overcomplete dictionary atom library D is constructed and defined as the EMD dictionary:

[0021]

[0022] The atoms in the EMD dictionary satisfy the following:

[0023]

[0024] Where, ω γ (t) represents the mother wavelet of the overcomplete dictionary atom library D. For modulated atoms, The control parameters for the seismic signal are time t, frequency f, and phase. The set of Γ represents the matrix of frequencies and phases corresponding to a certain time range, and a(t) is the instantaneous amplitude. It is the instantaneous phase.

[0025] Furthermore, the step of using the EMD dictionary to perform matching and tracing on the seismic signal to be decomposed to obtain the time-frequency atom combination of the seismic signal includes:

[0026] The seismic signal s(t) is decomposed using the EMD dictionary through matching pursuit. After n iterations, the seismic signal s(t) is decomposed into a linear combination of n matching atoms and the sum of the residuals, expressed as follows:

[0027]

[0028] Where, ω γn (t) represents the nth matching atom obtained by scanning the EMD dictionary, a n For ω γn The amplitude of (t), R n s is the residual after n iterations;

[0029] ω γn (t) can be expressed by the expression To describe, where t n ,f n and The control parameters are denoted as peak time, peak frequency, and phase, respectively. The core task of the matching pursuit algorithm in each iteration is to determine the optimal control parameters for the matching atoms.

[0030] Furthermore, for the atoms in the EMD dictionary, they are represented in the time domain as follows: Its representation in the frequency domain is as follows

[0031] According to Euler's formula, the frequency domain expression of an atom is:

[0032]

[0033] Furthermore, the matching atoms obtained from the decomposition of the seismic signal s(t) are frequency-varying single-component signals, which are defined in the frequency domain as:

[0034]

[0035] Where, A(ω), Time-frequency atoms The amplitude and phase in the frequency domain, where ω is the frequency.

[0036] Furthermore, the multiple synchronous compression transformation of the time-frequency atoms of the seismic signal includes:

[0037] For the time-frequency atoms Time-frequency analysis is performed, and the time-spectrum expression is as follows:

[0038]

[0039] For the time-frequency atoms Perform a short-time Fourier transform to obtain the fundamental time spectrum:

[0040]

[0041] in, This is a Gaussian window function, where the parameter ξ is used to adjust the size of the Gaussian window. It is the time-frequency atom The second-order Taylor expansion;

[0042] The time-frequency atom The second-order Taylor expansion is:

[0043]

[0044] Furthermore, it also includes:

[0045] For the time-frequency atoms Two-dimensional group delay GD trajectory estimation is performed, and the GD trajectory estimate is... For time parameters that include frequency information:

[0046]

[0047] Where σ is the damping coefficient, which is used to stabilize the auxiliary equation;

[0048] When GD trajectory is estimated hour, show yes The stable point;

[0049] Use fixed-point iterative algorithm to reduce and The error between them, through the By performing N iterations of differentiation and repeatedly constructing new GD trajectory estimates, the energy of the time-frequency signal is effectively compressed into the GD trajectory.

[0050]

[0051] By performing N iterations of integration on equation (13) in the time dimension, the time-frequency atom is obtained. Time spectrum:

[0052]

[0053] Where u represents the position of different time points in the time-frequency domain.

[0054] Furthermore, the time spectra of each time-frequency atom are added together to obtain the time spectrum of the seismic signal.

[0055] Based on the same inventive concept, the present invention also provides an electronic device, comprising: a memory and a processor; the processor being configured to read and execute a computer program stored in the memory to implement the time-spectrum decomposition method described above.

[0056] Based on the same inventive concept, the present invention also provides a computer-readable storage medium storing computer-executable instructions, which, when executed, implement the above-described time-spectrum decomposition method.

[0057] The technical effects and advantages of this invention are as follows: By constructing an Empirical Mode Decomposition (EMD) dictionary suitable for time-frequency analysis, and using the EMD dictionary to perform matched-tracking decomposition on seismic signals, a new time-frequency characterization method is derived by performing multiple synchronous compression transformations on the decomposed time-frequency atoms. This scheme designs a time-spectrum decomposition strategy based on empirical matched-tracking. By introducing multiple synchronous compression transformations based on stable points, the time-spectrum features of seismic signals can be extracted at high resolution, which can be used to accurately identify oil and gas reservoirs, thereby meeting the geological requirements of oil and gas exploration and development. Attached Figure Description

[0058] The accompanying drawings are provided to further illustrate the present invention and form part of the specification. They are used together with the embodiments of the present invention to explain the invention and do not constitute a limitation thereof. The drawings are as follows to more clearly illustrate the specific implementation process or technical solution of the present invention:

[0059] Figure 1 This is a schematic diagram of the time-spectrum decomposition method based on empirical matching pursuit according to an embodiment of the present invention;

[0060] Figure 2a This is a theoretical seismic signal;

[0061] Figure 2b The time spectrum of the theoretical seismic signal based on conventional matched pursuit;

[0062] Figure 2c The time spectrum of the theoretical seismic signal based on empirical matching tracing;

[0063] Figure 3a This is an actual single-channel seismic signal;

[0064] Figure 3b The time spectrum of a real single-channel seismic signal based on conventional matched pursuit;

[0065] Figure 3c The time spectrum of a real single-channel seismic signal based on synchronous compression transform;

[0066] Figure 3d for Figure 3c Enlarged view of point 1 in the middle;

[0067] Figure 3e for Figure 3c Enlarged view of point 2 in the middle;

[0068] Figure 3f The time spectrum of an actual single-channel seismic signal based on empirical matching pursuit;

[0069] Figure 3g for Figure 3f Enlarged view of point 1 in the middle;

[0070] Figure 3h for Figure 3f Enlarged view of point 2 in the middle;

[0071] Figure 4a This is a record of actual small-angle earthquakes;

[0072] Figure 4b This is a single-spectral profile based on conventional matched pursuit at 20 Hz.

[0073] Figure 4c A single-spectral profile of 20Hz based on empirical matching tracking;

[0074] Figure 4d for Figure 4b and Figure 4c Overlay display;

[0075] Figure 5a This is an actual pre-stack earthquake record;

[0076] Figure 5b The result is a fan-shaped characterization based on experience-based matching and tracking. Detailed Implementation

[0077] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0078] Starting from P-wave seismic data, this invention proposes a time-spectrum decomposition method based on empirical matching and tracking, which is used to perform high-resolution time-spectrum decomposition of seismic signals, thereby improving the stability and reliability of reservoir oil and gas identification.

[0079] like Figure 1 As shown, this invention provides a time-spectrum decomposition method based on empirical matching pursuit, comprising:

[0080] Step S1: Construct an Empirical Mode Decomposition (EMD) dictionary suitable for time-frequency analysis based on the input seismic data;

[0081] Step S2: Use the EMD dictionary to match and track the seismic signal to be decomposed to obtain the time-frequency atom combination of the seismic signal;

[0082] Step S3: Perform multiple synchronous compression transformation on the time-frequency atoms of the seismic signal to obtain the time-frequency distribution of the seismic signal.

[0083] Empirical Mode Decomposition (EMD) is used to decompose complex signals into a finite number of Intrinsic Mode Functions (IMFs) of increasing order. Each IMF component contains local features of the original signal at different time scales. In this invention, the time-frequency characteristics of seismic signals are obtained through EMD decomposition.

[0084] According to a preferred embodiment, step S1, which involves constructing an Empirical Mode Decomposition (EMD) dictionary suitable for time-frequency analysis based on the input seismic data, includes the following steps:

[0085] S11. Input the seismic signal set, perform EMD decomposition on the input signal to obtain a set of intrinsic mode functions (IMFs) containing time-frequency characteristics;

[0086] The expression for each IMF function is:

[0087]

[0088] Among them, D imf (t) is the IMF function after EMD decomposition, a(t) is the instantaneous amplitude, and t is time. For the instantaneous phase, the derivative of the instantaneous phase. Indicates instantaneous frequency;

[0089] instantaneous phase The subspace formed by the defined harmonic column vectors is expressed as follows:

[0090]

[0091] in, For phase, parameter k is used to adjust the phase amplitude, parameter λ is used to adjust the smoothness of the IMF function, and span{} is the spatial function;

[0092] The range of adjacent phase changes is obtained using a floor function:

[0093]

[0094] S11, the IMF function D imf(t) serves as the atom of the overcomplete dictionary. An adaptive overcomplete dictionary atom library D is constructed and defined as the EMD dictionary:

[0095]

[0096] The atoms in the EMD dictionary satisfy the following:

[0097]

[0098] Where, ω γ (t) represents the mother wavelet of the overcomplete dictionary atom library D. For modulated atoms, The control parameters for the seismic signal are time t, frequency f, and phase. The set of Γ represents the matrix of frequencies and phases corresponding to a certain time range, and a(t) is the instantaneous amplitude. It is the instantaneous phase.

[0099] For the seismic signal s(t) to be decomposed, the present invention uses the above-mentioned EMD dictionary as a redundant library for matching tracing decomposition to decompose the seismic signal s(t) into atomic combinations suitable for time-frequency analysis.

[0100] According to a specific implementation, the seismic signal s(t) is decomposed using the EMD dictionary through matching pursuit. After n iterations, the seismic signal s(t) is decomposed into a linear combination of n matching atoms and the sum of the residuals, expressed as:

[0101]

[0102] Where, ω γn (t) represents the nth matching atom obtained by scanning the EMD dictionary, a n For ω γn The amplitude of (t). R n s is the residual after n iterations. Iteration stops when the residual signal is less than or equal to a preset threshold, and when n = 0, R 0 s = s, where s is the original seismic signal s(t).

[0103] ω γn (t) can be expressed by the expression To describe, where t n ,f n and The control parameters are denoted as peak time, peak frequency, and phase, respectively. The core task of the matching pursuit algorithm in each iteration is to determine the optimal control parameters for the matching atoms.

[0104] Furthermore, for the atoms in the EMD dictionary, they are represented in the time domain as follows: Its representation in the frequency domain is as follows

[0105] According to Euler's formula, the frequency domain expression of an atom is:

[0106]

[0107] The matching atom obtained from the decomposition of the seismic signal s(t) also satisfies the above formula (7). This matching atom is a frequency-varying single-component signal, and therefore can be defined as follows in the frequency domain:

[0108]

[0109] Where, A(ω), Time-frequency atoms The amplitude and phase in the frequency domain, where ω is the frequency.

[0110] Furthermore, based on the time-frequency atomic derivation of the seismic signal and the multiple synchronous compression transform formula based on empirical matching pursuit, a high-resolution time-frequency distribution is obtained.

[0111] Step S3 specifically includes:

[0112] S31, regarding the time-frequency atom Perform time-frequency analysis;

[0113] The expression for the time spectrum is:

[0114]

[0115] S32, regarding the time-frequency atom Perform a short-time Fourier transform to obtain the fundamental time spectrum with lower resolution;

[0116]

[0117] in, This is a Gaussian window function, where the parameter ξ is used to adjust the size of the Gaussian window. It is the time-frequency atom The second-order Taylor expansion;

[0118] Assuming the time-frequency atom It is a high-frequency signal. A′(ω)≤ε, and The time-frequency atom The second-order Taylor expansion is:

[0119]

[0120] S33, regarding the time-frequency atom Perform two-dimensional group delay GD trajectory estimation;

[0121] GD trajectory estimation This is a time parameter that includes frequency information;

[0122]

[0123] Where σ is the damping coefficient, used to stabilize the auxiliary equations; in GD trajectory estimation hour, show yes The stable point;

[0124] S34. Use a fixed-point iterative algorithm to reduce... and The error between them, through the By performing N iterations of differentiation, new GD trajectory estimates are repeatedly constructed, effectively compressing the energy of the time-frequency signal into the GD trajectory.

[0125]

[0126] Since time-frequency energy diffuses around the GD trajectory, for seismic signals containing multiple frequencies, it is impossible to obtain the time point where the energy focuses in a single solution. Therefore, it is necessary to repeatedly differentiate the signals. For each iteration, the newly constructed two-dimensional GD trajectory estimate is closer to the stable point. Based on the fixed-point concept, it is believed that there is a point in time in the energy trajectory of a frequency domain signal that always satisfies the law of energy conservation. Therefore, by iteratively solving the stable point in the time domain for the frequency domain data, the signal energy can be squeezed into the GD trajectory.

[0127] In this embodiment of the invention, by means of By performing N iterations of differentiation until a stable time parameter point is obtained, the ambiguous time-frequency energy is effectively compressed into the corresponding GD trajectory, preventing the ambiguous divergence of time-frequency energy and thus improving the time resolution of the time spectrum.

[0128] S35. Perform N iterations of integration on formula (13) in the time dimension to obtain the time-frequency atom. Time spectrum:

[0129]

[0130] Where u represents the position of different time points in the time-frequency domain, and δ represents the Dirac function.

[0131] For the time point obtained in step S34, perform N integration iterations until the function no longer changes, thereby obtaining the time-frequency energy spectrum at this time point, which is the time-frequency atom. The time spectrum.

[0132] In this embodiment of the invention, each time-frequency atom The time spectrum of the seismic signal s(t) is obtained by adding the time spectra of the two components. The time spectrum is a heatmap describing the changes of each frequency component of the signal over time, used to represent the time-frequency distribution of the seismic signal. The vertical axis of the time spectrum plot shows the frequency distribution of the signal within a small time interval, and the horizontal axis shows the change of each frequency over time.

[0133] Conventional matching pursuit typically uses wavelet dictionaries for time-frequency decomposition (this is existing technology and will not be elaborated here), resulting in relatively dispersed spectral energy. In this embodiment of the invention, the completeness of empirical matching pursuit is fully considered, and a new time-frequency representation method is derived. A time-frequency decomposition strategy based on empirical matching pursuit is designed, and the resolution of time-frequency representation is improved by introducing multiple synchronous compression transform based on stable points.

[0134] Examples 1 and 2 verify the effectiveness and reliability of the present invention:

[0135] Example 1

[0136] See Figures 2a-2c , Figure 2a This is a theoretical seismic signal; Figure 2b The time spectrum of the theoretical seismic signal based on conventional matched pursuit; Figure 2c The time spectrum of the theoretical seismic signal is based on empirical matching tracing.

[0137] The theoretical seismic signal consists of zero-phase Riker wavelets with different amplitudes at 15Hz, 25Hz, 35Hz, 45Hz, and 65Hz. For this theoretical seismic signal, time-spectrum decomposition was performed using both conventional matched pursuit (time-spectrum decomposition technique based on wavelet dictionary) and empirical matched pursuit, and the results were compared. Figure 2b and Figure 2c , Figure 2c The temporal resolution of seismic signals is significantly higher, and the time-frequency energy is more concentrated, making the reservoir appear as a bright spot or obvious anomalous response in the image. Therefore, the present invention has a higher time-frequency resolution than the time-frequency decomposition technique based on conventional matching pursuit.

[0138] Example 2

[0139] See Figures 3a-3h , Figure 3a This is an actual single-channel seismic signal; Figure 3b The time spectrum of a real single-channel seismic signal based on conventional matched pursuit; Figure 3c The time spectrum of a real single-channel seismic signal based on synchronous compression transform; Figure 3d for Figure 3c Enlarged view of point 1 in the middle; Figure 3e for Figure 3cEnlarged view of point 2 in the middle; Figure 3f The time spectrum of an actual single-channel seismic signal based on empirical matching pursuit; Figure 3g for Figure 3f Enlarged view of point 1 in the middle; Figure 3h for Figure 3f Enlarged view of point 2 in the middle.

[0140] For actual single-channel seismic signals, traditional time-frequency decomposition based on conventional matching pursuit, time-frequency decomposition based on synchronous compression transform, and time-frequency decomposition based on empirical matching pursuit were carried out respectively. The comparison shows that the time-frequency decomposition technology based on empirical matching pursuit provided by this invention performs excellently in improving time-frequency resolution. The time-frequency energy of the seismic signal can be presented with higher clarity and concentration, which is beneficial for the identification of thin reservoirs. At the same time, it provides a favorable basis for the description of deep oil and gas-bearing sandstones and lays a solid foundation for subsequent seismic interpretation.

[0141] The high-resolution characteristics of time-spectrum decomposition according to the present invention were verified by comparing the time-spectrum data obtained by conventional methods with the time-spectrum data based on empirical matching pursuit.

[0142] Examples 3 and 4 verify the applicability of the present invention:

[0143] Example 3

[0144] To apply this invention to reservoir prediction in the F oilfield, see [reference needed]. Figures 4a-4d , Figure 4a This is a record of actual small-angle earthquakes. Figure 4b This is a single-spectral profile based on conventional matched pursuit at 20 Hz. Figure 4c A single-spectral profile of 20Hz based on empirical matching tracking; Figure 4d for Figure 4b and Figure 4c Overlay display; Figure 5a This is an actual pre-stack earthquake record; Figure 5b The result of depicting the fan body.

[0145] from Figure 4b It can be seen that the time of the target fault is approximately 1.15–1.25 seconds, and the dominant frequency is approximately 19 to 20 Hz. Figure 4c By focusing the signal energy into a time-frequency energy ridge, the resolution in the time-frequency domain is significantly improved. Figure 4c and Figure 4d The breakpoint curves in the figure are the interpreted fault development curves, proving that the present invention can be used to predict faults. Figure 4d for Figure 4b and 4cThe overlay plots, compared with actual well data on oil and gas, demonstrate that the present invention can accurately detect reservoir fluids and assist in determining reservoir development locations. Even for noisy seismic data, the time-spectrum obtained according to the present invention shows a significant improvement in resolution compared to traditional methods, strongly demonstrating the universality of the present invention.

[0146] Example 4

[0147] See Figures 5a-5b , Figure 5a The actual pre-stack seismic records show that the P-wave seismic recording method is insufficient to effectively characterize the fan distribution. Figure 5a The seismic data was subjected to time-spectrum decomposition based on empirical matching tracking to obtain, as follows: Figure 5b The fan-shaped depiction results shown are based on Figure 5b The characteristics of the fan body are clearly visible, and the boundaries of the fan body are depicted more precisely.

[0148] Based on the research results of Examples 1 and 2, the conventional matching pursuit-based seismic signal time-spectrum decomposition method has limitations in terms of time-frequency resolution, making it difficult to effectively identify deep and thin reservoirs. This invention extends the seismic time-spectrum decomposition method by designing a time-spectrum decomposition strategy based on empirical matching pursuit theory. It introduces a fixed-point-based multiple synchronous compression transform to focus time-frequency energy, thereby improving time-frequency resolution and reducing the interpretive ambiguity of seismic data. Applying this method to theoretical model processing can distinguish the development location of effective reservoirs within the target area and effectively identify favorable reservoirs, demonstrating the reliability and practical application prospects of this method. Revealing subsurface geological and fluid characteristics from multiple levels, angles, and scales enables truly precise exploration paths, meeting the geological needs of oil and gas exploration and development in various fields.

[0149] Based on the same inventive concept, embodiments of the present invention also provide an electronic device, including: a memory and a processor, wherein the processor is used to read and execute a computer program stored in the memory to implement the aforementioned time-spectrum decomposition method based on empirical matching and tracking.

[0150] Based on the same inventive concept, embodiments of the present invention also provide a computer storage medium storing computer-executable instructions, which, when executed, implement the aforementioned time-spectrum decomposition method based on empirical matching and tracking.

[0151] It should be noted that, for the sake of simplicity, the foregoing embodiments are all described as a series of actions. However, those skilled in the art should understand that the present invention is not limited to the described order of actions, because according to the present invention, some steps can be performed in other orders or simultaneously. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to the present invention.

[0152] In the above embodiments, the descriptions of each embodiment have their own emphasis. Parts not described in detail in a particular embodiment can be found in the relevant descriptions of other embodiments. Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A time-spectrum decomposition method based on empirical matching pursuit, characterized in that, include: Construct an Empirical Mode Decomposition (EMD) dictionary suitable for time-frequency analysis based on the input seismic data; The seismic signal to be decomposed is matched and tracked using the EMD dictionary to obtain the time-frequency atom combination of the seismic signal; Multiple synchronous compression transformations are performed on the time-frequency atoms of the seismic signal to obtain the time-frequency distribution of the seismic signal.

2. The time-spectrum decomposition method according to claim 1, characterized in that, The adaptive Empirical Mode Decomposition (EMD) dictionary, constructed based on the input seismic data, includes: The input seismic signal set is subjected to EMD decomposition to obtain a set of intrinsic mode functions (IMFs) containing time-frequency characteristics; The expression for each IMF function is: Among them, D imf (t) is the IMF function after EMD decomposition, a(t) is the instantaneous amplitude, and t is time. For the instantaneous phase, the derivative of the instantaneous phase. Indicates instantaneous frequency; instantaneous phase The subspace formed by the defined harmonic column vectors is expressed as follows: in, For phase, parameter k is used to adjust the phase amplitude, parameter λ is used to adjust the smoothness of the IMF function, and span{} is the spatial function; The range of adjacent phase changes is obtained using a floor function: The IMF function D imf (t) is used as an atom of an overcomplete dictionary. An overcomplete dictionary atom library D is constructed and defined as the EMD dictionary: The atoms in the EMD dictionary satisfy the following: Where, ω γ (t) represents the mother wavelet of the overcomplete dictionary atom library D. For modulated atoms, The control parameters for the seismic signal are time t, frequency f, and phase. The set of Γ represents the matrix of frequencies and phases corresponding to a certain time range, and a(t) is the instantaneous amplitude. It is the instantaneous phase.

3. The time-spectrum decomposition method according to claim 2, characterized in that, The step of matching and tracing the seismic signal to be decomposed using the EMD dictionary to obtain the time-frequency atom combination of the seismic signal includes: The seismic signal s(t) is decomposed using the EMD dictionary through matching pursuit. After n iterations, the seismic signal s(t) is decomposed into a linear combination of n matching atoms and the sum of the residuals, expressed as follows: Where, ω γn (t) represents the nth matching atom obtained by scanning the EMD dictionary, a n For ω γn The amplitude of (t), R n s is the residual after n iterations; ω γn (t) can be expressed by the expression To describe, where t n ,f n and The control parameters are denoted as peak time, peak frequency, and phase, respectively. The core task of the matching pursuit algorithm in each iteration is to determine the optimal control parameters for the matching atoms.

4. The time-spectrum decomposition method according to claim 2 or 3, characterized in that, For the atoms in the EMD dictionary, in the time domain, they are represented as: Its representation in the frequency domain is as follows According to Euler's formula, the frequency domain expression of an atom is:

5. The time-spectrum decomposition method according to claim 4, characterized in that, The matching atoms obtained from the decomposition of the seismic signal s(t) are frequency-varying single-component signals, which are defined in the frequency domain as: Where, A(ω), Time-frequency atoms The amplitude and phase in the frequency domain, where ω is the frequency.

6. The time-spectrum decomposition method according to claim 5, characterized in that, The multiple synchronous compression transformation of the time-frequency atoms of the seismic signal includes: For the time-frequency atoms Time-frequency analysis is performed, and the time-spectrum expression is as follows: For the time-frequency atoms Perform a short-time Fourier transform to obtain the fundamental time spectrum: in, This is a Gaussian window function, where the parameter ξ is used to adjust the size of the Gaussian window. It is the time-frequency atom The second-order Taylor expansion; The time-frequency atom The second-order Taylor expansion is:

7. The time-spectrum decomposition method according to claim 6, characterized in that, Also includes: For the time-frequency atoms Two-dimensional group delay GD trajectory estimation is performed, and the GD trajectory estimate is... For time parameters that include frequency information: Where σ is the damping coefficient, which is used to stabilize the auxiliary equation; When GD trajectory is estimated hour, show yes The stable point; Use fixed-point iterative algorithm to reduce and The error between them, through the By performing N iterations of differentiation and repeatedly constructing new GD trajectory estimates, the energy of the time-frequency signal is effectively compressed into the GD trajectory. By performing N iterations of integration on equation (13) in the time dimension, the time-frequency atom is obtained. Time spectrum: Where u represents the position of different time points in the time-frequency domain.

8. The time-spectrum decomposition method according to claim 1, characterized in that, The time spectrum of the seismic signal is obtained by adding the time spectra of each time-frequency atom.

9. An electronic device, characterized in that, include: Memory, processor; The processor is configured to read and execute the computer program stored in the memory to implement the time-spectrum decomposition method according to any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed, implement the time-spectrum decomposition method according to any one of claims 1-8.

Images