High-precision instantaneous frequency inversion method of continuous instantaneous phase

Abstract

The application discloses a high-precision instantaneous frequency inversion method of continuous instantaneous phase, relates to the technical field of data processing, and comprises the following steps: S1, inputting a real signal, processing, and acquiring a frequency spectrum; S2, acquiring an analytic signal based on the frequency spectrum; and S3, using high-precision instantaneous frequency inversion based on polynomial fitting based on the analytic signal to obtain a final polynomial fitting high-precision instantaneous frequency. The application can remove periodic jumps in the instantaneous phase obtained by Hilbert transform and arctangent function, thereby obtaining a continuous instantaneous phase in which the phase periodic jump is eliminated and a monotone increasing continuous instantaneous phase used for high-precision instantaneous frequency inversion.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and specifically to a high-precision instantaneous frequency inversion method for continuous instantaneous phase. Background Technology

[0002] Instantaneous frequency inversion is a key technical step in seismic data processing and interpretation. Its core lies in extracting time-varying frequency features from seismic signals to achieve a detailed characterization of the physical properties of the subsurface medium. This process not only directly affects the resolution and fidelity of seismic data but also lays an important foundation for subsequent processing and interpretation work.

[0003] High-precision instantaneous frequency results can more reliably reveal lithological variations, fluid identification, and reservoir characteristics within formations. For example, in hydrocarbon detection, frequency attenuation properties are often correlated with hydrocarbon content; in thin-layer identification, frequency information helps improve the resolution of formation thickness. Furthermore, instantaneous frequency data can be used to improve the accuracy of deconvolution, acoustic impedance inversion, and seismic attribute analysis, thereby supporting more reliable geological modeling and reservoir prediction.

[0004] As seismic exploration expands into deeper, more complex geological formations and unconventional resource areas, the demands for accuracy and stability in instantaneous frequency inversion are increasing. Advances in modern signal processing methods and time-frequency analysis techniques, such as high-resolution time-frequency transform and synchronous compression transform, provide effective means to obtain higher-precision instantaneous frequencies. Therefore, continuously optimizing instantaneous frequency inversion algorithms to improve their noise resistance and resolution is of significant scientific importance and practical application value for deepening the geological interpretation of seismic data and reducing exploration and development risks.

[0005] In existing technologies, the first type is the instantaneous frequency inversion method based on the first-order difference of the instantaneous phase (or principal argument), which is named the instantaneous frequency inversion method based on phase deperiodization and removal of discontinuities in the first-order differential of the instantaneous phase. The second type is the instantaneous frequency inversion method based on the first-order difference of the real and imaginary parts, which is named the instantaneous frequency inversion method based on the first-order differential of the real and imaginary parts. Traditional instantaneous frequency inversion methods are severely affected by the periodic jumps in the instantaneous phase and the sampling time interval, resulting in low accuracy and limited application. Instantaneous frequency inversion is a key technical step in seismic data processing and interpretation. Its core lies in extracting time-varying frequency features from seismic signals to achieve a detailed characterization of the physical properties of the subsurface medium. This process not only directly affects the resolution and fidelity of seismic data but also lays an important foundation for subsequent processing and interpretation work.

[0006] The first category is the instantaneous frequency inversion method based on the first-order difference of the instantaneous phase (or principal parameter), named the instantaneous frequency inversion method based on the removal of discontinuous instantaneous phase first-order differential without phase periodicity. The second category analyzes the signal based on the instantaneous frequency inversion method based on the first-order difference of the real and imaginary parts, named the instantaneous frequency inversion method based on the first-order differential of the real and imaginary parts. The inversion results are severely affected by the periodic jumps in the instantaneous phase and the time sampling interval, resulting in low accuracy and limited application. The instantaneous phase inversion results obtained by the instantaneous phase inversion method based on the first-order differential of the real and imaginary parts can avoid the influence of periodic jumps in the instantaneous phase, but are severely affected by the time sampling interval, resulting in low accuracy and limiting application. Summary of the Invention

[0007] To address the above problems, this invention proposes a high-precision instantaneous frequency inversion method for continuous instantaneous phase.

[0008] The technical solution of this invention is: a high-precision instantaneous frequency inversion method for continuous instantaneous phase includes the following steps:

[0009] S1. Input the real signal, process it, and obtain the spectrum;

[0010] S2. Obtain the analytical signal based on the spectrum;

[0011] S3. Based on the analytical signal, a high-precision instantaneous frequency inversion based on polynomial fitting is used to obtain the final high-precision instantaneous frequency of polynomial fitting.

[0012] Furthermore, S1 includes the following sub-steps:

[0013] S11, Input the actual signal;

[0014] S12. Noise attenuation is applied to the real signal to obtain a high signal-to-noise ratio signal;

[0015] S13. Perform Fourier transform on the high signal-to-noise ratio signal to obtain the spectrum.

[0016] Furthermore, S2 includes the following sub-steps:

[0017] S21. Perform Hilbert transform on the analytic signal to obtain the spectrum of the analytic signal;

[0018] S22. Perform an inverse Fourier transform on the spectrum of the analytic signal to obtain the analytic signal.

[0019] Furthermore, S3 includes the following sub-steps:

[0020] S31. Apply the arctangent function to the analytic signal to obtain the instantaneous phase;

[0021] S32. Apply the continuous instantaneous phase inversion method to the instantaneous phase to obtain the continuous instantaneous phase after removing the phase period and the monotonically increasing continuous instantaneous phase;

[0022] S33. Based on the continuous instantaneous phases after removing the phase period and the monotonically increasing continuous instantaneous phases, the final high-precision instantaneous frequency of the polynomial fitting is obtained.

[0023] Furthermore, S33 includes the following sub-steps:

[0024] S331. Use high-precision instantaneous frequency inversion based on polynomial fitting to obtain the sign function and high-precision instantaneous frequency based on polynomial fitting of continuous instantaneous phases with phase period removed.

[0025] S332. Use polynomial fitting-based high-precision instantaneous frequency inversion on the monotonically increasing continuous instantaneous phase to obtain the polynomial fitting high-precision instantaneous frequency based on the monotonically increasing continuous instantaneous phase.

[0026] S333, based on the high-precision instantaneous frequency and sign function obtained from S331 and S332, the final high-precision instantaneous frequency of the polynomial fitting is obtained.

[0027] Furthermore, in S21, the expression for the spectrum Z(f) of the analytic signal is:

[0028] ;

[0029] in, This represents the spectrum of a high signal-to-noise ratio real signal, where F represents the Nyquist frequency. Indicates frequency.

[0030] Furthermore, in S31, the instantaneous phase The expression is:

[0031] ;

[0032] Where x(t) represents a high signal-to-noise ratio signal and y(t) represents the imaginary part of the analytic signal.

[0033] The beneficial effects of this invention are:

[0034] (1) The continuous instantaneous phase inversion method can remove the periodic jumps in the instantaneous phase obtained by Hilbert transform and arctangent function, thereby obtaining a continuous instantaneous phase that eliminates the periodic phase jumps and a monotonically increasing continuous instantaneous phase for high-precision instantaneous frequency inversion.

[0035] (2) The high-precision instantaneous frequency inversion method based on polynomial fitting applies the polynomial fitting method based on least squares algorithm to the continuous instantaneous phase and monotonically increasing continuous instantaneous phase obtained by the continuous instantaneous phase inversion method, thereby eliminating the influence of time sampling interval in the instantaneous frequency inversion process and finally obtaining the ideal high-precision instantaneous frequency inversion result.

[0036] (3) The test of one-dimensional synthetic cosine (or single-frequency) signals and the application of three-dimensional field seismic datasets show that the high-precision instantaneous frequency inversion method with continuous instantaneous phase can obtain high-precision instantaneous frequency inversion results and can be widely applied in the field of digital signal processing and interpretation. Attached Figure Description

[0037] Figure 1 A flowchart of a high-precision instantaneous frequency inversion method for continuous instantaneous phase;

[0038] Figure 2(a) is a cross-sectional view of the third generation coherence (C3) of Inline 50;

[0039] Figure 2(b) is a cross-sectional view of the third generation coherence (C3) of Crossline 50;

[0040] Figure 2(c) is a time slice of the third-generation coherent (C3) coherence at 1100 ms;

[0041] Figure 2(d) is a time slice of the third-generation coherent (C3) coherence at 1300 milliseconds;

[0042] Figure 3(a) is a cross-sectional view of the third generation coherence (C3) of the discontinuous instantaneous phase without removing the phase period;

[0043] Figure 3(b) is a cross-sectional view of the third generation coherence (C3) of the Crossline 50 without removing the phase period;

[0044] Figure 3(c) is a 1100-millisecond third-generation coherence (C3) time slice of the discontinuous instantaneous phase without removing the phase period;

[0045] Figure 3(d) is a 1300-millisecond third-generation coherence (C3) time slice of the discontinuous instantaneous phase without removing the phase period;

[0046] Figure 4(a) is a cross-sectional view of the third generation coherent (C3) Inline 50 based on the fitting of high-frequency instantaneous frequencies by a monotonically increasing continuous instantaneous phase polynomial.

[0047] Figure 4(b) is a cross-sectional view of the third generation of Crossline 50 coherence (C3) based on the fitting of high-frequency instantaneous frequencies by a monotonically increasing continuous instantaneous phase polynomial.

[0048] Figure 4(c) is a 1100-millisecond third-generation coherent (C3) time slice plot based on the high-frequency instantaneous frequency fitted by a monotonically increasing continuous instantaneous phase polynomial.

[0049] Figure 4(d) is a 1300-millisecond third-generation coherent (C3) time slice plot based on the high-frequency instantaneous frequency fitted by a monotonically increasing continuous instantaneous phase polynomial. Detailed Implementation

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

[0051] like Figure 1 As shown, this invention provides a high-precision instantaneous frequency inversion method for continuous instantaneous phase, comprising the following steps:

[0052] S1. Input the real signal, process it, and obtain the spectrum;

[0053] S2. Obtain the analytical signal based on the spectrum;

[0054] S3. Based on the analytical signal, a high-precision instantaneous frequency inversion based on polynomial fitting is used to obtain the final high-precision instantaneous frequency of polynomial fitting.

[0055] This invention aims to eliminate the influence of periodic jumps in instantaneous phase and time sampling intervals during instantaneous frequency inversion, thereby obtaining ideal high-precision instantaneous frequency inversion results. A high-precision instantaneous frequency inversion method using continuous instantaneous phase is proposed. This method includes a flowchart of the continuous instantaneous phase high-precision instantaneous frequency inversion process, the continuous instantaneous phase inversion method, and a polynomial fitting-based instantaneous frequency inversion method. The flowchart of the continuous instantaneous phase high-precision instantaneous frequency inversion method aims to utilize noise attenuation, Fourier transform, Hilbert transform, inverse Fourier transform, arctangent function, continuous instantaneous phase inversion method, least squares polynomial fitting, and the polynomial fitting-based instantaneous frequency inversion method to construct a detailed workflow for high-precision instantaneous frequency inversion, thereby obtaining ideal high-precision instantaneous frequency inversion results. The purpose of the continuous instantaneous phase inversion method is to remove the periodic jumps in the instantaneous phase obtained from the Hilbert transform and arctangent function, thereby obtaining a continuous instantaneous phase with the periodic phase jumps removed and a monotonically increasing continuous instantaneous phase, achieving high-precision instantaneous frequency inversion. The instantaneous frequency inversion method based on polynomial fitting aims to apply the polynomial fitting of the least squares algorithm to the continuous instantaneous phase with periodic phase jumps and the monotonically increasing continuous instantaneous phase obtained by the continuous instantaneous phase inversion method, thus eliminating the influence of the time sampling interval during the instantaneous frequency inversion process. Ultimately, it obtains the ideal high-precision instantaneous frequency inversion result.

[0056] In this embodiment of the invention, S1 includes the following sub-steps:

[0057] S11, Input the actual signal;

[0058] S12. Noise attenuation is applied to the real signal to obtain a high signal-to-noise ratio signal;

[0059] S13. Perform Fourier transform on the high signal-to-noise ratio signal to obtain the spectrum.

[0060] In this embodiment of the invention, S2 includes the following sub-steps:

[0061] S21. Perform Hilbert transform on the analytic signal to obtain the spectrum of the analytic signal;

[0062] S22. Perform an inverse Fourier transform on the spectrum of the analytic signal to obtain the analytic signal.

[0063] In this embodiment of the invention, S3 includes the following sub-steps:

[0064] S31. Apply the arctangent function to the analytic signal to obtain the instantaneous phase;

[0065] S32. Apply the continuous instantaneous phase inversion method to the instantaneous phase to obtain the continuous instantaneous phase after removing the phase period and the monotonically increasing continuous instantaneous phase;

[0066] S33. Based on the continuous instantaneous phases after removing the phase period and the monotonically increasing continuous instantaneous phases, the final high-precision instantaneous frequency of the polynomial fitting is obtained.

[0067] In this embodiment of the invention, S33 includes the following sub-steps:

[0068] S331. Use high-precision instantaneous frequency inversion based on polynomial fitting to obtain the sign function and high-precision instantaneous frequency based on polynomial fitting of continuous instantaneous phases with phase period removed.

[0069] S332. Use polynomial fitting-based high-precision instantaneous frequency inversion on the monotonically increasing continuous instantaneous phase to obtain the polynomial fitting high-precision instantaneous frequency based on the monotonically increasing continuous instantaneous phase.

[0070] S333, based on the high-precision instantaneous frequency and sign function obtained from S331 and S332, the final high-precision instantaneous frequency of the polynomial fitting is obtained.

[0071] In this embodiment of the invention, in S21, the expression for the spectrum Z(f) of the analyzed signal is:

[0072] ;

[0073] in, This represents the spectrum of a high signal-to-noise ratio real signal, where F represents the Nyquist frequency. Indicates frequency.

[0074] In this embodiment of the invention, in S31, the instantaneous phase The expression is:

[0075] ;

[0076] Where x(t) represents a high signal-to-noise ratio signal and y(t) represents the imaginary part of the analytic signal.

[0077] In this embodiment of the invention, the purpose of the continuous instantaneous phase inversion method is to remove the periodic jumps in the instantaneous phase obtained by the Hilbert transform and the arctangent function, thereby obtaining a continuous instantaneous phase with the periodic phase jumps removed and a monotonically increasing continuous instantaneous phase, which is used for high-precision instantaneous frequency inversion. It includes a method for inverting continuous instantaneous phases with periodic phase jumps and a method for inverting continuous instantaneous phases with monotonically increasing phases.

[0078] Let real number ( () represents time, a real number ( () represents the time sampling interval; real number ( () represents a high signal-to-noise ratio real signal; real number ( () represents frequency; the real number F represents the Nyquist frequency. ;plural ( Let represent the spectrum of the high signal-to-noise ratio real signal X(t), i.e., the high signal-to-noise ratio real signal x(t) in its Fourier transform; the complex number z(t) represents the analytic signal corresponding to the high signal-to-noise ratio real signal x(t), which is derived from the Hilbert transform; the complex number Z(f) represents the spectrum of the analytic signal Z(t); then we have:

[0079] (1);

[0080] (2);

[0081] In the formula, I = −1, Accordingly, let the real number... ( () represents the accurate (or theoretical) instantaneous phase of a real signal x(t) (or an analytic signal z(t)); real number ( Let be the precise (or theoretical) instantaneous frequency of the real signal x(t) (or the analytic signal z(t)); then we have:

[0082] (3);

[0083] (4);

[0084] Therefore, the core of accurate instantaneous frequency inversion is how to obtain accurate (or theoretical) instantaneous phase. .

[0085] set up ( Let ) represent the instantaneous phase inversion of the real signal x(t) (or the analytic signal z(t)), and let be the principal argument (or the analytic signal z(t)); then we have:

[0086] (5);

[0087] Here, arctan[] represents the arctan function. It can be seen that the inverted instantaneous phase... Severe phase periodic jumps. Therefore, his inversion instantaneous phase... This can be considered as a discontinuous instantaneous phase without removing the period. Accordingly, let... ( , t0 represents the first sampling time, t i Indicates the first At each sampling time, t N-1 This represents the last sampling time, where i represents an imaginary number. Represents natural numbers, Real numbers ( ( () represents the continuous instantaneous phase after removing the phase period; therefore, it can be expressed as:

[0088] (6);

[0089] (7);

[0090] In the formula, It is an integer. express The continuous instantaneous frequencies after the phase periodic transition are removed at any given time. express The discontinuous instantaneous phase due to phase periodic transitions was not removed at any given moment. This indicates the discontinuous instantaneous phase without removing the periodic phase transition. Time and The first difference at time, express The discontinuous instantaneous phase due to phase periodic transitions was not removed at any given moment. express The continuous instantaneous frequency after removing the phase periodic transition is denoted by Min[]. According to equations (3) and (5)-(7), we have:

[0091] (8);

[0092] Furthermore, considering the complexity of formulas (4), (6), and (7), performing accurate instantaneous frequency inversion using formulas (4), (6), and (7) will face severe challenges. Therefore, the continuous instantaneous phase after phase period removal can be replaced by a corresponding monotonically increasing continuous instantaneous phase.

[0093] Accordingly, let real numbers ( The ) indicates that a monotonically increasing continuous instantaneous phase corresponds to a continuous instantaneous phase after removing the phase period. Then we have:

[0094] (9);

[0095] (10);

[0096] in, To construct a monotonically increasing, continuous instantaneous phase accumulation term, It is a natural number;

[0097] Therefore, we have:

[0098] (11);

[0099] (12);

[0100] in, express A monotonically increasing continuous instantaneous phase at time;

[0101] This indicates that: ① Both continuous instantaneous phases with and without phase periods can remove instantaneous phase period jumps. ② The complexity of monotonically increasing continuous instantaneous phases is lower than that of continuous instantaneous phases without phase periods, resulting in high-precision polynomial fitting results (or high-precision instantaneous frequency inversion results). ③ The absolute phase increment of continuous instantaneous phases without phase periods is the same as that of monotonically increasing continuous instantaneous phases. ④ The absolute value of the first-order difference (or absolute first-order difference) of continuous instantaneous phases without phase periods is the same as the absolute value of the first-order difference of monotonically increasing continuous instantaneous phases.

[0102] The instantaneous frequency inversion method based on polynomial fitting aims to apply polynomial fitting of the least squares algorithm to the continuous instantaneous phase after phase deperiodization and the monotonically increasing continuous instantaneous phase obtained by the continuous instantaneous phase inversion method. This eliminates the time sampling interval affecting the instantaneous frequency inversion process, ultimately obtaining ideal, high-precision instantaneous frequency inversion results. It includes the phase-deperiod continuous instantaneous phase polynomial fitting high-precision instantaneous frequency inversion method, the monotonically increasing continuous instantaneous phase polynomial fitting high-precision instantaneous frequency inversion method, the phase-deperiod continuous instantaneous phase method, and the monotonically increasing continuous instantaneous phase polynomial fitting high-precision instantaneous frequency inversion method.

[0103] According to equations (4) and (6)-(8), in order to eliminate the influence of the time sampling interval during the instantaneous frequency inversion process, the continuous instantaneous phase of the phase removal period can be polynomially fitted using the least squares algorithm. This allows for the acquisition of highly accurate instantaneous frequency inversion results.

[0104] Based on equations (4) and (8), equation (4) can be rewritten as:

[0105] (13);

[0106] Therefore, if we let real numbers ( () represents the fitted phase of the continuous instantaneous phases of the phase removal period, which is obtained by performing polynomial fitting on the continuous instantaneous phases of the phase removal period using the least squares algorithm. Real numbers ( This represents a high-precision instantaneous frequency inversion method based on phase-deperiodic continuous instantaneous phase polynomial fitting, utilizing... The first-order derivative is obtained and named Phase-Deperiodic Continuous Instantaneous Phase Polynomial Fitting High-Precision Instantaneous Frequency (PCHF); then, considering... The complexity is addressed by using the following formula. By performing N least squares fitting algorithms, we can obtain... .

[0107] (14);

[0108] (15);

[0109] in, Indicates the first Fitted continuous instantaneous phase at each sampling time point Indicates the first Each sampling time The local least squares polynomial fitting function centered at , Representing local time variables of Power of 1 This indicates that the local polynomial fitting function is at the central time. The value of , Indicates the first The coefficients of the first-order polynomial term in the fitted window. ( ; Represent natural numbers; Represent natural numbers, and Represents an integer; Let represent a real number. According to equations (13)-(15), we have: ① The high-precision instantaneous frequency based on polynomial fitting of continuous instantaneous phase with phase period removed can completely eliminate the influence of time sampling interval in the instantaneous frequency inversion process. ② The accuracy of the high-precision instantaneous frequency based on polynomial fitting of continuous instantaneous phase with phase period removed depends on the fitting accuracy of the fitted phase. ③ Due to the complexity of the deperiodized continuous instantaneous phase, the fitted phase of the deperiodized continuous instantaneous phase cannot achieve the ideal fitting accuracy. Therefore, the high-precision instantaneous frequency based on polynomial fitting of continuous instantaneous phase with phase period removed usually cannot achieve the ideal high accuracy, which shows that the high-precision instantaneous frequency inversion method based on polynomial fitting of phase period removed continuous instantaneous phase cannot obtain the ideal high-precision instantaneous phase inversion result.

[0110] The monotonically increasing continuous instantaneous phase polynomial fitting high-precision instantaneous frequency inversion method aims to eliminate the influence of time sampling interval in the instantaneous frequency inversion process, and further improve the accuracy of high-precision instantaneous frequency based on continuous instantaneous phase polynomial fitting (high-precision instantaneous frequency obtained by phase deperiod continuous instantaneous phase polynomial fitting high-precision instantaneous frequency inversion method) after removing phase period, so as to obtain ideal high-precision absolute instantaneous frequency inversion results.

[0111] According to formulas (4), (8) and (12), we have:

[0112] (16);

[0113] Therefore, if we let the real number ( ) represents the fitted phase of a monotonically increasing continuous instantaneous phase, which is obtained by applying a polynomial fitting to the monotonically increasing continuous instantaneous phase using the least squares algorithm; the high-precision absolute instantaneous frequency is obtained by the high-precision instantaneous frequency inversion method of polynomial fitting of real monotonically increasing continuous instantaneous phase, which is obtained by the first derivative of the high-precision instantaneous frequency inversion method of polynomial fitting of monotonically increasing continuous instantaneous phase, and is named the high-precision instantaneous frequency of polynomial fitting of monotonically increasing continuous instantaneous phase.

[0114] Through the Performing N least squares fitting algorithms and using the following equations yields the result. .

[0115] (17);

[0116] (18);

[0117] In the formula, Indicates the first The fitted monotonically increasing continuous instantaneous phase at each sampling time. Indicates the first Each sampling time The local least dichotomous polynomial fitting function centered at the y-axis. Represents natural numbers, Represent real numbers, Representing local time of Power of 1 This indicates that the local polynomial fitting function is at the central time. The value of , Indicates the first The coefficients of the first-order polynomial term of each fitting window. From equations (4), (6) to (18), it can be seen that: ① The high-precision instantaneous frequency fitted by a polynomial based on a monotonically increasing continuous instantaneous phase can completely eliminate the influence of the time sampling interval during the instantaneous frequency inversion process. ② The high-precision instantaneous frequency fitted by a polynomial based on a monotonically increasing continuous instantaneous phase depends on the fitting accuracy of the fitted phase. ③ Since the complexity of a monotonically increasing continuous instantaneous phase is lower than that of a continuous instantaneous phase without a phase period, the fitting accuracy of the fitted phase is higher than that of the fitted phase. ④ As the fitting accuracy phase, the high-precision instantaneous frequency fitted by a polynomial based on a monotonically increasing continuous instantaneous phase is higher than that of the fitted phase, therefore the accuracy of the high-precision instantaneous frequency fitted by a polynomial based on a monotonically increasing continuous instantaneous phase is higher than that of the high-precision instantaneous frequency fitted by a polynomial based on a continuous instantaneous phase without a phase period. Therefore, the high-precision instantaneous frequency obtained by polynomial fitting based on monotonically increasing continuous instantaneous phases has achieved the ideal high precision, which shows that the high-precision instantaneous frequency inversion method based on monotonically increasing continuous instantaneous phase polynomial fitting has obtained the ideal high-precision absolute instantaneous phase inversion result.

[0118] The purpose of the phase deperiod continuous instantaneous phase method and the monotonically increasing continuous instantaneous phase polynomial fitting high-precision instantaneous frequency inversion method is to obtain the sign function of the high-precision instantaneous frequency obtained by the phase deperiod continuous instantaneous phase polynomial fitting high-precision instantaneous frequency inversion method and the high-precision absolute instantaneous frequency obtained by the monotonically increasing continuous instantaneous phase polynomial fitting high-precision instantaneous frequency inversion method to obtain the ideal high-precision instantaneous frequency inversion result.

[0119] Let real number Let represent the sign function of the high-precision instantaneous frequency obtained by polynomial fitting based on continuous instantaneous phases after removing the phase period (the high-precision instantaneous frequency obtained by the phase-period-removing continuous instantaneous phase polynomial fitting high-precision instantaneous frequency inversion method); The real number represents the high-precision instantaneous frequency obtained by the phase-period-removing continuous instantaneous phase method and the monotonically increasing continuous instantaneous phase polynomial fitting high-precision instantaneous frequency inversion method (instantaneous frequency inversion method based on polynomial fitting or high-precision instantaneous frequency inversion method based on continuous instantaneous phases), which is named the high-precision instantaneous frequency based on polynomial fitting of continuous instantaneous phases after removing the phase period, or the high-precision instantaneous frequency based on polynomial fitting, or the high-precision instantaneous frequency based on continuous instantaneous phases; then:

[0120] (19);

[0121] (20);

[0122] From equations (19) and (20), we can see that: ① The high-precision instantaneous frequency based on polynomial fitting with phase period removed has the same sign as the high-precision instantaneous frequency based on polynomial fitting or the high-precision instantaneous frequency based on continuous instantaneous phase. ② The high-precision instantaneous frequency based on monotonically increasing continuous instantaneous phase has the same precision as the high-precision instantaneous frequency based on polynomial fitting or the high-precision instantaneous frequency based on continuous instantaneous phase. ③ Since the high-precision instantaneous frequency based on polynomial fitting or the high-precision instantaneous frequency based on continuous instantaneous phase combines the advantages of both the high-precision instantaneous frequency based on phase period removed and the high-precision instantaneous frequency based on monotonically increasing continuous instantaneous phase, the precision of the high-precision instantaneous frequency based on polynomial fitting or the high-precision instantaneous frequency based on continuous instantaneous phase is higher than that of the high-precision instantaneous frequency based on monotonically increasing continuous instantaneous phase.

[0123] Figures 2(a) and 2(b) show the inline50 and crossline50 profiles of the third-generation coherence (C3) extracted from the 128×128×512 size 3D third-generation coherence (C3) dataset, respectively; Figures 2(c) and 2(d) show the 1100ms and 1300ms time slices of the third-generation coherence (C3) extracted from the 128×128×512 size 3D third-generation coherence (C3) dataset, respectively.

[0124] Figures 3(a) and 3(b) show the discontinuous instantaneous phase of the third-generation coherence (C3) profiles of inline50 and crossline50 extracted from the 128×128×512 size 3D third-generation coherence (C3) without removing the phase period, respectively; Figures 3(c) and 3(d) show the third-generation coherence (C3) time slices of 1100ms and 1300ms, respectively, extracted from the 128×128×512 size 3D third-generation coherence (C3) without removing the phase period.

[0125] Figure 4(a) and Figure 4(b) are the third-generation coherence (C3) profiles of the in-line 50 and the intersection 50 extracted from the 128×128×512 size three-dimensional MCHFs. Figure 4(c) and Figure 4(d) are the 1100ms and 1300ms third-generation coherence (C3) time slices extracted from the 128×128×512 size three-dimensional third-generation coherence (C3) of high-precision instantaneous frequency based on polynomial fitting of monotonically increasing continuous instantaneous phase.

[0126] Figure 2-4 shows that: ① The third-generation coherence (C3) results of the field seismic dataset detected major geological anomalies, but with low accuracy. ② Compared with the third-generation coherence (C3) results of the field seismic dataset, the third-generation coherence (C3) results with discontinuous instantaneous phases without phase period removal detected more small-scale geological anomalies and had higher accuracy in geological anomaly identification; however, it was greatly affected by phase period jumps. ③ The third-generation coherence (C3) results based on polynomial fitting of monotonically increasing continuous instantaneous phases to obtain high-precision instantaneous frequencies (or high-precision instantaneous frequencies based on continuous instantaneous phases) can avoid the influence of phase period jumps and phase period jumps, thus obtaining ideal high-precision geological anomaly identification results.

[0127] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A high-precision instantaneous frequency inversion method for continuous instantaneous phase, characterized in that, Includes the following steps: S1. Input the real signal, process it, and obtain the spectrum; S2. Obtain the analytical signal based on the spectrum; S3. Based on the analytical signal, a high-precision instantaneous frequency inversion based on polynomial fitting is used to obtain the final high-precision instantaneous frequency of polynomial fitting.

2. The high-precision instantaneous frequency inversion method for continuous instantaneous phase according to claim 1, characterized in that, S1 includes the following sub-steps: S11, Input the actual signal; S12. Noise attenuation is applied to the real signal to obtain a high signal-to-noise ratio signal; S13. Perform Fourier transform on the high signal-to-noise ratio signal to obtain the spectrum.

3. The high-precision instantaneous frequency inversion method for continuous instantaneous phase according to claim 1, characterized in that, S2 includes the following sub-steps: S21. Perform Hilbert transform on the analytic signal to obtain the spectrum of the analytic signal; S22. Perform an inverse Fourier transform on the spectrum of the analytic signal to obtain the analytic signal.

4. The high-precision instantaneous frequency inversion method for continuous instantaneous phase according to claim 1, characterized in that, S3 includes the following sub-steps: S31. Apply the arctangent function to the analytic signal to obtain the instantaneous phase; S32. Apply the continuous instantaneous phase inversion method to the instantaneous phase to obtain the continuous instantaneous phase after removing the phase period and the monotonically increasing continuous instantaneous phase; S33. Based on the continuous instantaneous phases after removing the phase period and the monotonically increasing continuous instantaneous phases, the final high-precision instantaneous frequency of the polynomial fitting is obtained.

5. The high-precision instantaneous frequency inversion method for continuous instantaneous phase according to claim 4, characterized in that, S33 includes the following sub-steps: S331. Use high-precision instantaneous frequency inversion based on polynomial fitting to obtain the sign function and high-precision instantaneous frequency based on polynomial fitting of continuous instantaneous phases with phase period removed. S332. Use polynomial fitting-based high-precision instantaneous frequency inversion on the monotonically increasing continuous instantaneous phase to obtain the polynomial fitting high-precision instantaneous frequency based on the monotonically increasing continuous instantaneous phase. S333: Based on the high-precision instantaneous frequency and sign function obtained from S331 and S332, the final high-precision instantaneous frequency of the polynomial fitting is obtained.

6. The high-precision instantaneous frequency inversion method for continuous instantaneous phase according to claim 3, characterized in that, In step S21, the expression for the spectrum Z(f) of the analytic signal is: ； in, This represents the spectrum of a high signal-to-noise ratio real signal, where F represents the Nyquist frequency. Indicates frequency.

7. The high-precision instantaneous frequency inversion method for continuous instantaneous phase according to claim 4, characterized in that, In S31, the instantaneous phase The expression is: ； Where x(t) represents a high signal-to-noise ratio signal and y(t) represents the imaginary part of the analytic signal.

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