CN112578440B - Extremum constraint three-parameter scanning wavelet decomposition method and system - Google Patents
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Abstract
The invention provides a three-parameter scanning wavelet decomposition method and a system of extremum constraint, wherein the method comprises the following steps: s1, complex seismic channel analysis is carried out on a current seismic signal, and an instantaneous attribute is calculated; s2, calculating initial parameters of local optimal atoms according to the transient attributes; s3, searching the phase, frequency and scale of the local optimal atom according to the initial parameters and extracting the time shift of the local optimal atom; s4, obtaining residual errors of local optimal atoms and seismic signals, marking the residual errors of the seismic signals as current seismic signals, and repeating the steps S1 to S4 until preset conditions are met, so that a series of wavelet combinations are obtained. The invention fully considers the relation among wavelet control parameters and the influence of the phase extremum in the local range on the optimal matching parameters, improves the calculation efficiency and can obtain more accurate local optimal time-frequency atoms at the same time, thereby realizing high-precision and high-efficiency seismic wavelet decomposition.
Description
Technical Field
The invention belongs to the field of geophysical exploration, and particularly relates to a three-parameter scanning wavelet decomposition method and system of extremum constraint.
Background
The spectral imaging technology is a reservoir prediction characteristic interpretation technology based on seismic spectral decomposition, which is developed in recent years, and is an important component in seismic attribute analysis. The method is a valuable post-treatment technology for researching complex oil and gas areas, and mainly uses a spectrum tuning principle to describe the thickness and distribution of a reservoir, and can also be used for describing sedimentary facies and sedimentary environments, detecting river channels and sand bodies, extracting various time-frequency attributes and the like.
The heart of the seismic spectrum decomposition is a time-frequency analysis technology of signals, and the time-frequency analysis is a conventional method for analyzing non-stationary signals. Common time-frequency analysis methods include linear time-frequency analysis methods, bilinear time-frequency analysis methods, parameterized time-frequency analysis methods, and the like. Traditional STFT, CWT and GST are typical linear time-frequency analysis methods, which are limited by uncertainty principle, and the time-channel set can not reach higher time-frequency resolution at the same time. Wigner-Ville distribution is a typical bilinear time-frequency analysis method, and a decomposed single-component stable signal has higher time-frequency resolution; WVD is bilinear, however, and severe cross terms can occur when decomposing multi-component non-stationary signals.
Matching pursuit (also called wavelet decomposition) is a typical parameterized time-frequency analysis method, which is proposed by s.mallat and z.zhang in 1993, and can decompose a seismic signal into a set of wavelets, and can obtain higher time-frequency resolution by decomposing a nonstationary signal by using a WVD to calculate a time spectrum for a single wavelet. The technique has been applied to various aspects of the geophysical field since its proposal, such as reflection coefficient inversion, resolution enhancement processing, denoising, strong reflection removal, thin sand body prediction, seismic inversion, seismic deposit interpretation, geologic body detection, and the like. However, the technology realizes the decomposition of the seismic signals by continuously searching the local optimal atoms, and has low calculation efficiency. In order to improve the calculation efficiency, yangHua Wang (2007) researches a matching tracking method combining global coarse granularity prediction and local optimization in the iterative process, so that the calculation efficiency is improved, but the relation among parameters is not considered in the local optimal wavelet searching process, and the decomposition precision is not guaranteed; zhang Fanchang (2010) proposes a dual-parameter dynamic scanning technique, which improves the decomposition efficiency, but does not consider the influence of wavelet scale, wherein the wavelet scale is a constant value, and does not accord with the actual situation.
Therefore, the problem of the local best atomic search efficiency and precision in wavelet decomposition still needs to be solved.
Disclosure of Invention
Features and advantages of the invention will be set forth in part in the description which follows, or may be obvious from the description, or may be learned by practice of the invention.
In order to overcome the problems in the prior art, the invention provides a three-parameter scanning wavelet decomposition method with extremum constraint, which comprises the following steps:
s1, complex seismic channel analysis is carried out on a current seismic signal, and an instantaneous attribute is calculated;
S2, calculating initial parameters of local optimal atoms according to the transient attributes;
s3, searching the phase, frequency and scale of the local optimal atom according to the initial parameters and extracting the time shift of the local optimal atom;
S4, obtaining a residual error x i+1 (t) of a local optimal atom and a seismic signal, recording the residual error x i+1 (t) of the seismic signal as a current seismic signal, and repeating the steps S1 to S4 until a preset condition is met, so as to obtain a series of wavelet combinations.
Optionally, the transient properties include transient amplitude, transient frequency and transient phase, and the initial parameters include initial time shiftInitial frequency/>Initial phase/>Initial dimensions/>The step S2 includes:
Searching for a maximum value of the instantaneous amplitude, the initial time shift For a corresponding time at the maximum of the instantaneous amplitude, the initial frequency/>For the instantaneous frequency corresponding to the time, the initial phase/>The instantaneous phase corresponding to the time;
Using initial time shifting Initial phase/>Initial frequency/>Obtaining initial scale by maximum matching projection principle
Optionally, the step S3 includes:
searching the phase phi i, the frequency f i and the scale sigma i of the locally optimal atoms in the given parameter variation range according to the maximum matching projection principle;
The monotone section of the instantaneous phase is searched for in a given time shift search section, and the position corresponding to the phase closest to the locally optimal phase phi i is searched for as the locally optimal time shift u i in the monotone section.
Optionally, the step S4 includes:
And obtaining the amplitude a i of the local optimal atom according to the phase, frequency, scale and time shift of the optimal atom, wherein the residual error x i+1 (t) of the seismic signal is the product of the seismic signal x i (t) minus the local optimal atom and the amplitude a i. Alternatively, the local optimum atom M i (t) and the amplitude a i of the local optimum atom are calculated by the following formulas, respectively:
Wherein, R (i) X is the seismic signal of the ith iteration, which is the optimal atom for the ith iteration.
Optionally, the preset conditions in step S4 are: the iteration number reaches a preset threshold or the energy of the residual x i+1 (t) of the seismic signal is less than P% of the energy of the original signal x (t).
Optionally, the preset threshold is less than 1/3 of the length of the seismic signal, and the p% is less than 20%.
The invention provides an extremum constraint three-parameter scanning wavelet decomposition system, which comprises:
the analysis unit is used for carrying out complex seismic channel analysis on the current seismic signal and calculating the instantaneous attribute;
an initial parameter calculation unit, configured to calculate initial parameters of locally optimal atoms according to the transient attribute;
the optimal parameter calculation unit is used for searching the phase, frequency and scale of the local optimal atoms according to the initial parameters and extracting the time shift of the local optimal atoms;
A local optimum atom obtaining unit for obtaining a local optimum atom;
An iterative calculation unit, configured to calculate a residual x i+1 (t) of the seismic signal, and record the residual x i+1 (t) of the seismic signal as a current seismic signal;
And the iteration judging unit is used for judging whether the preset condition is met, if so, ending the iteration calculation and obtaining a series of wavelet combinations.
Optionally, the optimal parameter calculating unit is specifically configured to: searching the phase phi i, the frequency f i and the scale parameter sigma i of the local optimal atoms in the given parameter variation range according to the maximum matching projection principle; the monotone section of the instantaneous phase is searched for in a given time shift search section, and the position corresponding to the phase closest to the locally optimal phase phi i is searched for as the locally optimal time shift u i in the monotone section.
The present invention provides a computer-readable storage medium storing at least one program executable by a computer, which when executed by the computer, causes the computer to perform the steps in the method provided by any of the embodiments of the present invention.
According to the extremum constraint three-parameter scanning wavelet decomposition method and system provided by the invention, the relation among wavelet control parameters and the influence of the phase extremum in the local range on the optimal matching parameters are fully considered, the computing efficiency is improved, and meanwhile, more accurate local optimal time-frequency atoms can be obtained, so that the high-precision and high-efficiency seismic wavelet decomposition is realized.
Drawings
FIG. 1 is a flowchart illustrating a three-parameter scanning wavelet decomposition method with extremum constraint according to an embodiment of the present invention.
FIG. 2 is a flowchart illustrating a three-parameter scanning wavelet decomposition method with extremum constraint according to an embodiment of the present invention.
FIG. 3 is a schematic diagram of an extremum constrained three-parameter scanning wavelet decomposition system according to an embodiment of the present invention.
Fig. 4 is a real seismic signal.
FIG. 5 shows the wavelets after decomposition by atomic wave decomposition technique.
Fig. 6 is a time-channel set of seismic signals obtained by atomic wave decomposition techniques.
FIG. 7 illustrates various wavelets decomposed using the present invention.
Fig. 8 is a time-channel set of seismic signals calculated using the present invention.
Detailed Description
The invention is described in further detail below with reference to the attached drawing figures:
as shown in FIG. 1, the present invention provides an extremum constrained three-parameter scanning wavelet decomposition method, comprising:
s1, complex seismic channel analysis is carried out on a current seismic signal, and an instantaneous attribute is calculated;
the instantaneous properties include instantaneous amplitude, instantaneous frequency, and instantaneous phase. And inputting the seismic signal x (t), and performing complex seismic trace analysis on the current seismic signal x i (t) to calculate three curves of instantaneous amplitude, instantaneous phase and instantaneous frequency. x i (t) is the signal of the ith iteration, and the first iteration is the original input seismic signal x (t). Complex seismic trace analysis of digital signals is a well-known common technique, and is often used in three-transient attribute analysis, and the calculation process and three-transient attribute extraction are described in detail in a well-known textbook, and are not described in detail herein.
S2, calculating initial parameters of local optimal atoms according to the transient attributes;
More specifically, a maximum value of the instantaneous amplitude is searched for, and the initial time shift is performed I.e. the corresponding time at the maximum of the instantaneous amplitude, the initial frequency/>I.e. the instantaneous frequency corresponding to the time, the initial phase/>I.e. the instantaneous phase corresponding to the time.
Using initial time shiftingInitial phase/>Initial frequency/>Obtaining initial scale by maximum matching projection principle
S3, searching the phase, frequency and scale of the local optimal atom according to the initial parameters and extracting the time shift of the local optimal atom;
the phase phi i, the frequency f i and the scale parameter sigma i of the local optimum are searched in the given parameter variation range according to the maximum matching projection principle.
The monotone section of the instantaneous phase is searched for in a given time shift search section, and the position corresponding to the phase closest to the locally optimal phase phi i is searched for as the locally optimal time shift u i in the monotone section.
In particular implementation, the initial dimensionsIs fixed in a group/>The method comprises the following steps of obtaining by calculating an optimization formula (1);
wherein D= { M r(t)}r∈Γ is a time-frequency atomic dictionary, Is a function R (i) X and/>Inner product of (2), andR (i) X represents the residual signal of the ith iteration, the 1 st iteration is X (t), M r (t) is a time-frequency atom determined by a parameter R, the time-frequency atom is obtained by a formula (2), R i＝{ui,σi,fi,φi }, and i represents the number of iterations.
At the initial time shiftIn the fixed case, the phase phi i, the frequency f i and the scale parameter sigma i are searched for locally optimal values within the given range of variation of the respective parameters according to the principle of maximum matching projection.
In this embodiment, the local optimization of the three parameters of phase, frequency and scale is to find the optimal value of r i＝{ui0,σi,fi,φi in the local area, where the initial time shift u i0 is fixed, and the search range is [ r i-Δr,ri +Δr ], where Δr= (Δu, Δσ, Δf, ΔΦ), i.e., Δu=0 is a time offset, Δσ=0.1 is a scale offset, Δf=5 Hz is a frequency offset, and ΔΦ=50 is a phase offset. In the specific implementation, different values are arbitrarily taken in the given range of each parameter, a group of time-frequency atoms is obtained by the formula (2), and the parameters corresponding to the maximum of the formula (1) are the locally optimal phi i、fi and sigma i.
The locally optimal time shift is obtained from the relationship of the locally optimal phase and the instantaneous phase profile. More specifically, at a given time-shifted search intervalEffective monotonic interval/>, of internal search transient phaseThe instantaneous phase is monotonically increasing or monotonically decreasing in the interval, and the phase position with the smallest difference with the local optimal phase phi i is searched in the interval, and the position is the searched local optimal time shift u i.
S4, obtaining residual errors of local optimal atoms and seismic signals, recording the residual error x i+1 (t) of the seismic signals as the current seismic signals, and repeating the steps S1 to S4 for iterative decomposition until the preset condition is met, so that a series of wavelet combinations are obtained.
Obtaining the amplitude a i of the local optimal atom according to the phase, frequency, scale and time shift of the optimal atom; and obtaining the residual error x i+1 (t) of the seismic signal according to the phase, frequency, scale, time shift and amplitude of the optimal atom. The residual x i+1 (t) of the seismic signal is the product of the seismic signal x i (t) minus the locally optimal atom and the amplitude a i.
More specifically, the amplitude a i of the locally optimal atom is obtained according to the phase Φ i, the frequency f i, the scale σ i, and the time shift u i of the locally optimal atom in combination with the formula (3). Equation (3) is shown below:
Wherein, For the locally optimal atoms determined by the optimal parameter R i＝{ui,σi,fi,φi of the ith iteration and equation (2), R (i) X is the seismic signal of the ith iteration and R (i) X of the 1 st iteration is the original seismic signal X (t).
The parameters of the phase phi i, the frequency f i, the scale sigma i and the time shift u i of the locally optimal atom are put into the formula (2) to obtain the locally optimal atom M i (t). The residual x i+1 (t) of the seismic signal is obtained by subtracting the product of the locally optimal atoms and the amplitude a i from the seismic signal x i (t). The formula for calculating the residual x i+1 (t) is as follows:
xi+1(t)＝xi(t)-aiMi(t) (4)
the preset condition includes the number of iterations reaching a preset threshold or the energy of the residual x i+1 (t) of the seismic signal being less than P% of the energy of the original signal x (t). Wherein the preset threshold is less than 1/3 of the length of the seismic signal, and P is not more than 20. In this embodiment, the exit condition is 167 times of iteration agreed in advance or the energy of the residual x i+1 (t) is less than 10% of the energy of the original signal x (t).
The final raw seismic signal is decomposed into a combination of wavelets as shown in equation (5):
Referring to fig. 2, the present invention provides a three-parameter scanning wavelet decomposition method with extremum constraint, comprising the steps of:
101. Starting.
102. Inputting a current seismic signal;
103. analyzing complex seismic traces;
complex seismic trace analysis is performed on the current seismic signal x i (t), and instantaneous amplitude, instantaneous phase and instantaneous frequency are calculated. Obtaining an initial time shift, an initial frequency and an initial phase according to the instantaneous amplitude; more specifically, a maximum value of the instantaneous amplitude is searched for, and the initial time shift is performed I.e. the corresponding time at the maximum of the instantaneous amplitude, the initial frequency/>I.e. the instantaneous frequency corresponding to the time, the initial phase/>I.e. the instantaneous phase corresponding to the time.
104. Matching the initial scale;
obtaining an initial scale on the basis of the initial time shift, the initial frequency and the initial phase; in this embodiment, an initial time shift is utilized Initial phase/>Initial frequency/>And the above formulas (1) and (2) obtain the initial scale/>
105. Local dynamic scanning;
at the initial time shift In the fixed case, the locally optimal phase phi i, frequency f i and scale parameter sigma are searched for in the given range of variation of the respective parameters according to the principle of maximum matching projection i
106. Extracting time shift of local optimal atoms;
The time shift of the local best atoms is extracted by using the instantaneous phase attribute calculated in the complex seismic trace analysis and the local best phase obtained by the local dynamic scanning. More specifically, at a given time-shifted search interval Effective monotonic interval/>, of internal search transient phaseThe instantaneous phase is monotonically increasing or monotonically decreasing in the interval, and the phase position with the smallest difference with the local optimal phase phi i is searched in the interval, and the position is the searched local optimal time shift u i.
107. Calculating a local optimal atom;
the parameters of the phase phi i, the frequency f i, the scale sigma i and the time shift u i of the locally optimal atom are put into the formula (2) to obtain the locally optimal atom M i (t).
108. Judging whether a preset condition is met, if yes, entering a step 11, namely ending the process; if not, go to step 109;
109. removing local optimal atoms to obtain residual errors;
Obtaining the amplitude a i of the local optimal atom according to the phase, frequency, scale and time shift of the optimal atom and the combination formula (3); and obtaining the residual error x i+1 (t) of the seismic signal according to the phase, frequency, scale, time shift and amplitude of the optimal atom. The residual x i+1 (t) of the seismic signal is the product of the seismic signal x i (t) minus the locally optimal atom and the amplitude a i.
The preset condition includes the number of iterations reaching a preset threshold or the energy of the residual x i+1 (t) of the seismic signal being less than P% of the energy of the original signal x (t). Wherein the preset threshold is less than 1/3 of the length of the seismic signal, and P is not more than 20. In this embodiment, the exit condition is 167 times of iteration agreed in advance or the energy of the residual x i+1 (t) is less than 10% of the energy of the original signal x (t).
110. The residual is noted as the current seismic signal and returns to step 102.
111. Ending the process.
The final raw seismic signal is decomposed into a combination of wavelets as shown in equation (5).
The present invention provides a computer-readable storage medium storing at least one program executable by a computer, which when executed by the computer, causes the computer to perform the steps in the method provided by any of the embodiments of the present invention.
As shown in FIG. 3, the present invention provides an extremum constrained three-parameter scanning wavelet decomposition system comprising: an analysis unit 10, an initial parameter calculation unit 20, an optimal parameter calculation unit 30, a local optimal atom acquisition unit 40, an iterative calculation unit 50, and an iterative judgment unit 60. Wherein:
the analysis unit 10 is used for carrying out complex seismic trace analysis on the current seismic signal and calculating the instantaneous attribute; more specifically, the analysis unit is configured to implement step S1, which is not described herein.
The initial parameter calculation unit 20 is connected with the analysis unit 10 and is used for calculating initial parameters of locally optimal atoms according to the transient attribute; more specifically, the initial parameter calculation unit is configured to implement step S2, which is not described herein.
The optimal parameter calculation unit 30 is connected with the analysis unit 10 and the initial parameter calculation unit 20, and the optimal parameter calculation unit 30 is used for searching the phase, frequency and scale of the local optimal atom according to the initial parameter and extracting the time shift of the local optimal atom; more specifically, the optimal parameter calculation unit is configured to implement step S30, which is not described herein.
The locally optimal atom acquisition unit 40 is configured to acquire locally optimal atoms; the parameters of the phase phi i, the frequency f i, the scale sigma i and the time shift u i of the locally optimal atom are put into the formula (2) to obtain the locally optimal atom M i (t).
The iterative calculation unit 50 is connected to the locally optimal atom acquisition unit 40, and is configured to calculate a residual x i+1 (t) of the seismic signal, and record the residual x i+1 (t) of the seismic signal as a current seismic signal. The residual x i+1 (t) of the seismic signal is the product of the seismic signal x i (t) minus the local optimum atom and the amplitude a i; and (3) obtaining the amplitude a i of the local optimal atom according to the phase, frequency, scale and time shift of the optimal atom and the combination formula (3).
The iteration determining unit 60 is connected to the iteration calculating unit 50, and is configured to determine whether a preset condition is satisfied, and if so, terminate the iteration calculation, and obtain a combination of a series of wavelets. The preset condition includes the number of iterations reaching a preset threshold or the energy of the residual x i+1 (t) of the seismic signal being less than P% of the energy of the original signal x (t). Wherein the preset threshold is less than 1/3 of the length of the seismic signal, and P is not more than 20. In this embodiment, the exit condition is 167 times of iteration agreed in advance or the energy of the residual x i+1 (t) is less than 10% of the energy of the original signal x (t).
The advantageous effects of the embodiments of the present invention are described below by way of a specific example.
Fig. 4 shows an actual seismic signal, from which it can be seen that the maximum and minimum values of the seismic waveform are between 800ms and 1000ms, and the calculated energy maximum of the time spectrum should be between 800ms and 1000 ms.
Fig. 5 shows wavelets obtained by decomposing by the original four-parameter dynamic scanning wavelet decomposition method, wherein the wavelets are sequentially output by each step of iteration from left to right, the iteration number is 80, and the iteration time is 381 seconds. The solid circles in the graph can show that a plurality of wavelets appear at the same position, the polarities are opposite, and the energy of the next wavelet is larger than that of the last wavelet, the phenomenon is that the position of the maximum value of the instantaneous amplitude is deviated when searching time shifting, the root cause is that when searching time shifting parameters of local optimal atoms, the instantaneous phase is jumped in the time shifting disturbance range, namely, the phase of the searched local optimal atoms suddenly changes from pi to pi, the phase of the searched local optimal atoms is not problematic, but the time shifting is different, the maximum position of the instantaneous amplitude is deviated, the local optimal atoms of the iteration are incorrect, then the calculated residual signal is incorrect, and the subsequent iteration process is directly influenced. Meanwhile, as can be seen from the graph, the situation generally occurs in pairs, because the instantaneous amplitude energy of the position is the largest in the ith iteration, but the local optimal atoms are picked up to have deviation, the energy of the residual signal near the position is enhanced, so that the wavelet energy of the next iteration search is higher than that of the last iteration, and the iteration logic is not met.
FIG. 6 shows the time spectrum of wavelet calculations decomposed by the original four-parameter dynamic scanning wavelet decomposition method. As shown in FIG. 5 of the original seismic signals, the maximum energy of the seismic signals should be between 800ms and 1000ms, and according to the principle of time-frequency analysis, the maximum energy cluster of the time-frequency analysis should also be between 800ms and 1000ms, but the maximum energy (the darkest part) in FIG. 6 is below 1400ms, which is consistent with the maximum energy wavelet in the first black circle shown in FIG. 5; a strong energy bin below 1000ms is associated with the wavelet in the right-most circle in fig. 5, and three wavelets (of opposite polarity) appear in the same position, which directly causes problems in energy bin energy generation in the time spectrum. Because the decomposition process does not consider the influence of the phase, the decomposition wavelet is incorrect, so the calculated time spectrum is also incorrect, and the subsequent application of the time spectrum is directly influenced.
FIG. 7 shows the wavelet decomposed by the extremum-constrained three-parameter scanning wavelet decomposition method of the present invention, with 60 iterations and 19 seconds iterations. From the figure, it can be seen that the wavelet energy is continuously reduced, which is consistent with the actual iterative decomposition concept, and no two wavelets are at the same position, which benefits from the constraint of the phase extremum proposed by the present invention. The maximum energy of the first wavelet, which occurs between 800ms and 1000ms, is shown in fig. 8, which shows the calculated time spectrum of the present invention, and from the energy relation of the time spectrum, it can be seen that the maximum energy of the time spectrum also occurs between 800ms and 1000ms and is consistent with the maximum energy position of the seismic signal. The iteration times are not quite different, but the calculation time is greatly reduced.
In a word, compared with the existing wavelet decomposition technology, the method fully considers the relation among the time-frequency atomic decision parameters, reduces the existing four-parameter dynamic search to three-parameter dynamic search, and improves the calculation efficiency; meanwhile, the influence of phase mutation on local optimal time shift is considered, the optimal phase is searched in a monotone interval of the instantaneous phase, the local optimal time shift is determined by the local optimal phase, and the accuracy of wavelet decomposition is improved.
The invention provides an extremum constraint three-parameter scanning wavelet decomposition method and system, which can realize higher-precision wavelet decomposition and improve calculation efficiency. The invention fully considers the relation among the time-frequency atomic decision parameters, reduces the existing four-parameter dynamic search to three-parameter dynamic search, and improves the calculation efficiency; meanwhile, the influence of phase mutation on local optimal time shift is considered, the optimal phase is searched in a monotone interval of the instantaneous phase, the local optimal time shift is determined by the local optimal phase, and the accuracy of wavelet decomposition is improved.
The foregoing technical solution is only one embodiment of the present invention, and various modifications and variations can be easily made by those skilled in the art based on the application methods and principles disclosed in the present invention, not limited to the methods described in the foregoing specific embodiments of the present invention, so that the foregoing description is only preferred and not in a limiting sense.
Claims (8)
1. An extremum constrained three-parameter scanning wavelet decomposition method, comprising:
s1, complex seismic channel analysis is carried out on a current seismic signal, and an instantaneous attribute is calculated;
S2, calculating initial parameters of local optimal atoms according to the transient attributes;
S3, searching the phase, frequency and scale of the local optimal atoms according to the initial parameters, and extracting the time shift of the local optimal atoms;
s4, obtaining a residual error x i+1 (t) of a local optimal atom and a seismic signal, recording the residual error x i+1 (t) of the seismic signal as a current seismic signal, and repeating the steps S1 to S4 until a preset condition is met, so as to obtain a series of wavelet combinations; i is the iteration number;
The step S3 includes:
searching the phase phi i, the frequency f i and the scale sigma i of the locally optimal atoms in the given parameter variation range according to the maximum matching projection principle;
The monotonic interval of the instantaneous phase is searched for in a given time shift search interval, and the position corresponding to the phase closest to the phase phi i of the locally optimal atom is searched for as the locally optimal time shift u i in the monotonic interval.
2. The extremum constrained three parameter scanning wavelet decomposition method of claim 1, wherein said transient properties include transient amplitude, transient frequency and transient phase, and said initial parameters include initial time shiftInitial frequency/>Initial phase/>Initial dimensions/>The step S2 includes:
Searching for a maximum value of the instantaneous amplitude, the initial time shift For a corresponding time at the maximum of the instantaneous amplitude, the initial frequency/>For the instantaneous frequency corresponding to the time, the initial phase/>The instantaneous phase corresponding to the time;
Using initial time shifting Initial phase/>Initial frequency/>Obtaining initial scale/>, based on maximum matching projection principle
3. The extremum constrained three parameter scanning wavelet decomposition method of claim 1, wherein said step S4 comprises: and obtaining the amplitude a i of the local optimal atom according to the phase, frequency, scale and time shift of the local optimal atom, wherein the residual error x i+1 (t) of the seismic signal is the product of the seismic signal x i (t) minus the local optimal atom and the amplitude a i.
4. The extremum-constrained three-parameter scanning wavelet decomposition method of claim 3, wherein the amplitudes of the locally optimal atoms M i (t) and the locally optimal atoms a i are calculated by the following equations, respectively:
Substituting the phase phi i, the frequency f i, the scale sigma i and the time shift u i of the locally optimal atom into the above formula to obtain a locally optimal atom M i (t);
Wherein, R (i) X is the seismic signal of the ith iteration, f is the frequency, u is the time shift, sigma is the scale, and phi is the phase.
5. The extremum-constrained three-parameter scanning wavelet decomposition method according to claim 1, wherein the preset conditions in step S4 are: the iteration number reaches a preset threshold or the energy of the residual x i+1 (t) of the seismic signal is less than P% of the energy of the original signal x (t).
6. The extremum constrained three parameter scanning wavelet decomposition method of claim 5, wherein said predetermined threshold is less than 1/3 of the length of the seismic signal and said p% is less than 20%.
7. An extremum constrained three parameter scanning wavelet decomposition system comprising:
the analysis unit is used for carrying out complex seismic channel analysis on the current seismic signal and calculating the instantaneous attribute;
an initial parameter calculation unit, configured to calculate initial parameters of locally optimal atoms according to the transient attribute;
the optimal parameter calculation unit is used for searching the phase, frequency and scale of the local optimal atoms according to the initial parameters and extracting the time shift of the local optimal atoms;
A local optimum atom obtaining unit for obtaining a local optimum atom;
An iterative calculation unit, configured to calculate a residual x i+1 (t) of the seismic signal, and record the residual x i+1 (t) of the seismic signal as a current seismic signal;
The iteration judging unit is used for judging whether a preset condition is met, if yes, ending the iteration calculation and obtaining a series of wavelet combinations; the preset conditions are as follows: the iteration times reach a preset threshold value or the energy of the residual x i+1 (t) of the seismic signal is smaller than P% of the energy of the original signal x (t); the preset threshold value is smaller than 1/3 of the length of the seismic signal, and the P% is smaller than 20%;
The optimal parameter calculation unit is specifically configured to: searching the phase phi i, the frequency f i and the scale parameter sigma i of the local optimal atoms in the given parameter variation range according to the maximum matching projection principle; the monotone section of the instantaneous phase is searched for in a given time shift search section, and the position corresponding to the phase closest to the locally optimal phase phi i is searched for as the locally optimal time shift u i in the monotone section.
8. A computer-readable storage medium storing at least one program executable by a computer, wherein the at least one program, when executed by the computer, causes the computer to perform the steps in the method of any one of the preceding claims 1 to 6.
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