Seismic signal adaptive time-frequency energy contraction transformation method

Abstract

The invention relates to a seismic signal high-precision time-frequency analysis method, in particular to a seismic signal self-adaptive time-frequency energy shrinkage transformation method, which comprises the following steps of: inputting a seismic signal to be analyzed and carrying out short-time Fourier transformation to obtain a time-frequency result of the signal; calculating a first-order moment and a second-order central moment of any point in a time-frequency domain according to a short-time Fourier result of the seismic signal; constructing an adaptive energy suppression operator based on the obtained first-order moment and the second-order central moment; constructing a self-adaptive energy recovery operator according to the law of conservation of energy; constructing a seismic signal adaptive time-frequency energy shrinkage transformation method based on the obtained adaptive energy suppression operator and adaptive energy recovery operator, and obtaining a seismic signal high-precision time-frequency representation result; the problems that a traditional time-frequency analysis method is low in time-frequency positioning capacity, and time-frequency energy of a time-frequency post-processing method is excessively focused are solved.

Description

Technical Field

[0001] The invention belongs to the field of high-precision characterization methods for seismic signals, and relates to a seismic signal adaptive time-frequency energy shrinkage transformation method. Background Art

[0002] Time-frequency analysis is a powerful tool for analyzing non-stationary seismic signals. It maps the signal from the one-dimensional time domain to the two-dimensional time-frequency domain, effectively describing the changing characteristics of the seismic signal at different frequencies, thereby achieving a detailed description of the seismic signal. Traditional time-frequency analysis methods, such as short-time Fourier transform, are limited by the uncertainty principle and cannot achieve the optimal balance between time resolution and frequency resolution at the same time. Although time-frequency post-processing methods, such as synchronous extraction transform, can improve the time-frequency positioning capability, these methods theoretically assume that the signal is narrowband. Seismic signals usually have a certain time width and bandwidth and contain rich geological information. Therefore, it is difficult for existing time-frequency analysis methods to accurately characterize the characteristics of seismic signals. Summary of the invention

[0003] The purpose of the present invention is to address the above-mentioned problems in the prior art and to propose a method for adaptive time-frequency energy shrinkage transformation of seismic signals. The method comprises the following steps:

[0004] Step 1: Input the seismic signal to be analyzed and perform short-time Fourier transform to obtain the time-frequency results of the signal, which is the basis for the subsequent analysis of the time and frequency characteristics of the signal;

[0005] Step 2: Based on the short-time Fourier transform result of the obtained signal, the first-order moment and the second-order center distance of any point in the time-frequency domain are calculated to provide a basis for the subsequent construction of an adaptive energy suppression operator;

[0006] Step 3: construct an adaptive energy suppression operator based on the obtained first-order moment and second-order center distance to adaptively suppress the diffused time-frequency energy;

[0007] Step 4: Use the law of conservation of energy to construct an adaptive energy recovery operator to ensure that the total time-frequency energy of the constructed new method is consistent with the short-time Fourier transform;

[0008] Step 5: Based on the obtained adaptive energy suppression operator and adaptive energy recovery operator, an adaptive time-frequency energy shrinkage transformation method for seismic signals is constructed to obtain high-precision time-frequency characterization results of seismic signals.

[0009] Furthermore, in step 1, the seismic signal to be analyzed is input, and the short-time Fourier result obtained is for:

[0010] ;

[0011] in, is the imaginary part of the complex number, whose value is , For time, is the frequency, represents the time-integrated variable. Through this step, the seismic signal Convert from time domain to frequency domain.

[0012] Furthermore, in step 2, the first-order moment constructed :

[0013] ;

[0014] ;

[0015] in represents the real part of a complex number, represents the imaginary part of a complex number, Represents a window function The short-time Fourier result under Display Window About time The first-order partial derivative of .

[0016] Furthermore, in step 2, the second-order center distance constructed for:

[0017] ;

[0018] ;

[0019] in Represents a window function The short-time Fourier result under Display Window About time The above formula provides the short-time Fourier domain results of the first-order moment and the second-order central moment. In fact, if the idea of ​​the first-order moment and the second-order central moment is substituted into other traditional time-frequency analysis methods, the first-order moment and the second-order central moment results based on this method can be obtained.

[0020] Furthermore, in step 3, the adaptive energy suppression operator is constructed for:

[0021] ;

[0022] Represents all the time-frequency energy within the second-order moment of the signal's time-frequency center of gravity. All time-frequency energy within the range can be concentrated, while improving the degree of time-frequency spectrum energy focusing, while retaining more time-frequency energy than time-frequency post-processing transformation.

[0023] Furthermore, in step 4, if you want to build , you need to first define the window function The Wigner-Ville distribution under , expressed as:

[0024] ;

[0025] Adaptive energy recovery operator based on this Built as:

[0026] ;

[0027] It is constructed using the deconvolution algorithm of the Wigner-Ville distribution in order to ensure that the time-frequency energy of the new method is conserved with the short-time Fourier transform, which is conducive to reconstruction.

[0028] Furthermore, in step 5, the seismic signal adaptive time-frequency energy shrinkage transformation method It is expressed as:

[0029] ;

[0030] This means that the method first As a result, all the time-frequency energy of the second-order moment of the time-frequency center of gravity is extracted, suppressing The energy diffused in the Multiply to ensure that the total time-frequency energy of the new method is Consistent.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] The present invention proposes an adaptive time-frequency energy shrinkage transform, which is based on the first-order moment and second-order central moment of any point in the time-frequency domain, proposes an adaptive energy suppression operator and an adaptive energy recovery operator on the short-time Fourier time-frequency transform result, and constructs an adaptive time-frequency energy shrinkage transform. The method proposed by the present invention can not only improve the time-frequency positioning ability of the time-frequency spectrum, but also retain the more detailed spectrum characteristics of the seismic signal. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the embodiments of the present invention or the prior art solutions and advantages, the following briefly introduces the drawings required to be used in the embodiments or the prior art descriptions:

[0034] Figure 1 It is a flow chart of the present invention;

[0035] Figure 2(a) simulated seismic signal waveform, (b) simulated seismic signal ideal time edge distribution; (c) simulated seismic signal ideal frequency edge distribution;

[0036] Figure 3 The time-frequency results obtained by (a) short-time Fourier transform, (b) synchronous extraction transform, (c) transient extraction transform and (d) adaptive time-frequency shrinkage transform methods respectively. DETAILED DESCRIPTION

[0037] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0038] See also Figure 1 , showing the process of some embodiments of a method for adaptive time-frequency energy shrinkage transformation of seismic signals, including the following steps:

[0039] The seismic signal to be analyzed Input and get the short-time Fourier result of the signal ,Right now:

[0040] ;

[0041] in, is the imaginary part of the complex number, whose value is , is the frequency, For time, represents the time-integrated variable; the short-time Fourier transform obtains the seismic signal The time-frequency domain characteristics of

[0042] According to the obtained Calculate several key statistics in time-frequency distribution, including the first-order moment of any point in the time-frequency domain and the second-order center distance :

[0043] ;

[0044] ;

[0045] ;

[0046] ;

[0047] in represents the real part of a complex number, represents the imaginary part of a complex number, and Represents window functions Xiahe The short-time Fourier result under and Respectively represent windows About time The first-order and second-order partial derivatives of . The first-order moment and the second-order central moment provide the basis for the subsequent construction of the adaptive energy suppression operator;

[0048] Based on the obtained first-order moment and second-order center distance, an adaptive energy suppression operator is constructed. ,Right now:

[0049] ;

[0050] Covers all the time-frequency energy within the second-order moment of the signal, and retains it through adaptive The calculated time-frequency energy can focus the energy in the time and frequency directions of the time-frequency spectrum, thereby achieving the purpose of improving the time-frequency resolution of the time-frequency spectrum;

[0051] Constructing an adaptive energy recovery operator based on the law of energy conservation for:

[0052] ;

[0053] in is the window function The Wigner-Ville distribution under , expressed as:

[0054] ;

[0055] The construction of the new method benefits from the deconvolution algorithm of the Wigner-Ville distribution, which ensures that the total time-frequency energy of the new method is Consistency;

[0056] Obtained through the above steps and , combined with the time-frequency transformation theory, a seismic signal adaptive time-frequency energy shrinkage transformation method is constructed , and obtain high-precision time-frequency characterization results of seismic signals.

[0057] As a preference, the It is expressed as:

[0058] ;

[0059] This means that the new method constructed by the present invention first adaptively extracts the time-frequency energy of the second-order moment of the time-frequency point, and then uses the recovery operator to ensure the consistency of the time-frequency energy. The advantage of this is that it not only improves the focusing degree of the time-frequency energy, but also retains more detailed time-frequency features in the time-frequency spectrum.

[0060] In a specific embodiment, referring to FIG. (a), a waveform diagram of a designed simulated seismic signal is shown, wherein the main frequency of the wavelet at the position of 0.15 s is 95 Hz, and the main frequency of the wavelet at the position of 0.35 s is 30 Hz. Figure 2 (b) and Figure 2 (c) shows the ideal frequency marginal distribution and ideal time marginal distribution of the simulated seismic signal, respectively.

[0061] Figure 3 The time-frequency results and time and frequency marginal distributions obtained by different methods are shown, where the red dashed line is the ideal value and the blue implementation is the calculated value of the corresponding method. Figure 3 (a) is the spectrum of the short-time Fourier transform, whose time-frequency energy is diffused, and both the time edge distribution and the frequency edge distribution are wider than the ideal value. Figure 3 (b) and Figure 3 (c) is the result of the time-frequency post-processing method, where Figure 3 (b) is the result of synchronous extraction transformation. The frequency method energy of the time-frequency spectrum is very focused, but the bandwidth information is lost in the time-frequency spectrum. Figure 3 (c) is the result of transient extraction transformation, which improves the time positioning ability of the spectrum, but the time-frequency spectrum does not contain the time width characteristics of the seismic signal. Figure 3 As shown in (d), it can not only improve the time-frequency positioning capability of the time-frequency spectrum, but also shrink the time-frequency energy to a range that matches the time width and bandwidth of the seismic signal, and can accurately characterize the time-frequency distribution of the seismic signal.

[0062] The above is a specific description of the implementation of the present invention, but the invention is not limited to the embodiments. Those skilled in the art may make various equivalent modifications or substitutions without violating the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. A method for adaptive time-frequency energy shrinkage transformation of seismic signals, characterized in that: The following steps are involved: First, input the seismic signal to be analyzed Perform short-time Fourier transform to obtain the time-frequency results of the signal ,Right now: ， in, For time, is the frequency, Represents a window function The conjugate of represents the time-integrated variable, is the imaginary part of the complex number, whose value is ; Secondly, according to the obtained Calculate the first-order moment of any point in the time-frequency domain and the second-order center distance ; Then, based on the obtained , , and Constructing an adaptive energy suppression operator : ， Furthermore, an adaptive energy recovery operator is constructed based on the law of energy conservation ; Finally, based on the obtained and Constructing an adaptive time-frequency energy shrinkage transformation method for seismic signals , and obtain high-precision time-frequency characterization results of seismic signals.

2. The method according to claim 1, characterized in that Said and The calculation expression is: ； ； in represents the real part of a complex number, represents the imaginary part of a complex number, Represents a window function The short-time Fourier result under Display Window About time The first-order partial derivative of .

3. The method according to claim 1, characterized in that Said and The calculation expression is: ； ； in Represents a window function The short-time Fourier result under Display Window About time The second-order partial derivative of .

4. The method according to claim 1, characterized in that: The The calculation expression is: ； in is the window function The Wigner-Ville distribution under , expressed as: 。 5. The method according to claim 1, characterized in that The The calculation expression is: 。

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