Generalized high-order synchronous extrusion seismic signal time-frequency decomposition and reconstruction method
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A technology of synchronous extrusion and seismic signal, applied in seismic signal processing, seismology, geophysical measurement, etc., can solve problems such as "affecting extrusion" effect, and achieve the effect of improving accuracy and computing efficiency.
Active Publication Date: 2020-10-30
CHENGDU UNIVERSITY OF TECHNOLOGY
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In the process of synchronous squeeze transformation, the accuracy of the real instantaneous frequency estimation of the signal is particularly important, which will affect the final "squeeze" effect to a large extent.
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Embodiment 1
[0047] Example 1: see figure 1 , a generalized high-order synchronous extrusion seismic signal time-frequency decomposition and reconstruction method, including the following steps:
[0048] (1) Obtain a seismic signal x(t);
[0049] (2) Preset the first-order number K and the time window function g(t), calculated in the window function t k Short-time Fourier transform value under g(t) Where K≤6, k=0,1,...,max{2K-2,1}; we use the following formula to calculate
[0050]
[0051]
[0052] In the formula, t is time, ω is frequency, σ is the adjustment factor of time window function;
[0053] (3) A threshold ε is preset, and the K-order matrix L is constructed according to the following formulaK (t,ω), and find the matrix L K All sequential principal subforms det(L in (t,ω) m (t,ω)) absolute value greater than the maximum value m of ε;
[0054]
[0055] m=max{j:|det(L j (t,ω))|>ε,j=1,2,...,K}
[0056] In the formula, det means to solve the matrix determinant, a...
Embodiment 2
[0064] Example 2: see figure 1 , on the basis of embodiment 1, also includes step (7), to step (6) in The modulo operation yields the final high-order synchrosqueezed transform-time spectrum This embodiment is used to output high-order synchronous squeeze transform time spectrum.
Embodiment 3
[0065] Example 3, see figure 1 , on the basis of embodiment 1, also include step (7), adopt following formula to step (6) Perform inverse transformation to reconstruct the seismic signal x(t);
[0066]
[0067] This embodiment is used to reconstruct seismic signals.
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Abstract
The invention discloses a generalized high-order synchronous extrusion seismic signal time-frequency decomposition and reconstruction method. The method comprises the following steps: inputting a one-dimensional signal seismic signal; selecting an order and a time window function, calculating a short-time Fourier transform value under the window function, setting a threshold value, calculating a K-order matrix LK (t, omega), and obtaining an m value according to the threshold value; constructing an m-order matrix Lm (t, omega) and an m-order matrix Mm (t, omega); and calculating a K-order instantaneous frequency estimated value on the two-dimensional time-frequency spectrum, and extruding the short-time Fourier transform value by using the K-order instantaneous frequency estimated value. According to the invention, a proper time window function is flexibly selected according to the characteristics of the signal; an aggregated short-time Fourier transform time-frequency spectrum is obtained; an estimated value of any order can be directly solved; the method effectively improves the calculation efficiency, improves the precision of an instantaneous frequency estimation value, enablesthe time-frequency spectrum energy of high-order synchronous extrusion transformation to be more concentrated, greatly improves the time and frequency resolution of a signal, also maintains the reversibility of the transformation in an extrusion process, and can achieve the high-precision reconstruction of an original signal.
Description
technical field [0001] The invention relates to a method for processing seismic signals, in particular to a method for time-frequency decomposition and reconstruction of generalized high-order synchronously squeezed seismic signals. Background technique [0002] As an important branch of non-stationary signal processing, time-frequency analysis has always been one of the research hotspots in modern signal processing. Common time-frequency analysis methods include short-time Fourier transform (STFT), wavelet transform (CWT), S-transform (ST) and generalized S-transform (GST). Although the resolution of these time-frequency analysis methods has been improved, because they all use a certain window function (improved window function) and estimate the frequency component of the signal within the window function interval, so that the time Frequency energy is always distributed in a range centered on the true instantaneous frequency of the signal. Therefore, the energy focus of t...
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