An effective method for evaluating the quantitative resolution of spectral decomposition techniques

Abstract

The present invention provides an effective method for evaluating the quantitative resolution of spectral decomposition technology, including: obtaining the time-frequency distribution map of the actual seismic signal; obtaining the energy density at any point of the time-frequency profile according to the time-frequency distribution map; obtaining the spectral density probability distribution at this point according to the energy density at this point, and calculating the spectral density probability distribution along the time direction and the spectral density probability distribution along the frequency direction; calculating the normalized standard deviation in the time domain and the normalized standard deviation in the frequency domain; obtaining the resolution product according to the product of the normalized standard deviation in the time domain and the normalized standard deviation in the frequency domain; using the resolution product as the measurement standard for quantitative resolution analysis of different time-frequency analysis methods. The conclusion obtained by using the uncertainty product as the measurement method for quantitative resolution analysis of the time-frequency analysis method in the present invention is consistent with the result of quantitative interpretation of spectral decomposition of actual seismic data, and can meet the needs of seismic data processing and quantitative interpretation.

Description

Technical Field

[0001] The present invention relates to the technical field of time-frequency analysis, and particularly relates to an effective method for quantitatively evaluating the resolution of spectral decomposition technology. Background Art

[0002] Seismic signals are essentially non-stationary signals, whose frequency component content changes with the change of time records and contains rich geological information. Spectral decomposition (also known as time-frequency analysis) can transform seismic traces into the time-frequency domain to describe the time-varying characteristics of seismic frequencies and the characteristics of seismic data, revealing geophysical responses related to frequencies, and these responses are usually directly related to frequency anomaly phenomena. The attributes calculated by time-frequency analysis methods can be used to describe the structure of geological bodies, such as thin interbeds, channels, faults, and structural anomalies, etc. It has been widely used in seismic data denoising, direct hydrocarbon indication, seismic attenuation measurement, thin layer reflectivity inversion, formation heterogeneity determination, reservoir phase illumination, and pore and permeability distribution mapping and other seismic interpretation aspects.

[0003] Since spectral decomposition is essentially a non-unique process, there is no absolute "right" or "wrong". Different spectral methods have different time and spectral resolutions. A variety of time-frequency analysis methods are used in actual seismic exploration, and the more common ones include: short-time Fourier transform, continuous wavelet transform, S transform, matching pursuit decomposition, quadratic time-frequency distribution method (Wigner-Ville distribution), empirical mode decomposition, synchrosqueezing transform, and regularized spectral inversion method, etc. "High resolution" is the preferred characteristic of time-frequency analysis, however, it is a relative concept. Quantitative methods are needed to evaluate the time resolution and frequency resolution of different spectral decomposition techniques. There are many methods for measuring resolution, such as the full width at half maximum (FWHM), or wavelet decomposition ability. But currently, these evaluation methods are not applicable to quantitatively evaluating the resolution in the time-frequency domain.

[0004] The Heisenberg uncertainty principle and the Fourier similarity theorem tell us that for a given spectral analysis time window, the size and shape of the time window determine that the product of the time and frequency resolutions is a constant. Therefore, in the time-frequency domain, an increase in the resolution of one domain will necessarily lead to a corresponding decrease in the resolution of the other domain; it is impossible to obtain arbitrarily narrow time and frequency resolutions simultaneously. However, the Heisenberg uncertainty principle does not tell us that all spectral decomposition methods have the same uncertainty product. Theoretically, some methods can combine time domain and frequency domain resolutions better than others. Due to the existence of the Heisenberg uncertainty principle, to a certain extent, it provides the possibility for realizing the quantitative resolution analysis of time-frequency analysis methods.

[0005] Therefore, the present invention proposes an effective method for quantitatively evaluating the resolution of spectral decomposition technology. Summary of the Invention

[0006] To solve the above problems, based on the Heisenberg uncertainty principle, the present invention defines a quantitative evaluation method for time-frequency spectrum resolution analysis through an extension in terms of concepts. By calculating the quantified time-frequency domain resolution parameters and combining analysis means such as instantaneous frequency and bandwidth, the resolutions of commonly used spectral decomposition methods are studied and compared.

[0007] To achieve the above object, the present invention provides the following technical solutions.

[0008] An effective quantitative resolution evaluation method for spectral decomposition technology, comprising the following steps:

[0009] Obtain the time-frequency distribution map of the actual seismic signal;

[0010] Obtain the energy density G(t, f) at any point on the time-frequency profile according to the time-frequency distribution map (t represents time, f represents frequency);

[0011] According to the energy density G(t, f) at this point, obtain the spectral density probability distribution P(t, f) at this point, and calculate the spectral density probability distribution P t (t, f) along the time direction and the spectral density probability distribution P f (t, f) along the frequency direction;

[0012] According to P t (t, f) and P f (t, f), calculate the normalized standard deviation in the time domain and the normalized standard deviation in the frequency domain;

[0013] Obtain the resolution product according to the product of the normalized standard deviation in the time domain and the normalized standard deviation in the frequency domain; use the resolution product as a metric for quantitative resolution analysis of different time-frequency analysis methods.

[0014] Preferably, the calculation formulas for the spectral density probability distribution P t (t, f) along the time direction and the spectral density probability distribution P f (t, f) along the frequency direction are:

[0015]

[0016] In the formula, G(t, f) is the energy density at this point, f 0 is the starting frequency, f Nyq is the Nyquist frequency, t 0 is the starting time of the signal, t N is the ending time.

[0017] Preferably, the calculation formulas for the normalized standard deviation in the time domain and the normalized standard deviation in the frequency domain are:

[0018]

[0019] In the formula, μ t (t, f) is the normalized expected value in the time domain, and σ t (t, f) is the normalized standard deviation in the time domain, and μ f (t, f) is the normalized expected value in the frequency domain, and σ f (t, f) is the normalized standard deviation in the frequency domain.

[0020] Preferably, the resolution product follows the uncertainty principle, and the lower the resolution product value, the higher the time-frequency resolution.

[0021] Preferably, the steps for obtaining the time-frequency distribution map of the actual seismic signal include the following:

[0022] Obtain a synthetic signal formed by 8 equally spaced Ricker wavelets and 8 equally spaced Gaussian signals;

[0023] Perform time-frequency analysis on the synthetic signal by means of a regularization spectral inversion method, short-time Fourier transform, or continuous wavelet transform, and obtain the time-frequency distribution map at different times.

[0024] Advantages of the present invention:

[0025] The conclusion obtained by using the uncertainty product as a measure for quantitative resolution analysis in the time-frequency analysis method of the present invention is consistent with the result of quantitative interpretation of spectral decomposition of actual seismic data, which proves that this resolution evaluation method is feasible and can meet the needs of seismic data processing and quantitative interpretation. Description of the Drawings

[0026] Figure 1 is a flowchart of an effective method for evaluating the quantitative resolution of spectral decomposition technology of the present invention;

[0027] Figure 2 is the time-frequency distribution map obtained by performing time-frequency analysis on the synthetic signal by three time-frequency analysis methods in the embodiment of the present invention;

[0028] Figure 3 is the quantitative resolution analysis diagram of three time-frequency analysis methods in the embodiment of the present invention;

[0029] Figure 4 is the equal-frequency volume profile diagram of applying three time-frequency analysis algorithms in the embodiment of the present invention to the seismic profile of the wedge-shaped sediment in the Cooper Basin in southern Australia;

[0030] Figure 5 is the time-frequency distribution map of the seismic traces at two locations, CDP 430 and CDP 650, of the wedge-shaped sediment in the Cooper Basin by three time-frequency analysis methods in the embodiment of the present invention. Detailed Embodiments

[0031] In order to make the objectives, technical solutions and advantages of the present invention more clear and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0032] Referring to Figure 1 , an effective method for evaluating the quantitative resolution of spectral decomposition technology includes the following steps:

[0033] Step 1: Obtain the time-frequency distribution diagrams of different time-frequency analysis methods of the actual seismic signal;

[0034] Step 2: Obtain the energy density G(t,f) at any point on the time-frequency profile according to the time-frequency distribution diagram;

[0035] Step 3: According to the energy density G(t,f) at this point, obtain the spectral density probability distribution P(t,f) at this point, and calculate the spectral density probability distribution P t (t,f) along the time direction and the spectral density probability distribution P f (t,f) along the frequency direction;

[0036] The spectral density probability distribution P t (t,f) along the time direction and the spectral density probability distribution P f (t,f) along the frequency direction are calculated by the following formulas:

[0037]

[0038] In the formula, G(t,f) is the energy density at this point, f 0 is the starting frequency, f Nyq is the Nyquist frequency, t 0 is the starting time of the signal, t N is the ending time.

[0039] Step 4: Calculate the time-domain normalized standard deviation TSD and the frequency-domain normalized standard deviation FSD;

[0040] The calculation formulas for the time-domain normalized standard deviation TSD and the frequency-domain normalized standard deviation FSD are:

[0041]

[0042] In the formula, μ t (t,f) is the time-domain normalized expected value, σ t (t,f) is the time-domain normalized standard deviation, μ f (t,f) is the frequency-domain normalized expected value, σ f (t,f) is the frequency-domain normalized standard deviation.

[0043] Step 5: Obtain the resolution product based on the product of the time-domain normalized standard deviation TSD and the frequency-domain normalized standard deviation FSD; use the resolution product as the metric for the quantitative resolution analysis of different time-frequency analysis methods.

[0044] Example 1: Refer to Figures 2-3 , Figure 2 : (A) is a synthetic signal composed of 8 equally spaced Ricker wavelets (main frequencies ranging from 10 Hz to 80 Hz, with an increment of 10 Hz) and 8 equally spaced Gaussian signals (full width at half maximum, i.e., FWHM ranging from 80 ms to 10 ms, decreasing in width by 10 ms); (B) is the time-frequency distribution of the regularized spectral inversion method (RSI) within a 10-ms time window; (C) is the time-frequency distribution of RSI within a 20-ms time window; (D) is the time-frequency distribution of RSI within a 40-ms time window; (E) is the time-frequency distribution of RSI within an 80-ms time window; (F) is the time-frequency distribution of the continuous wavelet transform (CWT); (G) is the time-frequency distribution of the STFT within a 10-ms window; (H) is the time-frequency distribution of the STFT within a 20-ms window; (I) is the time-frequency distribution of the STFT within a 40-ms window; (J) is the time-frequency distribution of the STFT within an 80-ms window. In this example, the synthetic signal is subjected to time-frequency analysis by three different time-frequency analysis methods. Figure 3 : (A) is the time-domain standard deviation (TSD) corresponding to 10 Hz; (B) is the frequency-domain standard deviation (FSD) corresponding to 10 Hz; (C) is the resolution product corresponding to 10 Hz; (D) is the time-domain standard deviation (TSD) corresponding to 50 Hz; (E) is the frequency-domain standard deviation (FSD) corresponding to 50 Hz; (F) is the resolution product corresponding to 50 Hz; (G) is the time-domain standard deviation (TSD) corresponding to 100 Hz; (H) is the frequency-domain standard deviation (FSD) corresponding to 100 Hz; (I) is the resolution product corresponding to 100 Hz. Obtain a synthetic signal formed by 8 equally spaced Ricker wavelets (main frequencies ranging from 10 Hz to 80 Hz, with an increment of 10 Hz) and 8 equally spaced Gaussian signals (full width at half maximum, i.e., FWHM ranging from 80 ms to 10 ms, decreasing in width by 10 ms). Perform time-frequency analysis on the synthetic signal by the regularized spectral inversion (RSI) method, the short-time Fourier transform (STFT), or the continuous wavelet transform (CWT) to obtain the time-frequency distributions at different times. Calculate the time-domain standard deviation TSD and the frequency-domain standard deviation FSD at different frequencies corresponding to the three time-frequency analysis methods for the central moments of each Ricker wavelet and Gaussian signal; calculate the corresponding resolution products at different frequencies for the central moments of each Ricker wavelet and Gaussian signal based on the Heisenberg uncertainty relation; conduct quantitative resolution analysis on the three time-frequency analysis methods to obtain an evaluation method and draw the following conclusions:

[0045] The Regularized Spectral Inversion method (RSI) has the best frequency resolution and does not depend on the selected time window length. Compared with the STFT frequency resolution, the frequency resolution of RSI has less dependence on the window length. For long time windows, STFT can sacrifice time resolution to obtain better frequency resolution than RSI. At high frequencies, the resolution of the Continuous Wavelet Transform (CWT) is close to that of RSI. RSI has the highest resolution at all frequencies and all time window lengths, except for low frequencies (10 Hz) and short windows (20 ms).

[0046] Example 2: Refer to Figure 4 , Figure 4 is the seismic profile (waveform part) of the wedge-shaped sediment body, and the isofrequency volume profiles at 10 Hz (first row), 40 Hz (second row), and 70 Hz (third row), the RSI isofrequency volume profile using a 40 ms Hanning window (first column), the STFT isofrequency volume profile using a 40 ms Hanning window (second column), and the isofrequency volume profile of CWT (third column). In this example, different time-frequency analysis algorithms are applied to the seismic profile of the wedge-shaped sediments in the Cooper Basin in southern Australia, the isofrequency volume profiles are calculated, and combined with time-frequency seismic attribute analyses such as peak frequency and bandwidth, qualitative and quantitative resolution comparisons are made. The following conclusions are drawn:

[0047] In the sediments, the reflection layers in the wedge-shaped sediment are laterally squeezed and interrupted by faults and gradually show lateral pinch-out. The irregular discontinuities of the reflection layers and the possible presence of many closely spaced faults make the spectral variation more complex. In the co-frequency volume profile at low frequencies (10 Hz), the Regularized Inversion Spectral Decomposition method (RSI) separates the closely spaced reflection layers more clearly in time compared with the Short-Time Fourier Transform (STFT) and the Continuous Wavelet Transform (CWT). At high frequencies, the time resolutions of various methods are similar.

[0048] Example 3, refer to Figure 5 , Figure 5 Perform time-frequency analysis on the seismic traces of CDP 430 and CDP 650 in the seismic profile of the wedge-shaped sediment body using RSI and STFT with a 40 ms Hanning window, and the Continuous Wavelet Transform CWT. In this example, time-frequency analysis is performed on the seismic traces of CDP 430 and CDP 650 in the wedge-shaped sediments of the Cooper Basin by using the Continuous Wavelet Transform (CWT), the Regularized Inversion Spectral Decomposition method (RSI) with a 40 ms window, and the Short-Time Fourier Transform (STFT). The following conclusions can be drawn:

[0049] At low frequencies, due to the interference between wavelets, the time-frequency distribution of CWT produces vertical stripes, and STFT has spectral leakage. RSI solves these problems and can resolve the near-distance reflection layers at low frequencies. Since low-cut filtering is applied during the data processing, there is no energy at low frequencies on the time-frequency spectra of RSI or CWT, while the time-frequency spectrum of STFT shows low-frequency energy caused by the time-window effect.

[0050] The conclusions drawn from the above three embodiments prove that it is feasible to use the product of the uncertainty principle as an evaluation method for the quantitative resolution of spectral decomposition and it can meet the needs of actual exploration.

[0051] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. An effective method for evaluating the quantitative resolution of spectral decomposition technology, characterized in that, it includes the following steps: Obtain the time-frequency distribution map of the actual seismic signal; Obtain the energy density G(t,f) at any point of the time-frequency profile according to the time-frequency distribution map; wherein, t represents time and f represents frequency; According to the energy density G(t, f) at this point, obtain the spectral density probability distribution P(t, f) at this point, and calculate the spectral density probability distribution P t (t, f) along the time direction and the spectral density probability distribution P f (t, f); Spectral density probability distribution P according to the time direction t (t, f) and the spectral density probability distribution P in the frequency direction f (t, f) to calculate the normalized standard deviation in the time domain and the normalized standard deviation in the frequency domain; Obtain the resolution product according to the product of the normalized standard deviation in the time domain and the normalized standard deviation in the frequency domain; use the resolution product as the measurement standard for the quantitative resolution analysis of different time-frequency analysis methods; The spectral density probability distribution P t (t, f) along the time direction and the spectral density probability distribution P f (t, f) along the frequency direction are calculated by the following formula: where G(t,f) is the energy density at this point, and f 0 is the starting frequency, and f Nyq is the Nyquist frequency t 0 is the signal start time, t N is the end time; The calculation formulas for the normalized standard deviation in the time domain and the normalized standard deviation in the frequency domain are: where, μ t (t, f) is the normalized expected value in the time domain, σ t (t, f) is the normalized standard deviation in the time domain, μ f (t, f) is the normalized expected value in the frequency domain, σ f (t, f) is the normalized standard deviation in the frequency domain.

2. The effective method for evaluating the quantitative resolution of spectral decomposition technology according to claim 1, characterized in that, the resolution product follows the uncertainty principle, and the lower the resolution product value, the higher the time-frequency resolution.

3. The effective method for evaluating the quantitative resolution of spectral decomposition technology according to claim 1, characterized in that, the obtaining of the time-frequency distribution map of the actual seismic signal includes the following steps: Obtain a synthetic signal formed by 8 equally spaced Ricker wavelets and 8 equally spaced Gaussian signals; Perform time-frequency analysis on the synthetic signal through the regularized spectral inversion method, short-time Fourier transform or continuous wavelet transform and obtain the time-frequency distribution map at different times.

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