Newton time redistribution multiple synchronous extrusion time-frequency analysis method

Abstract

The invention relates to the technical field of thin reservoir identification, in particular to a Newton time redistribution multiple synchronous extrusion transform time-frequency analysis method, which comprises the following implementation steps of: 1, inputting a seismic signal to be analyzed to carry out short-time Fourier transform to obtain a time-frequency result of the signal; step 2, calculating a group delay estimation formula of the signal according to the obtained short-time Fourier result of the signal; 3, calculating to obtain signal Newton group delay estimation based on short-time Fourier transform properties and a Newton algorithm; and step 4, defining an extrusion operator according to an extrusion principle and calculating to obtain Newton time multiple extrusion transformation of the seismic data, and obtaining a single-frequency profile according to single-frequency feature extraction. According to the method, more accurate time positioning is realized, and when the method is used for thin reservoir identification, a more stable characterization effect of Newton time multiple extrusion transformation in the aspect of fine geological structure characterization is reflected.

Description

Technical Field

[0001] The invention belongs to the field of oil and gas geophysical signal processing, and particularly relates to a Newton time redistribution multiple synchronous extrusion transformation time-frequency analysis method. Background Art

[0002] China's tight gas is widely distributed in Ordos, Sichuan, Tarim, Bohai Bay, Songliao and Junggar basins, with rich resources. It is estimated that my country's tight gas production will reach about 80 billion cubic meters in 2025, and will enter the peak of production growth around 2030, with tight gas production reaching about 100 billion cubic meters. Tight sandstone reservoirs have become one of the leading sources of tight gas, with broad development prospects. However, due to the poor quality of tight sandstone reservoirs, effective development still faces many challenges.

[0003] Time-frequency analysis studies the time-varying law of the spectrum of non-stationary seismic signals. This method decomposes the one-dimensional time signal into the time-frequency domain, which can effectively describe the seismic signal in detail. The time-redistribution synchronous squeezing transform (TSST) greatly improves the time positioning capability and is widely used in the analysis of seismic sequences. It can more clearly highlight the geological structure characteristics. However, there is a phenomenon of energy non-concentration in the actual application effect. This is because the group delay estimation formula of TSST is directly derived from the pulse-like signal. In the "squeezing" process, the time redistribution point will be wrong, resulting in its insufficient ability to describe the stratigraphic structure. Summary of the invention

[0004] The purpose of the present invention is to address the above-mentioned problems in the prior art and propose a Newton time redistribution multiple synchronous extrusion transformation time-frequency analysis method. The method comprises the following steps:

[0005] Step 1: Input the seismic signal to be analyzed and perform short-time Fourier transform to obtain the time-frequency result of the signal;

[0006] Step 2: Calculate the group delay estimation formula of the signal according to the short-time Fourier result of the obtained signal;

[0007] Step 3: Calculate the Newton group delay estimation formula of the signal based on the short-time Fourier transform property and Newton algorithm;

[0008] Step 4: Define the squeezing operator according to the squeezing principle and calculate the Newton time multiple squeezing transform of the seismic data, and obtain the single-frequency profile according to the feature extraction of the single frequency.

[0009] Furthermore, in step 1, the formation signal x(t) to be analyzed is input, and the obtained short-time Fourier transform G(t,ω) is:

[0010]

[0011] in is the imaginary unit of the complex number, ω is the frequency (ω≠0), t is the time, τ is the movement of the center position of the window during the movement process, controls the movement of the window center in the t direction, and g(t) is the Gaussian window function, which is in the form of:

[0012]

[0013] Where δ represents the standard deviation of the Gaussian window in the t direction.

[0014] Further, in step 2, the group delay estimation formula of the signal is calculated based on the short-time Fourier result of the obtained signal: The formula is:

[0015]

[0016] Among them, Re(·) and They represent the real part of a complex number and the first-order partial derivative of (·) with respect to ω.

[0017] Furthermore, in step 3, the Newton group delay estimation formula of the signal is obtained based on the short-time Fourier transform and the properties of the Newton iterative algorithm: Right now:

[0018]

[0019] in It means to find the first-order partial derivative of (·) with respect to t.

[0020] Further, in step 4, a squeezing operator is defined according to the squeezing principle and the Newton time multiple squeezing transform of the seismic data is calculated, and a single frequency profile is obtained according to the feature extraction of the single frequency, which includes the following steps:

[0021] a. According to the squeezing principle, the squeezing operator NTSTO is defined as:

[0022]

[0023] where δ(·) represents the Dirac function

[0024] b. The Newton time redistribution multiple synchronous squeezing transform NTMSST(t,ω) of seismic data is calculated based on the multiple squeezing principle, that is:

[0025]

[0026] c. The process of iteratively applying multiple squeezing operations to NTSST(t,ω) according to step a above to construct the Newton time redistribution multiple synchronous squeezing transform NTMSST(t,ω) is as follows:

[0027]

[0028] NTSST [1] (t,ω) is the NTSST(t,ω) of formula (6), M is the number of iterations, and NTSST is obtained by formula (7) [M] (t,ω) can be written as:

[0029]

[0030]

[0031] Here we define the Newton time redistribution multiple synchronous squeezing transformation NTMSST(t,ω) as:

[0032]

[0033] d. Perform feature extraction of the calculation result (9) obtained in step c above at a frequency of ω0 to obtain the single-frequency profile NTMSST(t,ω0).

[0034] Compared with the prior art, the present invention has the following beneficial effects:

[0035] The present invention proposes a Newton time redistribution multiple synchronous extrusion transform time-frequency analysis method. The method is based on the time redistribution synchronous extraction transform, further improves the group delay estimation formula (GD) on the short-time Fourier time-frequency transform result, and proposes a Newton group delay estimation formula (NGD) calculated based on the time-frequency result. The method proposed in the present invention is more accurate in time positioning when depicting the internal structure of the formation. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] 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:

[0037] Figure 1 The process of the present invention Figure 1 A flow chart of a Newton time redistribution multiple synchronous squeezing transformation time-frequency analysis method;

[0038] Figure 2 This is a seismic thin-layer profile of a tight sandstone gas field in western Sichuan, China;

[0039] Figure 3 (a) and (b) are single-frequency profiles with a frequency of 30 Hz extracted after processing the tight sandstone gas field using the time redistribution synchronous compression transformation and the Newton time redistribution multiple synchronous compression transformation, respectively.

[0040] Figure 4(a) and (b) are single-frequency profiles with a frequency of 48 Hz extracted after processing the tight sandstone gas field using the time redistribution synchronous compression transform and the Newton time redistribution multiple synchronous compression transform, respectively. DETAILED DESCRIPTION

[0041] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0042] Example 1: See Figure 1 , showing a process of some embodiments of a Newton time redistribution multiple synchronous extrusion transformation time-frequency analysis method, including the following steps:

[0043] Step 1: Input the formation signal x(t) to be analyzed, and the obtained short-time Fourier transform G(t,ω) is:

[0044]

[0045] in is the imaginary unit of the complex number, ω is the frequency (ω≠0), t is the time, τ is the movement of the center position of the window during the movement process, controls the movement of the window center in the t direction, and g(t) is the Gaussian window function, which is in the form of:

[0046]

[0047] Where δ represents the standard deviation of the Gaussian window in the t direction.

[0048] Step 2: Calculate the group delay estimation formula of the signal based on the short-time Fourier result of the signal The formula is:

[0049]

[0050] Among them, Re(·) and They represent the real part of a complex number and the first-order partial derivative of (·) with respect to ω.

[0051] Step 3: Obtain the Newton group delay estimation formula of the signal based on the short-time Fourier transform and the properties of the Newton iterative algorithm Right now:

[0052]

[0053] in It means to find the first-order partial derivative of (·) with respect to t.

[0054] Step 4: Define the squeezing operator according to the squeezing principle and calculate the Newton time multiple squeezing transform of the seismic data, and extract the single frequency feature to obtain the single frequency profile, including the following steps:

[0055] a. According to the squeezing principle, the squeezing operator NTSTO is defined as:

[0056]

[0057] where δ(·) represents the Dirac function.

[0058] b. The Newton time redistribution multiple synchronous squeezing transform NTMSST(t,ω) of seismic data is calculated based on the multiple squeezing principle, that is:

[0059]

[0060] c. The process of iteratively applying multiple squeezing operations to NTSST(t,ω) according to step a above to construct the Newton time redistribution multiple synchronous squeezing transform NTMSST(t,ω) is as follows:

[0061]

[0062] NTSST [1] (t,ω) is the NTSST(t,ω) of formula (6), M is the number of iterations, and NTSST is obtained by formula (7) [M] (t,ω) can be written as:

[0063]

[0064]

[0065] Here we define the Newton time redistribution multiple synchronous squeezing transformation NTMSST(t,ω) as:

[0066]

[0067] d. Perform feature extraction of the calculation result (9) obtained in step c above at a frequency of ω0 to obtain the single-frequency profile NTMSST(t,ω0).

[0068] Embodiment 2:

[0069] The time redistribution synchronous compression transform and Newton time redistribution multiple synchronous compression transform (M=2) are used, and the same window length and sampling points are set to 1100 according to the signal length. The single-frequency profiles with a frequency of 30 Hz extracted after processing the tight sandstone gas field are obtained respectively. Figure 3 (a), (b). Similarly, after extraction and processing, the single-frequency profile with a frequency of 48 Hz is obtained Figure 4 (a), (b).

[0070] It can be seen that although the seismic profiles processed by the time redistribution squeezing algorithm at 30 Hz and 48 Hz have a certain degree of hierarchy, the resolution is very low. However, compared with the single-frequency profiles of 30 Hz or 48 Hz, the seismic profiles processed by the method of the present invention have better hierarchy, retain the continuity of seismic data, accurate time positioning, obvious geological stratification, rich texture details, and more reasonable results.

Claims

1. A Newton time redistribution multiple synchronous extrusion transformation time-frequency analysis method, characterized in that: The following steps are involved: Step 1: Input the seismic signal to be analyzed and perform short-time Fourier transform x(t) to obtain the time-frequency result G(t,ω) of the signal, that is: in is the imaginary unit of the complex number, ω is the frequency (ω≠0), t is the time, and τ is the movement of the window center during the movement process, which controls the movement of the window center in the t direction; Step 2: Calculate the group delay estimation formula of the signal based on the short-time Fourier result of the signal Right now: Among them, Re(·) and They represent the real part of a complex number and the first-order partial derivative of (·) with respect to ω respectively; Step 3: Based on the short-time Fourier transform properties and the Newton algorithm, the Newton group delay estimation formula of the signal is calculated Right now: in It means to find the first-order partial derivative of (·) with respect to t; Step 4: Define the squeezing operator according to the squeezing principle and calculate the Newton time multiple squeezing transform of the seismic data, and obtain the single-frequency profile according to the feature extraction of the single frequency.

2. The method according to claim 1, characterized in that In step 1, g(t) is a Gaussian window function, which is in the form of: Where δ represents the standard deviation of the Gaussian window in the t direction.

3. The method according to claim 1, characterized in that: In step 4, a squeezing operator is defined according to the squeezing principle and the Newton time redistribution multiple squeezing transformation of the seismic data is calculated. According to the feature extraction of a single frequency, a single frequency profile is obtained, which includes the following steps: a. According to the squeezing principle, the squeezing operator NTSTO is defined as: where δ(·) represents the Dirac function; b. The Newton time redistribution multiple synchronous squeezing transform NTMSST(t,ω) of seismic data is calculated based on the multiple squeezing principle, that is: c. The process of iteratively applying multiple squeezing operations to NTSST(t,ω) according to step a above to construct the Newton time redistribution multiple synchronous squeezing transform NTMSST(t,ω) is as follows: NTSST [1] (t,ω) is the NTSST(t,ω) of formula (6), M is the number of iterations, and NTSST is obtained by formula (7) [M] (t,ω) can be written as: Here we define the Newton time redistribution multiple synchronous squeezing transformation NTMSST(t,ω) as: d. Perform feature extraction of the calculation result (9) obtained in step c above at a frequency of ω0 to obtain the single-frequency profile NTMSST(t,ω0).

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