Three-dimensional synchronous extraction linear chirplet transformation thin reservoir boundary depicting method

Abstract

The invention discloses a three-dimensional synchronous extraction linear chirplet transformation method which is used for thin reservoir boundary depiction. Comprising the steps of inputting to-be-analyzed seismic data; setting parameters; deriving a partial derivative of frequency domain linear chirplet transform (LCT) of given data to define a group delay (GD) equation and a slope equation of a GD trajectory; extracting a time-frequency coefficient which meets a formula, and obtaining three-dimensional synchronous extraction linear chirplet transform (TDSELCT); integrating the result obtained by the TDSELCT along the slope direction of the GD track to obtain a two-dimensional time-frequency result; performing time-frequency transformation on the seismic data according to the method to obtain a final time-frequency result; and extracting a time sequence corresponding to a constant frequency from different seismic channel time-frequency spectra obtained by TDSELCT, synthesizing to obtain a profile map to represent reservoir features, and depicting a thin reservoir boundary.

Description

Technical Field

[0001] The present invention relates to the fields of seismic signal processing and seismic reservoir identification, and in particular to a thin reservoir boundary characterization method based on three-dimensional synchronous extraction linear chirplet transform (TDSELCT). Background Art

[0002] Time-frequency analysis plays a crucial role in the processing of nonstationary signals. Traditional time-frequency transform methods, such as the short-time Fourier transform (STFT), continuous wavelet transform, S transform (ST), and W transform, are constrained by the Heisenberg uncertainty principle and require a trade-off between frequency and time resolution. This limitation results in suboptimal time-frequency representations for seismic signal analysis. Compared with traditional methods, high-precision time-frequency post-processing methods, including empirical mode decomposition (EMD), synchronized squeezing (SST), and synchronized extraction (SET), significantly improve time-frequency resolution. When applied to real seismic data using frequency decomposition, these methods achieve relatively high signal characterization accuracy, enabling reservoir prediction and identification to a certain extent. However, when processing real seismic data from thin reservoirs, especially for boundary characterization, methods based on time-dependent squeezing or extraction, such as the time-shuffled synchronized squeezing transform (TSST) and the transient extraction transform (TET), are prone to the generation of non-time-frequency response points, resulting in an inability to accurately describe boundary features.

[0003] The chirplet transform (CT) is another parametric time-frequency analysis method. CT can achieve excellent analytical results for linear frequency modulated signals. However, when the instantaneous frequency of the signal to be analyzed is a nonlinear function, such as a strong frequency modulated signal, CT cannot accurately estimate the instantaneous frequency of such signals. The linear chirplet transform (LCT) provides a new approach to capturing the temporal variation of frequency. However, these methods fail to produce satisfactory time-frequency results when the pulse signals are too close together, which in turn results in poor characterization of thin reservoir boundaries. Therefore, it is necessary to develop a new time-frequency transform method that can effectively characterize thin reservoir boundaries. Summary of the Invention

[0004] The purpose of this invention is to propose a new time-frequency analysis method - three-dimensional synchronous extraction linear chirplet transform, which is used to characterize thin reservoir boundaries to solve the problem that existing methods such as TSST and TET cannot clearly characterize thin reservoirs when processing seismic signals.

[0005] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0006] Step 1: Input the seismic signal to be analyzed ;

[0007] Step 2: Set parameters according to signal characteristics, including window length and threshold , constant term and ;

[0008] Step 3: Define the group delay (GD) equation by deriving the partial derivatives of the LCT in the frequency domain given the signal and the slope equation of the GD trajectory , and then calculate and ;

[0009] Step 4: Extract Satisfaction and The time-frequency coefficients are used to obtain the three-dimensional synchronous extraction linear chirplet transformation value;

[0010] Step 5: Integrate the 3D synchronously extracted linear chirplet transform value along the slope direction of the GD trajectory to obtain the TDSELCT 2D time-frequency result;

[0011] Step 6: Perform time-frequency transformation on the seismic signal according to the above method to obtain the final time-frequency result;

[0012] Step 7: Extract the time series corresponding to the constant frequency from the time-frequency spectra of different seismic traces obtained by TDSELCT, and then synthesize them to obtain a cross-section to characterize the reservoir characteristics and depict the thin reservoir boundary.

[0013] Preferably, in step 3, the frequency domain LCT is first derived, and:

[0014]

[0015] in, represents the result of LCT in frequency domain, is the time variable, is the frequency variable, is the slope variable of the GD trajectory, It's a signal The Fourier transform of is the window function The Fourier transform of is an imaginary unit, Represents the frequency shift factor. The frequency domain LCT and the time domain LCT have a certain corresponding relationship. Corresponding to the chirp rate in the time domain LCT, and their product is 1;

[0016] Then define the GD equation by taking the partial derivative of LCT in the frequency domain ( ) and the slope equation of the GD trajectory ( ):

[0017]

[0018]

[0019] in, represents the real part, Indicates taking the imaginary part, Indicates the partial derivative of the time variable. In the joint equation This is to strengthen the constraints and provide a more accurate GD estimate. In fact, the GD equation Can extract satisfaction The time-frequency coefficients ( is the GD of the signal), and the slope equation of the GD trajectory is Can extract satisfaction The time-frequency coefficients ( is the slope of the GD trajectory), and and satisfy .in, Indicates the signal phase with respect to The first derivative of Indicates the signal phase with respect to The second derivative of Express about The first derivative of .

[0020] Preferably, the combined equation in step 4 is and , extract the time-frequency coefficients that simultaneously satisfy formula (4):

[0021]

[0022]

[0023] in, represents the exponential function, Represents the three-dimensional result of the three-dimensional synchronous extraction of linear chirplet transform, is the Dirac function. The significance of formula (4) is to eliminate the negative impact of the slope equation of the GD trajectory on the extraction of time-frequency coefficients, so that the final time-frequency representation can more accurately reflect the GD trajectory and no non-time-frequency response points will be generated when processing seismic data.

[0024] Preferably, step 5 integrates the three-dimensional synchronously extracted linear chirplet transformation value along the slope direction of the GD trajectory to obtain a two-dimensional time-frequency result:

[0025]

[0026] in, represents the 2D time-frequency representation of the 3D synchronously extracted linear chirplet transform, Represents a variable The purpose of integrating to obtain a two-dimensional time-frequency representation is to facilitate comparison with other two-dimensional time-frequency analysis methods and to better demonstrate the results of processing seismic data.

[0027] The present invention provides a thin reservoir boundary characterization method based on three-dimensional synchronous extraction of linear chirplet transformation, which has the following beneficial effects:

[0028] The three-dimensional synchronous extraction linear chirplet transform of the present invention can accurately extract the time-frequency coefficients on the GD trajectory, obtain a more concentrated and clearer time-frequency representation than TSST and TET, and effectively improve the resolution of the time-frequency analysis of seismic signals; the characterization results of cross signals at the cross position are better; when applied to actual seismic data, it can greatly improve the positioning ability of seismic signals in the time direction and effectively reveal the characteristics of thin reservoir boundaries. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 Flowchart of the present invention;

[0030] Figure 2 This is a seismic cross-section, where the rectangular box represents stacked multiple thin reservoirs;

[0031] Figure 3 for Figure 2 20 Hz frequency slices of 2D seismic profiles;

[0032] (a) Short-time Fourier transform (STFT) results; (b) Time-reassigned synchronized squeezing transform (TSST) results; (c) Time-reassigned multiple synchronized squeezing transform (TMSST) results; (d) Second-order time-reassigned synchronized squeezing transform (TSST2) results; (e) Time-reassigned synchronized extraction transform (TET) results; (f) Three-dimensional synchronized extraction linear chirplet transform (TDSELCT) results. DETAILED DESCRIPTION

[0033] The present invention will be further described below with reference to the accompanying drawings.

[0034] See also Figure 2-Figure 3 The performance of this method was tested using actual field data. Different time-frequency analysis methods were used to analyze seismic data from a certain region. The two-dimensional seismic data contained 360 seismic traces, each with 501 sampling points and a sampling interval of 1 ms. The specific implementation steps are as follows:

[0035] 1) Input the earthquake data to be analyzed and obtain the following Figure 2 The original seismic profile is shown;

[0036] 2) Set various parameters, including window length, threshold , constant term and ; The window length determines the quality of the time-frequency representation produced by the proposed method to a certain extent. The unified window length value of the present invention is 500; Threshold , constant term and Then the influence of the slope equation of the GD trajectory can be eliminated, which are 0.9, 20, and 30 respectively;

[0037] 3) For the input seismic signal, calculate the partial derivative of its LCT in the frequency domain to define the GD equation and the slope equation of the GD trajectory;

[0038] First derive the frequency domain LCT, we have:

[0039]

[0040] in, represents the result of LCT in frequency domain, is the time variable, is the frequency variable, is the slope variable of the GD trajectory, It's a signal The Fourier transform of is the window function The Fourier transform of is an imaginary unit, Represents the frequency shift factor.

[0041] Then define the GD equation by taking the partial derivative of LCT in the frequency domain ( ) and the slope equation of the GD trajectory ( ):

[0042]

[0043]

[0044] in, represents the real part, Indicates taking the imaginary part, It represents the partial derivative with respect to the time variable.

[0045] 4) Joint equation and , extract the time-frequency coefficients that simultaneously satisfy formula (10):

[0046]

[0047]

[0048] in, represents the exponential function, Represents the three-dimensional result of the three-dimensional synchronous extraction of linear chirplet transform, is the Dirac function.

[0049] 5) Integrate the 3D synchronously extracted linear chirplet transform values ​​along the slope direction of the GD trajectory to obtain the 2D time-frequency results:

[0050]

[0051] in, represents the two-dimensional time-frequency representation of the three-dimensional synchronously extracted linear chirplet transform, Represents a variable Perform integration.

[0052] 6) Perform time-frequency transformation on the seismic signal according to the above method to obtain the final time-frequency result;

[0053] 7) Extract the time series corresponding to the constant frequency from the time-frequency spectra of different seismic traces obtained by TDSELCT, and then synthesize them to obtain a cross-section to characterize the reservoir characteristics and depict the thin reservoir boundary.

[0054] Through Figure 3 A comparative analysis of (a) (b) (c) (d) (e) (f) revealed that:

[0055] (a) The time-frequency representation produced by the short-time Fourier transform (SFT) of the traditional time-frequency analysis method has a rough time-frequency response, and the time-frequency energy is roughly distributed around the reflection interface, which is not conducive to accurately characterizing the thin reservoir boundary.

[0056] (b), (c), and (d) TSST, TMSST, and TSST2 using compressed time-frequency coefficients. Compared with the traditional time-frequency analysis method STFT, the time-frequency results obtained by TSST, TMSST, and TSST2 are more concentrated and sparse. It can be seen that the sparse effect of TMSST and TSST2 is better than that of TSST. However, both methods exhibit time-frequency energy dispersion around the reflection interface.

[0057] (e) Compared with TSST, TMSST, and TSST2, TET uses an extraction operator to sharpen the STFT time-frequency spectrum. The time-frequency energy is further concentrated near the reflection interface, which can better describe the position of the reflection interface. However, the time-frequency energy is incorrectly distributed between the two reflection interfaces, which can easily cause confusion.

[0058] (f) The time-frequency energy distribution of TDSELCT is the most sparse and clear. This is because TDSELCT can accurately estimate the GD of seismic signals. Combined with the test results of theoretical signals, this method can also accurately locate close-range pulse signals. Therefore, it can be concluded that the proposed TDSELCT has more advantages in characterizing the boundary characteristics of thin reservoirs.

[0059] The above analysis shows that in the characterization of thin reservoir boundaries, TDSELCT has clearer and sparser time-frequency representation results, higher time resolution, more advantages in revealing the characteristics of thin reservoir boundaries, and has more potential than other methods in actual seismic data interpretation.

[0060] Although the specific embodiments of the invention are described in detail in conjunction with the accompanying drawings, this should not be construed as limiting the scope of protection of this patent. Within the scope described by the claims, various modifications and variations that can be made by those skilled in the art without creative work still fall within the scope of protection of this patent.

Claims

1. A thin reservoir boundary characterization method based on three-dimensional synchronous extraction of linear chirplet transform, characterized by: The following steps are involved: Step 1: Input the seismic signal to be analyzed ; Step 2: Set parameters; Step 3: Define the GD equation by deriving the partial derivatives of LCT in the frequency domain given the signal and the slope equation of the GD trajectory , and then calculate and ; Step 4: Extract Satisfaction and The time-frequency coefficients are used to obtain the three-dimensional synchronous extraction linear chirplet transform value ; Step 5: Integrate the 3D synchronously extracted linear chirplet transform value along the slope direction of the GD trajectory to obtain the 2D time-frequency result ; Step 6: Perform time-frequency transformation on the seismic signal according to the above method to obtain the final time-frequency result; Step 7: Extract the time series corresponding to the constant frequency from the time-frequency spectra of different seismic traces obtained by TDSELCT, and then synthesize them to obtain a cross-section to characterize the reservoir characteristics and depict the thin reservoir boundary.

2. The thin reservoir boundary characterization method based on three-dimensional synchronous extraction linear chirplet transformation according to claim 1 is characterized in that: In step 2, various parameters are set, including window length, threshold , constant term and , making the time-frequency representation more accurate.

3. The thin reservoir boundary characterization method based on three-dimensional synchronous extraction linear chirplet transformation according to claim 1 is characterized in that: In step 3, the partial derivatives of the frequency domain LCT are calculated to define the GD equation ( ) and the slope equation of the GD trajectory ( ),have: ； ； ； in, represents the result of LCT in frequency domain, is the time variable, is the frequency variable, is the slope variable of the GD trajectory, It's a signal The Fourier transform of is the window function The Fourier transform of is an imaginary unit, represents the frequency shift factor, represents the real part, Indicates taking the imaginary part, It means to find the partial derivative of the time variable and use the slope equation of the GD trajectory to further constrain the GD equation.

4. The thin reservoir boundary characterization method based on three-dimensional synchronous extraction linear chirplet transformation according to claim 3 is characterized in that: Joint equation and , extract the time-frequency coefficients that simultaneously satisfy formula (4): ； ； in, represents the exponential function, Represents the three-dimensional result of the three-dimensional synchronous extraction of linear chirplet transform, is the Dirac function, and the time-frequency coefficients on the accurate GD trajectory are extracted in three-dimensional space.

5. The thin reservoir boundary characterization method based on three-dimensional synchronous extraction linear chirplet transformation according to claim 1 is characterized in that: In step 5, the three-dimensional synchronous extraction linear chirplet transformation value is integrated along the slope direction of the GD trajectory to obtain a two-dimensional time-frequency result: ； in, represents the 2D time-frequency representation of the 3D synchronously extracted linear chirplet transform, Represents a variable By performing integration, the three-dimensional time-frequency representation is converted to two dimensions, which facilitates direct comparison with other time-frequency analysis methods.

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