Transient matching extrusion transformation reservoir boundary description method

Abstract

The invention discloses a transient matching extrusion transformation method which is used for depicting a reservoir boundary. Comprising the steps of inputting to-be-analyzed seismic data; calculating group delay (GD) and a group delay band center for the short-time Fourier transform time-frequency domain of the given data; calculating the boundary of a group delay band, and matching all GD estimators in the group delay band with the GD at the center of the GD band to obtain a matched GD estimator; extruding the time-frequency coefficient to obtain transient matching extrusion transformation (TMST); performing time-frequency transformation on the seismic data according to the TMST to obtain a time-frequency result; and extracting a time sequence corresponding to a constant frequency from different seismic channel time-frequency spectra obtained by TMST, synthesizing the time sequence to obtain a profile map to characterize reservoir features, and positioning the position of a reflection interface. The method integrates the advantages of time redistribution synchronous extrusion transformation (TSST) and transient extraction transformation (TET), and has both strong sharpening performance and reconstruction performance.

Description

Technical Field

[0001] The invention relates to the field of seismic signal processing and seismic reservoir identification, and in particular to a reservoir boundary characterization method based on transient matched squeeze transform (TMST). Background Art

[0002] Time-frequency analysis (TFA) plays a vital role in processing non-stationary signals such as seismic signals. Traditional time-frequency transforms such as short-time Fourier transform (STFT), continuous wavelet transform, S transform (ST) and W transform are limited by the Heisenberg uncertainty principle and require a trade-off between frequency and time resolution. Their time-frequency representation (TFR) results are not ideal for analyzing seismic signals. To overcome the shortcomings of traditional TFA methods, many time-frequency post-processing methods have been developed. Among them, the redistribution method (RM) provides a more concentrated TFR result by redistributing the time-frequency coefficients in the STFT domain to the centroid of the signal energy distribution, but RM loses the signal reconstruction ability of the TFA method. The synchronous squeezing transform (SST) only redistributes the time-frequency coefficients along the frequency direction, which sharpens the original spectrum while retaining the reconstruction properties. The synchronous extraction transform (SET) obtains sparse TFR results by extracting the time-frequency coefficients at the fixed points of the instantaneous frequency (IF) estimator. However, the sharpness of SST and SET depends on the accuracy of the IF estimator. For signals with strong frequency variation, it is difficult for the basic IF estimator to accurately estimate the IF of the signal.

[0003] For pulse signals, many scholars have improved the time resolution of TFR results by redistributing time-frequency coefficients in the time domain, which are mainly divided into two categories: SST (TSST) method based on time redistribution and transient extraction transform (TET) method. TSST method can reconstruct the original signal, but its sharpening effect is not good; TET method has strong sharpening performance, but due to the loss of a large number of time-frequency coefficients, the signal reconstruction effect is poor. Therefore, it is necessary to develop a new time-frequency transform method with both strong sharpening performance and reconstruction performance. Summary of the invention

[0004] The purpose of the present invention is to propose a new time-frequency transformation method, the transient matched squeeze transform (TMST), for seismic reservoir boundary characterization to solve the problem that the existing TSST and TET methods cannot take into account both sharpening and reconstruction performance 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 x(t) to be analyzed;

[0007] Step 2: Define the GD estimator by calculating the partial derivatives of the STFT of a given signal Then calculate the center of the group delay band;

[0008] Step 3: Determine the left and right boundaries of the group delay band (GDB) and And all GD estimators in GDB are matched with the GD estimator at the center of the GD band to obtain the matched GD (MGD) estimator

[0009] Step 4: Squeeze the time-frequency coefficients to obtain the transient matched squeeze transform (TMST) value Tm x (t,ω);

[0010] Step 5: Perform time-frequency transformation on the seismic signal x(t) according to TMST to obtain the time-frequency result;

[0011] Step 6: Extract the time series corresponding to the constant frequency from the time-frequency spectra of different seismic traces obtained by TMST, and then synthesize them to obtain a profile to characterize the reservoir characteristics and locate the position of the reflection interface.

[0012] Preferably, the partial derivative of its STFT is calculated in step 2 to define the GD estimator, which is:

[0013]

[0014] in, represents the group delay estimator in the STFT time-frequency domain, represents the real part, j is the imaginary unit, represents the partial derivative of the variable ω, S x (t,ω) represents the STFT of the signal x(t), where t is the time variable and ω is the frequency variable.

[0015] Then calculate the center of the group delay band:

[0016]

[0017] Among them, t c represents the center of the group delay band, and st represents limited by.

[0018] Preferably, the left and right boundaries of the group delay band (GDB) in step 3 are and

[0019]

[0020] in, represents the left edge of the group delay band, represents the partial derivative of the time variable, Indicates that in the GD estimator, time is t c .

[0021] All GD estimators in GDB are matched with the GD estimator at the center of the GD band to obtain the matched GD (MGD) estimator:

[0022]

[0023] in, Denotes the matched GD (MGD) estimator.

[0024] Preferably, step 4 obtains a transient matched squeeze transform (TMST) value:

[0025]

[0026] Among them, Tm x (t,ω) represents the transient matching squeeze transformation, represents the infinite integration of the variable u, and δ(·) represents the unit impulse function.

[0027] Preferably, the transient matched squeeze transform (TMST) mentioned in step 4 can be reconstructed losslessly without information loss, and the signal x(t) can be reconstructed, and the reconstruction formula is:

[0028]

[0029] in, Represents the value of the Fourier transform of the window function at 0.

[0030] The present invention provides a reservoir boundary characterization method based on transient matched squeeze transformation (TMST), which has the following beneficial effects:

[0031] The transient matched squeeze transform (TMST) of the present invention squeezes the scattered time-frequency coefficients onto the GD center trajectory, and can obtain a more concentrated TFR result than TSST and TET, effectively improving the resolution of time-frequency analysis of seismic signals; while achieving sharpening, it can also accurately reconstruct the original signal, overcoming the problem of poor reconstruction effect caused by the loss of a large number of time-frequency coefficients in TET; when applied to actual seismic data, it can effectively reveal the characteristics of the seismic reflection interface, accurately locate the position of the reflection interface, and provide a more powerful tool for seismic interpretation. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a flow chart of the present invention;

[0033] Figure 2 This is a seismic profile of a certain region in China;

[0034] Figure 3 for Figure 2 20Hz frequency slices of 2D seismic profiles;

[0035] (a) Short-time Fourier transform (STFT) result; (b) SST (TSST) result based on time redistribution; (c) Second-order TSST (TSST2) result based on time redistribution; (d) Transient Extraction Transform (TET) result, threshold γ α = 0.0001; (e) Based on the transient extraction transform (TET) result, the threshold γ α =0.001; (f) transient matched squeeze transform (TMST). DETAILED DESCRIPTION

[0036] The present invention will be further described below in conjunction with the accompanying drawings.

[0037] See also Figure 2-Figure 3 , using actual field data to test the performance of the method, using different time-frequency analysis methods to analyze earthquake data in a certain region of China. The two-dimensional seismic data contains 210 seismic traces, 501 sampling time points, and the time interval is 1ms. The specific implementation steps are as follows:

[0038] 1) Input the seismic data to be analyzed and obtain Figure 2 The original seismic profile shown;

[0039] 2) For the input seismic signal, calculate the partial derivative of its STFT to define the GD estimator Then calculate the center of the group delay band;

[0040] First calculate the GD estimator have:

[0041]

[0042] in, represents the group delay estimator in the STFT time-frequency domain, represents the real part, j is the imaginary unit, represents the partial derivative of the variable ω, S x (t,ω) represents the STFT of the signal x(t), where t is the time variable and ω is the frequency variable.

[0043] Then calculate the center of the group delay band:

[0044]

[0045] Among them, t c Indicates the center of the group delay band.

[0046] 3) Determine the left and right boundaries of the group delay band (GDB) and And all GD estimators in GDB are matched with the GD estimator at the center of the GD band to obtain the matched GD (MGD) estimator;

[0047] First calculate the left and right boundaries of the group delay band (GDB) and have:

[0048]

[0049] in, represents the left edge of the group delay band, represents the partial derivative of the time variable, Indicates that in the GD estimator, time is t c .

[0050] Then all GD estimators in GDB are matched with the GD estimator at the center of the GD band to obtain the matched GD (MGD) estimator:

[0051]

[0052] in, Denotes the matched GD (MGD) estimator.

[0053] 4) Squeeze the time-frequency coefficients to obtain the transient matched squeeze transform (TMST) value:

[0054]

[0055] Among them, Tm x (t,ω) represents the transient matching squeeze transformation, represents the infinite integration of the variable u, and δ(·) represents the unit impulse function.

[0056] 5) Perform time-frequency transformation on seismic data according to TMST to obtain time-frequency results of different seismic traces;

[0057] 6) Extract the time series corresponding to the constant frequency from the time-frequency spectra of different seismic traces obtained by TMST, and then synthesize them to obtain a profile to characterize the reservoir characteristics and locate the position of the reflection interface.

[0058] Through Figure 3 A comparative analysis of (a)(b)(c)(d)(e) revealed that:

[0059] (a) The TFR result produced by the traditional TFA method STFT has a rough TF response, and the TF energy is roughly distributed around the reflectivity position, which is not conducive to accurately identifying the reflective interface position;

[0060] (b) and (c) TSST and TSST2 using compressed TF coefficients. Compared with the traditional STFT, the constant spectrum lines obtained by TSST and TSST2 are more sparse. It can be seen that the sparse effect of TSST2 is better than that of TSST. However, both methods show the dispersion of TF energy around the reflection interface.

[0061] (d) and (e) Compared with TSST and TSST2, TET uses the extraction operator to sharpen the STFT time spectrum, which can better describe the position of the reflection interface. Here, we use two versions of TET to analyze the response curves. (d) The threshold γ α =0.0001,(e)γ α = 0.001, it can be seen that the TET time-frequency results with smaller thresholds are sparser, but the selection of thresholds is challenging in practice;

[0062] (f) TMST uses a compression operator to redistribute the TF coefficients, which combines the advantages of TET and leads to sparser time-frequency results with higher temporal resolution. Therefore, it can be concluded that the proposed TMST is more advantageous in revealing the characteristics of reflection interfaces.

[0063] The above analysis shows that in the characterization of reservoir boundaries, TMST's TFR has sparser time-frequency results, higher time resolution, and greater advantages in revealing the characteristics of reflection interfaces. It has more potential than other methods in the interpretation of actual seismic data.

[0064] The present invention is based on SST based on time reallocation (TSST) and transient extraction transform (TET), combining the lossless reconstruction performance advantages of SST based on time reallocation (TSST) and the strong sharpening performance advantages of transient extraction transform (TET). It is a new time-frequency transform with both strong sharpening performance and reconstruction performance.

[0065] Although the specific implementation of the invention is described in detail in conjunction with the drawings, it should not be understood as limiting the scope of protection of this patent. Within the scope described in 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 reservoir boundary characterization method based on transient matching squeeze transformation, characterized in that: The following steps are involved: Step 1: Input the seismic signal x(t) to be analyzed; Step 2: Define the GD estimator by calculating the partial derivatives of the STFT of a given signal Then calculate the center of the group delay band; Step 3: Determine the left and right boundaries of the group delay band and And all GD estimators in the group delay band are matched with the GD estimator at the center of the GD band to obtain the matched GD estimator Step 4: Squeeze the time-frequency coefficients to obtain the transient matching squeeze transformation value Tm x (t,ω); Step 5: Perform time-frequency transformation on the seismic signal x(t) according to the transient matching squeeze transformation to obtain the time-frequency result; Step 6: Extract the time series corresponding to the constant frequency from the time-frequency spectra of different seismic traces obtained by transient matching and squeezing transformation, and then synthesize them to obtain a profile to characterize the reservoir characteristics and locate the position of the reflection interface.

2. The reservoir boundary characterization method based on transient matching squeeze transformation according to claim 1 is characterized in that: In step 2, the partial derivative of the STFT is calculated to define the GD estimator, which is: in, represents the group delay estimator in the STFT time-frequency domain, represents the real part, j is the imaginary unit, represents the partial derivative of the variable ω, S x (t,ω) represents the STFT of the signal x(t), where t is the time variable and ω is the frequency variable.

3. The reservoir boundary characterization method based on transient matching squeeze transformation according to claim 2 is characterized in that: The group delay band center can be expressed as: Among them, t c represents the center of the group delay band, and st represents limited by.

4. The reservoir boundary characterization method based on transient matching squeeze transformation according to claim 1 is characterized in that: Step 3 determines the left and right boundaries of the group delay band t c l and t c r : in, represents the left edge of the group delay band, represents the partial derivative of the time variable, Indicates that in the GD estimator, time is t c .

5. The reservoir boundary characterization method based on transient matching squeeze transformation according to claim 4 is characterized in that: Match all GD estimators in the group delay band with the GD estimator at the center of the GD band to obtain a matched GD estimator: in, Represents the matched GD estimator.

6. The reservoir boundary characterization method based on transient matching squeeze transformation according to claim 1, characterized in that: The transient matching extrusion transformation obtained in step 4 is: Among them, Tm x (t,ω) represents the transient matching squeeze transformation, represents the infinite integration of the variable u, and δ(·) represents the unit impulse function.

7. The reservoir boundary characterization method based on transient matching squeeze transformation according to claim 1 is characterized in that: The transient matching squeeze transform obtained in step 4 is a lossless inverse transform, and there is no information loss. The signal x(t) can be reconstructed, and its inverse transform expression is: in, Represents the value of the Fourier transform of the window function at 0.

Images