Method for dividing deep carbonate rock sedimentary cycle based on matching chirplet squeezing transform

Abstract

This invention discloses a method for classifying deep carbonate sedimentary cycles based on matched Chirplet compression transform (MCST). The method includes: inputting the seismic signal to be analyzed; calculating the instantaneous frequency and group delay in the short-time Fourier transform domain to obtain the chirp rate function; deriving the IF band center and constructing the time-frequency energy focusing domain in the chirplet transform domain; accurately obtaining the local rate of change of the instantaneous frequency trajectory in the chirplet transform domain by constructing a matched Chirplet rate estimator; redistributing the time-frequency coefficients to the true instantaneous frequency trajectory in the time-frequency energy focusing domain through compression transform, thereby obtaining the time spectrum of matched chirplet compression transform (MCST); applying this method to perform time-frequency characterization of seismic trace data, and classifying deep carbonate sedimentary cycles by analyzing the changing trends of the tuned frequencies in the time spectrum.

Description

Technical Field

[0001] This invention relates to the fields of seismic signal processing and oil and gas exploration, and in particular to a method for classifying deep carbonate sedimentary cycles based on matched Chirplet compression transform. Background Technology

[0002] Sedimentary cycles play a crucial role in sequence stratigraphy, reservoir prediction, and oil and gas exploration. Deep carbonate reservoirs are an important area of ​​current oil and gas exploration. Studies have shown that seismic data contains rich information on sedimentary cycles, and frequency-modulated tuning can reflect complex sedimentary structures. Through time-frequency analysis, sedimentary cycle patterns can be intuitively identified. The principle is that an increase (decrease) in formation thickness will cause a decrease (increase) in the tuning frequency.

[0003] Traditional time-frequency characterization methods include Short-Time Fourier Transform (STFT), Continuous Wavelet Transform (CWT), S-Transform (ST), Generalized S-Transform (GST), and W-Transform (WT). All of these are constrained by the Heisenberg uncertainty principle, making it difficult to balance time and frequency resolution. Time-frequency energy often exhibits severe dispersion. In sedimentary cycle delineation, this dispersion leads to blurred boundaries between different cycles and difficulty in accurately tracing tuned frequency trajectories. Especially when cycle thickness changes slowly or the stratigraphic structure is complex, traditional methods struggle to effectively characterize the subtle changes within a cycle.

[0004] To further improve the resolution of time-frequency characterization, researchers introduced a series of post-processing techniques. Among them, the redistribution method (RS) simultaneously redistributes the TF coefficients along both the time and frequency axes to the centroid of the signal's energy distribution in the STFT domain. While this significantly improves the concentration of time-frequency energy, it cannot reconstruct the signal. The subsequent development of Synchronous Compression Transform (SST) and Synchronous Extraction Transform (SET) achieved energy compression along the frequency direction. SST squeezes the time-frequency energy along the frequency direction onto the instantaneous frequency (IF) trajectory, ensuring signal reversibility. SET further improves the energy concentration of the time-frequency characterization by extracting the IF trajectory. At this stage, time-frequency characterization methods began to be widely used in reservoir prediction, resulting in sharper and more concentrated frequency features compared to traditional time-frequency maps. However, they still have shortcomings. Because SST's improvement in time-spectral resolution after processing FM signals is limited, and it fails to clearly characterize the suppressed signal, the TFR generated by SST exhibits ambiguity. SET remains ineffective in signal reconstruction. Therefore, it is necessary to develop a new type of time-frequency transform that combines high energy focusing performance with robust reconstruction capability, laying the foundation for accurate segmentation of sedimentary cycles. Summary of the Invention

[0005] The purpose of this invention is to propose a novel time-frequency analysis method—the matched Chirplet compressional transform—for the classification of sedimentary cycles in deep carbonate rocks. This invention possesses highly focused energy performance and robust reconstruction capabilities, accurately characterizing changes in tuning frequencies caused by variations in formation thickness.

[0006] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0007] Step 1: Input the seismic signal to be analyzed ,in It is a time variable;

[0008] Step 2: Calculate the instantaneous frequency in the short-time Fourier transform domain Group delay According to instantaneous frequency Group delay The chirp rate was calculated. ,in Indicates frequency;

[0009] Step 3: Introduction The Chirplet transform is obtained. And calculate Instantaneous frequency band center in the domain , Indicates the sequence number of different components in the signal;

[0010] Step 4: Construct the time-frequency energy focusing domain TFEFD, and the left boundary of TFEFD. and right boundary ,in, This is an abbreviation for left. Abbreviation for right;

[0011] Step 5: Based on the positioning time frequency band The location is matched to the Chirp rate estimator MCR: ;

[0012] Step 6: Calculate the Chirplet transform in TFEFD And perform a squeezing operation to obtain a matching Chirplet squeezing transform. ;

[0013] Step 7: Apply the matched Chirplet compression transform to the seismic signal Perform time-frequency transformation to obtain the time-frequency result;

[0014] Step 8: From the time-frequency results obtained by matching the Chirplet compression transform, the increasing and decreasing trends of the tuning frequency are analyzed to characterize the deep carbonate sedimentary cycles.

[0015] Preferably, in step 2, the instantaneous frequency in the short-time Fourier transform is calculated. Group delay Calculated in the following way:

[0016] definition:

[0017] definition:

[0018] (1)

[0019] (2)

[0020] Then according to and Calculate chirp rate :

[0021] (3)

[0022] in, Represents the Gaussian window function. Represents the imaginary unit. Represents the variable Perform infinite integration, Represents the integral variable. This indicates that the window function is a Gaussian function. The short-time Fourier transform, This indicates that the window function is the derivative of the Gaussian function. The short-time Fourier transform, and They are respectively taking the real part and taking the imaginary part. Indicates to Find the partial derivative. Indicates to Find the partial derivative; the chirp rate can describe the rate of change of the instantaneous frequency of a signal over time.

[0023] Preferably, the Chirplet transform in step 3 The construction method is as follows:

[0024] (4)

[0025] And calculate the instantaneous frequency band center in the Chirplet transform domain. :

[0026] (5)

[0027] in, Indicates the retrieved first The frequency center of each component Represents the modulo operation; Chirplet transform It enables the slope of the analysis window to perfectly match the instantaneous frequency change rate of the signal, which helps to obtain a more focused time-frequency characterization. The point where the estimated frequency is exactly the same as the actual frequency can be retrieved, which can accurately locate the ideal instantaneous frequency trajectory.

[0028] Preferably, the time-frequency energy focusing domain TFEFD in step 4 is defined as follows:

[0029] definition: Its left boundary and right boundary Defined as:

[0030] (6)

[0031] (7)

[0032] in Indicates the sampling frequency. This represents the total number of sampling points over time. TFEFD prevents energy overlap between different components, ensuring that different components do not interfere with each other.

[0033] Preferably, in step 5, according to The matching Chirp rate estimator MCR is obtained as follows:

[0034] (8)

[0035] Calculate different components of the signal within the TFEFD range. It can accurately match the frequency slope.

[0036] Preferably, in step 6, the Chirplet transformation is... Defined as:

[0037] (9)

[0038] And on Perform matching Chirplet extrusion transformation in TFEFD operate:

[0039] (10)

[0040] in Represents the Dirac function; Concentrating time-frequency energy at the instantaneous frequency within the TFEFD range yields a more concentrated time-frequency characterization; MCST compresses the time-frequency coefficients within the TFEFD region to a level that conforms to... The instantaneous frequency trajectory of the location can significantly improve the time-frequency accuracy, which is conducive to better analyzing the changes in tuning frequency caused by the change in thin layer thickness, and thus accurately characterizing the sedimentary cycles of deep carbonate rocks.

[0041] Preferably, the matched Chirplet squeeze transform in step 6 can perform lossless mode reconstruction, which can reconstruct the signal. The reconstruction formula is as follows:

[0042] (11)

[0043] And the modal reconstruction formula is:

[0044] (12)

[0045] in The original signal The amount, This indicates that MCST did not cause any information loss.

[0046] The method for classifying deep carbonate sedimentary cycles based on matched Chirplet compressional transformation provided by this invention has the following beneficial effects:

[0047] The Matched Chirplet Squeeze Transform (MCST) proposed in this invention first calculates the instantaneous frequency and group delay in the short-time Fourier transform domain to obtain the chirp rate function. Second, in the chirplet transform domain, the IF band center is derived and a time-frequency energy focusing domain is constructed. Then, by constructing a matched chirp rate estimator, the local rate of change of the instantaneous frequency trajectory is accurately obtained within the chirplet transform domain. Finally, within the time-frequency energy focusing domain, the time-frequency coefficients are redistributed to the true instantaneous frequency trajectory through a squeezing transform, thereby obtaining the time-frequency spectrum of the matched chirplet squeeze transform (MCST). This achieves sharpening while accurately reconstructing the original signal. This invention demonstrates excellent time-frequency characterization capabilities, significantly improving the focusing of time-frequency energy and better characterizing the sedimentary cycles of deep carbonate rocks. Attached Figure Description

[0048] Figure 1 This is a flowchart of the present invention;

[0049] Figure 2 This is a seismic profile of a region in China.

[0050] Figure 3 for Figure 2The characterization results of the Naka-A seismic data under different time-frequency methods include (a) redistribution method (RS), (b) multiple synchronous compression transformation (MSST), (c) second-order synchronous compression transformation (2nd-SST), (d) synchronous extraction transformation (SET) and (e) MCST processing results.

[0051] Figure 4 for Figure 2 The characterization results of the Naka-B seismic data under different time-frequency methods include (a) redistribution method (RS), (b) multiple synchronous compression transformation (MSST), (c) second-order synchronous compression transformation (2nd-SST), (d) synchronous extraction transformation (SET) and (e) MCST processing results. Detailed Implementation

[0052] The invention will now be further described with reference to the accompanying drawings.

[0053] See Figure 1 The specific implementation steps of the deep carbonate sedimentary cycle partitioning method based on matching Chirplet compression transformation are as follows:

[0054] Step 1: Input the seismic data to be analyzed, and obtain the following results: Figure 2 The original seismic profile shown;

[0055] Step 2: Process the input seismic signal Calculate its instantaneous frequency in the short-time Fourier transform domain. Group delay Then based on the instantaneous frequency Group delay The chirp rate was calculated. , Indicates time, Indicates frequency;

[0056] First, the short-time Fourier transform is defined:

[0057] definition

[0058] definition

[0059] in, Represents the imaginary unit. Represents the Gaussian window function. This represents the derivative of the Gaussian function. Represents the variable Perform infinite integration, and The window functions are respectively: and The short-time Fourier transform, and then according to and The instantaneous frequency was calculated from the results. and :

[0060] (1)

[0061] (2)

[0062] in, and They are respectively taking the real part and taking the imaginary part. Indicates to Find the partial derivative, and then use the instantaneous frequency. Group delay The chirp rate was calculated. :

[0063] (3)

[0064] in, Indicates to Find the partial derivative. To obtain optimal localization performance in the time-frequency domain, here... The standard Gaussian window function is used.

[0065] Step 3: Introduction Obtain the Chirplet transform And calculate Instantaneous frequency band center in the domain , Indicates the sequence number of different components in the signal;

[0066] First, introduce Obtain the Chirplet transform :

[0067] (4)

[0068] And in Within the domain, automatic search satisfies The instantaneous frequency trajectory is determined in the Chirplet transform domain without the need for manual parameter preset, and the instantaneous frequency band center is calculated. :

[0069] (5)

[0070] in, Indicates the retrieved first The frequency center of each component This indicates the modulo operation.

[0071] Step 4: Construct the time-frequency energy focusing domain (TFEFD) and determine the left boundary of the TFEFD. and right boundary ,in, This is an abbreviation for left. Abbreviation for right;

[0072] Through the center of the instantaneous frequency band The position index is used to cut each component along the frequency direction. First, TFEFD is defined: , and The left and right boundaries of the time-frequency energy focusing domain are represented as follows:

[0073] (6)

[0074] (7)

[0075] in This indicates the sampling frequency of the seismic signal. This indicates the total number of sampling points within the selected seismic signal time period.

[0076] Step 5: Based on the center frequency of the instantaneous frequency band. By determining the distribution location of the signal components and matching their corresponding chirp rate values ​​within the TFEFD domain, the matched chirp rate estimator (MCR) is derived. ;

[0077] (8)

[0078] Step 6: Calculate the Chirplet transform within the TFEFD region. And through the extrusion operation, the matched Chirplet extrusion transformation (MCST) is obtained.

[0079] First, by introducing the Matched Chirp Rate Estimator (MCR) into the Chirplet transform, we can obtain a Chirplet transform in which the signal components match the chirp rate. :

[0080] (9)

[0081] Finally, through the principle of compression... Within the domain, the time-frequency coefficients are squeezed to the center of the corresponding instantaneous frequency band. Finally, the matching Chirplet squeeze transformation is obtained:

[0082] (10)

[0083] in This represents the Dirac function.

[0084] Step 7: Seismic signals ,Right now Figure 2 The seismic traces corresponding to the two well passages were subjected to time-frequency transformation using a matched Chirplet compression transform to obtain high-resolution time-frequency results for different seismic traces, such as... Figure 3 and Figure 4 ;

[0085] Step 8: From the time-frequency results obtained by matching Chirplet compression transform, the increasing and decreasing trends of the tuning frequency are analyzed to characterize the deep carbonate sedimentary cycles. In the time-frequency diagram, the trends from high frequency to low frequency (or from low frequency to high frequency) represent reverse cycles and positive cycles, respectively.

[0086] See Figures 1 to 4 Let's take two specific seismic signals as examples. Figure 2 This displays a seismic profile of a certain area. The two-dimensional seismic data contains 578 seismic traces with a sampling interval of 2ms. The input seismic signals are the seismic signals corresponding to the well traces (Well A and Well B) in the figure. Figure 3 and Figure 4 Time-frequency analysis results of seismic signals corresponding to Well A and Well B seismic traces using different time-frequency analysis methods are presented, including: (a) RS, (b) MSST, (c) 2nd-SST, (d) SET, and (e) a comparison of the results from the MCST method of this invention. The horizontal axis represents frequency in Hertz (Hz). The comparison shows that RS and SET exhibit significant dispersion in their time-frequency characterization results, especially RS, which shows obvious artifacts, making it difficult to define the specific boundaries of cycles. While MSST and 2nd-SST improve the concentration, ridges are prone to breakage or bifurcation in areas with drastic changes in signal frequency (i.e., abrupt changes in stratigraphic thickness), making it impossible to accurately determine stratigraphic layers based on frequency trends. It is noteworthy that the MCST time-frequency results not only demonstrate high resolution and high accuracy but also completely preserve the frequency variation trend, with the frequency decreasing as stratigraphic thickness increases, accurately characterizing deep carbonate sedimentary cycles.

[0087] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for deep carbonate depositional cycle division based on matched Chirplet squeezing transform, characterized in that, Includes the following steps: Step 1 : inputting the seismic signal to be analyzed wherein is the time variable; Step 2: Calculate the instantaneous frequency in the short-time Fourier transform domain and group delay and from the instantaneous frequency and group delay the chirp rate is calculated where denotes the frequency; Step 3: Introduction The Chirplet transform is obtained. And calculate the instantaneous frequency band center in the Chirplet transform domain. , Indicates the sequence number of different components in the signal; Step 4: Construct the time-frequency energy focusing domain TFEFD, and the left boundary of TFEFD. and right boundary ,in, This is an abbreviation for left. This is an abbreviation for "right". Step 5: Based on the positioning time frequency band Location-based matching Chirp rate estimator (MCR): ; Step 6: Calculate the Chirplet transform in TFEFD And perform a squeezing operation to obtain a matching Chirplet squeezing transform. ; Step 7: Apply the matched Chirplet compression transform to the seismic signal Perform time-frequency transformation to obtain the time-frequency result; Step 8: From the time-frequency results obtained by matching the Chirplet compression transform, the increasing and decreasing trends of the tuning frequency are analyzed to characterize the deep carbonate sedimentary cycles.

2. The method for classifying deep carbonate sedimentary cycles based on matched Chirplet compressional transformation according to claim 1, characterized in that, In step 2, the instantaneous frequency in the short-time Fourier transform is calculated. Group delay Calculated in the following way: definition: ; definition: ; (1)； (2)； in, This represents the Gaussian window function. This represents the derivative of the Gaussian function. Represents the integral variable. Represents the imaginary unit. and The window functions are respectively: and The short-time Fourier transform, and They are respectively taking the real part and taking the imaginary part. Indicates to Find the partial derivative.

3. The method for classifying deep carbonate sedimentary cycles based on matched Chirplet compressional transformation according to claim 1, characterized in that, chirp rate in step 2 It can be obtained in the following ways: (3)； in, Indicates to Find the partial derivative.

4. The method for classifying deep carbonate sedimentary cycles based on matched Chirplet compressional transformation according to claim 1, characterized in that, The introduction in step 3 Obtain the Chirplet transform : (4)。 5. The method for classifying deep carbonate sedimentary cycles based on matched Chirplet compressional transformation according to claim 1, characterized in that, In step 3 Defined as: (5)。 6. The method for classifying deep carbonate sedimentary cycles based on matched Chirplet compressional transformation according to claim 1, characterized in that, The left boundary of TFEFD in step 4 and right boundary Defined as: (6)； (7)； in Indicates the sampling frequency. This represents the total number of sampling points over time.

7. The method for classifying deep carbonate sedimentary cycles based on matched Chirplet compressional transformation according to claim 1, characterized in that, In step 5, according to The matching Chirp rate estimator MCR is obtained as follows: (8)。 8. The method for classifying deep carbonate sedimentary cycles based on matched Chirplet compressional transformation according to claim 1, characterized in that, In step 6, the Chirplet transformation is... for: (9)。 9. The method for classifying deep carbonate sedimentary cycles based on matched Chirplet compressional transformation according to claim 1, characterized in that, Step 6 involves matching the Chirplet extrusion transformation. for: (10)； in This represents the Dirac function.

10. The method for classifying deep carbonate sedimentary cycles based on matched Chirplet compressional transformation according to claim 1, characterized in that, The matching Chirplet squeeze transform obtained in step 6 is a lossless reconstruction, and its expression is: (11)； Furthermore, a single component signal can be recovered from the MCST time-frequency domain. The mathematical formula is expressed as: (12)； in The original signal The amount, .

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