Carbonate multi-stage reservoir characterization method based on time-varying gaussian window transient extraction transform

Abstract

This invention discloses a method for characterizing multi-stage carbonate reservoirs based on time-varying Gaussian window transient extraction transform, used for characterizing multi-stage carbonate reservoirs. The method includes: inputting the seismic signal to be analyzed, where is time; constructing a short-time Fourier transform containing the time-varying window width parameter to be optimized, where represents frequency; determining the optimal window width parameter at each time step based on the local Rényi entropy minimization criterion; substituting and calculating its time partial derivative; constructing a transient extraction operator based on the time partial derivative results, including a local maximum criterion, an energy derivative zero-point criterion, and a group delay migration criterion; and proposing a time-varying Gaussian window transient extraction transform under the action of this operator for characterizing multi-stage carbonate reservoirs.

Description

Technical Field

[0001] This invention belongs to the field of oil and gas exploration technology, and specifically designs a multi-stage reservoir characterization method for carbonate rocks based on time-varying Gaussian window transient extraction transformation. Background Technology

[0002] Carbonate reservoirs are highly heterogeneous, exhibiting significant lateral discontinuities and vertical stacking relationships. Having undergone multiple phases of diagenesis and tectonic alteration, their seismic responses display strong non-stationary signals and transient phase abrupt changes. This necessitates time-frequency analysis with both high temporal resolution and high energy focusing capabilities to accurately characterize the reservoir boundaries and internal structure. Traditional time-frequency analysis methods, such as Short-Time Fourier Transform (STFT), S-Transform (ST), and W-Transform (WT), are constrained by the fixed window function under the Heisenberg uncertainty principle, often facing problems such as energy divergence, severe background interference, and blurred reservoir boundaries.

[0003] Building upon the preliminary findings of heterogeneous responses from traditional time-frequency analysis, high-precision time-frequency post-processing methods have emerged to further enhance the granularity of reservoir boundary characterization. Squeezing algorithms, originating from Synchronous Squeezing Transform (SST), aim to obtain a high-resolution time-frequency representation by squeezing the signal's time-frequency energy along the frequency direction to the instantaneous frequency trajectory. Subsequent developments include Temporal Rearrangement Synchronous Squeezing Transform (TSST) and Temporal Rearrangement Multiple Synchronous Squeezing Transform (TMSST), which enhance the lateral continuity of the phase axis by squeezing the signal's time-frequency energy along the time direction to the estimated group delay (GD) trajectory. However, these methods suffer from insufficient tracking accuracy when dealing with structurally complex reservoirs such as carbonate rocks, exhibiting gaps and distortions when depicting the internal features of discontinuous, non-layered reservoirs. Another type is extraction-based algorithms, represented by Transient Extraction Transform (TET). Their core idea is to extract the signal's energy along the estimated group delay trajectory, rather than redistributing the energy, thus maintaining high temporal resolution. Faced with the challenge of complex seismic responses and low signal-to-noise ratios in multi-stage carbonate reservoirs, making reservoir characterization difficult, extraction methods such as TET still encounter bottlenecks in window adaptability and group delay estimation robustness. This can easily lead to extracted energy deviating from the true trajectory, making it difficult to reliably support the fine-grained partitioning of reservoir units. Therefore, it is necessary to develop a time-frequency analysis method that can better reveal the temporal resolution of signals and is more suitable for the characteristics of multi-stage carbonate reservoir development. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing methods by providing a method for characterizing multi-stage carbonate reservoirs based on time-varying Gaussian window transient extraction transform. This invention significantly improves signal temporal resolution and can be used to accurately characterize multi-stage carbonate reservoirs.

[0005] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0006] Step 1: Input the signal to be analyzed ,in Indicates time;

[0007] Step 2: Construct a time-varying window width parameter to be optimized Short-time Fourier Transform ;

[0008] Step 3: Calculate the optimal window width parameter at each time step under the local Rényi entropy minimization criterion. ;

[0009] Step 4: Optimal window width parameters and calculate Results of partial derivatives with respect to time ;

[0010] Step 5: Construct a transient extraction operator that includes the local maximum criterion, the zero-point energy derivative criterion, and the group delay offset criterion. ;

[0011] Step 6: Transient Extraction Operator Applying time-frequency focusing to seismic data to obtain high-frequency focusing performance based on time-varying Gaussian window transient extraction transform The results were used to characterize multi-stage carbonate reservoirs.

[0012] Preferably, in step 2, the time-varying Gaussian window short-time Fourier transform The calculation is as follows:

[0013]

[0014] in, For frequency, For time-varying window width functions, It is a Gaussian window function. This is the time integration variable. Here, the width parameter of the window function... It is no longer a constant, but a function of time t.

[0015] Preferably, the optimal window width parameter in step 3 It can be represented as:

[0016]

[0017] in, Represented as:

[0018]

[0019] in, Represents a sparsity measure. The unit is the imaginary unit. This calculation allows for a better matching of the window width where energy is more concentrated at each time step, thus enhancing the time-frequency characterization performance.

[0020] Preferably, in step 4 Results regarding time partial derivatives Represented as:

[0021]

[0022] in, express Regarding time The first derivative of the formula establishes the correspondence between the non-stationary rate of change of the signal and different weighted window transformations. The second term of the formula reflects the influence of the scale change rate on the energy evolution trajectory of the signal. , , According to The auxiliary transformation defined by the result has the following calculation expression:

[0023]

[0024] Preferably, the local maximum criterion in step 5 can be defined as follows:

[0025]

[0026] in, This represents the modulo operation. Indicates the time sampling point. This represents the frequency sampling point. Here, the energy peak value satisfies the zero-crossing point of the energy's time derivative, thus preserving the point with the strongest energy.

[0027] Preferably, the step 5 involves finding the squared modulus. First-order partial derivative with respect to time, energy derivative operator The calculation can be expressed as:

[0028]

[0029] in, To calculate using the real part, It represents The conjugate of the complex number, the zero-point criterion for the energy derivative is defined as:

[0030]

[0031] in, This selection mechanism, with a minimum value, can identify points that truly reflect the transient characteristics of the signal, thus improving the signal's temporal resolution.

[0032] Preferably, the group delay offset criterion in step 5 helps to further remove spurious energy interference, and it is defined as follows:

[0033]

[0034] in, This approximates the offset of the energy center of gravity relative to the window center. Here, the tolerance coefficient is used because extracting only extreme points may result in spurious peaks caused by noise. Introducing the group delay offset criterion ensures that the extracted points are located at the center of the effective support domain of the current adaptive window, thus better eliminating interference from incoherent components.

[0035] Preferably, the transient extraction operator in step 5 It can be defined as:

[0036]

[0037] This transient extraction operator matches local signal features with an adaptive window width and effectively removes spurious extremum interference.

[0038] Preferably, the transient extraction transform based on the time-varying Gaussian window in step 6... The calculation method is as follows:

[0039]

[0040] Here, a time-frequency representation with highly concentrated energy and adaptively matched signal transient characteristics is generated. This better reveals the multi-stage development characteristics of carbonate rocks, a complex reservoir structure characterized by strong heterogeneity, lateral discontinuity, and vertical stacking.

[0041] The method for characterizing multi-stage carbonate reservoirs based on time-varying Gaussian window transient extraction transformation provided by the invention has the following beneficial effects:

[0042] The proposed method for characterizing multi-stage carbonate reservoirs based on time-varying Gaussian window transient extraction transform firstly, according to the input signal... Construct a time-varying window width parameter to be optimized. Short-time Fourier Transform Next, the optimal window width parameter at each time step is calculated based on the local Rényi entropy minimization criterion. and bring in calculate Partial derivative results with respect to time Then, a transient extraction operator incorporating the local maximum criterion, the zero-point energy derivative criterion, and the group delay offset criterion was constructed. Finally, the transient extraction operator constructed based on the above constraints... Obtain time-frequency representation This invention is a method for characterizing multi-stage carbonate reservoirs based on time-varying Gaussian window transient extraction transformation. It demonstrates good performance in improving the temporal resolution of signals and can effectively characterize multi-stage carbonate reservoirs. Attached Figure Description

[0043] Figure 1 This is a flowchart of the present invention;

[0044] Figure 2 The time spectrum diagrams are obtained by (a) Short Time Fourier Transform (STFT), (b) Synchronous Extraction Transform (SET), (c) Time Rearranged Synchronous Extraction Transform (TSST), (d) Multiple Synchronous Extraction Transform (TMSST), (e) Transient Extraction Transform (TET), and (f) Time Rearranged Synchronous Extraction Transform (TGTET). Detailed Implementation

[0045] The invention will now be further described with reference to the accompanying drawings.

[0046] See Figure 1 A method for characterizing carbonate reservoirs across multiple phases based on time-varying Gaussian window transient extraction transform includes the following steps:

[0047] Step 1: Input the signal to be analyzed ,in Indicates time;

[0048] Step 2: Construct a time-varying window width parameter to be optimized Short-time Fourier Transform ;

[0049]

[0050] in, For frequency, For time-varying window width functions, It is a Gaussian window function. As a time-integral variable, by introducing a time-varying window width function This can better reflect the local time-frequency energy variation characteristics caused by changes in complex signals.

[0051] Step 3: Calculate the optimal window width parameter at each time step based on the local Rényi entropy minimization criterion. :

[0052]

[0053] Rényi entropy is an effective indicator of the sparsity of time-frequency distribution; the smaller the entropy value, the more concentrated the energy. Represented as:

[0054]

[0055] in, This represents the sparsity metric, typically set to 3 for a more robust sparsity measure. The unit is the imaginary unit. This calculation allows for better selection of windows where energy is more concentrated at different times, which is beneficial for enhancing time-frequency characterization performance.

[0056] Step 4: Substitute the optimal window width parameter ,calculate Results with respect to the partial derivative with respect to time :

[0057]

[0058] in, express Regarding time The first derivative of this calculation establishes a correspondence between the non-stationary rate of change of the signal and different weighted window transforms. The second term in the formula reflects the influence of the scale change rate on the signal energy evolution trajectory. To facilitate subsequent calculations, auxiliary Fourier transforms with different weighted window functions are introduced. , , The corresponding calculation expression is:

[0059]

[0060] Step 5: Construct a transient extraction operator that includes the local maximum criterion, the zero-point energy derivative criterion, and the group delay offset criterion. ;

[0061] First, define the local maximum criterion:

[0062] in, This represents the modulo operation. Indicates the time sampling point. The sampling point represents the frequency. This extraction condition can retain the point with the strongest energy, which is more conducive to separating the two reflection interfaces in actual seismic interpretation.

[0063] The energy derivative operator is then given. :

[0064]

[0065] in, To calculate using the real part, for Conjugate complex numbers, therefore, the zero point of the energy derivative must satisfy the following:

[0066]

[0067] in, This is a minimum value, usually set to a minimum positive value, and is selected here. .pass The constraint that the first derivative of energy is less than a local minimum, combined with the local maximum criterion, can better eliminate spurious signals that are not located on the energy center line, select points that can truly reflect the transient characteristics of the signal, and improve the signal time resolution.

[0068] The group delay offset criterion is then given, in which a group delay error is calculated. This approximates the offset of the energy centroid relative to the window center, and from this, a group delay offset criterion is constructed, which can be expressed as:

[0069]

[0070] in, This is the tolerance factor, selected here. The selection of the tolerance coefficient is related to factors such as the quality of seismic data. For multi-stage carbonate reservoirs, in practical applications, its value is set within the range of 0.1 to 0.5. In particular, in low signal-to-noise ratio regions, appropriately increasing this coefficient can better ensure the lateral continuity of the reservoir's phase axis. Following the aforementioned group delay migration criterion ensures that the extraction point is located at the effective support center of the current adaptive window, better eliminating interference from incoherent components.

[0071] Finally, the transient extraction operator is constructed. satisfy:

[0072]

[0073] This operator achieves adaptive window width matching of signal local features and removes spurious extrema by combining higher-order statistics, thus providing a prerequisite for generating a time-frequency representation of highly concentrated energy and adaptively matched signal features.

[0074] Step 6: Transient Extraction Operator Applying this to seismic data, a transient extraction transform based on a time-varying Gaussian window is obtained. Used to characterize multi-stage carbonate reservoirs. Specifically, it is expressed as follows:

[0075]

[0076] This result preserves the continuity of the mid-frequency trajectory while removing interference artifacts in the diffusion region on the time-frequency plane, providing more stable technical support for boundary identification and internal contour characterization of deep-ultra-deep carbonate heterogeneous reservoirs.

[0077] See Figures 1 to 2 Taking the processed results of a carbonate rock profile as an example, from... Figure 2 The processing results (a)-(f) show the results obtained using STFT, SET, TSST, TMSST, TET, and TGTET, respectively. The horizontal axis represents the seismic traces, specifically the data from traces 100-600; the vertical axis represents time, with a sampling interval of 2ms. The results show that STFT has low time-frequency resolution, making it difficult to clearly characterize the fine internal structure of the reservoir. SET fails to continuously track layered interfaces in many locations, making it difficult to characterize multi-stage reservoirs. While TSST, TMSST, and TET improve the identification accuracy of this region to varying degrees, their tracking accuracy significantly decreases when facing areas with rapidly changing reservoir structures, leading to gaps and distortions in the depiction of internal features of discontinuous and non-layered reservoirs. Compared to the above methods, TGTET achieves higher energy concentration in the time-frequency domain, clearly characterizing the continuous lateral distribution of layered reservoirs and reconstructing their geometric contours more completely in areas with complex reservoir structures, effectively revealing the distribution of internal features.

[0078] Although specific embodiments of the invention have been described in detail with reference to the accompanying drawings, this should not be construed as limiting the scope of protection of this patent. Various modifications and variations that can be made by a person skilled in the art without inventive effort within the scope described in the claims still fall within the scope of protection of this patent.

Claims

1. A method for characterizing multi-stage carbonate reservoirs based on time-varying Gaussian window transient extraction transform, characterized in that, Includes the following steps: Step 1: Input the signal to be analyzed ,in Indicates time; Step 2: Construct a time-varying window width parameter to be optimized Short-time Fourier Transform ; Step 3: Calculate the optimal window width parameter at each time step based on the local Rényi entropy minimization criterion. ; Step 4: Substitute the optimal window width parameter ,calculate Results with respect to the partial derivative with respect to time ; Step 5: Construct a transient extraction operator that includes the local maximum criterion, the zero-point energy derivative criterion, and the group delay offset criterion. ; Step 6: Transient Extraction Operator Applying time-frequency focusing to seismic data to obtain high-frequency focusing performance based on time-varying Gaussian window transient extraction transform The results were used to characterize multi-stage carbonate reservoirs.

2. The method for characterizing multi-stage carbonate reservoirs based on time-varying Gaussian window transient extraction transformation according to claim 1, characterized in that, Step 2, the time-varying Gaussian window short-time Fourier transform The calculation is as follows: in, For frequency, For time-varying window width functions, It is a Gaussian window function. This is the time integration variable.

3. The method for characterizing multi-stage carbonate reservoirs based on time-varying Gaussian window transient extraction transformation according to claim 1, characterized in that, The optimal window width parameter in step 3 It can be represented as: ； in, Represented as: ； in, Represents a sparsity measure. It is the imaginary unit.

4. The method for characterizing multi-stage carbonate reservoirs based on time-varying Gaussian window transient extraction transformation according to claim 1, characterized in that, In step 4 Results regarding time partial derivatives Represented as: ； in, express Regarding time The first derivative, , , The corresponding calculation expression for the auxiliary Fourier transform using different weighted window functions is: 。 5. The method for characterizing multi-stage carbonate reservoirs based on time-varying Gaussian window transient extraction transformation according to claim 1, characterized in that, The local maximum criterion in step 5 is calculated as follows: in, This represents the modulo operation. Indicates the time sampling point. Indicates the frequency sampling point.

6. The method for characterizing multi-stage carbonate reservoirs based on time-varying Gaussian window transient extraction transformation according to claim 1, characterized in that, The zero-point criterion for the energy derivative in step 5 requires finding the square of the modulus. The first-order partial derivative with respect to time, i.e., the calculated energy derivative operator. The calculation can be expressed as: ； in, To calculate using the real part, for The zero-point criterion for the energy derivative of a conjugate complex number is defined as follows: ； in, It is a local minimum.

7. The method for characterizing multi-stage carbonate reservoirs based on time-varying Gaussian window transient extraction transformation according to claim 1, characterized in that, The group delay offset criterion in step 5 is defined as follows: ； in, This is the tolerance coefficient.

8. The method for characterizing multi-stage carbonate reservoirs based on time-varying Gaussian window transient extraction transformation according to claim 1, characterized in that, The transient extraction operator constructed in step 5 satisfy: 。 9. The method for characterizing multi-stage carbonate reservoirs based on time-varying Gaussian window transient extraction transformation according to claim 1, characterized in that, Step 6 involves a transient extraction transformation based on a time-varying Gaussian window. The calculation method is as follows: 。

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