A method for estimating instantaneous frequency of seismic signals based on interpretable deep networks

Abstract

The present invention provides a method for estimating the instantaneous frequency of seismic signals based on an interpretable deep network. The method is based on a U-Net network, combines the sparsity of the instantaneous frequency, adds a convolutional sparse coding module, and utilizes the upsampling and feature fusion characteristics of the U-Net network to obtain a more effective instantaneous frequency estimation.

Description

Technical Field

[0001] The present invention belongs to the field of seismic signal processing and relates to an instantaneous frequency estimation method based on sparse representation, in particular to an instantaneous frequency estimation method that utilizes convolutional sparse coding and an interpretable deep network, and uses the instantaneous frequency estimation method to estimate the instantaneous frequency of oil and gas reservoirs. Background Art

[0002] Seismic data is a typical non-stationary signal. The commonly used Fourier transform cannot characterize the localized characteristics of non-stationary seismic signals. The time-frequency representation converts the one-dimensional signal into a two-dimensional time-frequency space, which can effectively reveal the localized characteristics of non-stationary seismic signals. The instantaneous frequency is an important physical quantity that describes the change of signal frequency over time. It has unique advantages and the concept of instantaneous effectiveness. The instantaneous frequency of seismic signals can be effectively extracted using the time-frequency representation method. The estimation of the instantaneous frequency of seismic signals is of great significance and application value for understanding reservoir characteristics, analyzing seismic data, improving quantitative prediction accuracy, and reducing exploration risks in oil and gas exploration.

[0003] In the past few decades, many time-frequency representation methods have been proposed to estimate instantaneous frequency, including short-time Fourier transform (STFT), continuous wavelet transform (CWT), S-transformation, and Wigner-Ville distribution (WVD). Traditional time-frequency transform methods are computationally efficient and widely used in seismic data processing and interpretation. However, they are limited by the Heisenberg uncertainty principle and may produce time-frequency spectra with energy diffusion. In order to obtain higher time-frequency resolution, time-frequency spectra based on sparse representation have attracted widespread attention from scholars. Gholami et al. (2012) applied the mixed l1-l2 norm to the classical STFT and proposed sparse STFT. Based on Gholami's work, Sattari (2017) proposed a sparse STFT based on mixed l1-l2 norm. l -l2 norm sparse S transform. However, the time-frequency representation method based on sparse representation requires a lot of computing time and is not suitable for actual seismic signal processing.

[0004] In recent years, with the rapid development of deep learning technology, more and more data-driven deep learning algorithms have been applied to time-frequency representation. Jiang et al. (2020) recently proposed a U-Net-assisted iterative shrinkage threshold algorithm to learn structural sparsity in the time-frequency domain, but its time-frequency representation reconstruction performance is still limited by the selection of fuzzy function samples. Lopac et al. (2022) proposed a deep learning algorithm based on time-frequency representation to classify noisy non-stationary time series signals. Zhang et al. (2022) proposed a method based on deep convolutional neural networks to obtain cross-term-free time-frequency representations, briefly described the concepts of automatic term preservation and cross-term suppression by training deep neural networks, and utilized and compared deep convolutional neural networks (FCNN; Fully Convolutional Neural Networks) and convolutional autoencoders. However, a series of network layers are simply stacked together, which leads to performance degradation and weakens the ability to extract features.

[0005] The existing technology has the following disadvantages:

[0006] 1) Traditional instantaneous frequency estimation methods based on sparse representation require a lot of computing time and cannot be directly applied to seismic signals and interpretation.

[0007] 2) Existing data-driven time-frequency representation methods do not consider the physical model of instantaneous frequency estimation and are unable to obtain accurate instantaneous frequency. Summary of the invention

[0008] The purpose of the present invention is to overcome the shortcomings of the prior art, integrate the prior art, and propose an interpretable deep network based on sparse coding. Based on the U-Net network, the network combines the sparsity of instantaneous frequency, adds a convolutional sparse coding module, and utilizes the upsampling and feature fusion characteristics of the U-Net network to obtain more effective instantaneous frequency estimation.

[0009] The present invention provides a method for estimating instantaneous frequency of seismic signals based on an interpretable deep network, the method comprising the following steps:

[0010] Obtaining a short-time Fourier transform representation of the analytical signal, obtaining an accurate instantaneous frequency according to the expression of the analytical signal, and constructing a sample data set according to the short-time Fourier transform representation and the accurate instantaneous frequency;

[0011] Constructing a convolutional sparse coding block according to a dictionary matrix composed of the input analytical signal and a short-time Fourier window function;

[0012] Constructing an interpretable deep network model according to the convolutional sparse coding block and the U-Net network model;

[0013] Using the training set in the sample data set to train the interpretable deep network model to obtain a trained network;

[0014] A test signal is input, the instantaneous frequency of the test signal is obtained, and the convergence of the trained network is verified through an error boundary.

[0015] According to the instantaneous frequency estimation method of seismic signals based on an interpretable deep network of the present invention, the method is based on the U-Net network, combines the sparsity of the instantaneous frequency, adds a convolutional sparse coding module, and utilizes the upsampling and feature fusion characteristics of the U-Net network to obtain a more effective instantaneous frequency estimation.

[0016] In addition, the instantaneous frequency estimation method of seismic signals based on an interpretable deep network according to the present invention also has the following technical features:

[0017] The sample data set includes three different analytical signals, and the three different analytical signals include a linear frequency modulation signal, a nonlinear frequency modulation signal and a sinusoidal frequency modulation signal.

[0018] The step of constructing a convolutional sparse coding block according to the input signal and the dictionary matrix specifically includes:

[0019] Calculate a sparse representation according to the input signal and the dictionary matrix, construct a sparse representation model equation according to the input signal, the dictionary matrix and the sparse constraint, find the most sparse representation in the sparse representation model equation, and construct the convolutional sparse coding block with the most sparse representation;

[0020] The sparse representation model equation is expressed as y=Dx, where y represents the input signal, D is the dictionary matrix, x is a sparse representation, and the most sparse representation is x*.

[0021] The step of finding the most sparse representation in the sparse representation model equation and constructing the convolutional sparse coding block with the most sparse representation specifically includes:

[0022] Characterizing a first value and a second value of the most sparse representation according to the sparse representation model equation, the first value including an l0 norm, the second value including an l1 norm, wherein the first value corresponds to a first most sparse representation equation, and the second value corresponds to a second most sparse representation equation;

[0023] Replacing the l0 norm in the first value with the l1 norm in the second value;

[0024] Using a least absolute shrinkage and selection algorithm to operate on the second sparsest representation equation to obtain a least absolute shrinkage and selection algorithm equation;

[0025] The least absolute shrinkage and selection algorithm equations are solved using an iterative soft thresholding algorithm to construct the convolutional sparse coding block.

[0026] The convolutional sparse coding block includes k layers, and the convolutional sparse coding block including k layers is expressed as x(k+1)=h θ (Wy+Sx(k)), where W, S, θ represent the trainable parameter set of the convolutional sparse coding block, and h θ Representing a non-negative soft threshold operator, the method also includes using a weighted ReLU activation function to replace the non-negative soft threshold operator to generate a ReLU activation function replacement equation, and the ReLU activation function replacement equation is expressed as x(k+1)=ReLU(Wy+Sx(k)).

[0027] The verifying the convergence of the convolutional sparse coding block by the error boundary specifically includes:

[0028] The convergence of the convolutional sparse coding block is verified by the error boundary equation, which is expressed as Among them, |x * |≤B, ||x * ||0≤s, ||ε||1≤σ, c>0 and C>0 are constants.

[0029] The sample data set is constructed using signals from three situations to verify the performance of the network. The signals from the three situations are:

[0030] Case 1: Two Crossed Chirp Signals

[0031]

[0032] Case 2: Two similar nonlinear FM signals

[0033]

[0034] Case 3: Crossed linear FM and sine FM signals

[0035]

[0036] a(t) represents amplitude, and a(t)=exp(-0.005t).

[0037] The convolutional sparse coding block, upsampling and feature fusion layers constitute a U-Net network model.

[0038] The U-Net network model is a semantic segmentation network model. The U-Net network model consists of 19 convolutional layers, 4 maximum pooling layers and 4 upsampling layers. The shape of the U-Net network model is U-shaped.

[0039] The signal-to-noise ratio of the sample data set is 5dB-45dB, and the sample data set includes a training sample data set and a verification sample data set, wherein the number of the training sample data set is greater than the number of the verification sample data set.

[0040] The present invention has the following beneficial effects:

[0041] The present invention estimates instantaneous frequency based on the idea of ​​sparse coding and deep network, and introduces the U-Net U-shaped network architecture, integrates upsampling and feature fusion into the sparse coding deep network, and is used for estimating the instantaneous frequency of seismic signals. Using seismic instantaneous frequency estimation can effectively predict the location and structure of underground reservoirs, providing favorable technical support for oil and gas exploration. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 Diagram of the two-layer LISTA network architecture.

[0043] Figure 2 Two-layer convolutional sparse coding block representation graph.

[0044] Figure 3 Interpretable deep network architecture diagram.

[0045] Figure 4 The instantaneous frequency estimation flow chart proposed by the present invention.

[0046] Figure 5 When the input signal-to-noise ratio is 15 dB, the reconstructed time-frequency representation results in three cases. From left to right: Case 1 to Case 3; from top to bottom: ideal time-frequency representation, STFT, WVD, FCNN, and the results of the present invention.

[0047] Figure 6 The time-frequency representation results of noisy seismic signals reconstructed by different methods; (a) STFT; (b) WVD; (c) FCNN; (d) the results of the present invention.

[0048] Figure 7 Estimation of the instantaneous frequency of the real signal; (a) GR and SP logging curves of the oil well; (b) actual seismic signal; (c) instantaneous frequency result estimated by the present invention. Specific implementation methods

[0049] The present invention is further described in detail below in conjunction with the accompanying drawings:

[0050] Seismic signals are a typical non-stationary seismic signal. Since the instantaneous frequency is sparse in the time-frequency space, it is considered to add sparsity to the deep network to obtain a more effective estimation. In order to solve this problem, the present invention proposes an interpretable convolutional sparse coding deep network for estimating the instantaneous frequency of non-stationary seismic signals.

[0051] The present invention provides a method for estimating instantaneous frequency of seismic signals based on an interpretable deep network, the method comprising the following steps:

[0052] Obtaining a short-time Fourier transform representation of the analytical signal, obtaining an accurate instantaneous frequency according to the expression of the analytical signal, and constructing a sample data set according to the short-time Fourier transform representation and the accurate instantaneous frequency;

[0053] Constructing a convolutional sparse coding block according to a dictionary matrix composed of the input analytical signal and a short-time Fourier window function;

[0054] Constructing an interpretable deep network model according to the convolutional sparse coding block and the U-Net network model;

[0055] Using the training set in the sample data set to train the interpretable deep network model to obtain a trained network;

[0056] A test signal is input, the instantaneous frequency of the test signal is obtained, and the convergence of the trained network is verified through an error boundary.

[0057] In a specific implementation, the sample data set includes three different analytical signals, and the three different analytical signals include a linear frequency modulation signal, a nonlinear frequency modulation signal, and a sinusoidal frequency modulation signal.

[0058] In a specific implementation, the step of constructing a convolutional sparse coding block according to the input signal and the dictionary matrix specifically includes:

[0059] Calculate a sparse representation according to the input signal and the dictionary matrix, construct a sparse representation model equation according to the input signal, the dictionary matrix and the sparse constraint, find the most sparse representation in the sparse representation model equation, and construct the convolutional sparse coding block with the most sparse representation;

[0060] The sparse representation model equation is expressed as y=Dx, where y represents the input signal, D is the dictionary matrix, x is a sparse representation, and the most sparse representation is x*.

[0061] In a specific implementation, the step of finding the sparsest representation in the sparse representation model equation and constructing the convolutional sparse coding block with the sparsest representation specifically includes:

[0062] Characterizing a first value and a second value of the most sparse representation according to the sparse representation model equation, the first value including an l0 norm, the second value including an l1 norm, wherein the first value corresponds to a first most sparse representation equation, and the second value corresponds to a second most sparse representation equation;

[0063] Replacing the l0 norm in the first value with the l1 norm in the second value;

[0064] Using a least absolute shrinkage and selection algorithm to operate on the second sparsest representation equation to obtain a least absolute shrinkage and selection algorithm equation;

[0065] The least absolute shrinkage and selection algorithm equations are solved using an iterative soft thresholding algorithm to construct the convolutional sparse coding block.

[0066] In a specific implementation, the convolutional sparse coding block includes k layers, and the convolutional sparse coding block including k layers is expressed as x(k+1)=h θ (Wy+Sx(k)), where W, S, θ represent the trainable parameter set of the convolutional sparse coding block, and h θ Representing a non-negative soft threshold operator, the method also includes using a weighted ReLU activation function to replace the non-negative soft threshold operator to generate a ReLU activation function replacement equation, and the ReLU activation function replacement equation is expressed as x(k+1)=ReLU(Wy+Sx(k)).

[0067] The instantaneous frequency estimation method of seismic signals based on an interpretable deep network of the present invention generally comprises the following steps:

[0068] (1) Obtain the STFT representation of the analytical signal:

[0069] The dataset consists of three different analytical signals, LFM (Liner Frequency Modulation), NLFM (Non-Liner Frequency Modulation) and SFM (Sinusoidal Frequency Modulation) and their complex structures. The signal-to-noise ratio level is set from 5dB to 45dB, and 2100 samples with different parameters are randomly generated. 70% of the samples are used for training and the remaining 30% are used for validation.

[0070] In order to prove the performance of the network, three complex cases are considered for verification, which are expressed as follows:

[0071] Case 1: Two intersecting LFM signals

[0072]

[0073] Case 2: Two similar NLFM signals

[0074]

[0075] Case 3: Crossed LFM and SFM signals

[0076]

[0077] The amplitudes of the three cases are all a(t)=exp(-0.005t).

[0078] (2) Construct convolutional sparse coding blocks:

[0079] The sparse representation model assumes that the signal y∈R N It can be expressed as

[0080] y=Dx

[0081] Where D∈R N×M is a matrix called a dictionary, x∈R M is a sparse representation. The task of sparse coding is to find the most sparse representation x*, that is

[0082]

[0083] Here ||x||0 represents the number of non-zero elements in x. Since the above problem is NP-hard, the l1 norm is usually used instead of the l0 norm, that is,

[0084]

[0085] By transforming the above problem into a LASSO problem,

[0086]

[0087] It can be solved using the iterative soft threshold algorithm (ISTA), namely:

[0088]

[0089] L is for D T The upper bound of the largest eigenvalue of D. h θ is a component vector shrinkage function with a threshold vector θ.

[0090] When the dictionary is a convolution matrix, the task of recovering the most sparse representation x* is called convolutional sparse coding, which assumes that a signal can be represented as the multiplication of a convolutional dictionary consisting of n0 local filters of length m1 and a sparse vector. The convolutional sparse coding model is extended to multiple layers to obtain a multi-layer convolutional sparse coding model.

[0091] Based on ISTA, some faster algorithm extensions have been proposed, such as LISTA. Figure 1 As shown in Figure 1, LISTA (LeCun, 2010) is a feedforward neural network whose parameters W, S and θ are learned from training data through the back-propagation algorithm. LISTA speeds up the extraction of sparse features, and after a certain number of iterations, a good sparse coding approximation result can be obtained.

[0092] (3) Construct an interpretable deep network based on convolutional sparse coding blocks:

[0093] Figure 3 The interpretable deep network based on convolutional sparse coding blocks proposed in the present invention is demonstrated, and the network is composed of 7 convolutional sparse coding blocks. Inspired by the U-Net network, the interpretable deep network proposed in the present invention includes upsampling and downsampling modules. First, the short-time Fourier transform of the input signal is downsampled. The downsampling module consists of three convolutional sparse coding blocks and three pooling layers to extract the features of the input short-time Fourier transform; then, a convolutional sparse coding block is used to further extract features; again, the features extracted in the previous step are upsampled. The upsampling module includes three convolutional sparse coding blocks and three deconvolution layers, and the upsampled and downsampled features are fused in the channel dimension; finally, a convolutional layer is used to output the instantaneous frequency estimated by the present invention. Among them, the network structure of the convolutional sparse coding block proposed in the present invention is as follows: Figure 2 As shown. A K-layer convolutional sparse coding block is represented as

[0094] x(k+1)=h θ (Wy+Sx(k))

[0095] Here, K=2 is selected. In each convolutional sparse coding block, W and S are 3*3 convolutional layers. θ , Papyan (2017) showed that the ReLU activation function is equivalent to the non-negative soft threshold operator, that is,

[0096] x(k+1)=ReLU(Wy+Sx(k))

[0097] For simplicity, θ=0 is set, and the ReLU activation function is selected. In addition, batch normalization is added before the ReLU activation function to prevent the model from overfitting. The present invention does not select the bilinear interpolation method but selects 3*3 deconvolution as the upsampling method, and finally uses a 1*1 convolution layer to output the final instantaneous frequency result. In addition, the commonly used mean square error (MSE; Mean Square Error; mean square error) is used as the loss function for training.

[0098] (4) Explain the convergence of the convolutional sparse coding block:

[0099] For the convergence of LISTA, Chen et al. (2018) gave an error bound through theorem and proved that the error bound is

[0100]

[0101] Among them, |x * |≤B, ||x * ||0≤s, ||ε||1≤σ, c>0 and C>0 are constants.

[0102] Numerical simulation results

[0103] The flowchart of the instantaneous frequency estimation method proposed by the present invention is as follows: Figure 4 First, in order to prove the performance of the proposed method, three cases consisting of analytical signals LFM, NLFM and SFM and their complex structures are considered for verification. The instantaneous frequency estimation results are shown in Figure 5 As shown. The first row is the ideal instantaneous frequency of the three signals, the second row is the time-frequency representation result of STFT, the third row is the time-frequency representation result of WVD, the fourth row is the time-frequency representation result of FCNN, and the fifth row is the time-frequency representation result of the method proposed in the present invention. Limited by the Heisenberg uncertainty principle, the STFT time spectrum energy is diffused and the time-frequency resolution is not high. The WVD method improves the diffusion phenomenon and has a higher time-frequency resolution, but it will produce cross-term interference. The time-frequency representation resolution obtained by FCNN is higher, but the instantaneous frequency is not continuous, especially at the intersection or in the middle. FCNN cannot fully recover the instantaneous frequency information. In contrast, the method proposed in the present invention maintains excellent time-frequency resolution and successfully recovers the signal time-frequency representation with higher time-frequency resolution regardless of the signal type. In order to quantitatively compare the performance of the method proposed in the present invention and FCNN, l1 distance and MSE are used as performance evaluation criteria. The synthetic signal is tested by changing the signal-to-noise ratio of the test data from 45db to 5db, and 50 tests are performed at each signal-to-noise ratio. The average l1 distance and MSE are recorded. The results show that the estimation effect of the proposed method is better than that of FCNN regardless of high or low signal-to-noise ratio.

[0104] Secondly, in order to further demonstrate the performance of the proposed method, its effectiveness was tested on the noisy seismic signal of the sedimentary cycle model. The noise signal contains 200 samples with a sampling period of 1 ms. The recovery results using different time-frequency transformation methods are shown in Figure 2. Figure 6 The time-frequency representation result obtained by the method proposed in the present invention has the highest resolution, maintains good signal energy, and reveals the thickening sedimentary cycle.

[0105] Finally, the instantaneous frequency of the real single trace was estimated in an oil well in the Bohai Bay Basin, based on the gamma-ray (GR) and spontaneous potential (SP) logs (e.g. Figure 7 a), Figure 7 b is the actual seismic signal in the time range of 1.2 to 1.5 s, of which the time range of 1.4 to 1.5 s can be interpreted as a sedimentary sand body with varying thickness. Figure 7 c is the time-frequency representation result reconstructed by the method proposed in the present invention, showing that the estimated instantaneous frequency value is between 18 and 30 Hz, which can delineate fluvial sandstone with variable thickness.

Claims

1. A method for estimating instantaneous frequency of seismic signals based on an interpretable deep network, characterized in that: The following steps are involved: Obtaining a short-time Fourier transform representation of the analytical signal, obtaining an accurate instantaneous frequency according to the expression of the analytical signal, and constructing a sample data set according to the short-time Fourier transform representation and the accurate instantaneous frequency; Constructing a convolutional sparse coding block according to a dictionary matrix composed of the input analytical signal and a short-time Fourier window function; Constructing an interpretable deep network model according to the convolutional sparse coding block and the U-Net network model; Using the training set in the sample data set to train the interpretable deep network model to obtain a trained network; A test signal is input, the instantaneous frequency of the test signal is obtained, and the convergence of the trained network is verified through an error boundary.

2. The method for estimating instantaneous frequency of seismic signals based on an interpretable deep network according to claim 1, characterized in that: The sample data set includes three different analytical signals, and the three different analytical signals include a linear frequency modulation signal, a nonlinear frequency modulation signal and a sinusoidal frequency modulation signal.

3. The method for estimating instantaneous frequency of seismic signals based on an interpretable deep network according to claim 2, characterized in that: The construction of the convolutional sparse coding block specifically includes: Calculate a sparse representation according to the input signal and the dictionary matrix, construct a sparse representation model equation according to the input signal, the dictionary matrix and the sparse representation, find the most sparse representation in the sparse representation model equation, and construct the convolutional sparse coding block with the most sparse representation; The sparse representation model equation is expressed as y=Dx, where y represents the input signal, D is the dictionary matrix, x is a sparse representation, and the most sparse representation is x*.

4. The method for estimating instantaneous frequency of seismic signals based on an interpretable deep network according to claim 3, characterized in that: The step of finding the most sparse representation in the sparse representation model equation and constructing the convolutional sparse coding block with the most sparse representation specifically includes: Characterizing a first value and a second value of the most sparse representation according to the sparse representation model equation, the first value including an l0 norm, the second value including an l1 norm, wherein the first value corresponds to a first most sparse representation equation, and the second value corresponds to a second most sparse representation equation; Replacing the l0 norm in the first value with the l1 norm in the second value; Using a least absolute shrinkage and selection algorithm to operate on the second sparsest representation equation to obtain a least absolute shrinkage and selection algorithm equation; The least absolute shrinkage and selection algorithm equations are solved using an iterative soft thresholding algorithm to construct the convolutional sparse coding block.

5. The method for estimating instantaneous frequency of seismic signals based on an interpretable deep network according to claim 4, characterized in that: The convolutional sparse coding block includes k layers, and the convolutional sparse coding block including k layers is expressed as x(k+1)=h θ (Wy+Sx(k)), where w, s, θ represent the trainable parameter set of the convolutional sparse coding block, and h θ Representing a non-negative soft threshold operator, the method also includes using a weighted ReLU activation function to replace the non-negative soft threshold operator to generate a ReLU activation function replacement equation, and the ReLU activation function replacement equation is expressed as x(k+1)=ReLU(Wy+sx(k)).

6. The method for estimating instantaneous frequency of seismic signals based on an interpretable deep network according to claim 5, characterized in that: The verifying the convergence of the convolutional sparse coding block by the error boundary specifically includes: The convergence of the convolutional sparse coding block is verified by the error boundary equation, which is expressed as ||x k (x * ,ε)-x * ||2≤sBexp(-ck)+Cσ, Among them, |x * |≤B, ||x * ||0≤s, ||ε||1≤σ, c>0 and C>0 are constants.

7. The method for estimating instantaneous frequency of seismic signals based on an interpretable deep network according to claim 2, characterized in that: The sample data set is constructed using signals from three situations to verify the performance of the network. The signals from the three situations are: Case 1: Two Crossed Chirp Signals Case 2: Two similar nonlinear FM signals Case 3: Crossed linear FM and sine FM signals a(t) represents amplitude, and a(t)=exp(-0.005t).

8. The method for estimating instantaneous frequency of seismic signals based on an interpretable deep network according to claim 1, characterized in that: The convolutional sparse coding block, upsampling and feature fusion layers constitute a U-Net network model.

9. The method for estimating instantaneous frequency of seismic signals based on an interpretable deep network according to claim 8, characterized in that: The U-Net network model is a semantic segmentation network model. The U-Net network model consists of 19 convolutional layers, 4 maximum pooling layers and 4 upsampling layers. The shape of the U-Net network model is U-shaped.

10. The method for estimating instantaneous frequency of seismic signals based on an interpretable deep network according to claim 7, characterized in that: The signal-to-noise ratio of the sample data set is 5dB-45dB, and the sample data set includes a training sample data set and a verification sample data set, wherein the number of the training sample data set is greater than the number of the verification sample data set.

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