Research on Seismic Signal Denoising Model Based on DnCNN Network

Abstract

Addressing the noise in seismic signals, a prevalent challenge within seismic signal processing, has been the focus of extensive research. Conventional algorithms for seismic signal denoising often fall short due to their reliance on manually determined feature functions and threshold parameters. These limitations hinder effective noise removal, resulting in suboptimal signal-to-noise ratios (SNRs) and post-denoising waveform distortion. To address these shortcomings, this study introduces a novel denoising approach leveraging a DnCNN network. The DnCNN framework, which integrates batch normalization with residual learning, is adept at swiftly identifying and eliminating noise from seismic signals through its residual learning capabilities. To assess the efficacy of this DnCNN-based model, it was rigorously tested against a curated test set and benchmarked against other denoising techniques, including wavelet thresholding, empirical mode decomposition, and convolutional auto-encoders. The findings demonstrate that the DnCNN model not only significantly enhances the SNR and correlation coefficient of the processed seismic signals but also achieves superior noise reduction performance.

1. Introduction

In the quest to refine seismic signal denoising techniques, a variety of traditional approaches have been explored, including the Fourier Transform, Wavelet Transform (WT), and Empirical Mode Decomposition (EMD). The Fourier Transform, a foundational method in seismic signal analysis, facilitates the transition of signals from the time domain to the frequency domain, targeting noise elimination through frequency range differentiation [1]. Yet, this method falls short in capturing simultaneous time and frequency characteristics, hindering the comprehensive analysis of nonstationary seismic signals. Wavelet Transform, on the other hand, extends the analysis to a two-dimensional time–frequency domain, offering a more nuanced processing of nonstationary signals [2]. However, its efficacy is contingent upon the selection of an appropriate threshold and basis function [3]. EMD offers a decomposition technique that operates based on the signal’s intrinsic time-scale attributes, yet it grapples with issues like mode aliasing and the challenge of selecting the right intrinsic mode functions [4,5]. Advanced versions of EMD, such as EEMD, CEEMDAN, and ICEEMDAN, have been developed to address these limitations and provide more robust denoising capabilities [6,7,8].

Since 2012, with the advent of AlexNet’s victory at the ILSVRC, deep neural networks have revolutionized fields like image recognition and noise reduction [9], leveraging their superior feature extraction and nonlinear mapping capabilities, along with reduced human intervention and computational costs. This has prompted researchers to explore their application in seismic signal denoising. In 2018, Siwei Yu and colleagues employed a multi-layer convolutional neural network for adaptive noise reduction [10], outperforming traditional methods. However, the effectiveness of such networks is constrained by their depth, with shallower networks failing to capture detailed signal features and deeper networks susceptible to gradient vanishing. Han Weixue and others validated the potential of multi-layer CNNs in seismic data, while Yuchen Jin’s team introduced an auto-encoder that leverages deep residual networks to mitigate gradient issues [11]. Despite these advances, challenges remain in distinguishing between seismic signals and noise, especially with nonstationary signals.

In 2019, Wang Yuqing and colleagues addressed the scarcity of labeled data in seismic denoising by employing data augmentation and CNN techniques [12]. Yangkang Chen utilized sparse auto-encoders to reduce noise while preserving data details, and Weiqiang Zhu investigated a U-Net-based method, DeepDenoiser, for noise suppression. Yet, U-Net’s reliance on shallow layer features can lead to the loss of significant signal information, impacting SNR improvement [13]. Xintong Dong and Wang Feng, in 2020, focused on regional noise suppression and predictive noise modeling through deep learning, respectively [14]. Despite the potential of deep learning to enhance denoising, issues such as low SNRs and signal distortion persist.

To overcome these challenges, this study introduces a DnCNN-based seismic signal denoising model. The DnCNN network is a convolutional neural network that combines batch normalization and residual learning. It uses the DnCNN residual learning method to efficiently and quickly learn the noise in seismic signals and then remove the learned noise from the noisy seismic signals.The DnCNN model can use the residual learning method to reduce the noise of seismic signals with different SNR without manual intervention. This model is designed to enhance the SNR of noisy seismic signals and to minimize distortion of the waveform, offering a promising advancement in the field of seismic signal processing.

2. Design of Seismic Signal Denoising Model Based on DnCNN

Seismic signal denoising is done to remove various kinds of noise from the noisy seismic signal and restore the original seismic signal, as shown in Formula (1):

$$x=y+v$$

(1)

In Formula (1), x is the seismic signal with noise, y is the original seismic signal without noise, and v is various kinds of noise contained in the seismic signal. The ultimate goal of seismic signal denoising is to accurately recover clean data y from noisy data x by using the DnCNN to obtain an estimate of the original seismic signal $y_0$ and make $y_0$ ≈ y.

2.1. Principle of Residual Learning

Deep learning advancements have led to increasingly deeper CNNs, enabling the extraction of more nuanced features, which is advantageous for training models. Yet, enhancing the depth of traditional CNNs can trigger gradient vanishing or explosion issues. To address these challenges, He Kaiming and his collaborators introduced ResNet, a network architecture predicated on residual learning units [15]. This architecture, as depicted in Figure 1, leverages skip connections to streamline the network’s structure and employs identity mapping to sidestep layers with nonlinear transformations.

ResNet’s architecture addresses depth-related training difficulties by introducing residual blocks, which simplify the training of very deep networks. These blocks allow the network to learn residuals, or the difference between the input and output, rather than the output itself. This approach alleviates the vanishing gradient issue by providing an alternative path for gradients, ensuring that signals can pass through the network without diminishing. As a result, ResNet facilitates the training of deeper networks by maintaining the flow of gradients and preventing the typical issues associated with network depth, as shown in Figure 1.

If the input is set to x, H(x) represents the mapping of the backbone neural network, F(x) represents the mapping of multiple convolutional layers, and F(x) can be expressed by Equation (2):

$$F\left(x\right)=H\left(x\right)-x$$

(2)

The mapping of the original neural network is expressed by Formula (3):

$$H\left(x\right)=F\left(x\right)+x$$

(3)

The optimization difficulty of the function F(x) + x is less than that of H(x), so the problem of gradient vanishing or exploding can be alleviated by using the residual learning unit.

2.2. Seismic Signal Denoising Model Structure Based on DnCNN Network

The seismic signal denoising model, which leverages the DnCNN network, adopts the principle of residual learning and employs residual mapping for processing [16]. Rather than attempting to model pristine seismic signals directly, this approach focuses on capturing the characteristics of noise, which are more tractable for the neural network. Throughout both the training and testing phases, the model takes in seismic signals laden with noise and produces an estimation of the noise present. The clean seismic signal is then derived by subtracting the predicted noise from the original noisy signal. A schematic representation of the DnCNN-based seismic signal denoising model is presented in Figure 2, illustrating its architecture and workflow.

The DnCNN-based seismic signal denoising model integrates several key components, including convolutional layers, batch normalization, ReLU activation functions, and residual learning. This model steers clear of the pooling layer, which is known to discard important features necessary for effective noise reduction, often leading to inferior signal recovery. Also, given that fully connected layers involve a multitude of parameters and are typically reserved for classification tasks, they are deemed inappropriate for seismic signal denoising, hence their exclusion from the DnCNN architecture. Instead, the model concludes with a convolutional layer to directly generate an output that matches the dimensions of the estimated signal, enhancing the model’s efficiency.

The initial layer of this model combines a convolutional layer with an activation function, which is tasked with extracting features from the input signal. It utilizes a $3\times 1$ kernel and 64 kernels for this purpose. Unlike DnCNN’s two-dimensional kernels designed for image data, the seismic signal denoising model employs one-dimensional kernels to process one-dimensional seismic signals. From the second to the sixteenth layer, the model replicates modules consisting of convolutional layers, batch normalization, and ReLU activations, each equipped with a $3\times 1$ kernel and 64 kernels. The final layer, which is responsible for noise prediction, uses a $3\times 1$ kernel and a single kernel. The DnCNN model comprises 17 layers in total, a configuration that has been optimized for image denoising and is similarly effective for seismic signal denoising. The denoised seismic signal is derived by subtracting the predicted noise from the noisy signal, capitalizing on the residual learning approach.

In this paper, the network structure of the DnCNN is used to construct a CNN model for seismic signal denoising. The model uses the residual learning method to predict the noise in the seismic signal. The final output of the model is the noise R(X) ≈ V. The estimation of the original seismic signal can be obtained by subtracting the noise R(X) from the noisy seismic signal, i.e., ${\mathit{y}}_0=\mathit{x}-\mathit{R}\left(\mathit{X}\right)$. The loss function is used to calculate the error between the estimated value and the expected value. The loss function used in this paper is the MSE (Mean Square Error) loss, as shown in Formula (4).

$$\psi \left(\rho \right)={\displaystyle \frac{1}{2M}}\sum _{i=1}^M\mid \mid R(x_i;\rho )-(x_i-y_i)\mid {\mid }_F^2$$

(4)

In Formula (4), $x_i$ (i= 1, 2,…, M) are M training samples of seismic signals with noise, $y_i$ (i = 1, 2,…, M) are M original seismic signal training samples without noise, $∥·∥$ denotes the Frobenius norm, and $\rho$ is the parameter of the model, which is obtained through the training process.

3. Dataset and Evaluation Metrics

3.1. Dataset and Data Preprocessing

A large amount of seismic data is required to train and test the model. The dataset used in this paper is the STEAD (Stanford Earthquake Dataset—STEAD), which is a high-quality, large-scale, and global dataset of local seismic and nonseismic signals recorded by seismic instruments. The seismic event signals contained in the dataset are labeled with the labels required for the training of various deep learning networks [17]. Examples of seismic event signals and nonseismic signals in the dataset are shown in Figure 3, Figure 4 and Figure 5.

For the purposes of training and evaluating our network, we require seismic signals that include noise. In this study, these noisy signals were artificially created by combining pristine seismic signals with noise. Given the challenge of acquiring truly clean seismic signals in the field, we chose 82,380 seismic event signals from the STEAD dataset, which have a high signal-to-noise ratio (SNR), to serve as our proxy for clean signals. Additionally, we selected 199,760 nonseismic signals from STEAD to act as our noise dataset. The synthesis of noisy seismic signals was achieved by blending these clean signal samples with noise samples in various ways.

To bolster our dataset of noisy seismic signals, we employed a random combination method. This involved randomly shifting each clean seismic signal, arbitrarily selecting a noise sample, arbitrarily adjusting its amplitude, and then superimposing this noise onto the clean signal to produce a range of seismic signals with varying SNRs. To enhance the network’s training convergence, the synthesized noisy seismic signals were normalized, as detailed by the normalization Formula (5), which refers to the amplitude value of the seismic event signal. This normalization step is crucial for maintaining the integrity of the signal features during the training process.

$$v_i={\displaystyle \frac{v_i}{max\mid v_i\mid }}$$

(5)

Each signal within our dataset was uniformly segmented to a duration of 30 s, with any excess length being truncated from the end. This 30-s window was chosen, as it sufficiently captures the primary waveform of high SNR seismic events within the initial 30 s. The dataset was then randomly partitioned into three subsets—the training set, the validation set, and the test set—in the ratios of 80% (65,904), 10% (8238), and 10% (8238), respectively. The training set was utilized for model training, the validation set for tuning the model’s hyperparameters, and the test set for evaluating the model’s denoising performance. This systematic division ensured a robust evaluation of the model’s capabilities across different phases of development and testing.

3.2. Model Evaluation Metrics

In this paper, the SNR and r (Correlation Coefficient) were used to quantitatively evaluate the effect of noise reduction. The SNR and r are calculated in Formulas (6) and (7):

$$SNR=10{log}_{10}{\displaystyle \frac{{\sigma }_s}{{\sigma }_n}}$$

(6)

$$r(X,Y)={\displaystyle \frac{Cov(X,Y)}{\sqrt{Var\left[X\right]Var\left[Y\right]}}}$$

(7)

In Formula (6), ${/sig}_s$ represents the energy of the clean signal, and ${/sig}_n$ represents the energy of the noise; in Formula (7), X is the signal before denoising, Y is the signal after denoising, Cov(X,Y) represents the covariance between the signal before and after denoising, Var[X] represents the variance of the signal before denoising, and Var[Y] represents the variance of the signal after the denoising.

SNR represents the ratio of signal to noise in the noisy signal, and the larger the SNR is, the lower the noise content is; r indicates the degree of correlation between the signal after denoising and the original signal, and its value is between 0 and 1. The closer the value is to 1, the more similar the signal waveform is to the original signal, and the better the denoising effect is.

4. Experimental Results and Analysis

The seismic signal denoising experiments utilizing the DnCNN-based model outlined in this paper were bifurcated into two principal phases: model training and denoising application.

During the training phase, we input seismic signals corrupted by noise, with the noise itself serving as the label for our network’s predictions. The loss function quantifies the discrepancy between the predicted noise and the actual noise. Through iterative forward and backward propagation, the network’s parameters were adjusted to minimize this loss, thereby learning to map noisy seismic signals to their noise components. This learned mapping constituted our trained model.

In the denoising phase, once the model was adequately trained, it was fed noisy seismic signals, and it output the estimated noise component. By subtracting this estimated noise from the original noisy signal, we extracted the denoised seismic signal, achieving the desired noise reduction.

For these experiments, TensorFlow was employed to build the model, which was trained on a GPU (specifically, a GTX1660). The training parameters included an initial learning rate of 0.001, optimization via the Adam algorithm, 100 epochs, and a batch size of 16. After approximately 25 h of training, the model typically converged around 85 epochs, yielding the final trained model.

4.1. Denoising Effect on Test Set

To assess the efficacy of the noise reduction model, the DnCNN-based seismic signal denoising model was subjected to evaluations using the established test dataset. The outcomes of these tests are depicted in Figure 6 and Figure 7. In these illustrations, segment (a) denotes the pristine seismic event signal, segment (b) is the signal post-noise addition, and segment (c) illustrates the signal following the denoising process. Figure 6 presents the outcomes for high-frequency noise, demonstrating the DnCNN model’s capability to efficiently eliminate noise and restore the original seismic signal when comparing (a) and (c). Figure 7, on the other hand, exhibits the results for low-frequency noise scenarios, showing that the DnCNN model is adept at mitigating the significant oscillations induced by such noise when comparing (a) and (c). These visual comparisons validate the model’s proficiency in noise reduction across different frequency bands.

4.2. Comparison with Other Algorithms

To evaluate and compare the denoising performance of the DnCNN model against other prevalent denoising techniques, this study employed the DnCNN model alongside Wavelet Transform (WT), Empirical Mode Decomposition (EMD), and convolutional auto-encoders to process seismic signals across a range of signal-to-noise ratios (SNRs). The test subjects, depicted in Figure 8, consist of seismic signals adulterated with noise to create signals with SNRs spanning from −6 dB to 10 dB in increments of 2 dB. These synthesized signals, which incorporate both noise and seismic components, served as the basis for the comparative analysis. The comparative denoising outcomes, as documented in

Table 1. Comparison of denoising effects of different denoising algorithms under different SNRs.

	Algorithm	Wavelet		EMD		Convolutional (Auto-Encoder)		DnCNN
SNR (dB)		SNR (dB)	r	SNR (dB)	r	SNR (dB)	r	SNR (dB)	r
−6		0.36	0.5488	−0.14	0.5907	2.98	0.6630	3.01	0.6634
−4		1.73	0.6533	1.74	0.6950	4.11	0.7512	4.46	0.7511
−2		3.02	0.7416	3.48	0.7822	5.48	0.8224	5.98	0.8223
0		4.24	0.8014	5.01	0.8385	7.16	0.8829	7.52	0.8831
2		5.79	0.8631	6.63	0.8874	8.37	0.9029	8.74	0.9014
4		7.23	0.9025	8.21	0.9215	9.69	0.9244	10.02	0.9251
6		8.95	0.9374	9.43	0.9412	11.02	0.9416	11.38	0.9415
8		10.57	0.9555	10.58	0.9554	12.46	0.9548	12.73	0.9552
10		12.17	0.9795	11.72	0.9665	13.81	0.9671	13.96	0.9687
Average		6.01	0.8203	6.30	0.8420	8.34	0.8678	8.64	0.8679

, offer insights into the efficacy of each algorithm at varying SNR levels, providing a comprehensive assessment of their respective denoising capabilities.

An analysis of Table 1 reveals that while both the WT and EMD techniques provided some enhancement in the seismic signal SNR, their effectiveness was constrained. In contrast, the DnCNN model surpassed these methods by learning noise patterns from the signals during training, resulting in a more substantial increase in the SNR for the denoised seismic signals. The DnCNN outperformed the WT and EMD across various SNR levels, demonstrating its superiority. Although the DnCNN model showed a slightly higher SNR compared to the convolutional auto-encoder, the difference is not markedly significant. Overall, the DnCNN model significantly outshined the traditional methods in terms of SNR improvement and denoising performance, highlighting the advantages of its residual learning approach. The DnCNN model achieved an average SNR improvement of 2.63 dB over the WT method and 2.34 dB over the EMD method. Additionally, the average improvement in the correlation coefficient for the DnCNN compared to the WT and EMD was 0.0476 and 0.0259, respectively. These enhancements underscore the DnCNN model’s optimized capability for seismic signal denoising.

5. Conclusions

This paper introduces a DnCNN-network-based seismic signal denoising model to tackle the limitations of traditional denoising algorithms, which are often hindered by manually selected features or threshold parameters, leading to suboptimal noise removal. The proposed DnCNN model leverages residual learning and batch normalization to efficiently capture the characteristics of seismic signals. Through rigorous training and testing with a curated dataset, the model has proven its proficiency in noise reduction within seismic signals. Comparative experiments with Wavelet Transform (WT), Empirical Mode Decomposition (EMD), and the DnCNN model on seismic signals across various noise levels demonstrate the superior performance of the DnCNN model. The results indicate that the DnCNN model not only surpasses traditional algorithms in denoising efficacy but also enhances the SNRs of seismic signals without being encumbered by the constraints of manual feature selection or thresholding.

Future work could explore the integration of the DnCNN model into real-time seismic monitoring systems, as well as the development of hybrid models combining DnCNN with other techniques (such as traditional methods) to achieve even more powerful denoising capabilities.