Improving the Signal‐to‐Noise Ratio of Seismological Datasets by Unsupervised Machine Learning

Abstract

Seismic waves that are recorded by near-surface sensors are usually disturbed by strong noise. Hence, the recorded seismic data are sometimes of poor quality; this phenomenon can be characterized as a low signal-to-noise ratio (SNR). The low SNR of the seismic data may lower the quality of many subsequent seismological analyses, such as inversion and imaging. Thus, the removal of unwanted seismic noise has significant importance. In this article, we intend to improve the SNR of many seismological datasets by developing new denoising framework that is based on an unsupervised machine-learning technique. We leverage the unsupervised learning philosophy of the autoencoding method to adaptively learn the seismic signals from the noisy observations. This could potentially enable us to better represent the true seismic-wave components. To mitigate the influence of the seismic noise on the learned features and suppress the trivial components associated with low-amplitude neurons in the hidden layer, we introduce a sparsity constraint to the autoencoder neural network. The sparse autoencoder method introduced in this article is effective in attenuating the seismic noise. More importantly, it is capable of preserving subtle features of the data, while removing the spatially incoherent random noise. We apply the proposed denoising framework to a reflection seismic image, depth-domain receiver function gather, and an earthquake stack dataset. The purpose of this study is to demonstrate the framework’s potential in real-world applications. INTRODUCTION Seismic phases from the discontinuities in the Earth’s interior contain significant constraints for high-resolution deep Earth imaging; however, they sometimes arrive as weak-amplitude waveforms (Rost and Weber, 2001; Rost and Thomas, 2002; Deuss, 2009; Saki et al., 2015; Guan and Niu, 2017, 2018; Schneider et al., 2017; Chai et al., 2018). The detection of these weak-amplitude seismic phases is sometimes challenging because of three main reasons: (1) the amplitude of these phases is very small and can be neglected easily when seen next to the amplitudes of neighboring phases that are much larger; (2) the coherency of the weak-amplitude seismic phases is seriously degraded because of insufficient array coverage and spatial sampling; and (3) the strong random background noise that is even stronger than the weak phases in amplitude makes the detection even harder. As an example of the challenges presented, the failure in detecting the weak reflection phases from mantle discontinuities could result in misunderstanding of the mineralogy or temperature properties of the Earth interior. To conquer the challenges in detecting weak seismic phases, we need to develop specific processing techniques. In earthquake seismology, in order to highlight a specific weak phase, recordings in the seismic arrays are often shifted and stacked for different slowness and back-azimuth values (Rost and Thomas, 2002). Stacking serves as one of the most widely used approaches in enhancing the energy of target signals. Shearer (1991a) stacked long-period seismograms of shallow earthquakes that were recorded from the Global Digital Seismograph Network for 5 yr and obtained a gather that shows typical arrivals clearly from the deep Earth. Morozov and Dueker (2003) investigated the effectiveness of stacking in enhancing the signals of the receiver functions. They defined a signal-to-noise ratio (SNR) metric that was based on the multichannel coherency of the signals and the incoherency of the random noise, and they showed that the stacking can significantly improve the SNR of the stacked seismic trace. However, stacking methods have some drawbacks. First, they do not necessarily remove the noise present in the signal. Second, they require a large array of seismometers. Third, they require coherency of arrivals across the array, which are not always about earthquake seismology. From this point of view, a single-channel method seems to be a better substitute for improving the SNR of seismograms (Mousavi and Langston, 2016; 2017). In the reflection seismology community, many noise attenuation methods have been proposed and implemented in field applications over the past several decades. Prediction-based methods utilize the predictive property of the seismic signal to construct a predictive filter that prevents noise. Median filters and their variants use the statistical principle to reject Gaussian white noise or impulsive noise (Mi et al., 2000; Bonar and Sacchi, 2012). The dictionary-learning-based methods adaptively learn the basis from the data to sparsify the noisy seismic data, which will in turn suppress the noise (Zhang, van der Baan, et al., 2018). These methods require experimenters to solve the dictionary-updating and sparse-coding methods and can be very 1552 Seismological Research Letters Volume 90, Number 4 July/August 2019 doi: 10.1785/0220190028 Downloaded from https://pubs.geoscienceworld.org/ssa/srl/article-pdf/90/4/1552/4790732/srl-2019028.1.pdf by Seismological Society of America, Mattie Adam on 09 July 2019 expensive, computationally speaking. Decomposition-based methods decompose the noisy data into constitutive components, so that one can easily select the components that primarily represent the signal and remove those associated with noise. This category includes singular value decomposition (SVD)-based methods (Bai et al., 2018), empirical-mode decomposition (Chen, 2016), continuous wavelet transform (Mousavi et al., 2016), morphological decomposition (Huang et al., 2017), and so on. Rank-reduction-based methods assume that seismic data have a low-rank structure (Kumar et al., 2015; Zhou et al., 2017). If the data consist of κ complex linear events, the constructed Hankel matrix of the frequency data is a matrix of rank κ (Hua, 1992). Noise will increase the rank of theHankel matrix of the data, which can be attenuated via rank reduction. Such methods include Cadzow filtering (Cadzow, 1988; Zu et al., 2017) and SVD (Vautard et al., 1992). Most of the denoising methods are largely effective in processing reflection seismic images. The applications in more general seismological datasets are seldom reported, partially because of the fact that many seismological datasets have extremely low data quality. That is, they are characterized by low SNR and poor spatial sampling. Besides, most traditional denoising algorithms are based on carefully tuned parameters to obtain satisfactory performance. These parameters are usually data dependent and require a great deal of experiential knowledge. Thus, they are not flexible enough to use in application to many real-world problems. More research efforts have been dedicated to using machine-learning methods for seismological data processing (Chen, 2018a,b; Zhang, Wang, et al., 2018; Bergen et al., 2019; Lomax et al., 2019; McBrearty et al., 2019). Recently, supervised learning (Zhu et al., 2018) has been successfully applied for denoising of the seismic signals. However, supervised methods with deep networks require very large training datasets (sometimes to an order of a billion) of clean signals and their noisy contaminated realizations. In this article, we develop a new automatic denoising framework for improving the SNR of the seismological datasets based on an unsupervised machine-learning (UML) approach; this would be the autoencoder method. We leverage the autoencoder neural network to adaptively learn the features from the raw noisy seismological datasets during the encoding process, and then we optimally represent the data using these learned features during the decoding process. To effectively suppress the random noise, we use the sparsity constraint to regularize the neurons in the hidden layer. We apply the proposed UML-based denoising framework to a group of seismological datasets, including a reflection seismic image, a receiver function gather, and an earthquake stack. We observe a very encouraging performance, which demonstrates its great potential in a wide range of applications. METHOD Unsupervised Autoencoder Method Wewill first introduce the autoencoder neural network that we use for denoising seismological datasets. Autoencoders are specific neural networks that consist of two connected parts (decoder and encoder) that try to copy their input to the output layer. Hence, they can automatically learn the main features of the data in an unsupervised manner. In this article, the network is simply a three-layer architecture with an input layer, a hidden layer, and an output layer. The encoding process in the autoencoder neural network can be expressed as follows: EQ-TARGET;temp:intralink-;df1;323;673 ξ W1x b1 ; 1 in which x is the training sample (x∈Rn), ξ is the activation function. The decoding process can be expressed as follows: EQ-TARGET;temp:intralink-;df2;323;608 x ⌢ ξ W2x b2 : 2 In equations (1) and (2), W1 is the weighting matrix between the input layer and the hidden layer; b1 is the forward bias vector; W2 is the weighting matrix between the hidden layer and output layer; b2 is the backward bias vector; and ξ is the activation function. In this study, we use the softplus function as the activation function: EQ-TARGET;temp:intralink-;df3;323;505 ξ x log 1 e : 3 Sparsity Regularized Autoencoder To mitigate the influence of the seismic noise on the learned features and suppress the trivial components associated with low-amplitude neurons in the hidden layer, we apply a sparsity constraint to the hidden layer; that is, the output or last layer of the encoder. The sparsity constraint can help dropout the extracted nontrivial features that correspond to the noise and a small value in the hidden units. It can thus highlight the most dominant features in the data—the useful signals. The sparse penalty term can be written as follows: EQ-TARGET;temp:intralink-;df4;323;335~ R p ; 4 in which R is the penalty function: EQ-TARGET;temp: