Seismic signals are oscillatory signals with nonstationary frequency content. These time-varying spectral structures have been shown to contain useful information for seismic signal characterization. Harmonic analysis can give us insight into the complex structure of seismic signals. Advanced reassignment techniques such as synchrosqueezing provide us with high-resolution imaging of this time-frequency structure. I used this new mathematical technique and developed one of its early applications for simultaneous denoising and onset picking and decomposing of earthquake signals and noise based on principles of wavelet shrinkage. Wavelet shrinkage is a widely popular statistic technique in signal processing that is used for Gaussian noise attenuation even when the signal and noise share the same frequency band. However, the conventional approach has been shown not to be effective for seismic denoising mainly due to the limitations of the original thresholding functions and the non-Gaussian nature of noise in seismic data that violate the assumptions commonly used for noise level estimations. I worked on this problem and improved the performance of time-frequency denoising for seismic data, by proposing more flexible thresholding functions specifically designed for earthquake signals and developing a more realistic noise level estimation approach. Building upon these, we showed that deep learning can provide even better denoising/decomposition performance by providing a more nonlinearity in sparse mapping between noisy and denoised signals while learning more realistic statistics of noise directly from data.
Langston, C.A., and Mousavi, S. M., (2019), Separating Signal from Noise and from other Signal using Non-linear Thresholding and Scale-Time Windowing of Continuous Wavelet Transforms, Bulletin of Seismological Society of America.
A procedure for removing noise or signal from seismic time series using the continuous wavelet transform (CWT) is developed through the common assumption of noise stationarity for pre‐event or post-event estimates of the noise. Noise and signal are efficiently separated using nonlinear thresholding of the CWT avoiding computationally intensive block thresholding algorithms on the wavelet scale‐time plane. Efficiency is gained by estimating the characteristic statistics of pre‐event noise using empirical cumulative distribution functions and then using these characteristics to threshold the entire time series using hard or soft nonlinear thresholding. In addition, scale‐time windowing of the CWT scalogram and inverse transforming into the time domain allows unprecedented control in partitioning a seismogram into component wave types that can subsequently be used to infer characteristics of Earth structure and source excitation. Noise can be separated from signals and signals decomposed into discrete wave groups. CWT techniques offer unique and intuitive alternatives to traditional Fourier methods for analyzing noise and signal useful for structure and source studies, event detection, and ambient‐noise interferometry.
Zhu, W., Mousavi, S. M., Beroza, G. C., (2019). Seismic Signal Denoising and Decomposition Using Deep Neural Networks, IEEE transaction in geoscience and remote sensing.
Frequency filtering is widely used in the routine processing of seismic data to improve the signal-to-noise ratio (SNR) of recorded signals and by doing so to improve subsequent analyses. In this paper, we develop a new denoising/decomposition method, DeepDenoiser, based on a deep neural network. This network is able to simultaneously learn a sparse representation of data in the time–frequency domain and a non-linear function that maps this representation into masks that decompose input data into a signal of interest and noise (defined as any non-seismic signal). We show that DeepDenoiser achieves impressive denoising of seismic signals even when the signal and noise share a common frequency band. Because the noise statistics are automatically learned from data and require no assumptions, our method properly handles white noise, a variety of colored noise, and non-earthquake signals. DeepDenoiser can significantly improve the SNR with minimal changes in the waveform shape of interest, even in the presence of high noise levels. We demonstrate the effectiveness of our method on improving earthquake detection. There are clear applications of DeepDenoiser to seismic imaging, micro-seismic monitoring, and preprocessing of ambient noise data. We also note that the potential applications of our approach are not limited to these applications or even to earthquake data and that our approach can be adapted to diverse signals and applications in other settings.
Mousavi, S. M., and Langston, C. A., (2017). Automatic Noise-Removal/Signal-Removal Based on the General-Cross-Validation Thresholding in Synchrosqueezed domains, and its application on earthquake data, Geophysics.
Recorded seismic signals are often corrupted by noise. We have developed an automatic noise-attenuation method for single-channel seismic data, based on high-resolution time-frequency analysis. Synchrosqueezing is a time-frequency reassignment method aimed at sharpening a time-frequency picture. Noise can be distinguished from the signal and attenuated more easily in this reassigned domain. The threshold level is estimated using a general cross-validation approach that does not rely on any prior knowledge about the noise level. The efficiency of the thresholding has been improved by adding a preprocessing step based on kurtosis measurement and a postprocessing step based on adaptive hard thresholding. The proposed algorithm can either attenuate the noise (either white or colored) and keep the signal or remove the signal and keep the noise. Hence, it can be used in either normal denoising applications or preprocessing in ambient noise studies. We tested the performance of the proposed method on synthetic, microseismic, and earthquake seismograms.
Mousavi, S. M., and Langston, C. A., (2016). Adaptive noise estimation and suppression for improving microseismic event detection, Journal of Applied Geophysics.
Microseismic data recorded by surface arrays are often strongly contaminated by unwanted noise. This background noise makes the detection of small-magnitude events difficult. A noise level estimation and noise reduction algorithm is presented for microseismic data analysis based upon minimally controlled recursive averaging and neighborhood shrinkage estimators. The method might not be compared with more sophisticated and computationally expensive denoising algorithms in terms of preserving detailed features of seismic signals. However, it is fast and data-driven and can be applied in the real-time processing of continuous data for event detection purposes. Results from the application of this algorithm to synthetic and real seismic data show that it holds great promise for improving microseismic event detection.
Mousavi, S. M., and Langston, C. A., (2016). Hybrid Seismic Denoising Using Wavelet Block Thresholding and Higher Order Statistics, Bulletin of Seismological Society of America.
We introduce a nondiagonal seismic denoising method based on the continuous wavelet transform with hybrid block thresholding (BT). Parameters for the BT step are adaptively adjusted to the inferred signal property by minimizing the unbiased risk estimate of Stein (1980). The efficiency of the denoising for seismic data has been improved by adapting the wavelet thresholding and adding a preprocessing step based on a higher‐order statistical analysis and a postprocessing step based on Wiener filtering. Application of the proposed method on synthetic and real seismic data shows the effectiveness of the method for denoising and improving the signal‐to‐noise ratio of local microseismic, regional, and ocean bottom seismic data.
Mousavi, S. M., Langston, C. A., Horton, S. P., (2016). Automatic Microseismic Denoising and Onset Detection Using the Synchrosqueezed-Continuous Wavelet Transform, Geophysics.
Typical microseismic data recorded by surface arrays are characterized by low signal-to-noise ratios (S/Ns) and highly nonstationary noise that make it difficult to detect small events. Currently, array or crosscorrelation-based approaches are used to enhance the S/N prior to processing. We have developed an alternative approach for S/N improvement and simultaneous detection of microseismic events. The proposed method is based on the synchrosqueezed continuous wavelet transform (SS-CWT) and custom thresholding of single-channel data. The SS-CWT allows for the adaptive filtering of time- and frequency-varying noise as well as offering an improvement in resolution over the conventional wavelet transform. Simultaneously, the algorithm incorporates a detection procedure that uses the thresholded wavelet coefficients and detects an arrival as a local maxima in a characteristic function. The algorithm was tested using a synthetic signal and field microseismic data, and our results have been compared with conventional denoising and detection methods. This technique can remove a large part of the noise from small-amplitudes signal and detect events as well as estimate onset time.