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Seismic Signal Denoising and Decomposition Using Deep Neural Networks
Weiqiang Zhu, S. Mostafa Mousavi, Gregory C. Beroza
TL;DR
Seismic denoising is difficult when noise overlaps the signal in frequency and when fixed filtering can distort waveforms. DeepDenoiser jointly learns sparse time-frequency features and nonlinear masks to separate signal from noise, improving denoising and earthquake detection while preserving waveform characteristics.
Problem
Conventional filtering struggles with overlapping signal and noise frequencies, parameter selection, and waveform preservation.
Method
DeepDenoiser uses a deep neural network to jointly learn sparse time-frequency representations and separate masks for seismic signal and noise.
Results
DeepDenoiser robustly denoises shared-band, colored, and non-earthquake noise while improving SNR, preserving waveform shape, and improving earthquake detection metrics.
Takeaways & Limitations
The method supports seismic denoising and decomposition with potential applications in earthquake detection, seismic imaging, micro-seismic monitoring, and ambient-noise preprocessing.
Takeaways & Limitations
Using one mask for both real and imaginary components cannot perfectly separate complex signal and noise or recover signal values larger than the noisy input.
Abstract
from arXiv · showhide
Denoising and filtering are widely used in routine seismic-data-processing 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 learn simultaneously 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. Our method properly handles 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 presence of high noise levels. We demonstrate the effect 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 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.
I. INTRODUCTION
DeepDenoiser addresses the limitations of conventional seismic filtering by jointly learning sparse time-frequency representations and nonlinear signal/noise masks. It is designed for signals and noise that overlap in frequency and vary across time.
- I. INTRODUCTION: Conventional spectral filtering is ineffective when seismic signals and noise occupy the same frequency range.Parameter selection is nonintuitive, often time-varying, and may substantially alter waveform shape.
- I. INTRODUCTION: Time-frequency denoising separates signal and noise by transforming data into domains where seismic signals can be represented sparsely.Thresholded coefficients are inverse-transformed to reconstruct the denoised signal.
- I. INTRODUCTION: Choosing a suitable thresholding function remains challenging, motivating improvements in both sparse representation and the mapping from noisy data to denoised signal.The paper focuses on using deep learning to improve both components.
- I. INTRODUCTION: DeepDenoiser jointly learns a sparse representation and a high-dimensional nonlinear mapping that produces separate masks for seismic signal and noise.It is trained on earthquake seismograms mixed with varied noise and non-earthquake signals, then evaluated on unseen noisy seismograms and earthquake detection.
II. METHOD
The method formulates seismic denoising as supervised learning in the time-frequency domain. A fully convolutional network learns adaptive signal and noise masks that are applied to noisy coefficients before inverse transformation.
- II. METHOD: Recorded data are modeled in the time-frequency domain as seismic signal superposed with additive natural, instrumental, or non-seismic noise.The denoising objective is to estimate the underlying seismic signal from its noise-contaminated version.
- II. METHOD: DeepDenoiser learns a sparse representation and an optimal mapping from training distributions of signal and noise data.The formulation uses separate masks for signal and noise and is described as analogous to Wiener deconvolution.
- II. METHOD: Each mask matches the input time-frequency representation and contains values from 0 to 1 that attenuate signal or noise components.The masks operate directly in time-frequency space.
- II. METHOD: The network uses descending and ascending fully convolutional layers with ReLU activations, batch normalization, and skip connections to learn sparse features.The input comprises real and imaginary time-frequency coefficients, while the final layer provides signal and noise masks trained with cross-entropy loss.
- II. METHOD: The noisy waveform is transformed with STFT, processed by the network to produce two masks, and reconstructed into denoised signal and noise using inverse STFT.Applying the masks to noisy coefficients yields estimated signal and noise time-frequency coefficients.
III. NETWORK TRAINING
The network is trained and tested on 30-second North California Seismic Network seismograms containing high-SNR earthquake signals and varied non-earthquake noise.
- III. NETWORK TRAINING: 30-second HN* seismograms from the North California Seismic Network provide the training and evaluation data.The dataset includes 56,345 earthquake waveforms and 179,233 non-earthquake waveforms, randomly split into training, validation, and test sets.
A. Test Set
On test data, DeepDenoiser decomposes noisy inputs into signal and noise while preserving the signal waveform and handling multiple noise characteristics. It also avoids recovering earthquake signal from pure-noise inputs.
- A. Test Set: The architecture receives real and imaginary noisy time-frequency components and outputs two masks through convolutional downsampling and deconvolutional upsampling.Batch normalization and skip connections support training convergence, while the final softmax layer predicts the masks.
- A. Test Set: The denoising pipeline transforms noisy data with STFT, applies learned signal and noise masks to the coefficients, and uses inverse STFT to recover time-domain outputs.The same flow produces both denoised seismic signal and extracted noise.
- A. Test Set: The network successfully decomposes noisy inputs with different characteristics into denoised seismic signal and noise.Recovered signal and noise preserve waveform shape, frequency content, and amplitude characteristics, with minimal signal leakage.
- A. Test Set: DeepDenoiser learns features of varied noise, including band-limited, low-frequency, and cyclic noise with time-varying frequency bands.Cyclic noise is especially challenging for traditional methods because its frequency band changes over time and overlaps the target signal.
- A. Test Set: On pure-noise waveforms, the method predicts no recovered earthquake signal and preserves the input noise.This contrasts with traditional denoising methods, which may contaminate the noise waveform.
B. Generalization
DeepDenoiser generalizes from synthetic training data to heavily contaminated real Northern California seismograms, recovering clean waveforms and improving SNR.
- 91,000 real Northern California seismograms were used to test generalizability despite heavy noise contamination.The samples came from detected earthquakes in the Northern California Earthquake Catalog.
- Around 15 dB SNR improvement was achieved while recovering clean seismic waveforms, including first arrivals.
- Although trained on synthetic data, DeepDenoiser generalized well to real seismograms and preserved clean, undistorted seismic signals for denoising tasks.
C. Comparison with Other Methods
Compared with normal filtering and GCV denoising, DeepDenoiser provides stronger denoising with less waveform distortion and more reliable arrival-time recovery across increasing noise levels.
- DeepDenoiser achieves better denoising performance while introducing smaller distortion to the signal waveform.The comparison evaluates SNR improvement, maximum amplitude, correlation coefficient, and picked arrival times.
- DeepDenoiser provides more significant and robust SNR improvement than the GCV method.
- At SNR above 2 dB, DeepDenoiser recovers maximum amplitude closer to the true signal, whereas GCV largely attenuates both noise and signal.
- DeepDenoiser yields accurate arrival times at SNR 2 dB, while noisy-signal arrivals delay by 0.5 s at 4 dB and fail beyond that level.
D. Application for Earthquake Detection
DeepDenoiser improves earthquake detection by sharpening STA/LTA characteristic functions after suppressing background noise and impulsive non-seismic signals. On 10,800 test samples, denoising substantially improves both detection precision and recall.
- STA/LTA improvement: Background noise can smooth arrival-related STA/LTA jumps and make small earthquakes undetectable, while impulsive non-seismic signals can create false earthquake peaks.The STA/LTA windows are 0.5 seconds and 5 seconds.
- Detection results: 35.14% to 92.34% precision and 17.69% to 93.76% recall are reported after denoising at an STA/LTA threshold of 5.These results compare noisy and denoised signals on a test dataset of 10,800 samples.
- STA/LTA improvement: DeepDenoiser sharpens arrival signatures and removes impulsive non-seismic peaks, improving recall and prediction precision respectively.The method is illustrated using two examples in which noise either masks arrivals or produces spurious detections.
V. DISCUSSION AND CONCLUSION
DeepDenoiser learns sparse features and adaptive masks to separate seismic signals from noise. The authors report robust denoising across shared frequency bands and varied noise types, while acknowledging that separation is not perfect.
- Method: DeepDenoiser simultaneously learns sparse data features and two adaptive masks that decompose input waveforms into signal of interest and noise.The masks are learned by optimizing the network loss function.
- Results: The method performs denoising when signal and noise share a frequency band and handles colored noise and non-earthquake signals.The authors also report applicability beyond the demonstrated earthquake-data setting.
- Results: DeepDenoiser significantly improves SNR while minimally changing the underlying waveform shape, including under high noise levels.The conclusion states that waveform shape is preserved more faithfully than with other denoising methods.
- Applications: Potential applications include seismic imaging, micro-seismic monitoring, testban treaty monitoring, and preprocessing ambient-noise data.The authors state that the approach can be adapted to different seismic and non-seismic signals and applications.
- Limitations: The method does not achieve perfect signal-noise separation because one bounded mask is applied to both real and imaginary time-frequency components.The authors identify direct prediction of signal and noise values as a future improvement.
APPENDIX A
The normal-filtering comparison uses a filter whose frequency distribution is based on the clean signal so that the signal’s frequency band is retained.
- Filter construction: The normal-filtering frequency distribution is constructed from the clean signal in Fig. 9(a) to preserve its frequency band.This design is used in the comparison section.