# Microseismic Signal Denoising and Separation Based on Fully Convolutional Encoder-Decoder Network
## 3 Results  
### Test Results  
Figure 3 shows the denoised results of some noisy signals selected from the test dataset, which are obtained by applying the two output masks to these noisy signals. It is possible to observe that the method can successfully separate the noisy signal with different characteristics into an estimated signal and estimated noise. The CNN-denoiser has an excellent denoising performance for microseismic signals with various types and intensities of noise. Noisy signals in Figure 3a,b indicate microseismic signals with cyclic noise at different frequencies, and Figure 3c indicates microseismic signals with a mixture of cyclic and other noise. For the most part, the cyclic noise changes over time, and its frequency band overlaps with that of the microseismic signals, which is a challenging issue for existing denoising  
Figure 2: Flow diagram of the method. 1 The noisy signal is transformed from the time domain into the time–frequency domain using Short Time Fourier Transform (STFT). 2 The real and imaginary parts of time–frequency coefficients of noisy signals are input into the neural network. 3 Two masks from the network are applied to the real and imaginary parts of time–frequency coefficients of the input noisy signal to estimate the time–frequency coefficients of microseismic signal and noise, respectively. 4 The estimated signal and noise in the time domain are obtained via the inverse STFT.  
methods. These above types of noisy signals cover all the noisy signal samples in the field. It can be found that CNN-denoiser can effectively suppress the microseismic signals with non-Gaussian noise (including cyclic noise, unknown noise, and their mixture). To further demonstrate the applicability of the proposed method to other noise (like Gaussian noise), CNN-denoiser was tested in noisy signals formed with clean microseismic signal and Gaussian noise (Figure 3d). The results show that the noises are significantly reduced regardless of types of noise. Further, the estimated signal leakage is minimal, and the shape and amplitude characteristics of the estimated signal are well preserved. These above characteristics are also applicable to estimated noise, even Gaussian noise.  
Figure 3: Cont.  
The proposed model not only learns the features of microseismic signals but also estimates noise. To validate this, the CNN-denoiser was tested for 12,000 real noise samples. Figure 4 shows the robustness of the neural network to some periodic non-microseismic signals (the frequency band varying with time). No estimated signals are predicted, and the estimated noise is almost equivalent to the input noise sample. It indicates that the CNN-denoiser can automatically produce a mask that adapts to the noise characteristics. The mask reflects the changes in frequency characteristics over time, as well as the frequency band of noise. Additionally, the distribution of the max amplitude difference between the real and estimated noise samples is shown in Figure 5. The results show that the max amplitude difference of more than 50% of noise samples is less than 0.05, which means the method only causes minor waveform distortion.  
Figure 3: Denoising performance of CNN-denoiser for noisy signals with various noise in the test dataset. The signals in the time domain and time–frequency domain for each sub-figure are clean signal, real noise, noisy signal, estimated signal, and estimated noise from top to bottom. (**a**,**b**) Microseismic signals with cyclic noises at different frequency; (**c**) microseismic signals with a mixture of cyclic noise and other noise; (**d**) microseismic signals with Gaussian noise.  
Figure 4: Denoising performance of CNN-denoiser for different types of real noise. The noises in the time domain and time–frequency domain are real noise, estimated signal and estimated noise from top to bottom of each sub-figure. (**a**) Mixture of cyclic noise and other noise; (**b**) cyclic noise.