DiffSD: Diffusion models for seismic denoising

Seismic waves contain information about the earthquake (EQ) source and many forms of noise deriving from the seismometer, anthropogenic effects, background noise associated with ocean waves, and microseismic noise. Separating the noise from the EQ signal is a critical first step in EQ physics and seismic waveform analysis. However, this is difficult because optimal parameters for filtering noise typically vary with time and may strongly alter the shape of the waveform. A few recent works have employed Deep Learning (DL) model for seismic denoising, among which we have taken as a benchmark Deep Denoiser and SEDENOSS. These models turn the noisy trace into a  2D signal (spectrograms) within the model to denoise the traces, making the process pretty heavy. We propose a novel DL-powered seismic denoising algorithm based on Diffusion Models (DMs), keeping the signal in 1D. DMs are the latest trend in Machine Learning (ML), having revolutionized the application fields of audio and image processing for denoising (DiffWave), synthesis (Stable Diffusion), and sequence modeling (STARS). The training of DMs proceeds by polluting a signal with noise until the signal has completely vanished into noise, then reversing the process by iterative denoising, conditioned on the latent signal representation. This makes DMs the ideal tool for seismic traces cleaning, as the model naturally learns from seismic sequences by denoising, which aligns the ML training procedure and the final task objective. In a preliminary evaluation, we used the Stanford Earthquake Dataset (STEAD); our proposed Diffusion-based Seismic Denoiser (DiffSD) outperforms the state-of-the-art DL methods on the Signal Noise Ratio (SNR),  Scale-Invariant Source to Distortion Ratio (SI-SDR), and Source to Distortion Ratio (SDR) metrics. DiffSD also yields qualitatively pleasing EQ traces out of visual inspection in time and frequency. Finally, DiffSD proceeds from regenerating clean EQ signals from noise, which opens the way to data-driven EQ sequence generations, potentially instrumental to further study and dataset augmentations.