Blind noise estimation and denoising filter for recovery of microquake signals

In this study, a data-driven linear filtering method is proposed to recover microseismic signals from noisy data/observations. The proposed method is based on the statistics of the background noise and the observation, which are directly extracted from the recorded data, obviating prior statistical knowledge of the microseismic source signal. The proposed method does not depend on any specific underlying noise statistics; therefore, it works for any type of noise, e.g. uncorrelated (random/white Gaussian), temporally correlated and spatially correlated noises. Consequently, the proposed method is suitable for microquake data sets that are recorded in contrastive noise environments. A mathematical analysis is presented to interpret the proposed method in two different ways. Furthermore, a number of practical concerns are discussed and their corresponding solutions are introduced. Finally, the proposed scheme is evaluated using both field and synthetic data sets and the experimental results show a reasonable and robust performance.