The frequency of microseismic data is higher than that of conventional seismic data. The range of effective frequency is usually from 100 to 500 Hz, and low-frequency noise is a common disturbance in downhole monitoring. Conventional signal analysis techniques, such as band-pass filters, have their limitation in microseismic data processing when the useful signals and noise share the same frequency band. We have developed a novel method to suppress low-frequency noise in microseismic data based on mathematical morphology theory that aims at distinguishing useful signals and noise according to their tiny differences of waveform. By choosing suitable structure elements, we have extracted low-frequency noise from a original data set. We first developed the fundamental principle of mathematical morphology and the formulation of our approach. Then, we used a synthetic data example that was composed of a Ricker wavelet and low-frequency noise to test the feasibility and performance of the proposed approach. Our results from the synthetic example indicate that the proposed approach can effectively suppress large-scale low-frequency noise while slightly decreasing the small-scale signals. Finally, we have applied the proposed approach to field microseismic data and obtained very encouraging results.

Multichannel singular spectrum analysis (MSSA) is an effective algorithm for random noise attenuation in seismic data, which decomposes the vector space of the Hankel matrix of the noisy signal into a signal subspace and a noise subspace by truncated singular value decomposition (TSVD). However, this signal subspace actually still contains residual noise. We have derived a new formula of low-rank reduction, which is more powerful in distinguishing between signal and noise compared with the traditional TSVD. By introducing a damping factor into traditional MSSA to dampen the singular values, we have developed a new algorithm for random noise attenuation. We have named our modified MSSA as damped MSSA. The denoising performance is controlled by the damping factor, and our approach reverts to the traditional MSSA approach when the damping factor is sufficiently large. Application of the damped MSSA algorithm on synthetic and field seismic data demonstrates superior performance compared with the conventional MSSA algorithm.

Multichannel singular spectrum analysis (MSSA) is an effective algorithm for random noise attenuation; however, it cannot be used to suppress coherent noise. This limitation results from the fact that the conventional MSSA method cannot distinguish between useful signals and coherent noise in the singular spectrum. We have developed a randomization operator to disperse the energy of the coherent noise in the time-space domain. Furthermore, we have developed a novel algorithm for the extraction of useful signals, i.e., for simultaneous random and coherent noise attenuation, by introducing a randomization operator into the conventional MSSA algorithm. In this method, which we call randomized-order MSSA, the traces along the trajectory of each signal component are randomly rearranged. Two ways to extract the trajectories of different signal components are investigated. The first is based on picking the extrema of the upper envelopes, a method that is also constrained by local and global gradients. The second is based on dip scanning in local processing windows, also known as the Radon method. The proposed algorithm can be applied in 2D and 3D data sets to extract different coherent signal components or to attenuate ground roll and multiples. Different synthetic and field data examples demonstrate the successful performance of the proposed method.

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