Runqiu Wang

Double Least-Squares Projections Method for Signal Estimation

A real-world signal is always corrupted with noise. The separation between a signal and noise is an indispensable step in a variety of signal-analysis applications across different scientific domains. In this paper, we propose a double least-squares projections (DLSPs) method to estimate a signal from the noisy data. The first least-squares projection is to find a signal-dimensional optimal approximation of the noisy data in the least-squares sense. In this step, a rough estimation of the signal is obtained. The second least-squares projection is to find an approximation of a signal in another crossed signal-dimensional space in the least-squares sense. In this step, a much improved signal estimation that is close to orthogonal to the separated noise subspace can be obtained. The DLSP implements projection operation twice to obtain an almost perfect estimation of a signal. The application of the DLSP method in seismic random noise attenuation and signal reconstruction demonstrates the successful performance in seismic data processing.

Unveiling the signals from extremely noisy microseismic data for high-resolution hydraulic fracturing monitoring

Microseismic method is an essential technique for monitoring the dynamic status of hydraulic fracturing during the development of unconventional reservoirs. However, one of the challenges in microseismic monitoring is that those seismic signals generated from micro seismicity have extremely low amplitude. We develop a methodology to unveil the signals that are smeared in the strong ambient noise and thus facilitate a more accurate arrival-time picking that will ultimately improve the localization accuracy. In the proposed technique, we decompose the recorded data into several morphological multi-scale components. In order to unveil weak signal, we propose an orthogonalization operator which acts as a time-varying weighting in the morphological reconstruction. The orthogonalization operator is obtained using an inversion process. This orthogonalized morphological reconstruction can be interpreted as a projection of the higher-dimensional vector. We first test the proposed technique using a synthetic dataset. Then the proposed technique is applied to a field dataset recorded in a project in China, in which the signals induced from hydraulic fracturing are recorded by twelve three-component (3-C) geophones in a monitoring well. The result demonstrates that the orthogonalized morphological reconstruction can make the extremely weak microseismic signals detectable.

Simultaneous Coherent and Random Noise Attenuation by Morphological Filtering With Dual-Directional Structuring Element

Seismic data are highly corrupted by noise or unwanted energies arising from different kinds of sources. In general, seismic noise can be divided into two categories, namely, coherent noise and random noise, and is treated with essentially different methods. Traditional methods often utilize the differences in frequency, wavenumber, or amplitude to separate signal and noise. However, the application of traditional methods is limited if the above-mentioned differences are too small to distinguish. For this reason, we have proposed a novel morphology-based technique to simultaneously attenuate random noise and coherent noise, i.e., to extract the useful signal. In this technique, we first flatten the signal by normal move out correction or other alternative approaches. For the extraction of the flatten reflections, we propose dual-directional mathematical morphological filtering, which can detect morphological information of the seismic waveforms from two orthogonal directions and then separate signal and other unwanted energy utilizing their difference in morphological scales. Application of the proposed technique on synthetic and field data examples demonstrates a successful performance.