Noise contamination is an important problem in microseismic data processing, due to the low magnitude of the seismic events induced during fluid injection. In this study, a noncoherent noise attenuation technique based on a constrained time-frequency transform is presented. When applied to 1C data, the transform corresponds to a sparse representation of the microseismic signal in terms of a dictionary of complex Ricker wavelets. The use of complex wavelets possesses the advantage that signals with arbitrary phase can be represented with enhanced sparsity. A synthetic example illustrates the superior performance of the sparse constraint for denoising objectives when compared to the standard least-squares regularization. As the arrival time and frequency content of any wavefront are equivalent in the three components of a single receiver, the extension of the sparse transform to 3C data is accomplished when the three components are considered to share the same sparsity pattern in the time-frequency plane. Application of the 3C sparse transform to synthetic and real microseismic data sets demonstrate the advantages of this technique when the denoised results are compared against the original and low-pass filtered version of the noisy data. Furthermore, a comparison of hodograms between original, low-pass, and denoised traces shows that the denoising process preserves the phase and relative amplitude information present in the input data. The benefits of the 3C transform are highlighted particularly in cases where the wave arrivals are measured in the three components of a receiver but are only visible in two components due to the prevailing signal-to-noise ratio.

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The nonlocal means algorithm is a noise attenuation filter that was originally developed for the purposes of image denoising. This algorithm denoises each sample or pixel within an image by utilizing other similar samples or pixels regardless of their spatial proximity, making the process nonlocal. Such a technique places no assumptions on the data except that structures within the data contain a degree of redundancy. Because this is generally true for reflection seismic data, we propose to adopt the nonlocal means algorithm to attenuate random noise in seismic data. Tests with synthetic and real data sets demonstrate that the nonlocal means algorithm does not smear seismic energy across sharp discontinuities or curved events when compared to seismic denoising methods such as f-x deconvolution.

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