Improving Microseismic Denoising Using 4D (Temporal) Tensors and High-Order Singular Value Decomposition

Microseismic data are used to understand fracture propagation by event detection, and this data acquisition and interpretation leads to improvement in fracture monitoring. This technology can provide an understanding of fluid and rock interaction in real-time once the handling of large volumes of data is achieved. In this research, we implement a high-order SVD (HOSVD) model reduction method for denoising and compressing microseismic and distributed acoustic sensing (DAS) data to obtain insights into the rock structure. This may be used as a basis for future planning of hydraulic fracturing for fracture propagation control. For the elaboration of the model, we developed a novel methodology based on Tucker tensor and high-order singular value decomposition. This latter can work with high-dimensional datasets, reducing the data volume and discovering hidden patterns. The workflow was divided into five stages: 1) data preprocessing where the datasets were converted into 3D and 4D tensors, 2) application of HOSVD, 3) compression ratio estimation, 4) singular value calculation and 5) a comparison between reduced and original microseismic tensors. The methodology was first evaluated using a synthetic 3D microseismic array and later tested on a field 3D DAS dataset. In addition, a 4D tensor was constructed for the analysis of temporal variation. For the 3D microseismic HOSVD implementation, results displayed a compression of approximately 75% with a reduction of the number of samples from 1,728,000 to 431,303. This compression was also associated with a core tensor of dimensions 181x34x11 and a tolerance of 0.0002. This tolerance value represents the requested relative error which designates the approximation error of the reduced tensor. Different tolerance levels were applied, providing a range of several compression ratios. This resulted in a direct relationship between tolerance and compression, where higher tolerance displayed higher compression. However, microseismic signals can be missing from the original data, failing to reconstruct the signal and preserved the most significant features. The core tensor revealed the reduced representation of the original 3D tensor where lower core dimensions are linked to higher compression ratios. Subsequently, we applied the model to the field DAS data obtaining a compression of 70.2% for a 3.5 GB data size. For 4D HOSVD, a compression ratio of 83% was achieved at a tolerance of 0.08. The reduced array also revealed denoising in the microseismic traces. Finally, a time variation analysis was performed by subtracting the first (e.g. 1 hour) and last (e.g. 5 hours) elapse times. This difference presented a lower amplitude response; however, the reduced 4D tensor was not affected by it. Hence, 4D HOSVD can be applied under mathematical operations, displaying the stability of the method. Results from application of this algorithm show that it holds great promise for improving microseismic and DAS detection.