## 1 Introduction  
The last decade has seen a great increase in hydrocarbon production from unconventional reservoirs. However, there are still many challenges in predicting their production potential. The quantity of hydrocarbons produced depends on the distribution and quantity of fractures present in the reservoir. Fracture identification and monitoring can be done by analyzing microseismic data [1]. With the goal of improving the ability to track the fracture distribution, the amount of seismic data acquired during reservoir monitoring has been increasing. Recent developments in reservoir monitoring use fiber optic cables to record both low frequency strain and seismic waves in a technique called distributed acoustic sensing (DAS) [2]. DAS provides a new and unique view of the reservoir by recording strain rate data with a high sample rate and dense spatial sampling. Higher recording rates and more receiver positions increase the amount of microseismic activity recorded while monitoring the reservoir. Recording microseismic events with DAS significantly increases the memory requirement of the monitoring data. Thus, data processing methods that can compress the data and reduce its noise would complement the new instrumental developments in reservoir monitoring. Signal processing algorithms are often based on the transformation of signal into a new domain. Early examples of compression involve discrete cosine transform [3] and wavelet transforms [4; 5; 6] which use cosine functions or wavelets to represent the data in order to reduce the memory requirements. Reduced-rank methods, which approximate the noiseless seismic data using low rank matrices and tensors, have been used in noise reduction [7] while also reconstructing missing data [8; 9]. In recent years, dictionary learning has seen wide application in seismic data. Because of its ability to provide a compact and informative representation of seismic signals, it has been used for both noise reduction [10; 11; 12] and data compression [13; 14]. Unfortunately, the drawback of the dictionary learning applications is the computation time that comes with learning and updating the dictionary. There have been successful efforts to reduce the associated computational times [15], but the computational cost of applying dictionary learning to microseismic DAS recordings is still to great. Thus far, dictionary learning methods have been applied to data collected by geophones, which can be very large but are still much smaller than data obtained by a single fiber-optic cable which can sample strain thousands of times a second on hundreds, even thousands of receiver locations. Since DAS is used for microseismic monitoring, the great amounts of data would need to be processed in real time, which puts a constraint on the computation time of processing methods. To achieve computationally efficient compression and denoising, we created a new data decomposition method by improving and further developing ideas developed as a part of the local SVD [16]. Similarly to the previously mentioned reduced-rank methods, local SVD applies SVD to a window in seismic data and represents the data using a small number of singular vectors. What makes local SVD unique is the process of shifting the columns of the window to maximize their correlation prior to applying SVD. This allows singular vectors to capture the signal in seismic data with high accuracy, while ignoring most of the noise. Once the data in the window is processed with SVD, the window is moved to the next location. This process is repeated until column shifting and SVD have been applied to every part of the data matrix. The path of the moving window as well as the number of singular vectors used at each location are predetermined. Local SVD can enhance a seismic data set even if it contains multiple wave arrivals. However, local SVD struggles to capture seismic signals if waves with different dips are interfering or present in the same window.