# Multi-Component Temporal-Correlation Seismic Data Compression Algorithm Based on the PCA and DWT
## 1 Introduction  
Decision making in industrial applications relies heavily on datasets and data acquisition systems. Statistical analysis for complex systems requires representative datasets and high data volume. Seismic data analysis [1] and data-driven prognostics [2, 3], for example, are applications with an increased need for high-frequency data sampling (i.e., vibration, acoustics) that increase storage demands. In specific application scenarios, such as seismic surveys conducted by oil and gas companies, seismic data can amount to tens of terabytes [4]. Consequently, storing and transferring such vast amounts of data pose significant cost and technical challenges [5]. Data in analytics can contain less relevant components depending on the application. In these cases, pruning the dataset can be considered to lower storage, that is, filtering less relevant data. While it is possible to automate such a process, it is challenging to balance meaningful storage reduction and maintain a relevant dataset. Therefore, these datasets tend to be compressed for storage using some form of classical lossless compression, even though lossless compression provides little benefit in reducing storage space.  
The seismic signal can be expressed as a linear combination of wavelets with varying bandwidths and time lags, contingent upon subsurface interactions with the source. The use of wavelet decomposition, extensively explored and recognized for its compression applications [6], and principal component analysis (PCA), a widely used method machinelearning (ML) in multivariate analysis for dimensionality reduction, have both been studied. The utilization of these techniques in seismic data compression has been documented [7]. Both algorithms aim to generate sparse data representations using as few coefficients as possible for effective compression. This involves transforming and discarding the least representative data and efficiently encoding the remaining information. In this work, we propose the usage of PCA as a filter to reduce the noise associated with seismic data, allowing discrete wavelet transform (DWT) to achieve higher compression rates. The main contributions of this work are as follows:  
* The modeling of a compression algorithm that combines PCA and DWT while employing thresholding, quantization, and entropy encoding strategies to increase compression performance;
* The analysis of a compression case study on seismic data from the Jubarte permanent reservoir monitoring.  
The remainder of this work is organized as follows: Section 2 presents the related works found in literature regarding the applications of principal component analysis (PCA), DWT, and their combination for data compression applications. Section 3 discusses the fundamentals of data compression using PCA, DWT, quantization, and thresholding, and explains the proposed data compression strategy. Section 4 presents the case study considered to evaluate the performance of the proposed compression strategy when applied to seismic data acquired during the monitoring process of an oil reservoir, as well as the results and discussion. Finally, Section 5 presents the concluding remarks of this work.