ARIMA-GARCH Seismic Data Compression via Residual Entropy Encoding
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Solution Overview
Problem
Seismic data compression is challenging due to its heteroscedastic nature, requiring effective models that account for both previous values and variance, which existing techniques struggle to address efficiently for lossless compression and transmission.
Innovation Solution
The use of an ARIMA-GARCH model estimation method, which applies Autoregressive Integrated Moving Average (ARIMA) and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models to reduce residual variance, followed by entropy encoding for efficient compression and decompression of seismic data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional signal data compression techniques are used, then compression is achieved, but the heteroscedastic nature of seismic data causes poor compression efficiency and loss of data integrity
Solution Approach 1:
The patent applies parameter changes by transitioning from conventional compression methods to ARIMA-GARCH model-based compression. The model parameters (ARIMA coefficients and GARCH variance parameters) are estimated to specifically capture the heteroscedastic characteristics of seismic data, changing the compression approach to match the data's statistical properties and achieve both high compression efficiency and data integrity preservation
Solution Approach 2:
The patent replaces conventional mechanical compression systems with a statistical modeling system. Instead of using generic signal processing techniques, the invention substitutes a specialized ARIMA-GARCH statistical model that mathematically captures the temporal dependencies and variance changes in seismic data, enabling superior compression performance
2Productivity
If ARIMA-GARCH model is applied to compress heteroscedastic data, then compression efficiency improves, but model complexity and computational requirements increase
Solution Approach 1:
The patent applies segmentation by dividing the compression process into distinct phases: data preparation, ARIMA-GARCH model estimation, residual calculation, and entropy encoding. The model itself is segmented into ARIMA components for mean prediction and GARCH components for variance modeling, allowing each part to be optimized independently and reducing overall computational complexity while maintaining high compression efficiency
3Reliability
If lossless compression is achieved through ARIMA-GARCH modeling, then data integrity is preserved, but processing time and computational resources increase
Solution Approach 1:
The patent applies preliminary action by pre-estimating the ARIMA-GARCH model parameters on a subset of the data before compressing the entire dataset. This preliminary model fitting captures the essential statistical characteristics of the seismic data, allowing the compression process to proceed more quickly using the pre-computed model rather than performing complex calculations on every data point during compression
Data Source
AI summary
Methods and apparatus are provided for compression and decompression of heteroscedastic data, such as seismic data, using Autoregressive Integrated Moving Average (ARIMA)-Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model estimation. Heteroscedastic data is compressed by obtaining the heteroscedastic data; applying the heteroscedastic data to an ARIMA-GARCH model; determining residuals between the obtained heteroscedastic data and the ARIMA-GARCH model; and compressing parameters of the ARIMA-GARCH model and the residuals using entropy encoding, such as an arithmetic encoding, to generate compressed residual data. Parameters of the ARIMA-GARCH model are adapted to fit the obtained heteroscedastic data. The compressed residual data is decompressed by performing an entropy decoding and obtaining the parameters of the ARIMA-GARCH model and the residuals. The ARIMA-GARCH model predicts heteroscedastic data values and then the decompressed residuals are added.