Seismic Signal Analysis using Multi-Scale/Multi-Resolution Transformations

Fast Fourier Transforms have been used since the early 1960s as a method of processing signals. Since the 1990s wavelet transformation has also been routinely used as method for signal processing. Their limitations include the inability to detect contours, curves and directional information of a signal. In the past few years, new approaches such as multi-scale and multi-resolution transformations have become more prevalent as methods to extrapolate information from signals and images. With roots in the Fourier transform and wavelet, multi-scale/multi-resolution transformations have recently given rise to even more advanced methods such as the bandelet, contourlet, ridgelet, and curvelet.[24] Additionally, advancements have been made to the standard wavelets to improve their analytical capabilities, resulting in methods such as the dual-tree discrete wavelet transformation and the dual density discrete wavelet transformation. Many studies have developed and validate algorithms for the wavelet multi-scale analysis but other types of transformations have not been as thoroughly studied. We propose a novel method of seismic signal analysis using the more advanced wavelet transformations to identify and extrapolate seismic information. The proposed analysis method makes the Double Density Dual Tree Discrete Wavelet Transform (D3WT) a viable alternative to the Discrete Wavelength Transform (DWT) and Fast Fourier Transform (FFT) during seismic signal processing, as well as paving the way for other multiscale transforms.[26] Further, the outcome can then be statistically analyzed for use in applications such as earthquake prediction. The initial results indicate that other transformation methods yield a better prediction than the DWT and FFT.