Theory and seismic applications of the eigenimage discrete wavelet transform

Abstract

A B S T R A C TDiscrete wavelet transforms are useful in a number of signal processing applications. To improve the scale resolution, a joint function of time, scale and eigenvalue that describes the energy density or intensity of a signal simultaneously in the wavelet and eigenimage domains is constructed. A hybrid method, which decomposes eigenimages in the wavelet domain, is developed and tested on field data with a variety of noise types. Several illustrative examples examine the ability of wavelet transforms to resolve features at several scales. Successful applications to time-lapse seismic reservoir monitoring are presented. In reservoir monitoring, the scale-dependent properties of the eigenstructure of the 4D data covariance matrix enable us to extract the lowfrequency time-lapse signal that is the result of internal diffusive losses caused by fluid flow. *

Multivariate model for surface microseismic denoising in the shearlet domain

“…As a classical time frequency analysis method, wavelet transform (WT) has been successfully used in seismic prospecting field [3]. But the optimal sparse representations of WT in one-dimension functions cannot be retained in higher dimensions.…”

The attenuated Ricker wavelet basis for seismic trace decomposition and attenuation analysis

“…This is one of the most direct and common applications for these MP‐like methods. Compared with other time–frequency analysis or decomposition methods, such as the short‐time Fourier transform (Cohen ), the discrete or continuous wavelet transform (Droujinine ; Sinha, Routh and Anno ), the S‐transform (Stockwell, Mansinha and Lowe ; Pinnegar and Mansinha ), the curvelet transform (Herrmann et al . ) and the local time–frequency analysis (Liu et al .…”

“…This is one of the most direct and common applications for these MP-like methods. Compared with other time-frequency analysis or decomposition methods, such as the short-time Fourier transform (Cohen 1995), the discrete or continuous wavelet transform (Droujinine 2006;Sinha, Routh and Anno 2009), the S-transform (Stockwell, Mansinha and Lowe 1996;Pinnegar and Mansinha 2003), the curvelet transform (Herrmann et al 2008) and the local time-frequency analysis (Liu et al 2011a;Liu and Fomel 2013), MP may generate sparser decomposition results. This is because that the wavelet basis employed in the MP iteration is more redundant, and * E-mail: fengxuan@jlu.edu.cn more types of wavelet basis are selectable (Wang 2007;Feng et al 2017).…”