Time‐frequency analysis based on curvelet transforms with time skewing

Abstract

Oil and gas exploration gradually changes to the deep and complex areas. The quality of seismic data restricts the effective application of conventional time‐frequency analysis technology, especially in the case of low signal‐to‐noise ratio. To address this problem, we propose a curvelet‐based time‐frequency analysis method, which is suitable for seismic data, and takes into account the lateral variation of seismic data. We first construct a kind of curvelet adapted to seismic data. By adjusting the rotation mode of the curvelet in the form of time skewing, the scale parameter can be directly related to the frequency of the seismic data. Therefore, the curvelet coefficients at different scales can reflect the time‐frequency information of the seismic data. Then, the curvelet coefficients, which represent the dominant azimuthal pattern, are converted to the time‐frequency domain. Since the curvelet transform is a kind of sparse representation for the signal, the screening process of the dominant coefficient masks most of the random noise, which enables the method to adapt for the low signal‐to‐noise ratio data. Results of synthetic and field data experiments using the proposed method demonstrate that it is a good approach to identify weak signals from strong noise in the time‐frequency domain.