Application of wavelet transform in reflection seismic data analysis

Abstract

A seismic signal is characterized by its travel time, frequency and phase information, as well as noises, especially coherent noises. The wavelet decomposition of a seismic signal involves simultaneous representation of its time and frequency characteristics. The key advantage of the wavelet transform (WT) over the conventional Fourier transform is that it can not only provide insight on the combined temporal and spectral character- istics of signals, but it can also localize the target information in the time-frequency domain simultaneously. The wavelet trans- form distinguished itself from the short time Fourier transform for time-frequency analysis in that it has a zoom-in and zoom-out capability. Thus the WT approach is suitable for time-frequency analysis of seismic signals. Application capability of the wavelet transform depends on the selection of the wavelet functions from which a basis function can be constructed for signal decomposition. There are two types of wavelet functions: orthogonal and non-orthogonal wavelet func- lions, thus the algorithms of the wavelet transform vary. The corn- moldy used wavelet functions are orthonormal and compactly supported, but do not have a finite impulse response and linear phase. These features are, however, undesirable for applications in exploration seismology, especially when further subsequent pro- ccssing is required in complex domain. Compactly supported non- orthogonal wavelets do not have phase distortion problem and provide a better choice for seismic data processing. Reflection and refraction events, coherent noises such as ground roll, air-wave, and ringing in seismic data have characteristic fea- tures and can be distinguished in the time-frequency space. The Morlet wavelet, a well-known example of non-orthogonal wave- lets, is tested in this study for effectively suppressing coherent noise. It was also demonstrated that the reconstructed signals after the weighted wavelet transform show significant improvements in the S/N ratio.