Wavelet Transforms For Seismic Data Processing

Considerable attention has been focussed on the use of wavelet transforms for seismic data compression. In addition to data compression, wavelet transforms also provide a powerful tool for analysis and processing of seismic data. In the frequency domain, wavelet transforms can be expressed as pairs of low and high pass filters that are repeatedly applied to a seismic trace. Using this framework, geophysical operations such as noise suppression and wave propagation can be readily derived for the wavelet domain. A unique feature of the wavelet transform is the availability of both time and frequency axes in the transform domain. Algorithms that require simultaneous access to time and frequency, such as attenuation analysis, can easily be implemented in the wavelet domain. Dual access to time and frequency comes at price, however. The filters used to implement the transform overlap in the frequency domain, which leads to internal aliasing for many algorithms, including data compression. Careful attention to the details of the aliasing terms in the transform is crucial for effective algorithms. A promising area for future research is the use of wavelet transforms for compressing integral operators. As an example, we describe the Radon transform in the wavelet domain, which results in compression of both the data processed and the operations performed.