Seismic data analysis with one‐dimensional seislet frame

Abstract

We introduce 1-D seislet frame – a novel domain for analyzing data that are composed primarily of sinusoidal signals (in 1-D) or plane waves (in 2-D). In the case of a single component, the 1-D seislet transform is a wavelet-like transform that breaks the input data into multiple scales. What makes the digital wavelet transform (DWT) different is that elementary prediction and update operations follow a sinusoid with a particular frequency. In these terms, the classic DWT is simply a 1-D seislet transform for a zero frequency. In the case of multiple components, the transform turns into a frame – an invertible overcomplete representation – and becomes suitable for analyzing data with multiple frequencies or multiple plane-wave slopes. Using simple synthetic and field data examples, we show that 1-D seislet frame can provide better compression quality for sinusoidal signals than either DWT or the digital Fourier transform. This superior compression property indicates the potential of the new domain for applications such as seismic data regularization or noise attenuation.