OC-seislet: Seislet transform construction with differential offset continuation

Many of the geophysical data-analysis problems such as signal-noise separation and data regularization are conveniently formulated in a transform domain, in which the signal appears sparse. Classic transforms such as the Fourier transform or the digital wavelet transform (DWT) fail occasionally in processing complex seismic wavefields because of the nonstationarity of seismic data in time and space dimensions. We present a sparse multiscale transform domain specifically tailored to seismic reflection data. The new wavelet-like transform — the OC-seislet transform — uses a differential offset-continuation (OC) operator that predicts prestack reflection data in offset, midpoint, and time coordinates. It provides a high compression of reflection events. Its compression properties indicate the potential of OC seislets for applications such as seismic data regularization or noise attenuation. Results of applying the method to synthetic and field data examples demonstrate that the OC-seislet transform can reconstruct missing seismic data and eliminate random noise even in structurally complex areas.