Dreamlet: A new representation and migration of seismic wavefield in full local domains

Seismic events have limited time duration, vary with space/traveltime and interact with the local subsurface medium during propagation. Partitioning is a valuable strategy for nonstationary seismic data analysis, processing and wave propagation. It has the potential for sparse data representation, flexible data operation and highly accurate local wave propagation. Various local transforms are powerful tools for seismic data segmentation and representation. In this paper, a detailed description of a multi-dimensional local harmonic transformed domain wave propagation and imaging method is given. Using a tensor product of a Local Exponential Frame (LEF) vector as the time-frequency atom (a drumbeat) and a Local Cosine Basis (LCB) function as the space-wavenumber atom (a beamlet), we construct a time-frequency-space-wavenumber local atom-dreamlet, which is a combination of drumbeat and beamlet. The dreamlet atoms have limited spatial extension and temporal duration and constitute a complete set of frames, termed as dreamlet frames, to decompose and represent the wavefield. The dreamlet transform first partitions the wavefields using time-space supporting functions and then the data in each time-space blocks is represented by local harmonic bases. The transformed wavefield is downward-continued by the dreamlet propagator, which is the dreamlet atom evolution weightings deduced from the phase-shift one-way propagator. The dreamlet imaging method is formulated with a local background propagator for large-scale medium propagation and combined with a local phase-screen correction for small-scale perturbations. The features of dreamlet migration and imaging include sparse seismic data representation, accurate wave propagation and the flexibility of localized time operations during migration. Numerical tests using Sigsbee 2A synthetic data set and real marine seismic data demonstrate the validity and accuracy of this method. With time-domain localization being involved, the dreamlet method can also be applied effectively to target-oriented migration and imaging.