Dreamlet: A New Representation and Migration of Seismic Wavefield in Full Local Domains (Communications in Computational Physics, 2020)
Seismic events have limited time duration, vary with space/traveltime andinteract 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 andhighly accurate local wave propagation. Various local transforms are powerful toolsfor seismic data segmentation and representation. In this paper, a detailed description of a multi-dimensional local harmonic transformed domain wave propagationand 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 andbeamlet. The dreamlet atoms have limited spatial extension and temporal durationand constitute a complete set of frames, termed as dreamlet frames, to decompose andrepresent the wavefield. The dreamlet transform first partitions the wavefields usingtime-space supporting functions and then the data in each time-space blocks is represented by local harmonic bases. The transformed wavefield is downward-continuedby the dreamlet propagator, which is the dreamlet atom evolution weightings deducedfrom the phase-shift one-way propagator. The dreamlet imaging method is formulatedwith a local background propagator for large-scale medium propagation and combined with a local phase-screen correction for small-scale perturbations. The featuresof 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 datademonstrate the validity and accuracy of this method. With time-domain localizationbeing involved, the dreamlet method can also be applied effectively to target-orientedmigration and imaging.
Keywords: Seismic imaging; wave equation; local harmonic transform; seismic migration; dreamlet transform.