Seismic wavefield reconstruction using a pre-conditioned wavelet–curvelet compressive sensing approach

Abstract

The proliferation of large seismic arrays have opened many new avenues of geophysical research; however, most techniques still fundamentally treat regional and global scale seismic networks as a collection of individual time-series rather than as a single unified data product. Wavefield reconstruction allows us to turn a collection of individual records into a single structured form that treats the seismic wavefield as a coherent 3-D or 4-D entity. We propose a split processing scheme based on a wavelet transform in time and pre-conditioned curvelet-based compressive sensing in space to create a sparse representation of the continuous seismic wavefield with smooth second-order derivatives. Using this representation, we illustrate several applications, including surface wave gradiometry, Helmholtz–Hodge decomposition of the wavefield into irrotational and solenoidal components, and compression and denoising of seismic records.