Superwide-angle One-way Wave Propagator Based On Gabor-Daubechies Frame

In this thesis, I introduced two basic one way wave propagators, the General Screen Propagator and G-D frame Propagator which are all based on one way wave equation. The advantages of one-way wave propagators are the fast speed of computation and the large savings in computer resources. We analyze the propagation characterizations of these two propagators and compare the images generated by them under BP velocity Benchmark (2004) respectively. And then we found that all of the main features, including the boundaries of the salt body, the thin layers and even sharp edges are imaged clearly with both G-D frame migration and General Screen migration. However, they all have inherent deficiency in imaging steep and overhanging flanks (>90°).In order to realize super-wide angle imaging, we first test super-wide angle GSP. The results show that it could model turning waves effectively and image overhanging flanks. Nevertheless, super-wide angle GSP depends on General Screen Propagator, which doesn't have good localization property such as local-angle-domain features. As a result, we develop super-wide angle Gabor-Daubechies frame propagator taking advantage of G-D frame propagator to overcome the intrinsic deficiency of super-wide GSP and realize the localization properties in both space and wavenumber domain. Finally, we get the following conclusions.1) Like super-wide angle GSP, super-wide angle G-D frame propagator could simulate turning waves well and imaging overhanging flanks because of its interpolation of two orthogonally propagated one way wavefields.2) This kind of propagator is obtained analytically by one-way wave G-D frame decomposition in the beamlet and beamlet-space mixed domain, hence it has superior localization properties. For example, it could image thin layers and deep seated anticline structures more accurately than GSP propagator.3) Since G-D frame decomposition of wavefields is overcomplete and nonorthogonal, more computations and storage space are required for super-wide angle G-D beamlet based method. But it has less noise than GSP method because of its good localization property, which is superior even than Gaussian beams in the sense that its localizations are not limited within short propagation distances. Numerical experiments demonstrate that Super-wide angle G-D frame propagator is valid and effective. Moreover, the localizations of the wavefield decomposition and propagation in the G-D beamlet domain allow detailed study of the directivity-involved features of local structures, which makes super-wide angle propagator of primary potential.