To model reflection seismograms, the one-way approximation is extended to one-return approximation based on the De Wolf approximation (Multiple-Forescattering-Single-Backscattering: MFSB) (Wu, 1996; Wu, Huang and Xie, 1995; Xie and Wu, 2001; Wu, 2002b; Wu and Wu, 2002). Both the thin-slab propagator and complex-screen propagator have been developed and tested. 2D numerical simulations have shown the validity, feasibility and advantages of the one-return methods. For moderate contracts the method is very fast and reasonably accurate. The method has been applied to calculations of synthetic seismograms and AVO (Amplitude vs. Offsets) analysis (Wu and Wu, 2002, 2002 submitted).
Based on the new theory and method, joint projects (with Los Almos National Laboratory, MIT, and industrial partners), have been supported by the ACTI (Advanced Computational Technology Initiative) and the Office of Basic Energy Sciences of DOE (The 3D Seismic Model ing and Imaging Project (Modeling and Imaging Laboratory) at UCSC ). A Research Consortium (WTOPI) ( The WTOPI Research Consortium at UCSC (Wavelet Transform On Propagation and Imaging applied to seismic exploration) ) has been also started and now is in its 6th years.
Collaborated with Jin and Xie and X. Wu, the theory and method of half-space screen propagators for the 2D SH case has been developed to model high-frequency (up to 25 Hz), long distance ( greater than 1000 km) Lg wave simulations in complex crustal waveguides including macro structures of the crust, small-scale random heterogeneities and rough interfaces (Wu, Jin, Xie, 2000a,b). Detailed accuracy verification and tests of the method have been conducted by comparing the results with the reflectivity and finite difference numerical methods. Excellent agreement between these methods demonstrated the high accuracy and efficiency of the half-space GSP method. For a medium size Lg problem, The GSP method is 300 times faster than the finite difference method. For large size problems, the saving could be much greater. The GSP method for SH Lg waves been extended to including the rough surface topography (collaborated with Xianyun Wu) (Wu and Wu, 2001). Some preliminary results of P-SV Lg wave propagation in the crust has also been obtained (in draft).
Boundary element (BE) method has also been applied to model Lg wave propagation for the case of rough free surface. Collaborated with L.Fu, the calculation of absorbing boundary condition for BE has been improved (Fu and Wu, 2000) and a connection formula has be developed for the hybrid BE-GSP method (Fu and Wu, 2001). Scattering attenuation due to rough surface has been investigated by the method (Fu et al., 2002).
The newly developed fast wavelet transform (WT) is considered to be a revolutionary breakthrough in signal analysis/processing. In the same time frame, there has been significant progress in one-way wave propagation theory and algorithms, including the recently developed fast acoustic and elastic generalized screen propagators from our group. The cross-breeding of these two new developments has the potential of revolutionizing modeling and imaging techniques for complex Earth media. Collaborated with Postdoctoral researchers and students Wu has done some investigation on propagator decomposition and compression and comparison has been made for adapted wavelet packet transform (best basis), standard wavelet transform, and adapted local cosine transform (Wu and Yang, 1997; Wu and Wang, 1998; Wang and Wu, 1998, 2000). It is shown that the one-way wave propagator in wavelet domain, which is called the beamlet (applying WT to the transversal space-coordinates) propagator, is a highly sparse matrix and has both the space and direction (wavenumber) localizations. Propagation and imaging in wavelet domain operate in local phase-space, and can adjust the resolutions in both space and directions, calculate and correct illumination and aperture effects in angle-domain (Wu and Chen, 2002), perform local AVA analysis and local inversion. Wu and his colleagues have developed a local perturbation theory for beamlet imaging (Wu, Wang and Gao, 2000) and implemented the theory for two kinds of beamlets. One is Gabor-Doubechies frame (GBF) beamlet (Weyl-Heisenberg coherent state) (Wu and Chen, 2001,2002; Chen and Wu, 2002); the other is the local cosine basis (LCB) beamlet (Wu,Wang and Gao, 2000; Wang and Wu, 2002; Wu, Chen and wang, 2002). Beamlet imaging has been applied to the SEG/EAGE salt model and Marmousi model. The imaging quality is superior to the traditional Kirchhoff migration and comparable to that of GSP. The Research Consortium (WTOPI) ( The WTOPI Research Consortium at UCSC (Wavelet Transform On Propagation and Imaging applied to seismic exploration) ) supported by the Oil/Gas and geophysical companies ( WTOPI Sponsors ) has been started to advance the theory and its applications, and now is in its 6th years.