Resolution Limits of LSM and FWI

As far as seismic imaging and inversion with the wave equation are concerned, the resolution limits are of fundamental interest, and understanding these limits allows us to economically parameterize the model and design an efficient inversion schedule. Although the resolution limits have been analyzed for traveltime tomography (Kravtsov and Orlov, 1990; Cerveny and Soares, 1992; Williamson, 1991) and for reflection imaging (Berkhout, 1984; Safar, 1985; Vermeer, 1997; Chen and Schuster, 1999), there lacks a comprehensive treatment of the resolution limits associated with fwi. In this dissertation I conduct a study to fill this gap by carrying out asymptotic analysis to the model resolution function for fwi. The results are summarized in Fig. 4.4 on page . Moreover, as noted by Jannane et al. (1989), the absence of intermediate wavenumbers recovered from diffraction and transmission migration poses a serious challenge for waveform inversion. I address this problem with the aid of diffractor and interbed multiples. The results are summarized in Fig. 4.9 on page . This line of work is covered in Chapter 4.