Abstract
One of the main problems in exploration Geophysics is to obtain an accurate velocity profile of the near surface Earth. The medium velocity of the near surface Earth is critical for the definition and interpretation of the shallow geology. It reflects the heterogeneity of the near surface Earth. Furthermore, the small variations of the near surface velocity result in scattering. Therefore the aim of this Thesis is to derive the linearized inversion of the scattered surface wavefield in order to determine the variations in the velocity profile of the near surface earth. In this Thesis, we will use the Green function and the method of perturbation in order to determine the variations in the velocity profile of the near surface Earth by means of linearized inversion of the scattered surface wavefield. Initially, we will give a general overview of the seismic waves, but with more emphasis on surface waves. Later, the construction of both the differential operators and the Green functions for Love and Rayleigh waves is presented. The perturbation methodology is deployed in order to obtain the linearized forward modeling formula. Finally, the linearized inversion formula is obtained analytically and numerical algorithm is also presented.
