Re-Exploration into Migration of Seismic Data

The formula of migration of seismic data is re-derived by using the forward propagation equations of seismic waves, in which the migration of seismic data is viewed as an approximate solution to the linear waveform inverse problem, a scattering migration method suitable for scattering seismic data and a reflection migration method suitable for reflection seismic data are proposed. Based on the scattering theory of seismic wave propagation, firstly we study and establish the migration theory for scattering seismic data through the linear equation describing the forward propagation of primary scattering wave. A subsurface reflectivity function is derived by applying the high frequency approximation to the spatial variation of velocity perturbation function generating the scattering field, and a forward propagation equation of reflection wave using the reflectivity function is derived from the propagation equation of scattering wave, then we study and establish the migration theory for reflection seismic data through the linear equation describing the forward propagation of primary reflection wave. We pointed out and corrected the shortcomings in Claerbout's migration method. The migration method of seismic data introduced in this paper is an improvement to current migration technique and theory, and establishes a solid theoretical base of mathematical physics for the migration of reflection seismic data. The migration results from the new methods have correct phase, accurate position and improved resolution.