Imageamento sísmico através do método de expansão rápida nos domínios do tempo e da frequência

Abstract

Our work proposes an alternative for the inversion of the matrix impedance present in the Helmholtz equation, used in the modeling and migration of seismic data. Initially implemented post-stacking and pre-stacking seismic migration algorithms in the frequency domain, using the non-recursive Rapid Expansion Method (REM).Which used non-recursive REM and based on the criterion of maximum amplitude, we obtain time tables used in the Kirchhoff migration method, improving the quality of the seismic images in complex media, when compared with the seismic images of the Kirchhoff migration using the time tables calculated through of the solution of the Iconal equation based on ray tracing. We developed a post-stacking frequency migration method that served as the theoretical and experimental framework for the development of the pre-stacked data algorithm. For this broader application the source and receiver wavefields are propagated and retropropagated respectively in the time domain in the same loop and at each extrapolation step are transformed to the frequency domain via the discrete Fourier transform (DFT), this is implemented efficiently. The image condition is calculated by multiplying the fields in the new domain. Different from what is usually done in reverse migration in conventional time, where the source field is stored and later correlated with the backpropagated field of the receivers constructing the migrated seismic image. The new method of calculating migration for pre-stack frequency domain data was used on synthetic data and real data with satisfactory results. In this method, the source field does not need to be saved for later access, making it promising for the migration of 3D seismic data. This new way of calculating the migration to pre-stack data in the frequency domain was used to implement Full Waveform Inversion (FWI) as presented in our results since it allows calculate of Green functions of source and receivers efficiently.