Reverse time migration by interpolation and pseudo-nalytical methods

Abstract

Within the seismic method, in order to obtain an accurate image, it is necessary to use some processing techniques, among them the seismic migration. The reverse time migration (RTM) uses the complete wave equation, which implicitly includes multiple arrivals, can image all dips and, therefore, makes it possible to image complex structures. However, its application on 3D pre-stack data is still restricted due to the enormous computational effort required. With recent technological advances and faster computers, 3D pre-stack RTM is being used to address the imaging challenges posed by sub-salt and other complex subsurface targets. Thus, in order to balance processing cost and with image’s quality and confiability, different numeric methods are used to compute the migration. This work presents two different ways of performing the reverse time migration using the complete wave equation: RTMby interpolation and by the pseudo-analytical method. The first migrates the data with different constant velocities and interpolate the results, while the second uses modifications in the computation of the Laplacian operator in order to improve the finite difference scheme used to approximate the second-order time derivative, making it possible to propagate the wave field stably even using larger time steps. The method’s applicability was tested by the migration of two-dimensional pre- and pos-stack synthetic datasets, the SEG/EAGE salt model and the Marmousi model. A real pre-stack data from the Gulf of Mexico was migrated successfully and is also presented. Through the numerical examples the applicability and robustness of these methods were proved and it was also showed that they can extrapolate wavefields with a much larger time step than commonly used.