Full wave equation 2D modeling and migration using a new finite difference scheme based on the Galerkin method (FDGM) for irregular grids are presented. Since these involve semi-discretization by the finite element method (FEM) in the depth direction with the linear element, spatially irregular grids can be used to compute the wavefield in modeling and reverse-time migration. The mesh can be made locally thin to better represent structural complexity and lower velocity zones, which are treated by a fine grid, while the remaining parts of the models are represented by a coarse grid with equal accuracy. No interpolation is needed between the fine and coarse parts due to the rectangular grid cells. The accuracy of the proposed technique has been tested with a comparison to an analytical solution. The effectiveness of the method is verified by its application to a thin-layer model. At the same time, its efficiency is shown through an impulse and an oblique interface with a variable velocity media.
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