Reverse time migration (RTM) is a method developed for performing non-invasive physical imaging. It aims to generate diagnostic images based on forward and backward modeling of waves, which can be solved with different type of techniques. A widely used one is Finite Differences (FD) due to its low computational cost and its simplicity, as compared to other methods, to implement. In this work we show how to implement RTM with curved coordinates using FD. In particular we focus on the application of curved coordinates to improve the quality of the resulting images and reduce the computational cost of RTM. Here, we apply a strategy to curve coordinates during the wave propagation modeling stage for a modified version of the Marmousi model. The results show that it is completely feasible the redistribution of grid nodes to locally improve quality of the migrated models and reduce the number of grid nodes at the same time. We also found that typical issues associated to the imaging condition and FD scheme remain.

Finite difference is a well-suited technique for modeling acoustic wave propagation in heterogeneous media as well as for imaging and inversion. Typically, the method aims at solving a set of partial differential equations for the unknown pressure field by using a regularly spaced grid. Although finite differences can be fast and cheap to implement, the accuracy of the solution is always restricted by the computational resources. This is a fundamental key point to treat when dealing with large-scale problems. In this work, we present and test a method that uses a non-uniform distribution of grid points to improve on accuracy or to reduce the required computational resources. The applied grid is generated through a coordinate transformation. Differential geometry and generalized coordinates are used to handle and analyze the effect of using a non-uniform grid. Results obtained with the presented method show that the applied transformation as well as the number of points-per-wavelength influences the stability and dispersion in the solution. We exploit this observation to locally improve the accuracy of our simulations. The work presented in this paper allows us to conclude that differential geometry for finite differences can be used to reduce dispersion and hence improve the accuracy when modeling acoustic wave propagation in heterogeneous media. In addition, it can be used to avoid oversampling through the optimization of the number of grid nodes required to have an accurate solution or just honor to the boundaries.