Mesh-free least-squares reverse-time migration

The reflectivity of the subsurface can be precisely determined using least-squares reverse-time migration (LSRTM). As LSRTM necessitates solving the wave equation, the numerical solution method of the wavefield directly determines the quality of the migration image. The conventional LSRTM method usually uses the finite difference method based on a regular grid to calculate the wavefield. Due to the stepwise approximation of an irregular surface with a regular grid, scattering noise may occur in the propagation of the wavefield, which affects the quality of the image. In addition, the conventional LSRTM cannot effectively handle the models with rugged topography. The finite difference method generated by radial basis functions (FD-RBF) is a mesh-free method and can construct interpolation functions to solve the wave equations numerically according to arbitrarily distributed spatial coordinate points. Therefore, we use the FD-RBF method to develop a mesh-free LSRTM approach to eliminate the influence of the inherent limitation of a regular grid on the imaging. Numerical examples show that the mesh-free LSRTM method can better represent the curved or steep interface within the model and is also suitable for models with rugged topography. The LSRTM method can provide higher-quality images and effectively reduce the memory required for calculations.