ACOUSTIC REVERSE-TIME MIGRATION BASED ON MESH-FREE FINITE-DIFFERENCE

Abstract eng:
As an important technique in many engineering and scientific fields, reverse-time migration (RTM) is a powerful tool for imaging geologically complex structures underground. The accuracy and efficiency of RTM are affected by many factors. One factor is the numerical solution of wave equations. Many methods have been developed to numerically solve wave equations, among them finite-difference (FD) is a popular one for its easy implementation, high efficiency and small memory cost. FD methods approximate derivatives through a weighted summation of function values from neighboring nodes. Traditionally, these neighboring nodes are assumed to be distributed regularly such as in square or rectangular lattices. To improve geometric flexibility, one option is to develop mesh-free FD (MFD), in which scattered nodes can be placed suitably with respect to irregular boundaries or arbitrarily shaped anomalies without generating irregular lattices or mesh elements. Another factor is the absorbing boundary condition (ABC). Reflections from limited model boundaries would degrade final images, therefore, the ABCs are in demand for suppressing the reflections. The ABC for wave propagation using a mesh-free method should maintain the flexibility of the mesh-free framework. In this paper, we develop an acoustic numerical modelling method by introducing radial-basis-functiongenerated finite difference (RBF-FD) and the hybrid absorbing boundary condition (HABC) for a homogenous model by mesh-free nodes. Moreover, the developed mesh-free numerical modelling is introduced into forward extrapolation and backward extrapolation of RTM to improve the migration geometric flexibility. It is demonstrated by an imaging profile for a simple and a complex models that the RBF-FD and HABC could offer high accuracy and algebraic simplicity in RTM.

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