Combination of FDTD with Analytical Methods for Simulating Elastic Scattering of 3-D Objects Outside a Fluid-Filled Borehole

We propose a hybrid method based on the finite-difference time-domain (FDTD) algorithm and analytical methods to solve the elastic scattering of 3-D objects outside a borehole. In the proposed method, the FDTD algorithm containing the incident waves generated by a borehole acoustic source is first used to calculate the wave fields inside a rectangular volume enclosing the object. Then, the reciprocity theorem for the wave fields in the fluid/solid configurations is employed to transform the near fields around the object into the far fields inside the borehole. This method uses the regional domain which tightly encloses the object, thus avoiding the simulation for the whole domain and leading to high efficiency for the large-scale and multiscale problems containing both the borehole and far-field objects. The validations with both analytical solutions and independent numerical methods demonstrate the accuracy and efficiency of the hybrid method.