A Direct Sampling Method For Recovering The Source Of 2D Elastic Wave

The main goal of the inverse sourse problems is to recover some parameter information,such as the strength,the size and the position,etc,of the unknown source from the measured radiated field.It has caused wide attention in geophysical,medical imaging,acoustic imaging optics,geology and other fields of science and engineering application.Since the inverse source prooblem is ill-posed and the cooresponding mathematical physics equations usually has no analytical solution,computing methods are usually used to solve these problems in practice.Therefore,the study of computing methods has not only thr theoretical significance,but application prospects as well.In the traditional inverse source problems of elastic wave,the iterative methods and regularization methods are used generally.But these methods are often very complex,and associated with difficulties,such as unstablity and slow convergence.This study is devoted to the inverse source problem for the two-dimensional time-harmonic Navier's equations.This problem is aimed at using the far-field data to predict the position and intensity of the the dipole source term of the equation.We propose a non-iterative sampling method for identifying locations and moments of the dipolar sources from the far-field data.The proposed direct sampling method is based on a special indicator function and some disadvantages in the traditional method,such as the ill-posed and the huge amount of calculation,can be avoided with this method.And then,the effectiveness and stability of this method are analyzed.Several numerical experiments are conducted to demonstrate the effectiveness and robustness of the proposed methods...