声波方程逆散射反演的近似方法

APPROXIMATE METHOD OF INVERSION OF THE ACOUS-TIC WAVE EQUATION BY INVERSE SCATTERING

我们在文献[1]里研究了介质参考波速沿某个方向线性变化时的三维声散射理论,导出了声波方程逆散射反演问题解的解析表达式.考虑到应用时的实际条件,本文根据上述反演方法导出2.5维模型的声波方程逆散射反演的波速扰动计算公式,给出该方法在“高频”近似条件下的波速扰动反演计算公式,从而使我们提出的“参考波速线性变化时的声波方程逆散射反演”理论更接近实际应用条件.本文给出的这些反演公式仍然具有原方法的优点,即不但可以使Born近似的假定在大多数情况下能得以满足,而且可以利用快速Fourier变换来快速实现介质波速扰动的反演成象.

In the previous paper, we have presented the acoustic inverse scattering theory for a linear reference velocity model, giving an analytic solution for the inverse scattering problem. Considering the practical applications of this method, we have introduced correspondent solutions for the following cases: 1. the two-and-one-half dimensional model with a point source, 2. high-frequency approximation of the solution. The extended studies shown in this paper make previously suggested methods of the inverse scattering more applicable while the advantages tn the previous approach proposed by the authors, e.g. high computational speed due to employment of the FFT algorithm and more endurable to the assumption of Born approximation, are still hold.