Higher-Order Rytov Approximation for Large-Scale and Strong Perturbation Media

Abstract

In the field of geophysics, although the first-order Rytov approximation is widely used, the higher-order approximation is seldom discussed. From both theoretical analysis and numerical tests, the accumulated phase error introduced in the first-order Rytov approximation cannot be neglected in the presence of strong velocity perturbation. In this paper, we are focused on improving the phase accuracy of forward scattered wavefield, especially for the large-scale and strong velocity perturbation case. We develop an equivalent source method which can update the imaginary part of the complex phase iteratively, and the higher-order scattered wavefield can be approximated by multiplying the incident wavefield by the exponent of the imaginary part of the complex phase. Although the convergence of the proposed method has not been proved mathematically, numerical examples demonstrate that our method can produce an improved accuracy for traveltime (phase) prediction, even for strong perturbation media. However, due to the neglect of the real part of the complex phase, the amplitude change of the scattered wavefield cannot be recovered. Furthermore, in the presence of multi-arrivals phenomenon, the equivalent scattering source should be handled carefully due to the multi-directions of the wavefield. Further investigations should be done to improve the applicability of the proposed method.