Higher-Order Rytov Approximation for Large-Scale and Strong Perturbation Media (Communications in Computational Physics, 2020)
In the field of geophysics, although the first-order Rytov approximation iswidely used, the higher-order approximation is seldom discussed. From both theoretical analysis and numerical tests, the accumulated phase error introduced in thefirst-order Rytov approximation cannot be neglected in the presence of strong velocity perturbation. In this paper, we are focused on improving the phase accuracy offorward scattered wavefield, especially for the large-scale and strong velocity perturbation case. We develop an equivalent source method which can update the imaginarypart of the complex phase iteratively, and the higher-order scattered wavefield can beapproximated by multiplying the incident wavefield by the exponent of the imaginarypart of the complex phase. Although the convergence of the proposed method has notbeen proved mathematically, numerical examples demonstrate that our method canproduce 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, inthe presence of multi-arrivals phenomenon, the equivalent scattering source should behandled carefully due to the multi-directions of the wavefield. Further investigationsshould be done to improve the applicability of the proposed method.
Keywords: Rytov approximation; higher-order approximation; large-scale strong perturbation; forward scattering; equivalent scattering source.