摘要
传统的波动方程线性化近似理论,如一阶Born近似或Rytov近似等,均隐含“弱散射”假设,因此仅适用于弱扰动模型.为克服“弱散射”假设的制约并将波动方程线性化近似理论推广至强扰动模型中,提出了适用于预测前向散射波相位扰动的保相位理论.通过将标量声波方程Rytov变换得到的非线性Ricatti方程中关于未知解(即散射场复相位)的积分,在Wentzel-Kramers-Brillouin-Jeffreys(WKBJ)近似下转化为对散射角和模型扰动的积分,给出了前向散射场相位扰动的显式积分表达.理论推导表明:对于一维波传播问题,保相位理论可以精确预测任意速度扰动模型中前向散射波的相位扰动.对于小角度前向散射,保相位理论可以进行线性化近似,得到广义Rytov近似.数值实验表明,对于高维问题,相比于一阶Rytov近似,广义Rytov近似可以更好地预测前向小角度散射场的相位扰动,且适用于强速度扰动模型.广义Rytov近似拓展了Rytov近似的成立条件和适用范围,可以直接应用于地震层析成像及医学超声透射成像中,从而降低层析反问题对初始模型的依赖性并加速反演收敛.
The conventional wave-equation linearization methods,such as the first-order Born or Rytov approximation,always implicitly imply a weak-scattering assumption,making it valid only for weak perturbation models.To extend the wave-equation linearization theory to strong perturbation models,we consider a scenario that the reference model is smooth within the scale of the incident wave length,and propose a phase-preserving method which can predict the phase perturbation of forward scattering wave field.First,we introduce the WKBJ approximation to the scattered-and incident wave fields so that the integral of the unknown solution(i.e.the scattered field)in the nonlinear Ricatti integral equation can be replaced by the integral of scattering-angle and model perturbation,yielding an explicit expression of the scattered field.Theoretical derivation shows that the proposed phase-preserving method can accurately predict the phaseperturbation of forward scattered wave field regardless of the strength of velocity perturbations for onedimensional wave propagation problem.To apply the phase-preserving approximation to the inverse problem,we further consider a scenario of small-angle forward propagation.In this case,the phase-preserving approximation can be linearized by neglecting the influence of scattering angles,leading to a linear relation between the scattered field and the model perturbation,which we refer to as the generalized Rytov approximation.Numerical experiments demonstrate that the generalized Rytov approximation can predict the phase perturbation of the scattered field with higher accuracy for small-angle forward propagation,and is suitable for strong model perturbations.The generalized Rytov approximation extends the validity and the scope of application of the traditional Rytov approximation.In specific application fields such as the seismic traveltime tomography or medical ultrasonic transmission imaging,a new traveltime/phase sensitivity kernel can be derived by replacing the conventional Rytov approximation with the proposed method,which can increase the inversion accuracy and speed up the convergence.
作者
冯波
徐文君
蔡杰雄
吴如山
王华忠
Feng Bo;Xu Wen-Jun;Cai Jie-Xiong;Wu Ru-Shan;Wang Hua-Zhong(Wave Phenomena and Intelligent Inversion Imaging Group(WPI),School of Ocean and Earth Science,Tongji University,Shanghai 200092,China;Key Laboratory of Intelligent Infrared Perception of the Chinese Academy of Sciences,Shanghai Institute of Technical Physics of the Chinese Academy of Sciences,Shanghai 200083,China;SINOPEC Geophysical Research Institute Co.,Ltd.,Nanjing 211103,China;Modeling and Imaging Laboratory,University of California,Santa Cruz 95060,CA,USA)
出处
《物理学报》
SCIE
EI
CAS
CSCD
北大核心
2023年第15期311-319,共9页
Acta Physica Sinica
基金
国家自然科学基金(批准号:42074143)
中央高校基本科研业务费专项资金资助的课题.
关键词
波动方程线性化
保相位近似
前向散射
强扰动模型
wave-equation linearization
phase-preserving approximation
forward scattering
strong perturbation model
