1. 同济大学海洋与地球科学学院, 上海 200092; 2. 同济大学海洋高等研究院, 上海 200092; 3. Modeling and Imaging Laboratory, University of California, Santa Cruz, CA 95060, USA
Wave-equation traveltime tomography using the ge-neralized Rytov approximation
FENG Bo1,2, WU Ru-Shan3, LUO Fei1, XU Rongwei1, WANG Huazhong1
1. Wave Phenomena Intelligent Inversion Imaging Group(WPI), School of Ocean and Earth Science, Tongji University, Shanghai 200092 China; 2. Institute for Advanced Study, Tongji University, Shanghai 200092 China; 3. Modeling and Imaging Laboratory, University of California, Santa Cruz, California 95060, USA
Abstract：The conventional finite-frequency tomography is usually derived from the Born or Rytov approximation which implies weak-scattering assumption. Therefore, the linearized forward problem in the finite-frequency theory is not satisfied for strong velocity perturbations. In the case of forward scattering and small-angle propagation, the generalized Rytov approximation (GRA) method recently developed can achieve improving phase accuracy of forward-scattered wavefield, making it more suitable for traveltime tomography. In this paper, we combine the conventional finite-frequency theory with GRA and propose a GRA-based traveltime sensitivity kernel, which works well regardless of the magnitude of velocity perturbations. Numerical examples show that the traveltime perturbation of forward-scattered waves can be correctly handled by the GRA-based traveltime sensitivity kernel. Then we propose an implicit matrix-vector product strategy which can calculate the Hessian matrix-vector product without explicitly forming the Hessian matrix, making it more attractive for 3-D problems. We solve the traveltime inverse problem with the Gauss-Newton method, where the Hessian matrix-vector product is obtained by the proposed implicit matrix-vector product method. Consequently, the Gauss-Newton method can be rea-lized in a matrix-free fashion, reducing the compu-ter memory and disk occupancy significantly. Numerical tests demonstrated that the proposed GRA-based traveltime tomography can estimate the near-surface velocity model with high resolution and at a fast convergence rate.
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