First-Arrival Traveltime Tomography Based on the Adjoint State Method with Independence of Surface Normal Vectors

Abstract

Summary The first-arrival traveltime tomography based on adjoint state method has gained widespread attention in recent years. Compared with the traditional method, this method does not need to perform any ray tracing. Only the eikonal equation and the adjoint equation need to be solved in order to obtain the inversion gradient. However, the result of commonly-used adjoint state traveltime tomography is related to the boundary normal vector of the computational domain. In the cases of complex surface, the calculation of adjoint field via the boundary normal vector makes the traveltime residual distributed according to structure-irrelevant parameters. As a result, the tomography gradient deviates from the true gradient and consequently contributes to a untrue tomographic model. In need of solving this issue, this paper derives a new form of adjoint equation that is independent from the boundary normal vector. This tomography method adapts to any kind of observation system. In situations of tough topography, it produces better results compared to the commonly-used adjoint state tomography method. The gradient calculated by this method is similar to that of the traditional ray-based method, but it offers better continuity and smoothness with significantly improved inversion efficiency proved by the synthetic experiments.