The improved first-arrival traveltime tomography based on the adjoint-state method

In the currently-used first-arrival traveltime tomography based on adjoint state method, the boundary normal vectors of the computational domain must be used to compute the adjoint field. As one result, it will get inaccurate gradients and produce unreasonable inversion results in the situation with complex topography. On the other hand, it cannot correctly deal with the problems for borehole observations. These limitations are discussed in this paper by theoretical analysis and numerical experiments. Furthermore, an improved adjoint state based first-arrival traveltime tomography method is proposed. Major improvements include: (1) The data of any observation geometry can be processed by this improved method, including surface and borehole observations simultaneously. (2) New adjoint equation is derived by perturbation method. It does not depend on the boundary normal vector so that the traveltime residuals of the receivers can be correctly back-propagated to the underground and a correct gradient can be obtained. As a result, the velocity inversion accuracy can be increased.