Joint transmission and reflection traveltime tomography using the fast sweeping method and the adjoint-state technique

We present a joint transmission and reflection traveltime tomography algorithm based on the Fast Sweeping Method and the adjoint-state technique. In contrast to classical ray based tomography, this algorithm utilizes a grid-based Eikonal equation solver to circumvent the non-linearity of conventional ray shooting and bending approaches in complex media. The adjoint-state technique is used to obtain the gradient of the objective function without the explicit estimation of the Frechet derivative matrix, which is usually computationally prohibitive for large-scale problems. When combined with Huygens Principle, the tomographic inversion can simultaneously use direct and reflected arrivals to optimize a final velocity model, further mitigate the ambiguity of the inverse problem and reveal deeper structures not visible to transmission tomography alone. In this paper, we describe the theoretical basis of our algorithm, evaluate its performance on synthetic models, and then apply it to a 20 km long 2-D seismic survey acquired in the Mackenzie Delta, Northwest Territories of Canada. The subsurface at that location is characterized by a thick permafrost (600 m) comprising high- and low-velocity areas associated with thermokarst lakes. Our results show the potential of the joint tomography in characterizing multi-scale heterogeneous velocity structures within the permafrost.