In this paper, we present a program, PATT (Parallel Arrival Time Tomography), to perform transmission and/or reflection travel time tomography based on adjoint-state technique and Fast Sweeping Method (FSM). In contrast to classical ray based tomography algorithm, this algorithm utilizes a finite difference based Eikonal equation solver to circumvent the non-linearity of conventional ray shooting and bending approaches. The adjoint-state technique is used to obtain the gradient of the objective function without estimation of Fréchet derivative matrix, which is usually computationally prohibitive for large scale problems. Based on Huygens’ Principle, we extend the capability of FSM to calculate reflection time and show that the joint tomography using both transmission and reflection time can further mitigate the non-linearity of inverse modeling and reveal deeper features not visible to transmission waves.
This paper describes the theoretical basis of the algorithm, provides the details of the parallel implementation and demonstrates the scalability of the high performance program on a distributed memory system. We then evaluate the performance of transmission, reflection and joint tomography on a synthetic model and a two-dimensional (2D) seismic survey conducted in Northwest Territories of Canada where complex thermokarst lakes and heterogeneous permafrost are present in the shallow subsurface. The accuracy of travel time using FSM and the resolution of the tomographic model in the presence of white noise are analyzed in the appendices.