A fast local level set adjoint state method for first arrival transmission traveltime tomography with discontinuous slowness

Abstract

SUMMARY We propose a numerical algorithm for solving first arrival transmission traveltime tomography problems where the underlying slowness is piecewise continuous. The idea is based upon our previously efficient approach for smooth slowness inversion (Leung & Qian) using the fast sweeping method and the adjoint state method. In this work, we further incorporate the level setmethodtoimplicitlyrepresentthediscontinuityinthevelocity.Onemainadvantageofsuch implicit representation is that there is no assumption on the number of disjoint components in the inverted structure. The evolution of the level set function will naturally take care of the change in the topology. Like in the previous work, the gradient of the mismatch functional is derived using the adjoint state method. The forward problem and the adjoint equation are efficientlysolvedbythefastsweepingmethod.Tofurtherimprovethecomputationalefficiency, we also propose a local level set method so that most computer power of updating the level set evolution is spent near the discontinuity in the slowness. Numerical results will be given to demonstrate the robustness of the algorithm.