Conventional full waveform inversion (FWI), which was first introduced by Tarantola (1984), has an objective function that is highly non-linear. The forward operator is linearized around the background velocity, which makes the initial model a determining factor for the convergence of the inversion. Therefore, a lot of previous work (Biondi, 2009; Biondi and Sava, 1999; Symes and Carazzone, 1991; Shen, 2004; Luo and Schuster, 1990) has focused on finding more tractable objective functions that have stronger dependence on the kinematics of the wavefield than on the amplitude of the waveform. One attractive method that uses such an objective function is wave-equation traveltime inversion (WT), which was first introduced by Luo and Schuster (1990). In this inversion, the objective function depends on the lag of maximum cross-correlation between the observed and modeled data. Conventionally, these lags are picked in a trace-by-trace scheme, which produce errors due to correlating noise, multiple events, and inconsistencies in the observed data. To overcome this problem, I cast the picking procedure as a global optimization problem in order to avoid local errors by making use of the redundancy of the data.

Wave-equation traveltime tomography by global optimization