Computational efficiency of full waveform inversion algorithms

For managing computational cost in full waveform inversion (FWI), attention to the details of the underlying nonlinear optimization procedure is essential. Here, we performed experiments with a variety of waveform inversion test problems. A quasi-Newton algorithm provided the best performance in all cases. Nonlinear conjugate gradient methods were less efficient and less robust, requiring occasional restarting to avoid numerical problems. Truncated Newton and Gauss "Newton methods, which can be implemented in a matrix-free manner to avoid assembling the Hessian or Jacobian, are shown to be cost-competitive for time domain waveform inversion" outperforming nonlinear conjugate gradient algorithms, though not yet outperforming quasi-Newton algorithms. Given the possibility of combining newly demonstrated computational efficiency with previously reported robustness, truncated Newton algorithms might one day surpass quasi-Newton algorithms as the method of choice for large-scale seismic inversions.