Full waveform inversion with optimal basis functions

The full waveform inversion for a 2D layered acoustic system, with point sources and receivers, perhaps the simplest test case for nonlinear inversion and a first-order approximation to the structure of Earth's subsurface was considered. By using the optimal basis functions alternately in the inversion process, the low frequency lacuna problem encountered before was not only overcame, but also obtained robust and accurate results. The physical reason for this success was elucidated by comparing 1D analytic solutions at a single interface, for both the step-function basis and the block function basis.