In full waveform inversion, the lack of low frequency information in the inversion results has been a long standing problem. In this work, we show that by using mixed basis functions this problem can be resolved satisfactorily. Examples of full waveform inversion on layered systems, using surface reflection data from point sources, have shown excellent results nearly indistinguishable from the target model. Our method is robust against additive white noise (up to 20\% of the signal) and can resolve layers that are comparable to or smaller than a wavelength in thickness. Physical reason for the success of our approach is illustrated through a simple example.
Ping Sheng. Gang Sun. Qianshun Chang. "Application of Optimal Basis Functions in Full Waveform Inversion\." Methods Appl. Anal. 11 (3) 345 - 352, September 2004.