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.