Summary
Inspired by interference beat tone, a phenomenon commonly used by musicians for tuning check, we developed a novel full waveform inversion (FWI) method called beat inversion for reliable velocity model building without low frequency seismic data. In this new method, by utilizing two recorded seismic waves with slightly different frequencies propagating through subsurface, we are able to extract very low wavenumber (large scale structure) components from high frequency seismic data. With the conventional FWI algorithms, this type of long wavelength information can only be obtained by inverting low frequency seismic data. We designed and investigated two algorithms for this new method, one is the so-called amplitude-frequency differentiation (AFD) beat inversion, and the other is the phase-frequency differentiation (PFD) beat inversion. The AFD algorithm works for transmission seismic data with accurate amplitude measurement. The PFD is a more robust algorithm applicable for both transmission data and reflection data inversion and can be used for complex velocity model building applications. The mathematical analysis and the numerical experiment validate that this new FWI algorithm overcomes the long existing difficulty in FWI – the cycle-skipping issue. Another unique and important feature of the PFD beat inversion algorithm is that it does not require accurate source estimation and it is insensitive to amplitude measurement error. The numerical example shows that, with high frequency seismic data, the beat inversion method produces very smooth velocity model with large scale structural information properly recovered. On the other hand, if we invert the same frequency seismic data using the conventional FWI algorithm, many artifacts arising from cycle-skipping are observed and the inversion is trapped in local minima.
