Grouping of Complex-valued Frequencies in the Laplace-Fourier Domain Waveform Inversion

Full waeform inversion is a method to estimate subsurface physical properties from seismic data. Laplace-Fourier domain waveform inversion can recover long-wavelength and medium- to short-wavelength velocity models despite lack of low frequency components in the data. For the Laplace-Fourier domain inversion, we propose a method of grouping complex-valued frequencies as an approach to optimize the usage of the complex-valued frequencies. The grouping method can be implemented by inverting grouped complex frequencies simultaneously while inverting each group sequentially. We applied three Laplace-Fourier inversion algorithms - simultaneous, sequential and grouping - to synthetic seismic data. Grouping method of fixed temporal freqeucny group with low-to-high order can recover long- to short- wavelength velocity models from scratch.