A novel source-free frequency-domain full waveform inversion

Full waveform inversion (FWI) is a challenging data-fitting procedure based on full wavefields to abstract quantitative information from seismograms. During the process, the wave propagation equation is solved for different sources and frequencies. Therefore, an efficient and effective wave propagation engine plays a critical role for FWI. The modelled data, theoretically, can be seen as the composites of Green’s function and source wavelet, convolution in the time domain, or multiplication in the frequency domain. So, the accurate source wavelet is essential for successfully applying full waveform inversion on a real dataset.  Yet, it remains a challenging task for data sets with sparse acquisition and noisy field datasets. In the traditional inversion procedure, the source signal can be estimated from observed seismograms as a part of FWI, which is time consuming and may result in inversion divergence. A source wavelet can also be extracted from the direct arrivals in the streamer dataset. However, the quality of the direct arrivals can be diminished by reflections and near-surface noise for land acquisition, vertical seismic profiling (VSP), and ocean bottom cable (OBC) datasets.

To avoid inaccurate source wavelet estimation, various source-independent methods are applied to FWI. Firstly, the deconvolution-based source-independent algorithm is proposed to mitigate the uncertainty of source wavelet estimation by normalizing the seismic data with a reference trace in the frequency domain. Then, the convolution-based source-independent algorithm is presented in the time domain to eliminate the source wavelet influence by convolving the observed data with a reference trace selected from a modelled wavefield, and the modelled data with a reference trace selected from an observed wavefield. To avoid an arbitrary or manual selection of the reference trace, we present a convolution-based source-free method implemented in the frequency domain. Thus, the convolution process becomes a multiplication in our source-free misfit function, achieving a significantly simpler implementation than in the time domain and requiring no artificial interposition.