Multiscale Virtual Wavefield Waveform Inversion Based on Multidimensional Interferometric Retrieval

Full waveform inversion (FWI) seeks a subsurface parameter model that optimally matches the true state by minimizing the differences between synthetic and observed data. However, when starting from a rough initial model, FWI is often limited by the weak low-frequency energy of the observed data and the difficulty of matching surface-related multiples (SRMs), especially when the source wavelet is not readily available. Source wavelet errors also affect the general inversion result. We propose a multiscale virtual wavefield waveform inversion (VWWI) based on multidimensional interferometric retrieval (MDIR) to mitigate these challenges. We use MDIR to retrieve the virtual response from the up- and down-going wavefields separated from the original data and infer the velocity using the virtual response instead of the original data. MDIR integrates the source functions using multidimensional cross correlation (MDCC) and then suppresses the source imprints from the original data through multidimensional deconvolution (MDD). The retrieved virtual responses have a broader bandwidth and are dominated by primary reflection events. It addresses simultaneously three major challenges that FWI faces through a one-time data retrieval. Assigning self-setting source functions with different dominant frequencies to the virtual response allows the extraction of virtual observed data to different frequency bands for multiscale velocity inversion. Considering the possible amplitude distortion and the computational cost, we propose the hybrid source cross-correlation objective function adapted to VWWI. Numerical examples of well-known models representing weak and strong scattering media show that the proposed VWWI method can stably achieve wide-scale velocity modeling from macroscopic background to delicate structures.