A Joint Inversion of Sources and Seismic Waveforms for Velocity Distribution: 1-D and 2-D Examples

Waveform inversion is theoretically a powerful tool to reconstruct subsurface structures, but a usually encountered problem is that accurate sources are very rare, causing the computation unstable and divergent. This challenging problem, although sometimes ignored and even imperceptible, can easily create discrepancies in calculated shot gathers, which will then lead to wrong residuals that must be migrated back to the gradients, hence jeopardizing the inverted tomograms. In practice, any shot gather may correspond to its own source even if some of them can be transformed alike after data processing. To resolve this problem, we propose a collocated inversion of sources and early arrival waveforms with the two submodules executing alternatively. Not only can this method produce a decent wavelet that approaches the true source or an equivalent source, but more importantly, it can also invert for credible background velocity models with the optimized sources. Part of the cycle skipping problems can also be mitigated because it avoids the trial and error experiments on various sources. Numerical tests upon a series of different conditions validate the effectiveness of this method. Restrictions on initial sources or starting velocity models will be relaxed with this method, and it can be extended to any other applications for engineering or exploration purposes.