Elastic full-waveform inversion (EFWI) updates high-resolution model parameters by minimizing the misfit function between the observed and modeled data. EFWI possesses strong nonlinearity and is likely to converge to a local minimum when the inversion begins with inaccurate initial models. Elastic reflection waveform inversion (ERWI) recovers the low-wavenumber components of P- and S-wave velocities along the "rabbit ear" wave paths to provide initial velocity models for EFWI. However, every iteration of ERWI requires six times as many forward calculations with elastic-wave equations which can be computationally expensive. Hence, we have developed a pure-wave reflection waveform inversion (PRWI) approach, which sequentially inverts low-wavenumber components of P- and S-wave velocity models. In our PRWI, we decompose elastic-wave operators into background and perturbed pure-wave parts and derive PRWI gradients using pure-wave operators. Both the background and perturbed wavefields in PRWI gradients are vector wavefields with single wave mode. PRWI can remove the high-wavenumber noise caused by S-wave stress decomposition, and reduce the computational cost of ERWI by almost 70%. Under the framework of PRWI, we have further developed the pure-wave reflection traveltime inversion (PRTI) approach to alleviate the issue of cycle skipping caused by waveform mismatch. In order to ensure the recovery of low-wavenumber components, we mute out the contribution of wavefields with small opening angles to PRTI gradients. Numerical examples have demonstrated that our PRTI method can provide good initial velocity models for EFWI efficiently.
Coarse-Grained Molecular Dynamics: Dissipation due to Internal Modes