Individual and Joint Inversions of Shallow-Seismic Rayleigh and Love Waves: Full-Waveform Inversion Versus Random-Objective Waveform Inversion

Abstract

Shallow-seismic full-waveform inversion (FWI) provides an effective way for the accurate reconstruction of near-surface models. The common 2D shallow-seismic FWI inverts either individual Rayleigh or Love waves, and the joint FWI of Rayleigh and Love waves can further improve the reliability of the result. Conventionally, FWI is formulated as a single-objective inverse problem and is solved with deterministic optimization algorithms. It suffers from a relatively high level of ill-posedness and high computational cost, which are two of the main problems that FWI faces. Recently, a random-objective waveform inversion (ROWI) method is proposed to mitigate these problems. ROWI reformulates waveform inversion as a multi-objective inverse problem and solves it with a stochastic optimization algorithm. The multi-objective framework and the stochastic nature provide ROWI relatively high freedom in searching for the optimal model and therefore improve its robustness against the poor initial model. In this paper, we perform a comprehensive comparison between the performance of shallow-seismic FWI and ROWI for the reconstruction of near-surface models. We compare their performance in the scenario of individual inversion of Rayleigh wave, individual inversion of Love wave, and joint inversion of both wave types. Besides, we also compare their effectiveness when using good and poor initial models. Synthetic examples of a highly heterogeneous model show that ROWI is more efficient and more robust than FWI in both individual and joint inversions. The individual ROWI of Love wave can reconstruct the model more efficiently than Rayleigh wave if a good initial model is available, and the other way around if a poor initial model is provided. The joint inversion, in both FWI and ROWI, outperforms the individual inversion of a single wave type. In both individual and joint inversions, ROWI is more efficient in reducing model error and more robust against the poor initial model than FWI. We also compare the performance of ROWI and FWI by using field data sets acquired in Rheinstetten, Germany. The results show that when a good initial model is available, both FWI and ROWI can nicely reconstruct the main structure of the subsurface model. The validity of the reconstructed model is proved by comparing it to a migrated ground-penetrating radar profile. ROWI can consistently reconstruct the model to a good level even when using a poor initial model, while the individual and joint FWIs fail to work when the initial model is poor. It confirms the relatively higher efficiency and robustness of ROWI than FWI in the reconstruction of near-surface models.

Appendix 1: field example with alternative misfit functions

We run FWIs with two other more convex misfit functions, namely the envelope misfit function (Fig. 19) and the FK-spectra misfit function (Fig. 20) on the field data sets starting with the poor initial model. The results reconstruct the subsurface model relatively better than the FWI results using the least-squares misfit (Fig. 16).

Fig. 19

Env FWI results in the field example when using the poor initial model. Three columns represent the reconstructed $V_S$, $V_P$, and density models, respectively. Three rows represent the results estimated from individual FWI of Rayleigh wave (a–c), individual FWI of Love wave (d and e), and joint FWI of Rayleigh and Love waves (f–h), respectively. The figures share the same color bars with Fig. 11

Fig. 20

FK FWI results in the field example when using the poor initial model. Three columns represent the reconstructed $V_S$, $V_P$, and density models, respectively. Three rows represent the results estimated from individual FWI of Rayleigh wave (a–c), individual FWI of Love wave (d and e), and joint FWI of Rayleigh and Love waves (f–h), respectively. The figures share the same color bars with Fig. 11