Concurrent elastic inversion of Rayleigh and body waves with interleaved envelope-based and waveform-based misfit functions

Abstract

Rayleigh and body waves are both solutions of the same propagation equation, but correspond to different wavenumber regions and boundary conditions, so their interaction with the elastic parameters (Vp, Vs and density) provides independent constraints during inversion. We develop and illustrate concurrent, elastic, full-waveform inversion of P and S body- and Rayleigh-waves using interleaved envelope- and waveform-based misfit functions, in a gradually-increasing frequency, multi-scale, inversion strategy. A wavelet and its envelope have different effective bandwidths, spectral shapes, and provide complementary frequency and wavenumber weighting in concurrent inversion. Because of the greater depth extent sampled by the exponentially decaying tail of a Rayleigh wave, compared to a body waveform, the depth extent of the model required to support both body and surface waves in concurrent inversion is defined by the Rayleigh waves. Correlation coefficients provide quantitative measures of the contributions of the data subsets to the fits of the solutions. For both smooth and constant starting models, concurrent interleaved inversion gives smaller data misfits than the envelope-only and waveform-only solutions. Treating the whole wavefield as a single data set means that it is not necessary to separate, or even to identify, different types of body and surface waves.

Keywords:

• Full waveform inversion
• Rayleigh waves
• near surface

Acknowledgements

Thanks to Hejun Zhu for valuable discussion and comments. Thanks to Yanhua Yuan from Princeton University, C. A. Pérez Solano from MINES ParisTech, PSL Research University and their co-authors for permission to use the modified synthetic near surface model. We also would like to thank Jeroen Tromp, Ryan Modrak and the Theoretical & Computational Seismology Research Group at Princeton University, for providing the software package SPECFEM2D and SeisFlows, which made this research much more efficient. We acknowledge the Texas Advanced Computing Center (TACC) for providing HPC resources that have contributed to the research results reported in this paper. This paper is Contribution No. 1699 from the Department of Geosciences at the University of Texas at Dallas.

Disclosure statement

The authors report there are no competing interests to declare.

Data availability statement

The data that support the findings of this study are available from the corresponding author, Li Ren, upon reasonable request.

Additional information

Funding

We would like to acknowledge the Sponsors of the UTD Geophysical Consortium for funding the research.