Solutions of Surface-Wave Dispersion and Attenuation in Stratified Viscoelastic Media Using a Spectral-Element Approach

Abstract

ABSTRACT Efficient and accurate calculation for the dispersion and attenuation of the surface waves in viscoelastic media is numerically challenging because the eigen wavenumbers are located in the complex domain. In this study, we propose a semianalytical spectral-element method (SASEM), which can determine the complex eigen wavenumbers by solving linear eigenvalue problems. By simplifying the structure of the eigenvalue problem, we significantly improve the calculation efficiency. The implementation of the frequency-dependent automatic discretization, semi-infinite element, and mode filter guarantees the correctness and accuracy of the modal solutions. Because no root-searching schemes are required, the root-skipping problem is naturally avoided. The numerical tests show that the SASEM can provide sufficiently accurate solutions with much less computation cost than traditional Muller’s method. Meanwhile, SASEM exhibits high flexibility when applied to media the parameters for which vary continuously with depth. To demonstrate the effectiveness of SASEM for complicated dispersion features, the dispersion curves and eigen wavefields of the viscoelastic media with a low-velocity layer are also analyzed. The results of numerical tests indicate the versatility, efficiency, and accuracy of our method. With further study, the proposed SASEM has the potential to become a promising tool for the investigation and retrieval of viscoelastic subsurface structures.