A unified description of surface waves and guided waves with relative amplitude dispersion maps

Abstract

Compared with surface waves, guided waves are rarely applied in near-surface investigation. The main reason may lie in the complexity of their dispersion curves. Besides, the study and understanding of guided wave dispersion characteristics are now also inadequate and not deep enough. In this paper, we derived the complete theoretical dispersion curves of P–SV-wave and pure P-wave systems in layered media based on the transmission matrix method and obtained the relative displacement amplitude coefficients at the free surface as a function of frequency and phase velocity for both surface and guided waves. By assigning the value of relative displacement amplitude coefficient to the corresponding point (f,v) on dispersion curve, we got a multi-information diagram called relative amplitude dispersion map (RADM). As a unified description of surface and guided waves, RADM not only shows the velocity–frequency relationship but also represents the polarized energy ratio at the free surface by display colours. The accuracy of RADM was proved by synthetic seismic records, in which RADMs fit well with the corresponding dispersion energy of surface and guided waves. In addition, we designed six models with different Poisson's ratio (PR) and different layer numbers for comparison. It shows that the dispersive vertical-to-horizontal amplitude ratio of guided waves is complex and discontinuous in RADM, which brings great difficulty for mode identification and even affects the subsequent inversion. Tests also show that for high PR layers, the trends of guided P–SV-wave dispersion curves are basically consistent with those of pure P wave. With the decrease of PR, dispersion curves of guided P–SV wave gradually deviate from those of pure P wave. However, RADMs can be greatly consistent with the dispersion energy in either case. This is of great significance for the inversion of near-surface P and S velocities by using dispersion relationships of multimode surface and guided waves.