Sensitivity of high-frequency Rayleigh-wave data revisited

Rayleigh-wave phase velocity of a layered earth model is a function of frequency and four groups of earth properties: Pwave velocity, S-wave velocity (Vs), density, and thickness of layers. Analysis of the Jacobian matrix (or the difference method) provides a measure of dispersion curve sensitivity to earth properties. Vs is the dominant influence for the fundamental mode (Xia et al., 1999) and higher modes (Xia et al., 2003) of dispersion curves in a high frequency range (>2 Hz) followed by layer thickness. These characteristics are the foundation of determining S-wave velocities by inversion of Rayleigh-wave data. More applications of surface-wave techniques show an anomalous velocity layer such as a high-velocity layer (HVL) or a low-velocity layer (LVL) commonly exists in near-surface materials. Spatial location (depth) of an anomalous layer is usually the most important information that surface-wave techniques are asked to provide. Understanding and correctly defining the sensitivity of high-frequency Rayleigh-wave data due to depth of an anomalous velocity layer are crucial in applying surface-wave techniques to obtain a Vs profile and/or determine the depth of an anomalous layer. Because depth is not a direct earth property of a layered model, changes in depth will result in changes in other properties. Modeling results show that sensitivity at a given depth calculated by the difference method is dependent on the Vs difference (contrast) between an anomalous layer and surrounding layers. The larger the contrast is, the higher the sensitivity due to depth of the layer. Therefore, the Vs contrast is a dominant contributor to sensitivity of Rayleigh-wave data due to depth of an anomalous layer. Modeling results also suggest that the most sensitive depth for an HVL is at about the middle of the depth to the half-space, but for an LVL it is near the ground surface.