Mode misidentification in Rayleigh waves: Ellipticity as a cause and a cure

Abstract

The surface wave method is a popular tool for geotechnical characterization because it supplies a cost-effective testing procedure capable of retrieving the shear wave velocity structure of the near-surface. Several acquisition and processing approaches have been developed to infer the Rayleigh wave dispersion curve which is then inverted. Typically, in active testing, single-component vertical receivers are used. In most cases, the inversion is carried out assuming that the experimental dispersion curve corresponds to a single mode, mostly the fundamental Rayleigh mode, unless clear evidence dictates the existence of a more complex response, e.g., in presence of low-velocity layers and inversely dispersive sites. A correct identification of the modes is essential to avoid serious errors. Here we consider the typical case of higher-mode misidentification known as “osculation” (“kissing”), where the energy peak shifts at low frequencies from the fundamental to the first higher mode. This jump occurs, with a continuous smooth transition, around a well-defined frequency where the two modes get very close to each other. Osculation happens generally in presence of strong velocity contrasts, typically with a fast bedrock underlying loose sediments. The practical limitations of the acquired active data affect the spectral and modal resolution, making it often impossible to identify the presence of two modes. In some cases, modes have a very close root and cannot be separated at the osculation point. In such cases, mode misidentification can create a large overestimation of the bedrock velocity and a large error on its depth. We examine the subsoil conditions that can generate this unwanted condition, and the common field acquisition procedures that can contribute to producing data having such deceptive Rayleigh dispersion characteristics. This mode misidentification depends strongly on the usual approach of measuring only the vertical component of ground motion, as the mode osculation is linked to the Rayleigh wave ellipticity polarization, and therefore we conclude that multicomponent data, using also horizontal receivers, can help discern the multimodal nature of surface waves. Finally, we introduce a priori detectors of subsoil conditions, based on passive microtremor measurements, that can act as warnings against the presence of mode osculation, and relate these detectors to the frequencies at which dispersion curves can be misidentified. Theoretical results are confirmed by real data acquisition tests.