Linearized Multimodal Inversion of Multichannel Surface Waves for Shallow Profiles Containing Stiff Layer

Abstract

Dispersion properties of surface waves find many useful applications in geophysical and geotechnical engineering projects [10]. It is normally assumed in these applications that the fundamental mode of surface waves (M0) dominates the recorded wavefield and higher modes can be ignored. In reality, however, experimental analysis indicates that higher modes are always generated and can sometimes possess significant amounts of energy [1], [13]. Two active-source methods that have proved valuable for determining shallow shear-wave velocity profiles are the spectral analysis of surface wave (SASW) method (See References [7] and [10] for further details) and the multichannel analysis of surface waves (MASW) method [8]. In both, dispersion curves are interpreted from the measured data, and a shear-wave profile is updated through inversion. The SASW method uses receiver pairs and, through spectral phase correlation, generates an effective dispersion curve that comprises a superposition of surface wave modes and other wave types, although historically, inversion of SASW data typically assumed that most of the energy making up the dispersion curve is associated with the fundamental mode Rayleigh wave. The second method builds dispersion curves by transforming the receiver array to a domain that allows independent interpretation of the fundamental and higher mode Rayleigh waves plus body waves. In this paper we present that inversion of the surface wave dispersion curves only by fun-damental mode will produce significant errors, especially where the generation of higher modes has been associated with presence of a velocity reversal (a lower Vs layer between higher Vs layers). In our proposed inversion algorithm, analyzing of the Jacobian matrix clearly shows the advantages of utilizing higher modes in inversion of surface wave data.