Wavelets in surface wave cavity detection - Theoretical background and implementation

摘要

A new approach based on representation of the surface response of a medium, in the time-frequency plane, is investigated in this study. Surface wave propagation in the soil medium is simulated by a transient response analysis on an axisymmetric finite element model. Cavities in a homogeneous half-space, as well as a pavement system with a variety of shapes and embedment depths, were considered. The continuous wavelet transform (CWT) has been introduced as a new analysis tool for extracting time and frequency information of nonstationary signals with good time and frequency resolutions. Different families of wavelets were examined for the analysis, and ultimately, Gaussian wavelets were chosen. It has been demonstrated that the surface response is of transient nonstationary nature with local time and frequency features. Using wavelet transform, the changing spectral composition of the surface transient response is presented in the time-frequency plane. Effects of different types of cavities on wavelet time-frequency maps (wavelet transform coefficients magnitude versus time and frequency for the response at different receiver locations) were analyzed. Time and frequency signatures of waves reflected from near and far faces of the cavity can be clearly observed in wavelet time-frequency maps. The pattern of changes of time-frequency maps at different receiver locations was reviewed. Based on these observations, a scheme for location of the cavities, and their size and depth estimation, using wavelet transform is suggested The proposed scheme has been used successfully to detect some known cavities in a pavement system. In addition, the applicability of the proposed method may be evaluated by a series of tests in a sand bin.