Application of the Unscented Kalman Filter to Estimate the Material Properties of a Layered Half-Space

Abstract

Full waveform inversion (FWI) to estimate physical properties of a system is one of the major research topics in science and engineering. This study proposes a probabilistic approach toward these solutions by applying the unscented Kalman filter (UKF). The responses of the vertical displacements of a layered half-space subjected to a harmonic vertical disk load on the surface are calculated from an estimated profile of shear-wave velocities and compared with measurements or observations. In the calculation of the dynamic responses, the thin-layer method (TLM), which is efficient for layered media, is employed. In order to improve the solutions to the considered inverse problem, regularization terms are included in the observations so that the differences in the material properties between two consecutive layers vanish. The proposed UKF method is demonstrated with a variety of FWI problems in a layered half-space. The results show that the proposed method can estimate the material properties of a layered half-space accurately.