Frequency Domain Waveform Inversion in a Tunnel Environment

The aim of the waveform inversion is to find an optimal model for the distribution of the elastic stiffness such that its response is consistent with the seismic data. In this study, a high-order finite element method is being used to solve the forward problem in the frequency domain and a gradient-based approach is followed to invert the model where an adjoint method eases the computational struggle by reducing the number of the required forward simulations significantly. Perfectly Matched Layers (PML) are implemented in order to absorb waves on the fictitious boundaries of the considered geometry. The model is inverted only over a limited number of frequencies. This reduces the number of the required forward simulations and the nonlinearity of the inverse problem. Every model is unique and has to be investigated before being inverted; appropriate boundary conditions, placement of the source and receiver locations, and an initial model close to the real model are crucial points to be considered separately and carefully. Applications to the reconnaissance problem in a tunnel environment are shown. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)