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Waveform inversion is an approach used to find an optimal model for the velocity field of a ground structure such that the dynamic response is close enough to the given seismic data. First, a suitable numerical approach is employed to establish a realistic forward computer model. The forward problem is solved in the frequency domain using higher-order finite elements. The velocity field is inverted over a specific number of discrete frequencies; thereby, reducing the computational cost of the forward calculation and the nonlinearity of the inverse problem. The results are presented for different frequency sets and with different source and receiver locations for a two-dimensional model. The influence of attenuation effects is also investigated. The results of two blind tests are presented where only the seismic records of an unknown synthetic model with an inhomogeneous material parameter distribution are provided to mimic a more realistic case. Finally, the result of the inversion in a three-dimensional space is illustrated.

The excavation process in mechanized tunneling can be improved by reconnaissance of the geology ahead. A nondestructive exploration can be achieved in means of seismic imaging. A full waveform inversion approach, which works in the frequency domain, is investigated for the application in tunneling. The approach tries to minimize the difference of seismic records from field observations and from a discretized ground model by changing the ground properties. The final ground model might be a representation of the geology. The used elastic wave modeling approach is described as well as the application of convolutional perfectly matched layers. The proposed inversion scheme uses the discrete adjoint gradient method, a multi-scale approach as well as the L-BFGS method. Numerical parameters are identified as well as a validation of the forward wave modeling approach is performed in advance to the inversion of every example. Two-dimensional blind tests with two different ground scenarios and with two different source and receiver station configurations are performed and analyzed, where only the seismic records, the source functions and the ambient ground properties are provided. Finally, an inversion for a three-dimensional tunnel model is performed and analyzed for three different source and receiver station configurations.