This thesis deals with the theory and application of full-waveform inversion. In the first part of this thesis the full-waveform inversion is mathematically described. Thereby the forward problem is explained, including a short discussion about numerical stability and dispersion. Following that, the inversion theory is given, once in the time-domain and once in the frequency-domain. The emphasis of the formulations lays here on the theory implemented in a newly developed inversion algorithm. This novel code is then tested by applying the inversion schemes to a simple cross-hole configuration. The inversion is carried out for Vp, Vs and Vp and Vs, simultaneously. The velocity anomalies were once placed at the same position and once at different positions, additionally showing different sign of perturbation. This cross-hole configuration is also applied to another 2-dimensional inversion code developed by the Institute of Technology in Karlsruhe (KIT). Both inversion algorithms could reliably reconstruct the velocity anomaly in terms of position, shape, size and sign of perturbation. The inversion converge very fast and the data misfit could be minimised in few iteration steps. In the second part of this thesis, the survey area is introduced, which is located in a closed down part of Mt. Erzberg. Old mine maps indicate an abandon tunnel in 25 m depth and with a diameter of 4 m. Two surveys in 2016 and 2018, were conducted, using two different sources for wave excitation, namely hammer blows and explosives. The data processing includes data quality control, normalisation routines, stacking, rotation and finally a velocity and spectral analysis. The data from the second survey are considered for a first-arrival travel-time tomography. The inverted travel-time tomography model serves as the initial model for the following synthetic study and the inversion of elastic parameters. The synthetic studies allow a characterization of wavefield behaviour in the presence of a subsurface cavity. Initially a comparable source wavelet is determined by transforming the amplitude spectra of the field data into the time-domain. Afterwards several forward simulations are done with different quality factors. The comparison of the amplitude spectra of measured field data and synthetically modelled data allows a determination of a reasonable Q-factor of 5. Now the simulations based on the tomography model without and with an implemented cavity are executed, allowing a comparison and development of inversion strategies. Three main strategies are considered, strategy A includes a trace killing without any filtering, strategy B includes a trace killing and a LP-filtering of the data and strategy C includes an offset mute until 50 m, a filtering and a time-windowing of the data for P-waves and Surface-waves. Those inversion strategies are applied to two different starting models in order to recreate the implemented cavity. The first model is the travel-time tomography model and the second one is a perturbed version of the travel-time tomography model. The synthetic inversion results show a good and reliable reconstruction of the cavity in nearly all inversion approaches and parameters. The implemented cavity can undoubtedly be reconstructed. With that knowledge at hand, finally the inversion strategies are applied to the measured field data. Here the cavity could not be reliably and undoubtedly resolved. The suspected cavity is not as well and clearly reconstructed as in the synthetic study. Considering all inversion approaches and the a priori knowledge of the cavity, it might be argued that the cavity is indicated