## 1 Introduction  
Vibration mitigation is becoming increasingly important due to the constant densification of urban areas, the expansion of transport networks, and the increase in traffic volume. The growing demand for the protection of residents, along with the use of heavier and faster vehicles with higher emissions places significant demands on the track-vehicle system. The current state of the art during planning procedures involves predicting environmental impacts based on empirical data or reference measurements in comparable scenarios. The propagation path from the source to the assessment point is typically split into separate sections referred to as the emission, transmission and immission domains, each with their respective transfer spectra [1, 2, 3, 4, 5]. This path encompasses the vehicle-track interaction (determined by superstructure stiffness, axle loads and vehicle speed), the propagation of seismic waves through the ground (determined by soil densities and elastic moduli) as well as the soil-structure interaction at the receiver location. While reference spectra for these subdomains typically require large safety factors or allowances to account for their variability, in situ investigations using artificial vibration sources can measure the actual vibration transfer behavior from the track to the immission points in question. In this article, the admittance-based prediction method, first presented by [PERSON] and [PERSON] [6], is explained and demonstrated in the context of railway applications at grade and in tunnels. The mechanical admittance is the ratio between the measured vibration velocity and the excitation force as a function of frequency. By using site-specific transfer admittances, which account for dynamic influences along the entire transmission path between the excitation point and the immission point, together with force density spectra of rail vehicles, which the authors of [6] claimed to represent site-independent vibration data of vehicles, would allow accurate immission predictions during planning. The process of determining these force density spectra for the most relevant train types in the Austrian rail network (see Table 1) and the associated pros and cons are illustrated in this article. Previous studies [7; 8; 9] have demonstrated that force density spectra can be calculated both numerically and experimentally. Theoretical models estimate the emitted forces based on the following method and considerations:  
* The admittance of the track or track compliance (in meters per Newton) is calculated by finite-element simulations, sometimes combined with boundary-element methods. Typical results are shown in [10];
* The vehicle compliance, which can be based on a single degree of freedom (SDOF) or a multi-degree of freedom (MDOF) system, needs to be determined;
* Track unevenness and wheel roughness also need to be considered. Challenges arise due to the complexity of soil stratification and underground structures in real world projects, which are not easily modeled. Assumptions must also be made regarding the track unevenness. The wheel roughness, as on-site measurements have shown, significantly influences emissions but is often overlooked. This typically leads to high uncertainties for frequencies above 25 Hz, as noted in [11]. Moreover, quasi-static effects or the impact of the moving load are generally neglected in such calculations, resulting in underestimated amplitudes at frequencies up to 25 Hz [11]. An alternative approach uses wheelset acceleration measurements, multiplied by the wheelset mass, to determine the excitation forces, as described in [12]. Typically, such measurements show that forces increase considerably with train speed at low frequencies, along with a frequency shift for individual components of roundness (6-16 Hz) and sleeper