During the operation of urban subway rail transit system, ground vibrations are generated that transmitted through the ground and cause vibrations in nearby buildings. The operation of these systems can be characterized as a linear source that generates vibrations transmitted through the ground. These ground borne vibrations are a consequence of local defects on the train wheels and/or onto the rail track. The transmission of vibrations from subway rail transit systems in a neighboring building is mostly described by the transfer function (TF) of vibration diffusion from the tunnel wall or invert towards the soil surface at the façade of the protected heritage or residential building. A methodology is proposed in order to determine the TF of vibration diffusion inside the given geological media demonstrating the vibration attenuation values in 1/3 octave band analysis. The tunnel boring with the usage of TBM requires the existence of a muck train to remove the excavation materials. This paper presents the metrological methodology of the relevant measurement campaign and analyses the findings in several sections of the tunnel using the TBM's muck train implementing simultaneous vibration recordings both in tunnel wall and the soil surface. This metrological approach is significant ensuring a high accurate estimation of the expected ground borne noise and vibration at the façade of sensitive receptors during operation and evaluate the need of implementation of mitigation measures, such as floating slabs (FS) where mandatory.