In this study, we determine spectral characteristics and amplitude decays of wind turbine induced seismic signals in the far field of a wind farm (WF) close to Uettingen, Germany. Average power spectral densities (PSDs) are calculated from 10 min time segments extracted from (up to) 6 months of continuous recordings at 19 seismic stations, positioned along an 8 km profile starting from the WF. We identify seven distinct PSD peaks in the frequency range between 1 and 8 Hz that can be observed to at least 4 km distance; lower-frequency peaks are detectable up to the end of the profile. At distances between 300 m and 4 km the PSD amplitude decay can be described by a power law with exponent b. The measured b values exhibit a linear frequency dependence and range from b=0.39 at 1.14 Hz to b=3.93 at 7.6 Hz. In a second step, the seismic radiation and amplitude decays are modeled using an analytical approach that approximates the surface wave field. Since we observe temporally varying phase differences between seismograms recorded directly at the base of the individual wind turbines (WTs), source signal phase information is included in the modeling approach. We show that phase differences between source signals have significant effects on the seismic radiation pattern and amplitude decays. Therefore, we develop a phase shift elimination method to handle the challenge of choosing representative source characteristics as an input for the modeling. To optimize the fitting of modeled and observed amplitude decay curves, we perform a grid search to constrain the two model parameters, i.e., the seismic shear wave velocity and quality factor. The comparison of modeled and observed amplitude decays for the seven prominent frequencies shows very good agreement and allows the constraint of shear velocities and quality factors for a two-layer model of the subsurface. The approach is generalized to predict amplitude decays and radiation patterns for WFs of arbitrary geometry. [ABSTRACT FROM AUTHOR]