Seismic radiation from wind turbines: observations and analytical modeling of frequency-dependent amplitude decays

Abstract

Abstract. In this study, we determine spectral characteristics and amplitude decays of\nwind turbine induced seismic signals in the far field of a wind farm (WF)\nclose to Uettingen, Germany. Average power spectral densities (PSDs) are\ncalculated from 10\u2009min time segments extracted from (up to) 6\xa0months of\ncontinuous recordings at 19 seismic stations, positioned along an 8\u2009km\nprofile starting from the WF. We identify seven distinct PSD peaks in the\nfrequency range between 1 and 8\u2009Hz that can be observed to at least 4\u2009km\ndistance; lower-frequency peaks are detectable up to the end of the profile.\nAt distances between 300\u2009m and 4\u2009km the PSD amplitude decay can be described by a power law with exponent b. The measured b\xa0values exhibit a linear frequency dependence and range from b=0.39 at 1.14\u2009Hz to b=3.93 at 7.6\u2009Hz. 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.\n