Joint optimization of seismometer arrays for the cancellation of Newtonian noise from seismic body waves in the Einstein Telescope

Seismic Newtonian noise (NN) is predicted to limit the sensitivity of the Einstein Telescope (ET). It can be reduced with coherent noise cancellation techniques using data from seismometers. To achieve the best results, it is important to place the seismic sensors in optimal positions. A preliminary study on this topic was conducted for the ET: it focused on the optimization of the seismic array for the cancellation of NN at an isolated test mass (TM). In this paper, we expand the study to include the nested shape of ET, i.e. four TMs of the low-frequency interferometers at each vertex of the detector. Results are investigated in function of the polarization content of the seismic field composed of body waves. The study also examines how performance can be affected by displacing the sensor array from its optimal position or by operating at frequencies other than those used for optimization.