NOTA: Per modificare l'immagine su questa diapositiva, selezionarla ed eliminarla. Fare quindi clic sull'icona delle Immagini nel segnaposto per inserire l'immagine personale. NEWTONIAN NOISES IN LOW FREQUENCIES 2. MITIGATION G. Cella – INFN Pisa 2015 International School on Numerical Relativity and Gravitational Waves July KISTI & KAIST, Daejeon in Korea

Lectures Plan Previous lecture (Estimation)  What is Gravity Gradient Noise?  Relevance  Seismic Gravity Gradient Noise  General formulation of the seismic GGN estimation problem This lecture (Mitigation):  A worked out estimation & mitigation case: seismic GGN of an homogeneous half space.  Going underground  Wiener subtraction  Sensor placement  Future developements

Simplified GGN model x y z

 Why pure longitudinal or transverse plane waves does not work?  A longitudinal wave, when reflected by the free surface, generate a superposition of a longitudinal and a transverse wave  Similarly a transverse wave is reflected in a superposition of a transverse and a longitudinal wave  An exception: a purely transverse wave with horizontal polarization and propagation  Surface waves (Raileigh waves) are allowed  They propagate on the horizontal direction  Exponentially damped with the depth T LT+L T+S TT+L T S No GGN Compression & Surface GGN

Simplified GGN model LT

Mitigation: going underground Surface -10 m -50 m -100 m -150 m ET-B ET-C

Mitigation: going underground The efficiency of the mitigation depends on the material in the ground As expected, when the sound speed increases for a given frequency the wavelength increases and the suppression is reduced At very low frequencies going underground is not an option for mitigation From c L =200 m/s to c L =2000 m/s Surface -10 m -50 m -100 m -150 m

Mitigation: Wiener subtraction

 The basic quantities which enters in the procedure are:  Optimal filters in the stationary case: the GGN power spectrum

Mitigation: Wiener subtraction

Another example: full optimization in three dimensions Using a simple model for the correlations 512 sensors At a fixed frequency Negligible auxiliary sensor noise When sensor noise is not negligible it is convenient to decrease the separation between sensors: a larger correlation can be tolerated to average the noise. Test mass here

Mitigation: Wiener subtraction Efficiency estimate Several coherences Regular grid Optimal arrangement of sensors

Mitigation: Wiener subtraction Optimal arrangement of sensors is frequency dependent More robust with an higher number of sensors Coherence improves the subtraction efficiency

Mitigation: Wiener subtraction From: Subtraction of Newtonian noise using optimized sensor arrays Jennifer C. Driggers, Jan Harms, and Rana X. Adhikari Phys. Rev. D 86,  Specific sensor placement is not critical  Detailed model needed:  Volume waves  Scattering effects  Enough improvement for a third generation detector  Good in the low frequency region

Atmospheric GGN From: T. Chreighton, Atmospheric Gravitational Noise, GWDAW LIGO-G Infrasonic Thermal turbulence

Atmospheric GGN  Thermal gradient effects  Rayleigh Bernard (G.C., E. Cuoco, P. Tomassini)  Thermal bubbles  Several scenarios, depending on the intensity of the thermal gradient  Lighthill process: turbulent generation of acoustic waves (C. Cafaro, G.C.)  Negligible in the «high frequency» region  Can be larger at lower frequencies (to be investigated) RB Bubbles Seismic

WD-WD at 10 kpc From: J. Harms et al, Phys. Rev. D 88, (2013) LF earth bound detectors

Conclusions  Good perspectives for beating GGN  Quiet site  Going underground  Subtraction  Lot of work to do  More investigation of atmospheric GGN  Atmospheric GGN subtraction?  «Realistic» estimates needed (FEM approach?)  «Realistic» study of subtraction procedure (FEM approach, non stationarity,….) Thank you for your attention….