1. Plans on table-top experiments towards Newtonian noise subtraction Frank Brückner, D. Brown, L. Carbone, P. Fulda, A. Freise University of Birmingham GEO-ISC Meeting, March 28, 2012

2. Slide 1 GEO-ISC Meeting, March 28, 2012Frank Brückner Outline 1.What is Newtonian Noise (NN)? 2.Why do we care about NN? 3.How to mitigate NN? Subtraction of NN 4.Plans on table-top experiments 5.Summary

3. Slide 2 GEO-ISC Meeting, March 28, 2012Frank Brückner What is Newtonian noise? (also known as gravity gradient noise)  Direct coupling between environmental fluctuations of mass density and test masses Bulk pressure waves (p-waves) Seismic displacement generates density perturbations These perturbations cause fluctuations of the gravitational force at point r 0 via J. Harms et al., Phys. Rev. D 80, 122001 (2009) Newton’s law:

4. Slide 3 GEO-ISC Meeting, March 28, 2012Frank Brückner  Direct coupling between environmental fluctuations of mass density and test masses Seismic displacement generates density perturbations These perturbations cause fluctuations of the gravitational force at point r 0 via Surface waves (Rayleigh-waves) What is Newtonian noise? J. Harms et al., Phys. Rev. D 80, 122001 (2009)

5. Slide 4 GEO-ISC Meeting, March 28, 2012Frank Brückner  Direct coupling between environmental fluctuations of mass density and test masses Both contributions can be combined into a single model: Describes a dipole perturbation with as the dipole moment What is Newtonian noise? J. Harms et al., Phys. Rev. D 80, 122001 (2009)

6. Slide 5 GEO-ISC Meeting, March 28, 2012Frank Brückner Why do we care? Strain noise spectral density of Advanced LIGO and its noise sources J. Driggers et al., LIGO Document P1200017 (2012)  Dominant noise source near 10 Hz: Pulsars and massive BH mergers

7. Slide 6 GEO-ISC Meeting, March 28, 2012Frank Brückner Estimates for contributions to the NN spectra at the LIGO sites Why do we care? J. Driggers et al., LIGO Document T1100237 (2011)

8. Slide 7 GEO-ISC Meeting, March 28, 2012Frank Brückner How to mitigate NN? Important: Test masses cannot be shielded from local gravitational fluctuations 1.Place detector at a quiet site 2.Going underground 3.Seismic shielding (Tidal barrage / seismic “metamaterial”) 1.Subtraction/Cancellation techniques B. Barr et al., LIGO Document T1200005 (2012) S.-H. Kim et al., arXiv: 1202.1586 (2012)

9. Slide 8 GEO-ISC Meeting, March 28, 2012Frank Brückner Newtonian Noise subtraction for GWD Differences to simple SISO scheme such as in active noise cancellation headphones: 1.Several witness sensors  MISO filter 2.Witness sensors do not measure the same physical quantity  Theoretical model has to be included ??? 3. …. IFO (Prim. Sensor) IFO (Prim. Sensor) Accelerometers (Second. Sensors) Accelerometers (Second. Sensors) GW- Signal Newtonian Noise Signal MISO- Filter online/ feed-forward offline/ post-processing Seismic field Seismic field Optimization

10. Slide 9 GEO-ISC Meeting, March 28, 2012Frank Brückner Ground Newtonian Noise subtraction for GWD (2D) Reasonable approach – Small sensor array + Filtering Accelerometers Assume only surface waves (reasonable for LIGO) ~ 10 m

11. Slide 10 GEO-ISC Meeting, March 28, 2012Frank Brückner Optimization of the sensor array By minimizing the subtraction residual R which is dependent on the sensor location C SN … cross-correlation vector between sensor and NN acceleration C SS … cross-correlation matrix between different sensors C NN … NN variance Optimizing the sensor locations of 10 sensors simultaneously gives:  “Almost” optimal pattern with R ~ 10 -12 at 10 Hz Newtonian Noise subtraction for GWD (2D) Reasonable approach – Small sensor array + Filtering J. Driggers et al., LIGO Document P1200017 (2012)

12. Slide 11 GEO-ISC Meeting, March 28, 2012Frank Brückner Off-line post subtraction Basic idea: Optimally construct a vector of filter coefficients (one per sensor) which form a linear superposition of the sensor channels as the NN estimate Minimize: Residual = IFO date – NN estimate from sensor data - Can use non-causal filters - To account for non-stationarity, filter coefficients should be re-evaluated after certain time  quasi- adaptive Comparison of subtraction perfor- mance for different sensor arrays:  Surprisingly all arrays perform equally well ??? Newtonian Noise subtraction for GWD (2D) Reasonable approach – Small sensor array + Filtering J. Driggers et al., LIGO Document P1200017 (2012)

13. Slide 12 GEO-ISC Meeting, March 28, 2012Frank Brückner Online feed-forward subtraction Can be implemented in two ways: -Exerting a cancellation force directly to the test masses -Cancellation can be done on interferometer data - Fundamental difference to post- subtraction: Can only use causal filters - To account for non-stationarity can use adaptive filter algorithms Impact of causality:  Can train filter on data series and apply it to next series  Surprisingly all arrays perform equally well ??? Newtonian Noise subtraction for GWD (2D) Reasonable approach – Small sensor array + Filtering J. Driggers et al., LIGO Document P1200017 (2012)

14. Slide 13 GEO-ISC Meeting, March 28, 2012Frank Brückner What are the challenges/open questions of active NN cancellation? 1.So far it is just an idea, not in practice yet 2.We need a detailed 3D model of the geology around the sites 3.With this model how accurately can a simulation of the full seismic spectra reproduce the measured data 4.How strong is the correlation between the motion of the ground near the test masses and the gravitational potential experienced at the test mass? 5.What is the impact of local inhomogeneities within the sensor network? 6.How large is the impact of non-seismic NN sources? 7.What is the maximum achievable level of NN subtraction? 8.What is the required density and size of the sensor network? 9.What is the optimal pattern of the sensor network? 10.Is online (feed-forward) or offline (post-processing) subtraction more efficient/practical? 11.Is static filtering sufficient or do we need adaptive filtering? 12.Which algorithms are most suitable in terms of performance and computation? 13.What kind of pre-conditioning of the sensor data is required?

15. Slide 14 GEO-ISC Meeting, March 28, 2012Frank Brückner How can we contribute with table-top experiments? Metal plate Accelerometer network Cavity Vibrational force Inhomogeneity Simplify the system: Witness sensors measure the same quantity as “primary sensor”: displacement Replace seismic motion by acoustic vibrations of a metal plate (several hundred Hz) Signals from sensor network MISO- Filter Displacement of mirror Cavity feedback system Error signal = 0 ? Optimization

16. Slide 15 GEO-ISC Meeting, March 28, 2012Frank Brückner Design of the metal plate Free quadratic plate c L … speed of sound (steel: 3100 m/s for transverse (shear) waves) d … thickness of the plate  … poisson ration (steel: 0.3) L … side length of plate  m,n … frequency ratios of modes Frequency ratios and modes of free quadratic plate For example: d = 2 mm L = 50 cm  f (1,1) = 150 Hz For an oscillation amplitude of 500  m this gives a maximum acceleration of: a = ± 44 g T. Görne (2009)

17. Slide 16 GEO-ISC Meeting, March 28, 2012Frank Brückner Case Accelerometers … measure proper acceleration (i.e. change in velocity) by determining the inertial force to a test mass -Double integration of the signal gives displacement -Most common are piezoelectric accelerometers Piezoelectric material Mass Voltage Case Piezoelectric material Mass Acceleration Triaxial accelero- meter Single axis accelero- meter Frequency range: 0.5 … ~ 20 kHz Measuring range: ± 55 g Sensitivity: 100 mV/g http://www.mmf.de

18. Slide 17 GEO-ISC Meeting, March 28, 2012Frank Brückner Research plan 1.Play with accelerometers, characterise internal noise level 2.Setup simple, extendable digital system, test static and adaptive filters on FPGA with single sensor (one accelerometer is primary sensor, the other one the witness sensor) 1.Design and set up simple suspension system with local damping for mechanical vibration plate with accelerometer sensor network and the end mirror of an optical cavity 2.Modelling of the vibrational modes of the plate using Comsol 3.Modelling of different sensor networks 4.Use sensor network to reconstruct plate vibration field 5.Test feed-forward and post-subtraction techniques Vibrational force causes noise Signal from witness sensor SISO- Filter Signal from primary sensor = 0 ? = noise Optimization...

19. Slide 18 GEO-ISC Meeting, March 28, 2012Frank Brückner 7.Test different filter types (filtered-x least mean square (fxLMS), fast recursive least-squares (fast RLS), fast transversal filters (fast FTF)) 8.Evaluate required pre-conditioning of accelerometer data 9.Test different sensor network configurations - Aliasing Research plan M. Wathelet, PhD thesis, Universite ́ de Liege (2005)

20. Slide 19 GEO-ISC Meeting, March 28, 2012Frank Brückner How can we contribute with table-top experiments?  ☐ ☐ ☐      ☐  ☐ 1.So far it is just an idea, not in practice yet 2.We need a detailed 3D model of the geology around the sites 3.With this model how accurately can a simulation of the full seismic spectra reproduce the measured data 4.How strong is the correlation between the motion of the ground near the test masses and the gravitational potential experienced at the test mass? 5.What is the impact of local inhomogeneities within the sensor network? 6.How large is the impact of non-seismic NN sources? 7.What is the maximum achievable level of NN subtraction? 8.What is the required density and size of the sensor network? 9.What is the optimal pattern of the sensor network? 10.Is online (feed-forward) or offline (post-processing) subtraction more efficient/practical? 11.Is static filtering sufficient or do we need adaptive filtering? 12.Which algorithms are most suitable in terms of performance and computation? 13.What kind of pre-conditioning of the sensor data is required? 

21. Slide 20 GEO-ISC Meeting, March 28, 2012Frank Brückner Summary Newtonian noise is going to be a limiting noise source for future detectors at low frequencies The most promising, maybe only option to reduce this noise is an active subtraction scheme Simulation work has already been carried out and the results support this hope There is yet a lot of open questions and foreseen challenges Table-top experiments can indeed be useful to address some of these questions They can serve as a test bed for several aspects of NN subtraction:  Size of sensor array relative to vibration wavelength  Amount of sensors, density of sensors  Pattern of sensor array  Filter algorithms  Wave scattering/inhomogeneities

22. Slide 21 GEO-ISC Meeting, March 28, 2012Frank Brückner Thank you for your attention!

23. Slide 22 GEO-ISC Meeting, March 28, 2012Frank Brückner Newtonian Noise subtraction for GWD (3D) Naive approach – No filtering Test mass at r 0 = 0 Seismic sensor at each grid point (70 3 grid points in grid volume of (3 P = 3km) 3 ) For 99% accuracy of NN prediction: monitored sphere with radius of about 2 p ( p = 1 km) J. Harms et al., Phys. Rev. D 80, 122001 (2009)

24. Slide 23 GEO-ISC Meeting, March 28, 2012Frank Brückner What is the error of fewer grid points? Seismic sensor at each grid point (15 3 grid points in grid volume of (3 km) 3 ) Non-uniform coarse grid (due to 1/r 3 dependence more sensors close to test mass, less far away) Acceptable errors for: 13 3 = 2197 grid points in grid volume of (3 km) 3 Newtonian Noise subtraction for GWD (3D) Naive approach – No filtering J. Harms et al., Phys. Rev. D 80, 122001 (2009)