Review of Folded Pendulum Seismometers, Accelerometers and Tiltmeters Fausto Acernese, Fabrizio Barone Università degli Studi di Salerno INFN – Sezione di Napoli VIRGO experiment

Outline Introduction Horizontal Accelerometers Vertical Accelerometers Tiltmeters The Folded Pendulum Mechanical Scheme Sensors based on FP Mechanical Scheme  Horizontal Accelerometers  Tiltmeters Conclusions

Introduction Inertial sensors were and are being developed to measure the cinematic of seismic attenuation chains of gravitational wave (GW) interferometric detectors. Because of the directionality requirements (> 10 3 ), GW accelerometers tend to be more specialized for sensing of different degrees of freedom (horizontal,vertical, and tilt) than the classical geophysics seismometers. Furthermore, with respect to geophysical sensor, the GW inertial sensor must have high vacuum compatibility as well as high low- frequency sensitivity. In the last years there was an hopeful knowledge sharing between GW and seismology community for the development of new kind of inertial sensors.

VIRGO Horizontal Accelerometer Single axis accelerometer Described in VIR-NOT-PIS-1380 and Braccini, S. et al. “Low noise wideband accelerometer using an inductive displacement sensor”, Rev. Sci. Inst. 66, no. 3, 2672 (1995). Mechanics based on Inverted Pendulum Position sensing based on LVDT device PID analog control loop with coil-magnet actuation system Resonant Frequency of about 3.5Hz with Quality Factor = 25 Mass about 450g UHV compliant

Mechanical scheme and picture of Horizontal Accelerometer A: Brass masses B: Blade springs D – E : Position sensor F – G : Coil-magnet actuation system

VIRGO Accelerometer readout noise Readout noise of LVDT ~ m/√Hz above few Hz. The sensing noise grows as 1/f below 300mHz De Salvo R., “Accelerometer development for use in gravitational wave-detection interferometers”, Bulletin of the Seismological Society of America (2009), 99(2B):

VIRGO Vertical Accelerometer Developed from 1996 and 1998 on Lacoste principle The test mass (A) is constrained to move in the vertical direction by a pair of leaf flexures (B). A spring (C) at roughly 45° provides preloading force. The LVDT readout (D-E) and Coil-magnet actuation system (F-G) are the same of horizontal sensor. De Salvo R., “Accelerometer development for use in gravitational wave-detection interferometers”, Bulletin of the Seismological Society of America (2009), 99(2B):

Anti-spring Vertical Accelerometer Position Readout based on differential capacitance Mechanical design based on geometric anti-spring Force Balanced configuration with a coil-magnet actuation system Thermal noise is the main noise source. Bertolini A. et al., “Geometric anti-spring vertical accelerometers for seismic monitoring”, Nuc. Instr. Meth. A 518, 233–235 (2004)

The thin vertical blade design allows better flexure loading and much less mechanical stiffness than the cross-blade Bendix flexure design. The flexure mount is designed to be easily replaceable to allow the testing of different materials and of surface and thermal treatments of the flexure. The instrument is designed to use different methods of sensing and actuation. LIGO/VIRGO “new” Mechanical Tiltmeter De Salvo R., “Accelerometer development for use in gravitational wave-detection interferometers”, Bulletin of the Seismological Society of America (2009), 99(2B): (C) flexure hinge (D) knife-edge hinge,

Tiltmeter Gyrolaser Based on Sagnac Effect: two propagating laser beams oscillate on the same mode of an active ring laser cavity. When the cavity is rotating, the angular velocity Ω is related to the frequency difference Δf between the two optical beams. A. Di Virgilio et al., “Performances of 'G-Pisa': a middle size gyrolaser”, Class. Quant. Grav. 27, 2010 This frequency difference is detected by simply beating the two beams on the same photodetector.

Optical schemeSensor Picture 1.35 m in side Two different orientation of the laser plane Since June 2010 the system is active in the VIRGO interferometer central area Perimeter control system using two opposite moving mirror

Gyrolaser Sensitivity Private comunication of April 2011 Below 1mHz the sensor is affected by backscattering noise, that cat be subtract offline. There no appreciated difference in sensitivity in the two different alignment

The Folded Pendulum The Folded Pendulum (FP) geometry, introduced, and used to build a seismometer by the UWA group (Blair, 1994; Liu, 1998). The Folded Pendulum configuration allows an arbitrary low resonant frequency changing the mass distribution (m p1 and m p2 ), using a calibration mass attached to the central mass. The restoring force is partially due to the gravity and so the internal thermal noise is reduced because it is causes only by the elastic force and not by the gravity.

140x134x40mm Single block of CuBe or Aluminum Gap of ≈ 250 μm (due to capacitive sensor) Resonant Frequency of ≈ 700mHz, reducible to 550 mHz 50 μm circular notch hinges Readout based on differential capacitive sensor Coil-magnet actuation system for closed loop configuration UHV compliant LIGO-TAMA Horizontal Accelerometer Bertolini, A., R. DeSalvo, F. Fidecaro, M. Francesconi, S. Marka, V. Sannibale, D. Simonetti, A. Takamori, and H. Tariq “Mechanical design of a single-axis monolithic accelerometer for advanced seismic attenuation systems”, Nuc. Instr. Meth. A 564, 579–586 (2006).

LIGO-TAMA Accelerometer Readout Noise Bertolini, A., R. DeSalvo, F. Fidecaro, M. Francesconi, S. Marka, V. Sannibale, D. Simonetti, A. Takamori, and H. Tariq “Readout system and predicted performance of a low-noise low frequency horizontal accelerometer”, Nuc. Instr. Meth. A 556, 616–623 (2006).

UNISA Horizontal Seismometer Full symmetric design 100 μm Elliptical Notch Hinges Enlargement of the the gap to 2.5mm to increase the open loop dynamics Optical Readout (Optical lever and/or Michelson Interferometer) Configurable in Open loop (absence of Actuation system) or in closed loop, as accelerometer. Developed mainly for very low frequency seismic noise monitoring. Acernese F. et al., “New architecture of tunable mechanical monolithic horizontal sensor for low frequency seismic noise measurement”, SPIE Proceedings Vol. 7831, (2010).

Frequency Calibration A stable resonant frequency of about 66mHz (red circle) has been archived. Acernese F. et al., “New architecture of tunable mechanical monolithic horizontal sensor for low frequency seismic noise measurement”, SPIE Proceedings Vol. 7831, (2010).

Optical Readout Sensitivity Acernese et al., “Tunable mechanical monolithic horizontal sensor with high Q for low frequency seismic noise measurement”, Journal of Physics: Conference Series 228 (2010)

Quality factor Linear dependence between Q and f 0 → Viscous Damping Quadratic dependence between Q and f 0 → Internal Thermal Noise Final report of PRIN2007 project (Italian Ministry of the University and of Scientific Research), Barone et al.

Q for FP sensors calibrated at ~ 700mHz Q = 1800 in air; Q lim = P = 2∙10 -4 mbar S. Vilasi, UNISA Internal Report, and Bertolini et al., Nucl. Instr. and Meth. A 564 (2006) 579–58

Tiltmeter based on FP Longer resonant period of Folded Pendulum → Higher sensitivity to ground tilt FP Compact design

Design by A. Takamori, A. Bertolini, R. DeSalvo, T. Kanazawa, M. Shinohara, A. Araya Mechanical design based on similar scheme of horizontal sensor 50 μm Elliptical notch hinges, reduced to < 30μm with electrochemical buffing. Lower resonant frequency of about 500mHz Optical readout based on Optical Fiber Transducer to realize a non contact position sensor immune to electromagnetic noise.

FP Tiltmeter Readout Noise Considering the equivalent length of the FP (1.1m), the readout sensitivity corresponds to 1 nrad/ 100mHz and 0.1 nrad/√Hz above 100Hz De Salvo, Private Comunication

Conclusion and future remarks Although the requirements for accelerometers and tiltmeter for use in GW detectors are quite different from the needs for geophysics measurements, both fields will profit in the future from extended collaboration. To compare the sensitivity of different inertial sensor based on different mechanical scheme, readout and actuation system, a correlation analysis is need, using two sensor in parallel, as shown in Rodgers P. W., Bulletin of the Seismological Society of America, 82 (2),1099 (1992), or in Barzilai et al., Review of Scientific Instruments, 69 (7), 2767 (1998).

Some of the data and schematics shown in this article were provided to the author by various scientists, as referenced. The other data and schematics shown were produced by the authors. Thanks for your attention