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Underground reduction of Gravity Gradient Noise.: 

Underground reduction of Gravity Gradient Noise. Giancarlo Cella INFN sez. Pisa/Virgo GWADW – La Biodola 2006

Introduction: 

Introduction In future advanced interferometers Newtonian (Gravity Gradient) Noise will be one of the fundamental limitations for the sensitivity in the low frequency region. Can it be estimated? What are the most important sources? Can it be reduced? What we gain going underground?

Outline: 

Outline Motivations Seismic GGN Atmospheric GGN Going underground Underground GGN estimates GGN reduction inside a cavity Other (but related) options Monitoring and subtraction Reference masses Conclusions

What is Gravity Gradient Noise: 

What is Gravity Gradient Noise Mass density fluctuations couple directly to the test masses: Example: Elastic material

Seismic GGN: 

Seismic GGN Estimate uses transfer function between seism and GGN

Atmospheric GGN: 

Atmospheric GGN

Atmospheric GGN: 

Atmospheric GGN

What we can expect by going underground: 

What we can expect by going underground

Going underground: seismic GGN reduction: 

Going underground: seismic GGN reduction A simple fact: surface waves die off exponentially with the depth Surface waves are probably the most important excitations for GGN Surface movement dominate the bulk compression effect Most efficient mechanism to transport energy from “far” sources Significative coupling with “local” sources (human activity) GGN is a “long range” effect: what is its depth dependence? h/l “Smearing effect”

GGN vs. depth: 

GGN vs. depth Surface/Bulk 100 Hz 50 Hz 10 Hz 5 Hz 100 Hz 50 Hz 10 Hz 5 Hz All this is pretty good, but Volume waves contributions will not share this fast decay Surface fluctuations in the depth? depth (m) Relative reduction of GGN with depth: Bulk Surface Total

A rough model for an underground cavity: 

A rough model for an underground cavity Test mass Spherical cavity in a homogeneous elastic medium: Elasticity eq. Free boundaries Mode Classification accordingly with rotation symmetry: Toroidal Spheroidal longitudinal For each ,l,m: 2 spheroidal modes (mixed transverse & longitudinal) 1 toroidal mode (transverse only) Incoming wave scattered to an outgoing one What is the contribution of each mode to GGN? Spheroidal transverse

A rough model for an underground cavity: 

A rough model for an underground cavity Volume fluctuation Surface fluctuation Test mass Bulk contribution to GGN: Surface contribution to GGN: Only “dipole” contribution to bulk GGN (cavity displacements) Both transverse & longitudinal contributions to surface GGN Toroidal modes: transverse, no surface motion, no Newtonian

R dependence of GGN inside the cavity: 

R dependence of GGN inside the cavity Surface longitudinal and transverse contributions Normalization: fixed incoming flux from infinity of elastic energy Statistical sum over modes Assumed absence of correlations between modes (weak dependence) Bulk longitudinal and transverse contributions Method: Surface contributions always dominant in the relevant frequency range

R dependence: final result: 

R dependence: final result Amplitude/Amplitude (R=1) 5 Hz 10 Hz 20 Hz 40 Hz Bulk + Surface Longitudinal + Transverse Good reduction with a reasonable cavity’s size.

Transfer function: 

Transfer function There is a relation between GGN in the cavity and seismic motion measured on the surface? Motion normal to the surface (as an example) Symmetries are not constraining enough…… Seismic motion get contributions from all GGN is controlled by modes only In other words: measuring the dipole mode is a difficult issue, without additional informations about the importance of each . In principle: measure the correlations

Other (related) options: 

Other (related) options

GGN subtraction: 

GGN subtraction Example: a set of 10 accelerometers with random initial position.... …and after the optimization

Subtraction in the cavity?: 

Subtraction in the cavity? We can apply the subtraction method to seismic measurements inside the cavity. Subtracted signal Subtraction efficiency The method can be applied We can’t anticipate its efficiency Performances and number of sensors will depend on the number of relevant modes

Measuring horizontal GGN: 

PD L Virgo mirror d δx δy L/21/2 Finesse F Measuring horizontal GGN Preliminary idea: Measure the GGN using as a reference “quiet” masses. Subtract Features: Decoupled from vertical GGN L large compared with L small compared with interferometer arms Problems: “Quiet” masses must be dominated by GGN “Quiet masses coupled to vertical seism (more refined schemes can cure this problem)

Conclusions:: 

Conclusions: The underground option seems promising Seismic surface waves contributions to GGN exponentially damped Atmospheric contributions should be damped also exponentially A cavity can be used to further reduce GGN Localized seismic waves on the gallery Small masses involved Monitorable Acoustic (pressure waves) resonances Could be reduced Monitorable Volume seismic waves Problems: Measurements in realistic scenarios are mandatory! Thank you for your attention!