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Underground reduction of Gravity Gradient

Noise.

Giancarlo CellaINFN sez. Pisa/Virgo

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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?

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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

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What is Gravity Gradient Noise

Mass density fluctuations coupledirectly to the test masses:

Example:Elastic material

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Seismic GGN

Estimate uses transfer functionbetween seism andGGN

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Atmospheric GGN

OtherOther

Effect of acoustic waves (Saulson) Negligible

Airborne objects, sonic booms, advection, … (Creighton)

Turbolent generation of acoustic waves (Lighthill process). (C. Cafaro, G. C.) Negligible

Well developed turbulenceWell developed turbulence

Method: extimation of the structure functions using simple scaling relations.

Rayleigh Bernard Scenarios (G.C., E. Cuoco, P. Tomassini)Rayleigh Bernard Scenarios (G.C., E. Cuoco, P. Tomassini)

Different possibilities accordingly with the intensity of thermal gradient.

Nucleation phase (slow)

Ascension phase

Thermal bubblesThermal bubbles

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Atmospheric GGN

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What we can expect by going underground

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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”

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20 40 60 80 100

0.00001

0.0001

0.001

0.01

0.1

1

GGN vs. depth

20 40 60 80 100

1

10

100

1000

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

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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:

Spherical cavity in a homogeneous elastic medium:

Elasticity eq.

Free boundaries

Mode Classification accordingly with rotation symmetry:

ToroidalSpheroidal longitudinal

For each ,l,m:

2 spheroidal modes (mixed transverse & longitudinal)

1 toroidal mode (transverse only)

Incoming wave scattered to an outgoing one

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

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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

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Am

plit

ude/

Am

plit

ude(

r=1)

5 Hz10 Hz20 Hz40 Hz

R dependence of GGN inside the cavity

Surface longitudinal andtransverse contributions

Am

plit

ude/

Am

plit

ude(

r=1)

Normalization: fixed incoming flux from infinity of elastic energy

Statistical sum over modes

Assumed absence of correlations between modes (weak dependence)

Bulk longitudinal andtransverse contributions

Method:

Surface contributions always dominant in the relevant frequency range

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R dependence: final resultA

mp

litu

de/

Am

plit

ude

(R

=1) 5 Hz

10 Hz20 Hz40 Hz

Bulk + Surface Longitudinal + Transverse

Good reduction with a reasonable cavity’s size.

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Transfer functionThere 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

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Other (related) options

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GGN subtractionExample: a set of 10 accelerometers with random initial position....

…and after the optimization

Test of subtraction: 3 environmental channels (acoustic) from dark fringe data

No

ise

PS

D (

log

arb

itra

ry u

nit

s)

Frequency (Hz)

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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

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PD

L

Virgo mirror

d δx

δy

L/21/2

Finess

e F

Measuring horizontal GGN

Preliminary idea:

1. Measure the GGN using as a reference “quiet” masses.

2. SubtractFeatures:

1. Decoupled from vertical GGN

2. L large compared with

3. L small compared with interferometer arms

Problems:

1. “Quiet” masses must be dominated by GGN

2. “Quiet masses coupled to vertical seism (more refined schemes can cure this problem)

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Conclusions:

The underground option seems promisingSeismic surface waves contributions to GGN exponentially dampedAtmospheric contributions should be damped also exponentially

A cavity can be used to further reduce GGN

Localized seismic waves on the gallerySmall masses involvedMonitorable

Acoustic (pressure waves) resonancesCould be reducedMonitorable

Volume seismic waves

Problems:Measurements in realistic scenarios are mandatory!

Thank you for your attention!