In addition to the papers listed at [http://ilog.ligo-wa.caltech.edu:7285/advligo/Seismic_Isolation the AdvLIGO wiki], I found [http://www.iop.org/EJ/abstract/0264-9381/15/11/004/ this VIRGO paper], which contains a section "Effect of the apparatus infrastructure".

[http://www.ligo.caltech.edu/docs/P/P040032-00.pdf Rana's thesis]

[http://www.ligo.caltech.edu/docs/G/G040557-00.pdf Rana's presentation with scale diagram of BSC]

[http://prola.aps.org/pdf/PRD/v58/i12/e122002 Published version of Hughes & Thorne paper]

I attached a plot (attachment:strain1.pdf) of the GG noise from the BSC vibration, calculated from real accelerometer data (from early this morning) and a generous estimate of the gravity coefficient (7.3e-9 (m/s^2)/m). It doesn't come close to the total noise curve, so unless another model says something very different, we might not have to worry about the BSC at all.

Okay, here's the worst case noise curve: attachment:worst-case-strain.pdf. I computed it by assuming

• Radius: 1.5 m
• Height: 5 m
• Mass: 8000 kg
• Test mass at center
• Each point of the BSC moves in the direction that maximizes the gravity gradient along the beam axis (not a physically reasonable vibration mode, but a limiting case).

This results in a gravity coefficient of 1.0e-7 (m/s^2)/m. It uses accelerometer data from the noisiest BSC at a noisy time of day, and also uses a real harmonic oscillator transfer function instead of a free mass TF (although the difference is negligible above 2 or 3 Hz).

Moving the test mass away from the center decreases the GG noise.

Next I'm going to model the piers, but since they're both less massive and farther away from the test mass, I don't think they'll be a problem either. -- KeenanPepper 2007-06-28 01:38:54

The worst-case gravity coupling coefficient for all four piers is about 7.3e-9 (m/s^2)/m, more than an order of magnitude smaller than for the BSC itself. So even if they are shaking an order of magnitude more than the BSC, we don't have to worry about them either. -- KeenanPepper 2007-07-05 21:16:22

Expression to integrate (for cutting and pasting):

((2*x^2-y^2-z^2)*u + 3*x*y*v + 3*x*z*w)/sqrt(x^2+y^2+z^2)^5

-- KeenanPepper 2007-07-10 02:12:13

To do

• Compare analytic solution of toy model with COMSOL to verify accuracy. Tried it with a dumbbell off to one side of the test point, whose axis passes through it, and the gravity coefficient of the near sphere matched up to the numerical precision. COMSOL automatically sets the phase of maximum deformation to zero, which corresponds to the phase of maximum gravity gradient in this simple case, but not in all cases. -- KeenanPepper 2007-07-16 21:29:36

• Create seismic feedforward matrix for the 40-meter. Use a neural network or something, and write up how to do it in detail.
• Create COMSOL model of 40-meter slab and estimate eigenfrequencies.
• Figure out how to import Dennis's models into COMSOL.
• Get new data from Hanford and put in into model.

• Figure out how to make COMSOL do [http://www.geo.mtu.edu/UPSeis/images/Rayleigh_animation.gif this].