Seismic gravity-gradient noise in interferometric gravitational-wave detectors - art. no. 122002

When ambient seismic waves pass near and under an interferometric gravitati onal-wave detector, they induce density perturbations in the Earth, which i n turn produce fluctuating gravitational forces on the interferometer's tes t masses. These forces mimic a stochastic background of gravitational waves and thus constitute a noise source. This seismic gravity-gradient noise ha s been estimated and discussed previously by Saulson using a simple model o f the Earth's ambient seismic motions. In this paper, we develop a more sop histicated model of these motions, based on the theory of multimode Rayleig h and Love waves propagating in a multilayer medium that approximates the g eological strata at the LIGO sites, and we use this model to reexamine seis mic gravity gradients. We characterize the seismic gravity-gradient noise b y a transfer function, T(f)=(x) over tilde(f)/(W) over tilde(f), from the s pectrum of rms seismic displacements averaged over vertical and horizontal directions, (W) over tilde(f), to the spectrum of interferometric test-mass motions, (x) over tilde(f)=L (h) over tilde(f); here L is the interferomet er arm length, (h) over tilde(f) is the gravitational-wave noise spectrum, and f is frequency. Our model predicts a transfer function with essentially the same functional form as that derived by Saulson, T similar or equal to 4 pi G rho(2 pi f)(-2)beta(f), where rho is the density of Earth near the test masses, G is Newton's constant, and beta(f)=gamma(f)Gamma(f)beta'(f) i s a dimensionless reduced transfer function whose components gamma similar or equal to 1 and Gamma similar or equal to 1 account for a weak correlatio n between the interferometer's two corner test masses and a slight reductio n of the noise due to the height of the test masses above the Earth's surfa ce. This paper's primary foci are (i) a study of how beta'(f)similar or equ al to beta(f) depends on the various Rayleigh and Love modes that are prese nt in the seismic spectrum, (ii) an attempt to estimate which modes are act ually present at the two LIGO sites at quiet times and at noisy times, and (iii) a corresponding estimate of the magnitude of beta'(f) at quiet and no isy times. We conclude that at quiet times beta'similar or equal to 0.35-0. 6 at the LIGO sites, and at noisy times beta'similar or equal to 0.15-1.4. (For comparison, Saulson's simple model gave beta=beta'=1/root 3=0.58.) By folding our resulting transfer function into the "standard LIGO seismic spe ctrum," which approximates (W) over tilde(f) at typical times, we obtain th e gravity-gradient noise spectra. At quiet times this noise is below the be nchmark noise level of "advanced LIGO interferometers" at all frequencies ( though not by much at similar to 10 Hz), at noisy times it may significantl y exceed the advanced noise level near 10 Hz. The lower edge of our quiet-t ime noise constitutes a limit, beyond which there would be little gain from further improvements in vibration isolation and thermal noise, unless one can also reduce the seismic gravity gradient noise. Two methods of such red uction are briefly discussed: monitoring the Earth's density perturbations near each test mass, computing the gravitational forces they produce, and c orrecting the data for those forces; and constructing narrow moats around t he interferometers' corner and end stations to shield out the fundamental-m ode Rayleigh waves, which we suspect dominate at quiet times. [S0556-2821(9 8)00424-X].