Human gravity-gradient noise in interferometric gravitational-wave detectors

Among all forms of routine human activity, the one which produces the strongest gravity-gradient noise in interferometric gravitational-wave detectors (e.g. LIGO) is the beginning and end of weight transfer from one foot to the other during walking. The beginning and end of weight transfer entail sharp changes (time scale $\tau \sim 20$ msec) in the horizontal jerk (first time derivative of acceleration) of a person’s center of mass. These jerk pairs, occurring about twice per second, will produce gravity-gradient noise in LIGO in the frequency band 2.5 $\mathrm{Hz}\lesssim f\lesssim 1/\left(2\tau \right)\simeq 25$ Hz with the form $\sqrt{S_h\mathrm{}\left(f\right)\mathrm{}}\sim 0.6\times {10}^{-23}$ ${\mathrm{Hz}}^{-1/2}(f/10\mathrm{}\hspace{0.5em}\mathrm{Hz}{)}^{-6}[{\sum }_i{(r}_i/10\mathrm{}$ $\mathrm{m}{)}^{-6}{]}^{1/2}.$ Here the sum is over all the walking people, $r_i$ is the distance of the $i$’th person from the nearest interferometer test mass, and we estimate this formula to be accurate to within a factor 3. To ensure that this noise is negligible in advanced LIGO interferometers, people should be prevented from coming nearer to the test masses than $r\simeq 10$ m. A $r\simeq 10$ m exclusion zone will also reduce to an acceptable level gravity gradient noise from the slamming of a door and the striking of a fist against a wall. The dominant gravity-gradient noise from automobiles and other vehicles is probably that from decelerating to rest. To keep this below the sensitivity of advanced LIGO interferometers will require keeping vehicles at least 30 m from all test masses.