Earth’s spheroidal motion induced by a gravitational wave in flat spacetime

Abstract

We revisit the theoretical modeling of astrophysical gravitational wave (GW) interaction with Earth's normal modes in the millihertz frequency band. We consider a force term associated with plane waves in a flat spacetime acting on a nonrotating anelastic Earth model. Our study confirms that the leading spheroidal induced displacement consists of an angular order-2 term, while the induced azimuthal order terms depend on the incident angles of the GW. We show that some of the previous estimates of the Earth's acceleration due to incoming gravitational waves were too optimistic. Current ground-based detectors are embedded in seismic and environmental noise that is several orders of magnitude larger than the expected GW signal. However, with the prospect of new technologies and improved noise reduction techniques, detection may become feasible.