An instrument for direct observations of seismic and normal-mode rotational oscillations of the Earth

The rotations around the vertical axis associated with the normal mode oscillations of the Earth and those induced by the seismic and other disturbances have been very difficult to observe directly. Such observations will provide additional information for 3D modeling of the Earth and for understanding earthquakes and other underground explosions. In this paper, we describe the design of an instrument capable of measuring the rotational motions associated with the seismic oscillations of the Earth, including the lowest frequency normal mode at ν ≈ 3.7 × 10^-4 Hz. The instrument consists of a torsion balance with a natural frequency of ν₀ ≈ 1.6 × 10^-4 Hz, which is observed by an autocollimating optical lever of high angular resolution and dynamic range. Thermal noise limits the sensitivity of the apparatus to amplitudes of ≈ 1.5 × 10^-9 rad at the lowest frequency normal mode and the sensitivity improves as μ^-3/2 with increasing frequency. Further improvements in sensitivity by about two orders of magnitude may be achieved by operating the balance at cryogenic temperatures. Alternatively, the instrument can be made more robust with a reduced sensitivity by increasing ν₀ to ≈10^-2 Hz. This instrument thus complements the ongoing effort by Igel and others to study rotational motions using ring laser gyroscopes and constitutes a positive response to the clarion call for developments in rotation seismology by Igel, Lee, and Todorovska [H. Igel, W.H.K. Lee and M.I. Todorovska, AGU Fall Meeting 2006, Rotational Seismology Sessions: S22A,S23B, Inauguration of the International Working Group on Rotational Seismology (IWGoRS)].