The seismic waves that spread out from the earthquake source to the entire Earth are usually measured at the ground surface by a seismometer which consists of three orthogonal components (Z (vertical), N (north-south), and E (east-west) or R (radial), T (transversal), and Z (vertical)). However, a complete representation of the ground motion induced by earthquakes consists not only of those three components of translational motion, but also three components of rotational motion plus six components of strain.
Altough theoretical seismologists have pointed out the potential benefits of measurements of rotational ground motion, they were not made until quite recently. This was mainly because precise instruments to measure ground rotational motion were not available.
The measurement of rotational motion induced by earthquakes is relatively new in the field of seismology. To the best of our knowledge, the first experiment to measure ground rotational motion using rotational sensor was done by Nigbor (1994}. He successfully measured translational and rotational ground motion during an underground chemical explosion experiment at the Nevada Test Site using a triaxial translational accelerometer and a solid-state rotational velocity sensor. The same type of sensor was also used by Takeo (1998} for recording an earthquake swarm on Izu peninsula, Japan. However, because of the limitation of the instrument sensitivity, this kind of sensor was only able to sensing the rotational ground motion near the earthquake sources of other artificial sources.
Another type of rotational sensor was assembled using two oppositely oriented
seismometers. This is possible since in principle the rotational component of the ground motions is equal to half the curl of the ground velocity. This kind of sensor was intensively researched and developed by the seismology group in Institute of geophysics, Polish Academy of Sciences. However, they report several problems especially due to the small differences in the seismometer's response function. Like the solid state rotational sensors, this sensor was only able to measure rotational motion near the seismic sources.
The application of the Sagnac effect for sensing the inertial rotation using optical devices were intensively investigated, since the advent of lasers in the sixties. However, the first application of a ring laser gyroscope as a rotational sensor applied in the field of seismology was reported by Stedman et al. (1995}. Fully consistent rotational motions were recorded by a ring laser gyro installed at the fundamental station Wettzell, Germany (Igel et al., 2005). They showed that the rotational motions were compatible with collocated recordings of transverse acceleration by a standard seismometer, both in amplitude and phase. They mentioned that "standard" rotational sensors with sufficient resolution may be possible in the near future. Among the other type of rotational sensor, ring lasers seem more reliable in seismic applications since it has been provenable to sensing the ground rotational motion from near source as well as teleseismic earthquake events with a broad magnitude range (Igel et al., 2007}.
In earthquake engineering, observations of rotational components of seismic strong motions may be of interest as this type of motion may contribute to the response of structures to earthquake-induced ground shaking. Most of rotational/torsional studies of ground motion in earthquake engineering are so far still carried out by indirect
measurements. It can be done since the rotational component of motion is a linear combination of the space derivatives of the horizontal component of the motion. However, to the best of our knowledge, there are no comparison of array-derived rotation rate and direct measurement from rotational sensors mentioned in the literature.
The first objective of my thesis is to study the effect of noise and various uncertainties to the derivation of rotation rate a