Rotational Motions in Seismology

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 and to compare directly the result with the ring laser data. Here we present for the first time a comparison of rotational ground motions derived from seismic array with those observed directly with ring laser. Our study suggest that - given accurate measurements of translational motions in an array of appropriate size and number of stations - the array-derived rotation rate may be very close to the "true" rotational signal that would be measured at the center of the array (or the specific reference station). However, it is important to note that it may be dangerous to use only the minimally required three stations as even relatively small noise levels may deteriorate the rotation estimates. Furthermore, it is clear that the logistic effort to determine rotations from array is considerably larger than direct measurements. In the light of this, the necessity to develop field-deployable rotational sensors with the appropriate resolution for use in local and regional seismology remains an outstanding issue. More recently, Igel et al. (2005) introduced a method to estimate the horizontal phase velocity by using collocated measurements from a ring laser and seismometer. A simple relationship between transverse acceleration and rotation rate (around a vertical axis) shows that both signals should be in phase and their ratio proportional to horizontal phase velocity. Comparison with synthetic traces (rotations and translations) and phase velocities determined in the same way showed good agreement with the observations. The second objective of my thesis is to study the accuracy of phase velocity determination using collocated measurement of rotational and translational motion and derive the Love wave dispersion curve using spectral ratio for both synthetic and real observed data. Whether the accuracy of the dispersion curves derived with the approach presented in this thesis is enough for tomographic purposes remains to be evaluated. Nevertheless, the results shown here indicate that through additional measurements of accurate rotational signals, wavefield information is accessible that otherwise requires seismic array data. However, to make this methodology practically useful for seismology will require the development of an appropriate high-resolution six-component broadband sensor. Efforts are underway to coordinate such developments on an international scale (Evans et al., 2006). The ground tilt is generally small but not negligible in seismology, especially in the strong-motion earthquake. It is well known that the tilt signal is most noticeable in the horizontal components of the seismometer. Ignoring the tilt effects leads to unreliable results, especially in calculation of permanent displacements and long-period calculations. The third objective of my thesis is to study the array-derived tilt, a further application of measuring tilt. An interesting result concerning tilt study based on a synthetic study is the possibility to derive the Rayleigh wave phase velocity as well as Rayleigh wave dispersion curve from collocated measurement of tilt rate and translational motions. The synthetic study shows that there is a frequency dependent phase velocity from collocated radial acceleration and transverse tilt.