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.