Rotational Motions in Seismology: Theory, Observation, Modeling

Theoretically, to fully describe the change in the medium around a
point one needs three components of translation, six components of
strain, and three components of rotation. It is expected that
collocated measurements of translations and rotations may help (1)
correcting translation signals recorded by classical seismometers
for contamination by ground rotations, (2) extracting additional
information on earthquake source properties, soil-structure
interactions, and properties of the subsurface, and (3) providing
additional ground motion information to earthquake engineers for
seismic design. Thus, in addition to translations and strains, the
rotational part of ground motions should also be recorded. However,
the lack of instrumental sensitivity did not allow seismologists to
observe rotational motions for decades. Recently, ring laser
technology has provided the means to develop instruments that allow
in principle the observation of rotational motions in a wide
frequency band and epicentral distance range. Here we present the
observations of rotational ground motions around a vertical axis in
the P coda (the section between the onsets of direct P- and S-
waves) of tele-seismic signals on a ring laser sensor at the
Fundamental Observatory Wettzell, southeast Germany. The studies
focus on finding the explanation for the observed P coda rotations
as well as the way to extract additional information from the use
of co-seismic rotational motions. First, the effects of co-seismic
tilts on ring laser measurements are quantified based on
magnitude-amplitude relations and translation derived tilts. Then
the phenomenon of scattering assuming three dimensional random
media and topography that may generate the observed P coda
rotations is investigated through analysis of observations and
forward modelling. The partitioning of P and S energy indicated by
the stabilization of the ratio of energies of the two is used to
constrain scattering properties. Finally, an analytical approach
focusing on the solution of plane waves in linear elastic
anisotropic media is used to quantify the anisotropic behavior
through the variations of rotational wavefield. The focus is on
quasi-P waves and transverse isotropic media. Kelvin-Christoffel
equation and the Thomson parameters, descriptive of the degree of
anisotropy, are used. The obtained results show that 1) P-SH
scattering in the random crust is the main cause of the P-coda
observations; and 2) rotational motions contain additional
information (at least) about scattering properties and anisotropic
coefficients and that joint measurements of translational and
rotational motions at only one point allow the extraction of
additional information. The results demonstrate the potential
benefit not only of measurements of co-seismic rotational ground
motions but also of the use of the amplitude content of seismic
signals.