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