Rotational motions excited by earthquakes

Abstract

There are many reports about rotations of tombstones and stone lanterns during large earthquakes (e.g. Yamaguchi and Odaka 1974). Only translational ground motions, however, have been observed in instrumental measurements of seismic waves, and quantitative measurements of rotational ground motions have not been made until quite recently. Bouchon and Aki (1982) simulated rotational ground motions near earthquake faults buried in layered media for strike-slip and dip-slip fault models, and obtained a maximum rotational velocity of 1.5-103 rad/s produced by a buried 30 km long strike-slip fault with slip of 1 m. Their simulation shows that the rotational motions are small compared with the amplitude of the translational motions. The difficulty experienced in measuring of rotational motions excited by earthquakes is caused by a lack of technology for measuring such small rotational motions. Recently, Nigbor (1994) succeeded in measuring rotational and translational motions using a new angular measurement sensor (Morris 1971) at a surface station during a non-proliferation experiment at the Department of Energy, Nevada Test Site, using a very large (1 kiloton) chemical explosion. The sensor will allow us to measure the rotational ground motions of seismic waves in the near future. What will rotational motions excited by earthquakes tell us? We will have accurate data for arrival times of SH waves, because the rotational component around the vertical axis is sensitive to SH waves although not to P-SV waves. A vertically heterogeneous, isotropic, elastic medium is the first-order approximation of the Earth's interior, so that we can expect to have a clear SH-wave onset in records of the rotational component around the vertical axis. When we try to separate SH waves from P-SV waves using translational motions, we need to rotate two horizontal components into radial and transverse components. To do this, we have to know the in cident directions of seismic waves. Now, we will be able simply to detect onsets of SH waves using the rotational component only. The purpose of this paper is to elucidate another possibility, which is related to seismic sources. The familiar source model of earthquakes is a dislocation model concerned with a discontinuity of displacement across internal surfaces in a continuum, but not with a rotation across the surfaces. The rotation naturally generates rotational seismic waves. Defects in the continuum other than dislocations inclusive of tensile fractures are sources of such rotational motions. Teisseyre (1973) discussed, based on the micropolar theory, the possibility of rotational motions in source processes. There are several theories that deal with elastic continua with internal defects inside (e.g. Kondo 1949a, b, 1957, Bilby et al. 1955, Kroner 1958, Amari 1962, 1968, Mura 1963, 1972, deWit 1973, Kossecka and deWit 1977a, b). Among them, the most general perspective is provided by the geometrical theory of defects (Kondo 1949a, b, 1957). Based upon the theory, we will derive a general expression for rotational motions of seismic waves. This, as well as a general expression for translational motion, completely specifies the seismic waves. We start with a sketch of the geometrical theory of defects. After outlining the fundamental concepts in Sect. 11.2.1, we present a space-time formulation in Sect. 11.2.2 so that we can treat time-dependent problems. An expression of defects is generalized by using geometrical quantities introduced in these subsections. Two kinds of defects, dislocations and disclinations, play important roles. Interestingly, their motions are closely related with each other, being characterized by continuity equations. Section 11.2.3 is devoted to their derivation, using the space-time of Section 11.2.2. The strain related to earthquakes will be less than 10-3; the magnitude of strain of granite rocks just before brittle fractures was measured in triaxial compression tests (e.g. Mogi 1978). So we can employ a linear approximation to obtain our main result, simple formulae (11.97) and (11.98) for rotational and translational motions excited by earthquakes are used. Finally in Section 11.4, we present a simulation of rotational motion excited by an earthquake, and discuss the possibility of detection in real situations. © 2006 Springer-Verlag Berlin Heidelberg.