Rotation motions: Recording and analysis

Abstract

Rotation motions can be classified as those associated to the body seismic waves (displacement-related component and micromorphic component) and those which form independent fields (pure rotation and twist waves); see Chaps. 4-6. The equipment that records rotation motions may use various sensors, like the Sagnac-effect based gyroscopes (see Chaps. 11, 12, 29, 30, 31, 37), seismometers (Chaps. 15, 32, 33, 34), tiltmeters (Chap. 36) or rotation sensors (Chap. 35). In this Chap. we present some records obtained with a system of two horizontal seismometer pairs, each containing two pendulums suspended on a common axis and aligned in opposite directions. The pairs were oriented perpendicular to each other. The system was constructed by J. Suchcicki (see Teisseyre et al. 2003). Its ability has been improved by some numerical procedures normalizing the signals at the antiparallel channels. The errors caused by the inevitable small differences in seismograph responses have been estimated and a reliability of recordings was tested in many ways: by filtering in the time domain (using some data obtained from the same equipment as a reference, see Nowoyski and Teisseyre KP 2003), or by numerical filtering procedure in the frequency domain and the learning procedure for filters (Teisseyre R et al. 2003a, b). Any serious analysis of rotation wave records would require, first of all, the existence of a network of recording stations; however, up to now, only few rotation-recording stations do exist, and these use various sensors. There is also a need for a more advanced theory describing propagation and reflection of the rotation waves. Such an advanced approach should follow the development of the classical seismology, starting with hodographs and separation of phases of rotation motions. The independent rotation waves may travel with different, rather lower velocities than those related to the body waves. This is due to the different material constants that describe the stress response to rotational deformations. Such constants enter in the constitutive relation between the stress moments (or equivalently, the antisymmetric stresses) and angular motion (see Chaps. 4-6). To better understand the role of pure rotation and twist, we shall take into account the fact that rotation of particles or grains induces antisymmetric stresses (equivalent to stress moments). We expect the rotation rigidity (see Chap. 5) to be smaller than the rigidity modulus; hence, we could expect the late arrivals of the related rotation waves. To discover such late arrivals we shall start with hodographs for near field and gradually extend the required time interval of registrations. A first trial of such a near field hodograph is presented by Jaroszewicz et al. in Chap. 31. However, we shall also take into account an interrelation between the displacement motion and rotation, which may lead to a kind of coupling of these motions; this is, among other things, discussed in this chapter. © Springer-Verlag Berlin Heidelberg 2006.