Journal of Seismology

, Volume 19, Issue 2, pp 491–509 | Cite as

Six-degree-of-freedom near-source seismic motions I: rotation-to-translation relations and synthetic examples

  • Johana BrokešováEmail author
  • Jiří Málek
Original Article


The paper deals with theoretical aspects of rotation-to-translation relations in six-degree-of-freedom short-period seismic records at close hypocentral distances. Rotation-to-translation ratios are introduced as the ratios relating peak amplitudes of the relevant rotational and translational components. Their frequency dependence is analyzed in simple models. The relations between translations and rotations are expressed by equations derived under the assumption of a spherical S wave radiated from a shallow point source in a homogeneous medium. A set of numerical experiments is performed to examine these relations for a double-couple source buried in simplified structure models. These experiments indicate that at local distances (up to several km), at lower frequencies (up to a few Hz), and at locations with rapid amplitude changes due to the radiation pattern (e.g., in the vicinity of nodal planes), the rotational components are a linear combination of terms proportional to translational velocity and acceleration, and none of the terms can be, in general, neglected. We also focus on the possibility to retrieve the S-wave phase velocity along the wavepath. The applicability of the equations is tested also in a layered velocity model. It has been found that, under certain conditions, the equations allow us to find correct values of wavepath velocity even in vertically inhomogeneous structures. The depth-range sensitivity is examined for a specific 1D model containing a thin surficial low-velocity layer. Based on these experiments, we have concluded that the retrieved velocity is representative down to the depth not exceeding one wavelength.


Seismic rotation Near-source region Rotation-to-translation relations Numerical simulations S-wave velocity 



This work was supported by the Czech Science Foundation, Projects No P210/10/0925 and P210/15-02363S.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Faculty of Mathematics and Physics, Department of GeophysicsCharles University in PraguePragueCzech Republic
  2. 2.Institute of Rock Structure and MechanicsAcademy of Sciences of the Czech RepublicPragueCzech Republic

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