Tutorial on rotational seismology and its applications in exploration geophysics

Traditionally, seismological interpretations are based on the measurement of only translational motions, such as particle displacement, velocity, and/or acceleration, possibly combined with pressure changes; yet theory indicates that rotational motions should also be observed for a complete description of all ground motions. The recent and ongoing development of rotational sensors renders a full analysis of the translational and rotational ground motion possible. We have developed the basic mathematical theory related to rotational motion. And we also evaluated several instruments used to directly measure the rotational ground motion, which may be applicable for exploration geophysics. Finally, we made several applications of rotational motion in exploration geophysics, namely, (1) P- and S-wavefield separation, (2) wavefield reconstruction, (3) ground-roll removal, (4) microseismic event localization and reflection seismic migration by wavefield extrapolation, and (5) moment tensor inversion. The cited research shows that in particular, the information on the spatial gradient of the wavefield obtained by rotational sensors is beneficial for many purposes. This tutorial is meant to (1) enhance familiarity with the concept of rotational seismology, (2) lead to additional applications, and (3) fast track the continued development of rotational sensors for global and exploration geophysical use.