First Comparison of Array-Derived Rotational Ground Motions with Direct Ring Laser Measurements

Abstract

Recently, ring laser technology has provided the first consistent observations of rotational ground motions around a vertical axis induced by earthquakes. "Consistent," in this context, implies that the observed waveforms and amplitudes are compatible with collocated recordings of translational ground motions. In particular, transverse accelerations should be in phase with rotation rate and their ratio proportional to local horizontal phase velocity assuming plane-wave propagation. The ring laser installed at the Fundamentalstation Wettzell in the Bavarian Forest, Southeast Germany, is recording the rotation rate around a vertical axis, theoretically a linear combination of the space derivatives of the horizontal components of motion. This suggests that, in principle, rotation can be derived from seismic-array experiments by "finite differencing." This has been attempted previously in several studies; however, the accuracy of these observations could never be tested in the absence of direct measurements. We installed a double cross-shaped array of nine stations from December 2003 to March 2004 around the ring laser instrument and observed several large earthquakes on both the ring laser and the seismic array. Here we present for the first time a comparison of array-derived rotations with direct measurements of rotations for ground motions induced by the M 6.3 Al Hoceima, Morocco, earthquake of 24 February 2004. With complete 3D synthetic seismograms calculated for this event we show that even low levels of noise may considerably influence the accuracy of the array-derived rotations when the minimum number of required stations (three) is used. Nevertheless, when using all nine stations, the overall fit between direct and array-derived measurements is surprisingly good (maximum correlation coefficient of 0.94).

Reducing nonuniqueness in finite source inversion using rotational ground motions

“…Alternatively, the seismogeodetic method [Bodin et al, 1997;Spudich et al, 1995;Spudich and Fletcher, 2008] may be used to derive rotational ground motion from translation recordings at the surface [e.g., Suryanto et al, 2006;Kendall et al, 2012;Pham et al, 2012]. This method requires, however, detailed knowledge of 3-D subsurface structure.…”

Rotational Motions in Seismology: Theory, Observation, Simulation

“…Indeed, in several array studies, rotation rate of seismic wavefields after large earthquakes was estimated (e.g., Huang 2003). However, there is only one study where array-derived rotation rate was compared with direct measurements (Suryanto et al 2005) and the results indicate that -as expected-array derived rotation is sensitive to noise. As indicated above and shown in Igel et al (2005b), with appropriate scaling the broadband transverse acceleration can be almost identical to rotation rate provided that the assumption of plane wave propagation holds.…”

“…There are now observations of ground rotations of several dozens of earthquakes with a wide magnitude and epicentral distance range. The accuracy of the phase velocity estimates is currently under investigation by comparison with complete wave simulations (see below), and array-derived phase velocities (Suryanto et al 2005) as well as theoretical predictions of Love-wave dispersion for local Earth models.…”

“…The instruments should be as close as possible for the finite difference approximations to be as close as possible to the true gradients. However, for a given instrumental noise level, the uncertainty in the gradients will be larger if the instruments are closer; see Suryanto et al (2005) for a more in-depth discussion of noise contribution. Finally, the assumption of linearity of the displacement will be greatly affected by site effects at the stations.…”

“…However, the subsequent development of ring laser technology indicates that a significant part of the gap has recently been filled, as demonstrated by Schreiber et al (2003b) and Igel et al (2005b) and exemplified later in this paper. Rotations can also be determined with array measurements, but with important limitations; see section 3.1 and Suryanto et al (2005).…”