Chin-Jen Lin

Review: Progress in Rotational Ground-Motion Observations from Explosions and Local Earthquakes in Taiwan

Rotational motions generated by large earthquakes in the far field have been successfully measured, and observations agree well with the classical elasticity theory. However, recent rotational measurements in the near field of earthquakes in Japan and in Taiwan indicate that rotational ground motions are 10 to 100 times larger than expected from the classical elasticity theory. The near-field strong-motion records of the 1999 Mw 7:6 Chi-Chi, Taiwan, earthquake suggest that the ground motions along the 100 km rupture are complex. Some rather arbitrary baseline corrections are necessary in order to obtain reasonable displacement values from double integra- tion of the acceleration data. Because rotational motions can contaminate acceleration observations due to the induced perturbation of the Earths gravitational field, we started a modest program to observe rotational ground motions in Taiwan. Three papers have reported the rotational observations in Taiwan: (1) at the HGSD station (Liu et al., 2009), (2) at the N3 site from two TAiwan Integrated GEodynamics Research (TAIGER) explosions (Lin et al., 2009), and (3) at the Taiwan campus of the National Chung-Cheng University (NCCU )( Wuet al., 2009). In addition, Langston et al. (2009) reported the results of analyzing the TAIGER explosion data. As noted by several authors before, we found a linear relationship between peak rotational rate (PRR in mrad=sec) and peak ground acceleration (PGA in m=sec 2 ) from local earthquakes in Taiwan, PRR 0:002 1:301 PGA, with a correlation coefficient of 0.988.

Observing Rotational and Translational Ground Motions at the HGSD Station in Taiwan from 2007 to 2008

Because of a lack of suitable instruments, rotational ground motions have not been observed until the last decade. Rotational measurements in the near field of earthquakes in Japan (Takeo, 1998) indicate that rotational ground motions are many times larger than expected from the classical elasticity theory. After failing to obtain useful rotational ground motions (using similar rotational sensors as Takeo did), we deployed a far more sensitive rotational velocity sensor (R-1) at the HGSD station in eastern Taiwan. From 7 December 2004 to 12 November 2006, several hundreds of earthquakes were recorded during our Phase 1 operation. This was mostly a learning exercise to solve field operation problems; Phase 1 operations ended when our two R-1 sensors ceased to operate. A K2 R1 instrument was deployed in the spring of 2007 to start our Phase 2 operation. From 8 May 2007 to 17 February 2008, we ob- served 52 local earthquakes with good rotational velocity signals (with signal-to-noise ratio >∼5), together with excellent translational acceleration signals (with signal-to- noise ratio >∼10). Unfortunately, field operation was interrupted due to flooding of the HGSD station site in mid-February 2008; we just resumed normal operation in June 2008. This article reports our observations of rotational and translational ground motions made at the HGSD station so far. We concentrate on describing our instru- mentation and the data obtained from 52 local earthquakes during our Phase 2 opera- tion and present some very preliminary results.

Application of Rotational Sensors to Correcting Rotation-Induced Effects on Accelerometers

Abstract Dynamic and permanent seismic displacements are important for seismologists and engineers and, in principle, can be derived from the double-time integral of translational acceleration. However, because translational accelerometers are sensitive not only to translational but also to rotational motions, it is not possible to recover with assurance the true displacement by direct double-time integration of acceleration without first applying corrections from separately recorded rotational motions. This paper applies an attitude equation from the navigational literature to obtain the time-dependent orientation of the accelerometer from colocated recordings of three-axis rotation rate and then applies an attitude-correction equation together with orientation and these rotational data to correct centrifugal and tilt-induced gravitational effects on accelerometers. Finally, we perform coordinate transformations to derive the dynamic motion in an inertially fixed (geographic) coordinates frame rather than in the body-attached coordinates in which they are recorded. To verify our algorithm, we attached a three-axis translational accelerometer and a three-axis rotation-rate sensor together to the end of a robot arm. By moving the robot arm simultaneously in translation and rotation, we find a good match between displacements calculated with our correction scheme and the actual robot-arm movements, as determined by the robot’s inputs and feedback system.

Seismic-Wave Strain, Rotation, and Gradiometry for the 4 March 2008 TAIGER Explosions

Abstract Acceleration spatial gradients, horizontal strains, and horizontal rotation were computed using strong-motion array data from the 4 March 2008 TAIGER explosions in northeastern Taiwan and used in conjunction with the original three component acceleration data to perform a gradiometric analysis of the strong ground motion wave train. The analysis yields a complex, frequency-dependent view of the nature of seismic-wave propagation over short propagation distances that imply significant lateral velocity changes in structure. Areal strain and rotation about the vertical axis have equal amplitudes and suggest significant wave scattering within the confines of the river valley where the experiment was performed and/or significant departure from an axisymmetric explosion source. Gradiometry shows that the P wave arrives at the array 35° off-azimuth clockwise from the straight-line path and appears to have been refracted from the northern side of the valley. Large, slowly propagating secondary surface waves initially arrive 45° counterclockwise from the straight-line path but later arrivals are seen to propagate in all directions, including back toward the explosion source. A frequency-dependent radiation pattern for the triple-borehole explosion in comparison to the single-borehole explosion explains the differences in the maximum amplitudes between the sources seen in the acceleration data. The use of seismic strain and rotation with standard particle motion wave fields at a single location allows for a direct view of seismic-wave propagation that illuminates the true nature of the seismogram.

Estimate of Rayleigh‐to‐Love wave ratio in the secondary microseism by a small array at Piñon Flat Observatory, California

Using closely located seismographs at Pinon Flat (PFO), California, for 1 year long record (2015), we estimated the Rayleigh-to-Love wave energy ratio in the secondary microseism (0.1-0.35 Hz) in four seasons. Rayleigh wave energy was estimated from a vertical component seismograph. Love wave energy was estimated from rotation seismograms that were derived from a small array at PFO. Derived ratios are 2-2.5, meaning that there is 2-2.5 times more Rayleigh wave energy than Love wave energy at PFO. In our previous study at Wettzell, Germany, this ratio was 0.9-1.0, indicating comparable energy between Rayleigh waves and Love waves. This difference suggests that the Rayleigh-to-Love wave ratios in the secondary microseism may differ greatly from region to region. It also implies that an assumption of the diffuse wavefield is not likely to be valid for this low frequency range as the equipartition of energy should make this ratio much closer.

Investigation of ground rotational motions caused by direct and scattered P-waves from the 4 March 2008 TAIGER explosion experiment

High-frequency rotational motions of P-waves and coda waves were analysed using rotation rate sensors and strong motion array data from the 4 March 2008 TAiwan Integrated GEodynamics Research (TAIGER) explosion experiment in northeastern Taiwan. Theoretical and observational investigations focussed on the effects of this experiment on the free surface. The main goal of this study was to explore possible applications of combined measurements of artificial explosion-derived translational and rotational motions. Also investigated was the consistent ground rotation observed directly by rotation rate sensors and derived using translational seismic arrays. Common near-source high-frequency rotational motion observations and array-recorded translational motions from one shallow borehole explosion are analysed in this study. Using a half-space assumption of plane P-wave propagation across the recording site, we conclude that: (1) rotational motions induced by direct P-waves interacting with a free surface in theory can be used to estimate wave radial direction, velocity and anisotropic properties; (2) rotational motions derived from scattering are predominant among the observed rotations during the TAIGER explosion experiments and allow us to image the heterogeneous structure of the medium at the investigated site; and (3) rotation sensor measurements undertaken during TAIGER explosion experiments may be affected by cross-axis sensitivities, which need to be considered when using the data obtained during these experiments.

Inversion of ground-motion data from a seismometer array for rotation using a modification of Jaeger's method

Abstract We develop a new way to invert 2D translational waveforms using Jaeger’s (1969) formula to derive rotational ground motions about one axis and estimate the errors in them using techniques from statistical multivariate analysis. This procedure can be used to derive rotational ground motions and strains using arrayed translational data, thus providing an efficient way to calibrate the performance of rotational sensors. This approach does not require a priori information about the noise level of the translational data and elastic properties of the media. This new procedure also provides estimates of the standard deviations of the derived rotations and strains. In this study, we validated this code using synthetic translational waveforms from a seismic array. The results after the inversion of the synthetics for rotations were almost identical with the results derived using a well-tested inversion procedure by Spudich and Fletcher (2009). This new 2D procedure can be applied three times to obtain the full, three-component rotations. Additional modifications can be implemented to the code in the future to study different features of the rotational ground motions and strains induced by the passage of seismic waves.