Rotational Seismology Workshop of 

February 2006 

By John R. Evans1, A. Cochard2, Vladimir Graizer3, Bor-Shouh Huang4, Kenneth W. Hudnut5, 

Charles R. Hutt6, H. Igel2, William H.K. Lee1,

 Chun-Chi Liu4

, Eugeniusz Majewski7, Robert Nigbor8, Erdal 

Safak9, William U. Savage1, U. Schreiber10, Roman Teisseyre7, Mihailo Trifunac11, J. Wassermann2, and 

Chien-Fu Wu12 (alphabetical throughout, excepting first author here) 

1 U.S. Geological Survey, Menlo Park CA 94025, USA 

2 Sektion Geophysik, Ludwig-Maximilians-Universität, D-80333 München, Germany 3 California Geological Survey, Sacramento CA 95814, USA 4 Institute of Earth Sciences, Academia Sinica, Taipei, Taiwan 

5 U.S. Geological Survey, Pasadena CA 91106, USA 

6 U.S. Geological Survey, Albuquerque NM 87198, USA 

7 Institute of Geophysics, Polish Academy of Sciences, 01-452 Warszawa, Poland 8 Department of Civil Engineering, University of California, Los Angeles CA 90095, USA 9 Bogazici University, Kandilli Observatory, 81220 Cengelkoy, Istanbul, Turkey 10 Fundamentalstation Wettzell, Technische Universität München, D-93444 Kötzting, Germany 11 Department of Civil Engineering, University of Southern California, Los Angeles CA 90089, USA 12 Seismology Center, Central Weather Bureau, Taipei, Taiwan

2007

Open-file Report 2007-1145 

U.S. Department of the Interior 

U.S. Geological Survey 
ii

U.S. Department of the Interior 

DIRK KEMPTHORNE, Secretary 

U.S. Geological Survey 

Mark D. Myers, Director 

U.S. Geological Survey, Reston, Virginia 2007 

For product and ordering information: 

World Wide Web: http://www.usgs.gov/pubprod

Telephone: 1-888-ASK-USGS 

For more information on the USGS—the Federal source for science about the Earth, 

its natural and living resources, natural hazards, and the environment: 

World Wide Web: http://www.usgs.gov

Telephone: 1-888-ASK-USGS 

Suggested citation: 

Evans, J.R., Cochard, A., Graizer, Vladimir, Huang, Bor-Shouh, Hudnut, Kenneth W., Hutt, Charles R., Igel, H., 

Lee, William H.K., Liu, Chun-Chi, Majewski, Eugeniusz, Nigbor, Robert, Safak, Erdal, Savage, William U., 

Schreiber, U., Teisseyre, Roman, Trifunac, Mihailo, Wassermann, J., and, Wu, Chien-Fu, 2007, Rotational 

seismology workshop of February 2006: U.S. Geological Survey, Open-File Report. 2007-1145, 20 p. 

[http://pubs.usgs.gov/of/2007/1145/]. 

Any use of trade, product, or firm names is for descriptive purposes only and does not imply 

endorsement by the U.S. Government. 

Although this report is in the public domain, permission must be secured from the individual 

copyright owners to reproduce any copyrighted material contained within this report. 
iii

Contents

Introduction ....................................................................................................................................................4 

Theoretical Basis for Rotational Effects in Strong Motion and Some Results 

 — V. Graizer, E. Safak, and M. D. Trifunac.................................................................................................6 

Observational Experience with Rotational Strong Motion 

 — B. S. Huang, W. H. K. Lee, C. C. Liu, R. Nigbor, and C. F. Wu.............................................................9 

Integrating GPS, Rotational, and Inertial Sensors 

 — K. Hudnut ...............................................................................................................................................11 

Teleseismic Rotational Seismology 

 — A. Cochard, H. Igel, E. Majewski, U. Schreiber, R. Teisseyre, J. Wassermann....................................12 

Instrument Testing 

 — J. R. Evans and C. R. Hutt......................................................................................................................14 

Discussion and Conclusions 

 — W. U. Savage..........................................................................................................................................16 

References ....................................................................................................................................................17 

Appendix. A Workshop on Measuring the Rotation Effects of Strong Ground Motion on 

16 February 2006..........................................................................................................................................20 
Rotational Seismology Workshop of February 2006 

By John R. Evans, A. Cochard, Vladimir Graizer, Bor-Shouh Huang, Kenneth W. Hudnut, 

Charles R. Hutt, H. Igel, William H.K. Lee, Chun-Chi Liu, Eugeniusz Majewski, Robert Nigbor, 

Erdal Safak, William U. Savage, U. Schreiber, Roman Teisseyre, Mihailo Trifunac, 

J. Wassermann, and Chien-Fu Wu

Introduction 

A successful workshop titled “Measuring the Rotation Effects of Strong Ground Motion” 

was held simultaneously in Menlo Park and Pasadena via video conference on 16 February 2006. 

The purpose of the Workshop and this Report are to summarize existing data and theory and to 

explore future challenges for rotational seismology, including free-field strong motion, structural 

strong motion, and teleseismic motions. We also forged a consensus on the plan of work to be 

pursued by this international group in the near term. 

At this first workshop were 16 participants in Menlo Park, 13 in Pasadena, and a few on the 

telephone. It was organized by William H. K. Lee and John R. Evans and chaired by 

William U. Savage in Menlo Park and by Kenneth W. Hudnut in Pasadena. Its agenda is given 

in the Appendix. 

This workshop and efforts in Europe led to the creation of the International Working Group 

on Rotational Seismology (IWGoRS), an international volunteer group providing forums for 

exchange of ideas and data as well as hosting a series of Workshops and Special Sessions. 

IWGoRS created a Web site, backed by an FTP site, for distribution of materials related to 

rotational seismology. At present, the FTP site contains the 2006 Workshop agenda (also given 

in the Appendix below) and its PowerPointTM presentations, as well as many papers (reasonableonly basis with permission of their authors), a comprehensive citations list, and related 

information. Eventually, the Web site will become the sole authoritative source for IWGoRS 

and shared information: 

http://www.rotational-seismology.org

ftp://ehzftp.wr.usgs.gov/jrevans/IWGoRS_FTPsite/

With contributions from various authors during and after the 2006 Workshop, this Report 

proceeds from the theoretical bases for making rotational measurements (Graizer, Safak, 

Trifunac) through the available observations (Huang, Lee, Liu, Nigbor), proposed suites of 

measurements (Hudnut), a discussion of broadband teleseismic rotational seismology (Cochard, 

Igel, Schreiber, Teisseyre, Wassermann, Majewski), sensor-calibration issues (Evans, Hutt), and 

finally the summary and conclusions (Savage). 

As a direct result of the 2006 Workshop and the formation of IWGoRS, we held a special 

session at the Fall 2006 AGU meeting (convened by H. Igel, W. H. K. Lee, and 

M. I. Todorovska). Currently, the first formal Workshop of the IWGoRS is being organized by 

W. H. K. Lee, M. Çelebi, and M. I. Todorovska with sponsorship by the USGS and assistance 

from many others; this First International Workshop on Rotational Seismology and Engineering 

Applications will be held in September 2007 at Menlo Park, California 

(http://pubs.usgs.gov/of/2007/1145/). 

4
The following summarizes presentations and discussions during and shortly after the 

informal Workshop of February 2006. 

5
Theoretical Basis for Rotational Effects in Strong Motion and Some 

Results — V. Graizer, E. Safak, and M. D. Trifunac 

In traditional earthquake engineering, structures are designed to resist only simplified 

representations of strong ground motions — horizontal translational accelerations. Occasionally, 

the vertical component of linear excitation also may be considered, however rotational excitation 

by torsional and rocking components is almost never considered. 

Recognition that the rocking is caused not only by soil compliance (soil-structure interaction) 

but also by the rocking of foundations caused by the passage of P, SV, and Rayleigh waves 

began to appear in the mid-1980s (Trifunac, 1982; Castellani and Bofi, 1986, 1989; Lee and 

Trifunac, 1987; Graizer, 1989). Many studies showed the significance of rocking excitations for 

both contiguous and base-isolated structures (e.g., Todorovska and Trifunac, 1990a,b; 1992a,b; 

Todorovska and Trifunac, 1993). Separating the effects of rotational excitation from rocking 

associated with soil-structure interaction is essential for interpreting observed inter-story drift. 

Current instrumentation does not permit this separation even approximately (Trifunac et al., 

2001). For buildings with large floor plans, warping and deformation of the foundation 

(Trifunac et al., 1999), and differential translation and rotation complicate both recording and 

analysis of structural response. Further work is needed in this area before the role of rocking 

excitation can be understood and included in engineering design. 

In the absence of recorded rotational components of strong motion, it is important for 

engineering studies of response to have at least preliminary, physically realistic simulations of 

such motions. The method of Lee and Trifunac (1985, 1987) for generating artificial torsional 

and rocking accelerograms meets most of these requirements. This method is an exact analytical 

solution if it is accepted that (1) the motion occurs in a linear elastic, layered half space and (2) 

that synthetic ground motion can be constructed by superposition of P, SV, and Rayleigh waves 

for rocking (Lee and Trifunac, 1987), and by SH and Love waves for torsion (Lee and Trifunac, 

1985). This method has been extended to predict associated strain (Lee, 1990) and curvature 

over time near the surface (Trifunac, 1990) during the passage of seismic waves. 

Simple models have been studied and used to evaluate the effects of torsional excitation 

(Gupta and Trifunac, 1987, 1989, 1990) and of rocking excitation (Gupta and Trifunac, 1988, 

1991), showing that such excitations can be significant. For example, rocking excitation 

becomes important for tall structures supported by soft soil while torsional excitations can 

dominate in the response of long and stiff structures supported by soft soils. 

Observations of building response to earthquake shaking led to similar findings. For 

example, for a seven-story, symmetric, reinforced concrete structure torsional response 

contributed up to 40% of the motion at the roof (Trifunac and Ivanovic, 2003). Torsional and 

rocking excitations contributed to significant damage in this building. In another well-studied 

building, asymmetry of the foundation and strong torsional excitation by surface waves 

propagating approximately along the longitudinal axis of the building resulted in a large torsional 

response (Trifunac et al., 2001). 

Recording, analysis, and interpretation of the contributions of torsional and rocking 

excitations to inter-story drift are essential for future development of earthquake-resistant design 

codes. Without proper consideration of these contributions, observed drifts may erroneously be 

assumed to result only from relative displacement of structures, leading to false confidence that 

current design methods are “conservative” (Trifunac and Ivanovic, 2003). 

6
Rotational motions in structures are generated by both the rotational components of ground 

shaking and dynamic characteristics (e.g., mass and stiffness distribution) of the structure. Body 

P, SV, Love, and Rayleigh waves are the main sources of rotational excitations. Rayleigh waves 

cause horizontal-axis rotational excitations at the base of any multi-story building. Love waves 

can create rotational excitations about vertical axis (i.e., torsion). The significance of rotational 

excitations varies with the wavelengths and dominant frequencies of surface waves and the 

foundation geometry and the natural frequencies of the structure. For tall buildings, Rayleighwave induced rotations can create significant “P-Δ Effects”, which are the overturning moments 

and horizontal shear forces generated by drift and the weight of the offset building. 

 Mass and stiffness characteristics of structures determine the amounts of rotation in 

structural components and their connections. These rotations significantly influence the 

structure’s natural frequency, a key parameter in calculation of seismic design forces. In multistory buildings, for example, it is often assumed that the floor slabs remain horizontal, that there 

are no rotations at beam-column connections. In fact, beam-column connections do rotate, and 

the amount of rotation is determined by the relative stiffness of beams and columns and the 

presence of shear walls. Indeed, in a multiple-story building the assumptions of no-rotations 

versus free-rotations at the beam-column connections can make more than a factor of two 

difference in the natural frequencies of the structure. Moreover, knowing rotations in a structure 

(e.g., rotations of beam-column or beam-shearwall connections, or in-plane rotations of floor 

slabs) allows one to calculate more precisely the distribution of seismic forces among 

components such as frames and shear walls. 

Thus, there is a need for measuring rotational motions during earthquakes, both on the 

ground and in the structure. Rotational motions are not now measured but calculated by taking 

differences between measured linear motions at separated sensors. This differencing operation 

amplifies the noise in the records significantly, particularly for vertical motions. 

Most instruments used to record ground motion are pivot-pendulum or linear-pendulum 

seismographs, velocigraphs, or accelerographs. It is often assumed that these sensors respond 

only to translational motions. However, Graizer (1989, 2005) showed that the differential 

equation of small oscillations of horizontal pivot-penduli can be written (3 = vertical axis): 

y ′ ′ 1 + 2ω1D1y ′

1 +ω1

2

y1 = −x ′′

1 + gψ2 −ψ ′′3l1 + x ′′2θ1 (1) 

where yi is the recorded response of the instrument, θi is the angle of pendulum rotation, li is the 

length of the pivot-pendulum arm, yi

 = θili at the end of the arm, ωi is the natural frequency, Di is 

the fraction of critical damping of the ith transducer, g is the acceleration due to gravity oriented 

vertically, xi

” is the linear ground acceleration in ith direction, and i is a rotation angle of the 

ground surface about axis xi. The following are functions of time: θi (thus y1) and x1. 

For small oscillations of all penduli, the vertical accelerometer is almost insensitive to tilts. 

Neglecting the cross-axis sensitivity terms, however, the differential equation of the first 

horizontal pendulum (Eqn. 1) simplifies to 

y ′ ′ 1 + 2ω1D1y ′

1 +ω1

2

y1 = −x ′′

1 + gψ2 (2) 

while that of the vertical pendulum becomes 

y ′ ′ 3 + 2ω3D3 y ′

3 +ω3

2

y3 = −x ′′ 3 (3) 

7
Thus, in a typical strong-motion tri-axial instrument both horizontal sensors are responding 

to a combination of horizontal linear accelerations and axial tilts while the vertical sensor is 

responding almost entirely to linear acceleration. 

Tilting of a horizontal accelerometer’s base therefore significantly impacts its output. As 

shown by Graizer (2005, 2006), the presence of unknown tilts in a record makes calculation of 

displacements impossible using only linear-accelerometer data. Consequently, direct methods of 

displacement calculation from linear acceleration are not applicable to those records. A 

conservative procedure based on filtering out the low-frequency portion of linear ground motion 

by Trifunac (1971) and similar methods are the only way to process existing strong-motion data. 

A method for evaluating tilts using uncorrected linear accelerograms proposed by Graizer

(1989) has been tested in laboratory experiments with various linear accelerometers. The 

method is based on the difference in the tilt sensitivity between the horizontal and vertical 

penduli. It was applied to a number of the large-amplitude records, including from the MW = 6.7 

Northridge earthquake of 1994. Residual tilt extracted from the strong-motion record at the 

Pacoima Dam reached 3.1° in the N45°E direction, in agreement with residual tilt as measured 

by an electronic level a few days after the earthquake (Shakal et al., 1994). Records from the 

Northridge earthquake yielded estimated tilt of 2.9° on the ground floor of a 12-story hotel in 

Ventura. Processing most of the largest-amplitude records of the Northridge earthquake did not 

resolve tilting greater than the error of the method, about 0.5°. 

Tilt estimates using existing strong-motion records demonstrate the importance of 

independent measurements of rotations. It may be especially important in recording the seismic 

response of buildings because structures can have significant rotational components even in 

cases when the corresponding free-field ground motion is purely translational. 

8
Observational Experience with Rotational Strong Motion — 

B. S. Huang, W. H. K. Lee, C. C. Liu, R. Nigbor, and C. F. Wu 

Nigbor (1994) documents early efforts to measure rotational strong ground motion, using the 

Systron-DonnerTM MEMS “GyroChipTM” Model QRS11TM rotational-velocity sensor. Nigbor 

integrated a prototype sensor into his 6-DOF (six degrees of freedom) measurement system. 

That sensor’s range (0.2 rad/s full scale and 100 μrad/s resolution) was appropriate for strong 

ground motions, based on theoretical results of Bouchon and Aki (1982) and others. The system 

was in the garage of a private home north of Landers, California, 2 km from the fault trace of the 

1992 mainshock. Over two months, six aftershocks were recorded with PGA •0.02 g, but no 

rotational motions were resolved above the ~1 mrad/s noise level. 

However, on 22 September 1993, the Department of Energy conducted a “Non-Proliferation 

Experiment” (NPE) at the Nevada Test Site, a one-kiloton chemical explosion 390 m 

underground. This event was densely monitored by the seismological community (Zucca, 1993); 

the prototype 6-DOF accelerograph was deployed on bedrock 1 km from ground zero and 

successfully recorded viable data on all six sensors, including rotation. Peak rotational velocity 

was 400 mrad/s, peak linear acceleration 0.8 g horizontal and >1 g vertical. 

The rotational sensors then were moved to the surface station of the Borrego Valley 

Downhole Array in Southern California, where they remain. Since 1994, several hundred 

earthquakes have been recorded by the BVDA array, with PGA •0.2 g, but no rotational motions 

have been resolved above the ~1 mrad/s sensor noise. 

In 2004, ATATM ARS-09TM magneto-hydrodynamic (MHD) rotational-velocity sensors were 

included in the SFSI (soil-foundation-structure interaction) test structure at the Garner Valley 

Digital Array in Southern California (part of the George E. Brown, Jr., Network for Earthquake 

Engineering Simulation; http://nees.ucsb.edu). The rotational sensors are installed on the bottom 

slab of the 4 m × 4 m × 4 m test structure, atop soft soil. Four vertical accelerometers in the 

corners of the foundation slab can be used independently of the ARS-09TM to measure rotational 

motions. Data from active (shaker) and passive (earthquake and microtremor) monitoring have 

been gathered for two years. Rocking motion of the structure has been measured using vertical 

accelerometers, on the order of 100 μrad/s, however, no rotational data have been resolved to 

date above the ~1 mrad/s rotational-sensor noise. 

Lessons from the 13 years of experience with COTS rotational sensors: 

• Resolution is ~1 mrad/s for both the QRS11TM and ATA-09TM. 

• Small rotational foundation motions can be resolved by closely-spaced vertical 

accelerometers, but obtaining all axes of motion will be difficult using this method. 

• The NEES SFSI test structure at GVDA can be a useful field test site for rotational sensors. 

Over the past 13 years Taiwan has begun to monitor the rotational components of strong 

ground motion in addition to translational acceleration measurements. Interest in rotational 

strong ground motion derive from theoretical results (Bouchon and Aki, 1982; Lee and Trifunac, 

1985). These studies concluded that rotational components of strong ground motion may be 

important in the near field. Graizer (1989) suggests inertial seismometry methods for weak and 

strong motions. Estimates of peak rotational velocities in these papers are on the order of 

0.1 rad/s, within the range of available inertial sensors. 

9
The at least 50 near-field strong-motion records from the 1999 Chi-Chi (Taiwan) earthquake 

indicate that ground motions along the 100-km long rupture are complex and may have included 

significant rotations. Huang (2003) inferred ground rotational motions of the Chi-Chi 

earthquake as inferred from dense array observations using the method of Spudich et al. (1995). 

C. C. Liu and B. S. Huang began recording at 200 sps with triaxial rotation transducers at station 

HRLT near Hualien on 12 December 2000 (a 12-channel KinemetricsTM K2TM data logger, an 

FBA, a PVC-5TM rotation transducer [0.2 V/rad/s], and a GyroChipTM rotation transducer 

[1.43 V/rad/s]). No useful rotation data were obtained after five years of observation. A more 

sensitive triaxial rotational transducer (eentec/PMDTM model R-1TM) was purchased and Liu and 

Huang began observations with it at station HGSD near Cheng-Kung in eastern Taiwan, 

07 December 2004. The sensitivity of the R-1TM is 50 V/rad/s, ~35 times higher than the 

GyroChipTM and 250 times higher than the PVC-5TM. Several hundred earthquakes yielded 

rotation data during this two-year interval. 

At HGSD a six-channel digitizer (QuanterraTM Q330TM) is being used to collect data from 

two sets of sensors: (1) a three-component GuralpTM CMG-3TDTM broadband velocity 

seismometer (down hole at 100-m depth) and (2) the triaxial eentec/PMDTM model R-1TM 

rotational transducer (at the surface). Data are continuously sampled at 100 sps and 24-bit 

resolution. At 18:50:20.3 UTC, 26 September 2005, an MW=5.1 earthquake occurred ~29 km 

south of the station at 23.23° N, 121.40° E, focal depth 21 km (CWB Earthquake Report 

No. 94139). At 17:01:37.2 UTC, 08 January 2006, an MW=4.6 earthquake occurred ~36 km 

south of the station at 23.16° N, 121.42° E, focal depth 8.7 km (CWB Earthquake Report No. 

95002). Preliminary observations of peak rotational velocities from these two earthquakes are: 

Earthquake Epicentral 

Distance (km) 

Maximum Rotation (μrad/s) 

Component EW NS Vertical 

26 September 2005 29 306 499 1863 

09 January 2006 36 98 183 217 

A preliminary analyses of these data was performed; these results are described for the 

26 September 2005 earthquake. To integrate the rotational velocity data, we first removed their 

mean and then high-pass filtered with corner at 0.2 Hz). Maximum rotation is a few tens of μrad 

for the horizontal components and about 100 μrad for the vertical. Since 1 μrad in-plane tilt will 

introduce about 1 μg deflection in a horizontal accelerometer, these results suggest that rotational 

motions even for an earthquake of MW=5 in the middle-field cannot be ignored in double 

integration of linear acceleration. 

Absent to date is in-field calibration of the rotational transducer, so we are not sure that the 

measurements are real. Also, the deployment also is not optimal; Huang, Lee, Liu, and Wu will 

deploy additional triaxial rotational transducers (eentec R-1TM or PMDTMRSB20TM) and 

accelerometer arrays in two new experiments in Taiwan in 2007 following some calibration tests. 

10
Integrating GPS, Rotational, and Inertial Sensors — K. Hudnut 

It is fair to say that no one sensor can do everything. Important earthquake-related motions 

occur over a wide range of amplitudes and periods. Technology evolves quickly, so there is an 

need to identify promising new devices and develop more capable earthquake-monitoring 

systems. A single sensor package that measures body and surface waves of teleseisms while also 

recording near-field strong-motion and permanent displacements is a key goal. GPS and gyros 

can be important augmentations to weak motion sensors and accelerometers (e.g., Boore, 2003). 

No site will be well suited to all requirements — quiet across the entire spectrum — and there is 

complexity in upgrading extant sites. However, there is room for innovation and improvement, 

particularly in the rapidly developing area known as “inertial-aided GPS”. 

Technological developments in GPS and inertial measurement units (IMUs) are progressing 

rapidly. Increasingly, GPS, gyros, and accelerometers are being integrated (the 6-DOF system 

and GPS covering each other’s weaknesses — drift of inertial systems versus obstruction of GPS 

signals — also providing higher frequency information for anti-skid, dynamic suspension, etc. 

Cell phones now commonly contain GPS receivers and soon will add inertial sensors. These and 

other markets have led to rapid improvements in performance while decreasing costs. 

Algorithms have improved greatly for analyzing real-time data from multiple sensors (e.g., 

Jekeli, 2001). 

The USGS requires such instrumentation for applications like earthquake early warning and 

fault slip quantification (e.g., for finite-fault source modeling and DamageMap). DamageMap is 

an automatic, preliminary tagging of structures as red, yellow, or green after a large event, based 

on the rotations, accelerations, and displacements (drift) of the structure. The DamageMap 

system is envisioned as a major new product of USGS for urban areas (e.g., Safak and Hudnut, 

2006). DamageMap testing has shown that current GPS and accelerometer systems are each 

inadequate in isolation for recording building motions that translate into structural damage 

estimates. Torsional and rocking motions are not uniquely measured by GPS or accelerometers, 

so gyros should be included. Gyros also will improve the redundancy and robustness of 

DamageMap, fault slip, and early-warning instrument packages. With current ANSS structural 

instrumentation funding a development and testing program has been initiated for GPS “Point 

Positioning” and extended “Real-Time Kinematic” GPS methods at the UCLA Factor building; 

gyros will be purchased and tested shortly. Partly through interactions at this workshop, new 

ideas went into a new NASA proposal by JPL and USGS, to expand development efforts in 

support of DamageMap. 

11
Teleseismic Rotational Seismology— A. Cochard, H. Igel, E. Majewski, 

U. Schreiber, R. Teisseyre, J. Wassermann 

Recently, precision ring laser technology has been developed for the Earth Sciences, 

primarily to detect small variations of the Earth’s rotation rate. The high resolution of these 

instruments led to the first measurements of earthquake-induced rotational weak ground motions, 

first observed at Christchurch, New Zealand (Schreiber et al., 2006). At teleseismic distances 

the seismic wave field is well approximated by plane waves; in this approximation a direct 

comparison between rotation rate around a vertical axis and transverse acceleration is possible — 

translations and rotations are in phase and their amplitudes scale by twice the horizontal phase 

velocity (similar relations hold for strains and translations). A study of collocated translations 

and rotations has been done with measurements from the 4×4-m ring laser at Wettzell, Germany. 

These observations showed, over a broad frequency range (1–150 s period), that the waveforms 

have the expected relationships and that amplitude ratios allow an accurate estimate of horizontal 

phase velocities (Igel et al., 2005; Cochard et al., 2006). These observations are corroborated by 

numerical modeling of rotations and translations of the M8.3, Tokachi-oki event, 25 September 

2003. A collection of local and distant event records are being accumulated at these sites, which 

observations led to a purpose-built ring laser system for seismology. One such 2×2-m prototype 

is now operational at the Piñon Flat Observatory, California. 

In principle, the vertical component of rotation rate can be estimated from seismic array data 

(e.g., Spudich et al., 1995), but — due to the lack of resolution of rotation sensors — were never 

compared to direct measurements of rotations. A star-shaped seismic array with an aperture of 

3 km was installed around the ring laser at Wettzell for four months and recorded several large 

earthquakes. The event recorded with the best signal-to-noise ratio (M6.3, Al Hoceima, 

24 February 2004) was modeled with synthetic seismograms; the influence of noise on 

individual stations were investigated systematically. The results have problems typical when 

using only a few noisy stations, but a comparison between directly measured rotation rate and 

array-derived rotations using all nine stations shows they match well (correlation coefficient 

0.94). While direct measurements are more practical, this result indicates that accurate smallscale array measurements can be used to test and validate rotational instruments (the method also 

can be used for rotations around horizontal axes, as vertical components are expected to be less 

noisy). 

Future studies will focus on the estimation of Love-wave dispersion (and other wavefield 

properties) from collocated measurements of translations and rotations. These new processing 

tools will be applied to extant events. 

Recently, new, sensitive rotation seismographs and laser/fiber ring interferometers (ring laser 

gyroscopes and fiber optic gyroscopes) exploiting the Sagnac principle have opened new 

opportunities. Acknowledging that real rotation and twist motions in a source zone exist, there is 

an open question of how far such fields can propagate from a source as well as unknown rates of 

attenuation. We should take into account the fact that even distal body and surface seismic 

waves, when entering a near-surface region characterized by complex structure, may give rise to 

conjugated microdisplacement motions (cf., microcontinuum theory of composites, porous 

media, rocks, etc.). That is, rotation and twist waves may again derive from interaction of 

incident seismic waves with these near-surface features. Theories of micropolar and 

micromorphic media (Teisseyre, 1973) predict a relationship between displacement derivatives 

and the microdisplacements. 

12
Recent experimental and theoretical results for rotational seismic motion motivated creation 

of a comprehensive monograph (Teisseyre et al., 2006) offering new insights into observations 

and theory. Teisseyre et al. address many subjects from a variety of viewpoints collected in a 

manner facilitating systematic coverage. 

13
Instrument Testing — J. R. Evans and C. R. Hutt 

The Albuquerque Seismological Laboratory (ASL) of the U.S. Geological Survey is being 

updated with new facilities and capabilities to provide a National testing capability for the ANSS 

(Advanced National Seismic System), providing ANSS with the ability to verify and maintain a 

wide variety of sensors, including broadband, strong motion, and perhaps rotational. 

ASL is located about 15 miles southeast of Albuquerque, just south of Kirtland AFB on the 

Isleta Indian Reservation. It is a seismologically quiet site with a large vault consisting of two 

rooms and a cross tunnel between them, ~15 m deep in granite. It also has downhole broadband 

instruments in granite (~100–200 m) and a set of WWSSN piers on the surface on granite. The 

underground facilities have excellent long- and short-term temperature stability in addition to 

noise signatures near the Low Noise Model (Peterson, 1993). 

ASL has a series of reference instruments, including an STS-1TM in the vault within a superisolated chamber (a sealed, barometric pressure resistant vessel) and both a GeotechTM 

KS54000TM and a GuralpTM CMG-3TBTM downhole (GSN site ANMO). ASL has several 

QuanterraTM Q680TM, high-resolution, 24-bit, 12-channel recorders. Personnel experienced in 

calibration issues are present, as is software for computing self noise, power spectra, and digital 

filters, and for performing automated calibration analyses. We have a low-distortion oscillator 

for testing linearity and distortion in recorders, but this device needs replacement. The facility 

has one standard LennartzTM/Wielandt step table that can be used to calibrate broadband and, 

perhaps, rotational sensors. ASL has two Russian-made shake tables that may be useful as 

isolators but would need substantial refurbishment to be useful as shakers and then would 

probably have too much cross-axis noise for many high-resolution calibration procedures. 

Upgrades for proposed ANSS testing include ASL acquisition of: additional low-noise highresolution recorders (either some of the Q680’sTM being retired from GSN or purpose-bought 

Q330HR’sTM, both high-resolution QuanterraTM recorders); new reference sensors dedicated to 

calibration and testing (STS-2TM and HoneywellTM QA2000-300TM accelerometers). ASL may 

also acquire an environmental test chamber (temperature ± humidity ± pressure), AgilentTM 

precision sampling multimeter (3458ATM) and dynamic signal analyzer (35670TM). A 

combination of a high-precision tilt table and a high-precision strong-motion shake table would 

allow for separation of linear and rotational sensitivities and cross-axis sensitivities of both 

accelerometers and rotational sensors. Additional upgrades may include EMI/RFI/magnetic field 

generation and test equipment, an additional, larger LennartzTM/Wielandt step/tilt table, a new 

low-distortion oscillator, an interferometric rotational reference sensor, a centrifuge, and new, 

GUI-based software for standardized testing following ANSS guidelines and those of the 

Guidelines for Seismometer Testing Workshop (May, 2005, Albuquerque). Finally, it may be 

appropriate to fit the Russian shake tables as isolation tables and possibly as functioning shake 

tables. 

We note that site noise may also be a limiting factor in the measurement of rotations just as it 

can be for linear-motion sensors, but we know little about what ambient-noise levels to expect, 

particularly in urban areas. At quiet sites at least, the best instruments can measure the rotation 

of the Earth, 72 μrad/s (0.004 °/s) as well as the rotational motions associated with large 

teleseisms. The sensitivity required for strong motion is comparable to the rotational velocity of 

the Earth. 

14
Finally, we mention that there has been significant work on the difficult method of measuring 

rotation by comparing adjacent linear sensors on the same pier (e.g., Huang et al., 2003; 

Suryanto et al., 2006). 

15
Discussion and Conclusions — W. U. Savage 

The focus of our general discussion at the Workshop was the immediate future, the near-term 

after the Workshop. The following comments and suggestions were made. 

We agreed to prepare this summary of our deliberations to inform and to include the larger 

community in subsequent discussions and developments; J. R. Evans and W. H. K. Lee took the 

lead. We recommend forming an International Working Group to implement our 

recommendations, to guide future developments, and to help promote theoretical and 

experimental contributions to the subject of rotational ground motion. 

Our consensus for the immediate future is to evaluate existing data and to collect additional 

data with both current instruments and with new rotational sensors at sites, in structures, and at 

near-field free-field sites. 

The impact of rotational data on engineering design and analysis needs to be explored 

further, theoretically and through experiments. Prior to a large-scale deployment of rotational 

sensors, the ultimate societal uses and benefits from expanded measurements should be studied. 

The Working Groups should review the objectives and benefits of making such measurements. 

Additional data are needed to evaluate a wide variety of available sensors and to be certain 

what is being measured. We should take advantage of both US and international testing and 

deployment capabilities as well as sensors already owned by any of us. Manufacturers should be 

invited to participate in development and testing of these systems. 

GPS is efficacious in static displacements, with both fact and promise of higher frequency 

observations. GPS has the advantage of being independent of and complementary to inertial 

systems. We recommend that GPS be incorporated in ANSS guidance material. 

Further evaluation of rotational sensors and rotational measurements can be accelerated by 

bench testing prior to deployment. These laboratory calibrations would help to verify the data 

from existing installations. Similarly, field calibration methods must be developed. 

Simultaneous measurement of acceleration, rotation, and GPS are needed to sort out tilt from 

the passage of seismic waves, to certify total displacements, and to broaden the bandwidth of the 

combined data. GPS is best at long periods while the high-frequency data are also needed and 

will come primarily from inertial sensors —1000-Hz GPS is in development but more testing is 

needed for confident use of high-frequency GPS instrumentation. 

16
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19
Appendix. A Workshop on Measuring the Rotation Effects of Strong 

Ground Motion on 16 February 2006 

Organized by W. H. K. Lee and John R. Evans 

(Speaker’s name is underlined.) 

Workshop Chairs: Woody Savage in Menlo Park and Ken Hudnut in Pasadena 

[Full presentation is allocated 20 minutes for presentation and 5 minutes for discussions] 

1:00 p.m. Welcome by Rufus Catchings, Chief Scientist, Western Earthquake Hazard Team 

1:05 p.m. Theoretical basis for rotational effects in strong motion and some results. V. Graizer 

1:30 p.m. Observational experience with rotational strong motion. R. Nigbor 

1:55 p.m. Significance of rotational motions in structures. E. Safak 

2:00 p.m. Measuring rotation in the free field of Taiwan. W. H. K. Lee, C. C. Liu, and 

C. F. Wu 

2:05 p.m. Plan for instrument testing in the ANSS project. C. R. Hutt and J. R. Evans

2:10 p.m. Discussions for the above three short presentations 

2:15 p.m. Break 

2:30 p.m. Integrating GPS, strong-motion, and rotation. K. Hudnut

2:55 p.m. Measurement of rotations — conditio sine qua non — for comprehensive 

interpretation of strong motion. M. D. Trifunac

3:20 p.m. A Preliminary Report of Two Taiwan Earthquakes Recorded by Both Broadband and 

Rotation Sensors. C. C. Liu, B. S. Huang, and W. H. K. Lee

3:40 p.m. General discussion: Recommendations to the community, and action plan. 

Moderated by R. Nigbor 

20