# Review of the Usefulness of Various Rotational Seismometers with Laboratory Results of Fibre-Optic Ones Tested for Engineering Applications

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## Abstract

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## 1. Introduction

^{−3}m and a tilt of <0.5 × 10

^{−6}rad at La Jolla, California, during the Borrego Mountain earthquake on 9 April 1968 (magnitude 6.5) [29]. Early efforts also included studies of explosions using seismological sensors to directly measure point rotations after nuclear explosions [30], as well as commercial rotational sensors based on microelectro-mechanical systems (MEMS) for identifying significant near-field rotational motions from a one-kiloton explosion [31]. Finally, it should be noted that rotations of and strains in the ground in the responses of structures have been indirectly deduced from accelerometer arrays using methods valid for seismic waves with wavelengths longer than the distances between sensors [32,33,34,35,36,37,38,39].

## 2. Fundamental Requirements for Rotational Seismometers Depending on Area of Interest

_{x}(t), u

_{y}(t) and u

_{z}(t) along the x, y and z axes and three rotations Ω

_{x}, Ω

_{y}and Ω

_{z}about the above axes. Despite the need for experimental evidence described in the previous section, these rotations were not measured for many years, due to a lack of appropriate measurement techniques and the sceptical approach of researchers towards the presence and/or importance of these types of recordings.

^{−7}rad/s at periods of between 10 and 100 s. These four requirements for seismological applications will be referred to as S1 to S4 respectively in the remainder of this paper.

^{−3}rad/s using a high-pass filter 0.2–30 Hz [31]. A vertical-axes peak rotation rate published for a set of data from an earthquake by Takeo [41] was nearly 5 × 10

^{−3}rad/s; however, it is likely that expected amplitudes and frequency ranges are much higher, and may fall into the rad/s range [42]. Recent work on collection of data from ground rotations at the surface measuring station located in the mining area of the Ziemowit coal mine in the Upper Silesian Coal Basin in Poland has identified rotation with magnitudes of up to 2.7 and respective rotation rates of up to 0.5 × 10

^{−3}rad/s; however, rockbursts with magnitudes exceeding 4 are expected in this area within a few more years [43]. For these reasons, the requirements for rotational seismometer in engineering applications should in the authors’ opinion be as follows: (1–3) the same requirements as for seismological applications (S1–S3); (4) a useful instrument needs to be able to measure amplitudes on the order of a few rad/s at a frequency range of between 10

^{−2}and 100 Hz, that is, even higher than that for engineering strong motion seismology [44]. In the remainder of this paper, these four requirements for engineering applications will be referred to as E1 to E4 respectively.

## 3. Rotational Seismometers for Indirect Measurement of Rotation

_{z}in radians per second around the z axis is [7]:

_{1}and v

_{2}are the velocities measured by sensors 1 and 2 along the x axis.

#### 3.1. Rotational Seismometer Using a Pair of Classical Pendulum Seismometers

_{z}= Ω(t), the electromotive force (EMF) f(t) recorded by each SM-3 contains a component of displacement ±u and rotational motion Ω multiplied by the proper length of the pendulum l [46]:

#### 3.2. Rotational Seismometers Using Pairs of Classical Geophones

_{z}(Equation (4)) and two horizontal components of the ground translational velocity [58].

_{i}is a suitable time derivative of the displacement components measured by geophone.

^{−6}rad/s) [57,58,62,63] and anthropogenic sources (blasts with measured rotation in order of 10

^{−3}rad/s) [58,60,63]. Regarding requirements (S1–S4) and (E1–E4), the 6DOFs are close to fulfilling the requirements for seismological applications; however their frequency ranges are still too narrow, and they should be treated as short-period systems.

## 4. Rotational Seismometers for Direct Measurement of Rotation

#### 4.1. Rotational Seismometer Using Mechanical Sensor Technology

#### 4.2. Rotational Seismometers Using Electrochemical Sensor Technology

^{−5}rad/s/(m/s

^{2}) and 2% cross-axis sensitivity are conservative at the maximum value [72] and were twice as high as expected [73]. The same doubt remains about the quality of the calibration, especially in the lower (<1 Hz) frequency range [39], since the frequency response does not have a flat shape, and at frequencies above 1 Hz the dynamic range is 80 dB instead of the claimed value of above 110 dB [72]. For this reason, it has been suggested that better resolution of one order of magnitude for the recording of weak earthquakes is required [40]. Finally, deviations from the nominal value of 27% and 18% in the scale factor values for R-1 and R-2 in a temperature range of 20 °C to 50 °C have been measured [40], giving rise to the suggestion that the liquid-based technology requires further improvement for reliable field measurements.

^{−3}rad/s for the vertical component with a dominant frequency band of about 2.5–5.5 Hz.

#### 4.3. Rotational Seismometers Using Optical Sensor Technology

**Ω**is [76]:

**A**is the vector of the geometrical area enclosed by the wave path, c

_{0}is the velocity of light in a vacuum and

**Ω**is the rotation vector. It can be seen that the Sagnac effect depends on the scalar product of two vectors (

**A**,

**Ω**), showing that the system detects only rotational components with an axis perpendicular to the geometrical area enclosed by the wave path; this axis can be positioned freely according to this area [76]. In general, the distance ∆L generated by the Sagnac effect is extremely small; for instance, the Earth’s rate of rotation (0.26 rad/h) gives a magnitude of ∆L equal to 9.7 × 10

^{−15}m for an area of 10

^{−2}m

^{2}. Hence, ring laser and fibre-optic type systems (Figure 7b,c) are technical implementations of the loop interferometer for appropriate detection of distances of this magnitude or lower.

^{q}along the (q = +) and (q = −) directions within the resonator (lower part of Figure 7b). In the presence of rotation

**Ω**, the frequency difference ∆f is given by:

**n**is the normal vector to the laser beam plane and P is the perimeter enclosed by the beam path. The ring-laser approach using a He-Ne amplifier [79] was the first successful ring-laser gyroscope (RLG) and is now being used in a number of civilian and military navigation systems. The implementation of this type of system for seismological research has been proposed in various systems including the C-II [80] and GEO ring-lasers [81] in Christchurch, New Zealand, and the G-ring laser in Wettzell, Germany [82] (Figure 8). These have two major advantages for applications in seismic studies compared to the other seismometers discussed above, since they measure absolute rotation with respect to the local universe, and they do not depend on accelerated masses. In particular, this last property ensures an extremely wide dynamic range of operation, from a few 10

^{−6}Hz for geophysical signals up to more than 10 Hz, as obtained from regional earthquakes [83]. Since the G-ring laser is at present the system with the best signal-to-noise performance, its parameters are included in Table 3 for comparison with other optical rotational seismometers.

_{0}is the wavelength of the light in a vacuum. In other words, the sensitivity of the Sagnac interferometer in this approach is enhanced not only by increasing the diameter of the physical sensor loop but also by increasing the total length of the used fibre.

^{−8}rad/s @ 1 Hz for an optimised sensor loop radius and optical fibre length. Limited information can be found in the literature on other applications of the commercial FOG as a rotational seismometer. Bernauer et al. [40] described a laboratory investigation of the temperature stability of the LCG-Demonstrator based on LCR-100 AHRS (Northrop Grumman LITEF GmbH, Freiburg im Breisgau, Germany), shown in Figure 9a, with parameters presented in Table 3. Within a temperature range of between 20 °C and 50 °C, these authors observed no scale factor error, whereas the Allan deviation of the seismometer indicated an amplitude-modulated white noise in periods from 0.1 to 500 s. A power consumption of 25 W and the rather low sensitivity of the LCG-Demonstrator restrict this device mainly to rotational engineering applications in the authors’ opinion. Similar conclusions can be drawn from a laboratory investigation and a field test of the μFORS-1 device at a wind generator [88] (Figure 9b with parameters in Table 3). The main reason for this limited application is probably related to the fact that commercial FOGs have integrated electronics which are optimised to measure angle changes but not rotational rates. In order to avoid this problem, new systems with special electronics have been proposed. The first is our autonomous fibre-optic rotational seismograph (AFORS-1), which is characterised in Table 3. This device, shown in Figure 9c, has been used continuously in the Książ Observatory, Poland since 21 July 2010. It records seismic events which are stored on the spot together with data from two sets of TAPS for comparison of their recordings [90,91,98,99] as well as sending this to a FORS-Telemetric Server via GPS (see http://fors.m2s.pl with login and password: AFORSbook). The main advantage of the AFORS-1 [99] is the possibility of using a full system remote control via the internet. However its main disadvantages are a frequency band which is too low, and a maximum detectable rate of a few mrad/s which limits parameters for AFORS application in the seismological area of interest. In view of this, the next rotational seismometer, known as the fibre-optic system for rotational events and phenomena monitoring (FOSREM) (the laboratory investigation of which is summarised in Section 5), has been proposed [100] as a device for seismological and engineering applications.

## 5. FOSREM as a System for Seismological as Well as Engineering Applications

#### 5.1. Construction, Operation and Main Parameters of FOSREM

^{−8}rad/s/Hz

^{1/2}. The electronic unit calculates and records rotational data through the use of open-loop synchronous detection in a digital form using a 32-bit DSP. This involves specific electronic solutions using signal processing to directly determine the component of rotation according to a previously developed approach [102] using the following formula [101]:

_{e}, S

_{o}are the electronic and optical constants of the system, and A

_{1ω}and A

_{2ω}are the first and second amplitudes of the harmonic output signal [u(t)].

^{−8}rad/s/Hz

^{1/2}to a few rad/s) as well as in a wide frequency band from DC to 328.12/n Hz (n = 1, …, 128). Dimensions are 470 mm × 360 mm × 230 mm for FOSREM-SS and 360 mm × 360 mm × 160 mm for FOSREM-BB; the weight is below 10 kg, and power supply is 230VAC + 14.4V/20Ah Li-On battery (12 h for the operational system) for FOSREM-SS and PoE 48V from PCU for FOSREM-BB. These aspects, combined with the remote control of the electronic module possible via the internet [93] mean that the FOSREMs are portable and autonomous devices. Beside these differences in weight, size and power management, the two FOSREMs have additional differences in maximum rotation rate measurement; this was optimised for FOSREM-BB according to its patent application [102].

_{E}= 4.45 × 10

^{−5}rad/s for φ = 52°20′). The obtained accuracies are in the range 3 × 10

^{−8}rad/s to 1.6 × 10

^{−6}for the abovementioned frequency bandpass [101]. Moreover, FOSREMs are stable during cooling and heating processes within a temperature range of 0 °C to 50 °C with temperature sensitivity of the scale factor <0.03%/°C [101].

#### 5.2. Recording Strong Rotational Motion with a New Set-Up Using Earthquake Simulations

## 6. Conclusions

^{−8}to 1.6 × 10

^{−6}rad/s in the abovementioned frequency bandpass, and in practice detects rotation with an amplitude of 0.25 rad/s. It is a remotely controlled sensor which is portable and works autonomously. Additionally, the use of cloud system by FOSREM allows the integration of dozen of sensors in a worldwide network, each transferring data to the central cloud-based system. The data can be viewed and analysed from anywhere in the world via the internet. The authors believe that the further application of FOSREM in the investigation of rotational seismology effects will contribute to the provision of interesting and useful data.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 2.**Principle of operation of a rotational seismometer for indirect measurement; sensors 1 and 2 are velocity seismometers.

**Figure 3.**The TAPS rotational seismometer: (

**a**) scheme [50]; (

**b**) general view. φ(t) is the angle of rotation for a given pendulum.

**Figure 5.**The Horizon™ MEMS angular rate sensor: (

**a**) general view of the HZ1-100-100; (

**b**) scheme of operation.

**Figure 7.**The Sagnac effect in a circular ring interferometer rotating with respect to an inertial frame of reference: (

**a**) interferometric systems for its detection; (

**b**) active method in the ring-laser approach; (

**c**) passive method in a fibre-optic interferometer approach. Notation: L

_{cw}, L

_{ccw}—distances in clockwise and counterclockwise directions; I

_{IN}, I

_{UOT}—intensities of input and output beams respectively [77].

**Figure 8.**The ring laser rotational seismometer [84]: (

**a**) C-II, horizontally installed; (

**b**) G, horizontally installed; (

**c**) GEO, vertically installed.

**Figure 10.**FOSREM: (

**a**) general scheme of the system; (

**b**) view of FOSREM-SS; (

**c**) view of FOSREM-BB; (

**d**) multi-sensor synchronous measuring system based on FOSREM-BB.

**Figure 11.**Modified shaking table: (

**a**) scheme (top image) and trigonometric dependence for Equation (9) (bottom image: H = 0.5 m, L = 3.7 m); (

**b**) general view of shaking table with mounted FOSREMs and HZ1-100-100.

**Figure 12.**Data obtained by various devices for (

**a**) sine excitation; (

**b**) sweep sine from 0.25 Hz to 10 Hz; (

**c**) El Centro earthquake; (

**d**) Loma Prieta earthquake.

**Figure 13.**Spectrum characteristics for sweep sine excitation: (

**a**) rotation from accelerometer PCB 333B52; (

**b**) FOSREM-SS; (

**c**) FOSREM-BB; (

**d**) HZ1-100-100.

**Table 1.**Overview of rotational seismometers using indirect measurement (only the most important parameters are listed).

Parameter | Unit | TAPS [55] | Rotaphone | ||
---|---|---|---|---|---|

3DOF [62] | 6DOF [62] | D [61] | |||

Frequency range | Hz | 7 × 10^{−1}–50 ^{(1),(2)} | 1–100 ^{(2)} | 2–60 ^{(2)} | 2–80 ^{(2)} |

Sampling frequency | Hz | 100 | 250 | 250 | 250 |

Sensitivity ^{(3)} | rad/s | 1 × 10^{−7} | 1.67 ×10^{−8} | 2.16 × 10^{−9} | 3.77 × 10^{−9} |

Maximum rate | rad/s | 1 × 10^{−1} | 1 × 10^{−2} | 2.87 × 10^{−1} | 3.17 × 10^{−2} |

Dynamic range | dB | 120 | 100 | 120 | 120 |

Paired sensor spacing | m | 0.28 | 0.30 | 0.30 | 0.40 |

Operating temperature | °C | −10–45 | −20–40 | −20–40 | −40–100 ^{(4)} |

Weight | kg | 15 | 4.5 | 9.5 | 15.3 |

Dimensions [L × W × H] | mm | 450 × 180 × 350 | 250 ^{(5)} × 10 | 350 × 350 × 430 | 445 ^{(5)} × 112 |

Sensors: [pcs × type] | 2 × SM-3 | 8 × LF-24 | 12 × SM-6 | 16 × SM-6 | |

Natural frequency | Hz | 4.5 | 1 | 4.5 | 4.5 |

A/D converter: | type | Sigma-Delta | 2 × AD16021 | 4 × Tedia | 1 × EE & S |

dynamic | Bit | 26 | 21 | 28 | 24 |

range | V | ±10 | ±5 | ±2.5 | ±1 or ±2.5 |

GPS receiver and antenna | Stationary system | Garmin GPS 18 (mobile) | |||

Software: | type | Own | Own | Own | Own |

output format | miniSEED | RotaCal | RotaCal | RotaCal |

^{(1)}Modified according to recorder MK-6 by IG PAS;

^{(2)}The instrument generally operates in a high-frequency range (above the natural frequency of the sensors used);

^{(3)}Understood as an expression for the smallest signal that can be resolved ([7], p. 79);

^{(4)}Data for geophone SM-6;

^{(5)}Disc diameter.

**Table 2.**Overview of rotational seismometers using direct measurement (only the most important parameters are listed).

Parameter | Unit | HZ1-200-100 [67] | R-1 [68] | R-2 [69] |
---|---|---|---|---|

Axial | uniaxial | triaxial | triaxial | |

Sensitivity ^{(1)} | rad/s/√Hz | 4.4 × 10^{−4} | 1.2 × 10^{−7} | 0.6 × 10^{−7} |

Clip level ^{(2)} | rad/s | 3.49 | 0.10 | 0.40 |

Dynamic range | dB | 78 | 110 | 117 |

Frequency band | Hz | >60 | 0.05–20 | 0.03–50 |

optional extended | n/a | 0.03–50 | 0.01–100 | |

Scale factor ^{(3)} | V/rad/s | 0.57(±2%) | 50 | 50 |

optional | n/a | 2 × 10^{2} | 5–2 × 10^{2} | |

Operating temperature | °C | −40 to +71 | −15 to +55 (extended −45 to +55) | |

Output signal | V | +0.5 to +4.5 | ±5, ±2.5 | ±20 differential |

Calibration (S.F. deviation from 20/22 °C) | %/°C | <0.08 | <0.03 | Internal calibration electronics |

Shock survival | g | 200 | 200 | 200 |

Power supply | VDC | 8–12 | 9–14 | 9–18 |

Supply current | mA | <20 | 20 | 30 |

Power consumption | W | 0.24 | 0.28 | 0.54 |

Weight | kg | <0.06 | 1.0 | 1.5 |

Dimensions [L × W × H] | mm | 58.3 × 25.3 × 25.3 | 120 × 120 × 90 | 120 × 120 × 100 |

NEMA rating | 4 | 4 | Waterproof (submersible) | |

Software | type | Own | Own | Own |

**Table 3.**Overview of optical rotational seismometers with RLG and FOG configurations (only the most important parameters have been listed).

Parameter | Unit | G-Ring [85] | μFORS-1 [88,89] | LCG ^{(1)} [40] | AFORS-1 [90,91] | BlueSeis-3A [92,93] |
---|---|---|---|---|---|---|

Axial | uniaxial | uniaxial | triaxial | uniaxial | triaxial | |

Sensitivity ^{(2)} | rad/s/√Hz | 9 × 10^{−11} | 3 × 10^{−5} | 6.3 × 10^{−7} | 4 × 10^{−9} | 2 × 10^{−8} |

Maximum Rate | rad/s | 1 | 17.5 | No data | 6.4 × 10^{−3} | 0.1 |

Dyn. Range | dB | 280 | 115 | No data | 124 | 135 |

Freq. Band | Hz | 0.003–10 | No data | DC–100 | 0.83–106.15 | DC–100 |

S. F. Error ^{(3)} | %/°C | Not observed | ≤0.05(1σ) | Not observed | No data | <0.01 |

Oper. Temp. | °C | Constant | −40 to 77 | No data | −10 to 50 | −10 to 50 |

Calibration | Needs | No data | Not needed | Remote | Not needed | |

Shock Survival | g | No data | 250 | 10 | No data | No data |

Power Supply | VDC | high | ±5, 3.3 | 24 | 12 | 24 |

Power Cons. | W | high | 2.5 | 25 | <24 | <20 |

Weight | kg | No data | 0.137 | 2.7 | 18 | 20 |

Dimensions [L × W × H] | mm | Area equal to 16 m^{2} | 22 × 73 × 58 | 278 × 102 × 128 | 700 diameter × 160 | 300 × 300 × 280 |

Ingress Protection | none | hermetically sealed | none | IP66 | ||

Sampling rate | Hz | 4 | 5 to 1000 | 200 | 212 | up to 200 |

Output format | No data | TIL/CMOS | miniSEED | miniSEED | miniSEED | |

Software | type | No data | No data | UDP Ethernet protocol | Web-based interface for configuration |

^{(1)}LCG-Demonstrator based on the LCR-1000 gyrocompass AHRS;

^{(2)}For unambiguous comparison with data in Table 1, this is output noise for SNR = 1 defined also as resolution @ 1 Hz in [rad/s];

^{(3)}Defined also as the temperature sensitivity of scale factor.

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Jaroszewicz, L.R.; Kurzych, A.; Krajewski, Z.; Marć, P.; Kowalski, J.K.; Bobra, P.; Zembaty, Z.; Sakowicz, B.; Jankowski, R.
Review of the Usefulness of Various Rotational Seismometers with Laboratory Results of Fibre-Optic Ones Tested for Engineering Applications. *Sensors* **2016**, *16*, 2161.
https://doi.org/10.3390/s16122161

**AMA Style**

Jaroszewicz LR, Kurzych A, Krajewski Z, Marć P, Kowalski JK, Bobra P, Zembaty Z, Sakowicz B, Jankowski R.
Review of the Usefulness of Various Rotational Seismometers with Laboratory Results of Fibre-Optic Ones Tested for Engineering Applications. *Sensors*. 2016; 16(12):2161.
https://doi.org/10.3390/s16122161

**Chicago/Turabian Style**

Jaroszewicz, Leszek R., Anna Kurzych, Zbigniew Krajewski, Paweł Marć, Jerzy K. Kowalski, Piotr Bobra, Zbigniew Zembaty, Bartosz Sakowicz, and Robert Jankowski.
2016. "Review of the Usefulness of Various Rotational Seismometers with Laboratory Results of Fibre-Optic Ones Tested for Engineering Applications" *Sensors* 16, no. 12: 2161.
https://doi.org/10.3390/s16122161