**1. Introduction**

22 Will-be-set-by-IN-TECH

334 Earthquake Research and Analysis – Statistical Studies, Observations and Planning

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> The possibility of a direct monitoring of rotational events has an important role in the seismological sciences as well as in the applied physics regarding large engineering structures.

> According to the first aspect, a possibility of existence of the rotational phenomena in the seismic field has been discussed from the beginning of the earthquakes investigations. The interest in these phenomena has been stimulated by strange, rotary and even screw-like deformations that occur after earthquakes, often appearing on parts of tombs and monuments (Ferrari, 2006; Kozák 2006). The classical textbooks on seismology deny the possibility that the rotational phenomena, especially in form of seismic rotational waves – SRW, could pass through a rock, so the earthquake rotational phenomena were explained by an interaction of standard seismic waves with a compound structure of objects they penetrate, which, in fact, might be the case (Teisseyre & Kozak, 2003). Nevertheless, it was theoretically proved that even the SRW could propagate through grained rocks; later on, this possibility was extended on rocks with microstructure or defects (Eringen, 1999; Teisseyre & Boratyński, 2002) or even without any internal structure (Teisseyre, 2005; Teisseyre et al., 2005; Teisseyre & Górski, 2009), due to the asymmetric stresses in the medium. It should be noticed that the SRW were for the first time effectively recorded in Poland in 1976 (Droste & Teisseyre, 1976). From this time, waves of this type have been studied in a few centers over the world. Taking into consideration large engineering structures, the rotational events monitoring is connected to the torsional effects in structures as well as to the interstory drift. Since the application of new materials and technologies for building constructions, they have irregular structures in-plane which causes difficulties in designing of the horizontal rotations of these structures especially during earthquakes (Schreiber et al., 2009). Recently in the above areas, the first monographs have been published (Teisseyre et al., 2006, 2008; Lee et al., 2009), covering the theoretical aspects of the rotation motion generation and propagation, as well as the examples of the field experiments.

> A further experimental verification of the existing rotational phenomena in seismic events needs a new approach to the construction of the measuring devices, because the

Fibre-Optic Sagnac Interferometer as Seismograph for Direct Monitoring of Rotational Events 337

Sagnac (1913) first demonstared the feasibility of an optical experiment capable of indicating the state of rotation of the frame of reference in which his interferometer was at rest. The basic principle of Sagnac's interferometer is given in Fig. 1a. The input light beam is split by a beam spliter into a beam circulating in the loop in a clockwise - cw direction and a beam circulating in the same loop in a counterclockwise - ccw direction. The two beams are reunited at a beam splier so that interference fringes are observed in the output light. When the whole interferometer with a light source and the fringe detector is set in rotation with an

in which **A** is the area enclosed by the light path. The vacuum wavelength is and the free-

cosine of angle between the axis of rotation and the normal to the optical circuit. Sagnac also established that the effect does not depend on the shape of the loop or the center of rotation.

Fig. 1. Schematic of Sagnac's interferometer (a) and its implementation in fibre optic

It should be noticed that a German graduate student, Harress (1912), performed a very similar experiment for a thesis project a few years before Sagnac did his experiment. Harress used an optical circuit which consisted of a ring of total reflecting prism, but his objective was quite different from Sagnac's. According to Sagnac's data (Sagnac, 1914), for the wavelength of indigo mercury light and a loop area *A*=866 cm2, a fringe shift of 0.07 fringes was clearly detectable for the rate of rotation of 2 rps. However, according to the other data (Post, 1967) the fringe shift detectability at that time was probably of an order of 0.01 of a fringe, so precision of the Sagnac's experiment therefore may have been close

A Sagnac experiment of great precision was subsequently performed by Pogany (1926).

demonstrating the rotation of the Earth by means of the Sagnac effect, also. To obtain the required sensitivity they had to choose an unusually large size (rectangular 0.4 x 0.2 mile) for the surface area enclosed by the beam. Summarizing, the experiments of Sagnac, Pogany, and Michelson-Gale and the results of Harress, as reinterpreted by Harzer (1914), the following features of the Sagnac effect according to the fringe shift can be given (Post, 1967):

=157.43 rad/s, and

*Z* with respect to the fringe position for stationary

*Z* =  **•A**/0c, (1)

0=546 nm, he reproduced within 2% the

=0.906. Michelson and Gale (1925) succeeded in

*Z* is proportional to the

 

space velocity of light is *c.* The scalar product  **•A** denotes that

**2. Sagnac effect and its application as FOG** 

interferometer is observed, which is given by the formula:

angular rate of rad/s, a fringe shift

technique (b)

to marginal.

With a loop area *A=*1178 cm2,

theoretically expected fringe shift

conventional seismometers are inertial sensors detecting only linear velocities. Similarly, the measurements of torsional response and interstory drift are reasonably easy on small scale models in a laboratory (Kao, 1998) but are much more difficult in real structures. The first of them can be measured by using a pair of accelerometers and then dividing differences in the horizontal accelerations by the distance between them in a direction perpendicular to the measured motion. Then this has to be integrated twice with respect to the time needed to give the torsional rotations (Schreiber et al., 2009). However, the inherent sensor drift and the small offset from zero in the absence of an input signals are the important limitations of this technique. According to the measurement of interstory drifts, it is, in principle, possible to arrange a frame from the floor below to near the ceiling above to set up the displacement transducers to measure the difference in displacements (McGinnis, 2004). However, again far from the hardware complexity of this approach, it is also vulnerable to building deformations.

For the above reason, the new instrumentations are important, especially those designed for an investigation of very small rotations. The near–field studies for the understanding of the mechanics of earthquakes is extensively reviewed by Kamamori (1994) and can be summarized as requirement for instruments with frequency range below 100 Hz and resolution in range of 10-6-10-9 rad/s/Hz1/2 for the SRW. Whereas the engineering strongmotion seismology needs devices operating in a frequency range of 0.05 – 100 Hz with resolution 10-1 – 10-6 rad/s/Hz1/2 (Cowsik et al., 2009).

Since the Sagnac effect (Sagnac, 1913) measures the rotation directly, an application of the sensor based on this effect seems to be ideal for the construction of the rotational seismometer - RS. Its greatest strength is the fact that it does measure absolute rotations or oscillations, so that it does not require any external reference frame for its measurement. This means that it measures true rotations even during an earthquake, where nothing remains static. Since it is an entirely optical device, it does not have the problems that characterize inertial mass transducers, also. We distinguish two systems based on the Sagnac interferometer: a ring laser rotational seismometer - RLRS (Schreiber et al., 2001), and a fibre-optic rotational seismometer - FORS (Takeo et al., 2002; Franco-Anaya et al., 2008; Schreiber et al., 2009). The first of them is a stationary system constructed for investigation disturbances in the Earth rotation, whereas the second one based on the application commercially available fibre-optic gyroscope - FOG.

Even though 40-ty years of the FOG investigation gives very precise systems useful for different areas including inertial navigation, their constructions are optimized for the detection of angular changes rather than rotation speed, then may generate the same difficulties during the investigation rotational phenomena. For the above reason in this chapter we conclude ours experiments connected to another approach to the rotation phenomena investigation (Jaroszewicz et al., 2003). We started the second part with a short description of the Sagnac effect with the same historical review of its application as FOG. In part 3, which is the main part of this chapter, we described the Autonomous Fibre-Optic Rotational Seismograph – AFORS, with its optical part based on the FOG construction, whereas the special autonomous signal processing unit – ASPU optimizes its operation for the measurement of rotation speed instead of angular changes. Finally, in part 4 we presented the same results obtained during the application of these systems for the rotational events investigation as well as a monitoring of building torsional moves.

### **2. Sagnac effect and its application as FOG**

336 Earthquake Research and Analysis – Statistical Studies, Observations and Planning

conventional seismometers are inertial sensors detecting only linear velocities. Similarly, the measurements of torsional response and interstory drift are reasonably easy on small scale models in a laboratory (Kao, 1998) but are much more difficult in real structures. The first of them can be measured by using a pair of accelerometers and then dividing differences in the horizontal accelerations by the distance between them in a direction perpendicular to the measured motion. Then this has to be integrated twice with respect to the time needed to give the torsional rotations (Schreiber et al., 2009). However, the inherent sensor drift and the small offset from zero in the absence of an input signals are the important limitations of this technique. According to the measurement of interstory drifts, it is, in principle, possible to arrange a frame from the floor below to near the ceiling above to set up the displacement transducers to measure the difference in displacements (McGinnis, 2004). However, again far from the hardware complexity of this approach, it is also vulnerable to building

For the above reason, the new instrumentations are important, especially those designed for an investigation of very small rotations. The near–field studies for the understanding of the mechanics of earthquakes is extensively reviewed by Kamamori (1994) and can be summarized as requirement for instruments with frequency range below 100 Hz and resolution in range of 10-6-10-9 rad/s/Hz1/2 for the SRW. Whereas the engineering strongmotion seismology needs devices operating in a frequency range of 0.05 – 100 Hz with

Since the Sagnac effect (Sagnac, 1913) measures the rotation directly, an application of the sensor based on this effect seems to be ideal for the construction of the rotational seismometer - RS. Its greatest strength is the fact that it does measure absolute rotations or oscillations, so that it does not require any external reference frame for its measurement. This means that it measures true rotations even during an earthquake, where nothing remains static. Since it is an entirely optical device, it does not have the problems that characterize inertial mass transducers, also. We distinguish two systems based on the Sagnac interferometer: a ring laser rotational seismometer - RLRS (Schreiber et al., 2001), and a fibre-optic rotational seismometer - FORS (Takeo et al., 2002; Franco-Anaya et al., 2008; Schreiber et al., 2009). The first of them is a stationary system constructed for investigation disturbances in the Earth rotation, whereas the second one based on the

Even though 40-ty years of the FOG investigation gives very precise systems useful for different areas including inertial navigation, their constructions are optimized for the detection of angular changes rather than rotation speed, then may generate the same difficulties during the investigation rotational phenomena. For the above reason in this chapter we conclude ours experiments connected to another approach to the rotation phenomena investigation (Jaroszewicz et al., 2003). We started the second part with a short description of the Sagnac effect with the same historical review of its application as FOG. In part 3, which is the main part of this chapter, we described the Autonomous Fibre-Optic Rotational Seismograph – AFORS, with its optical part based on the FOG construction, whereas the special autonomous signal processing unit – ASPU optimizes its operation for the measurement of rotation speed instead of angular changes. Finally, in part 4 we presented the same results obtained during the application of these systems for the

rotational events investigation as well as a monitoring of building torsional moves.

resolution 10-1 – 10-6 rad/s/Hz1/2 (Cowsik et al., 2009).

application commercially available fibre-optic gyroscope - FOG.

deformations.

Sagnac (1913) first demonstared the feasibility of an optical experiment capable of indicating the state of rotation of the frame of reference in which his interferometer was at rest. The basic principle of Sagnac's interferometer is given in Fig. 1a. The input light beam is split by a beam spliter into a beam circulating in the loop in a clockwise - cw direction and a beam circulating in the same loop in a counterclockwise - ccw direction. The two beams are reunited at a beam splier so that interference fringes are observed in the output light. When the whole interferometer with a light source and the fringe detector is set in rotation with an angular rate of rad/s, a fringe shift *Z* with respect to the fringe position for stationary interferometer is observed, which is given by the formula:

$$
\Delta \mathbf{Z} = \mathbf{Q} \bullet \mathbf{A} / \lambda\_0 \mathbf{c}, \tag{1}
$$

in which **A** is the area enclosed by the light path. The vacuum wavelength is and the freespace velocity of light is *c.* The scalar product  **•A** denotes that *Z* is proportional to the cosine of angle between the axis of rotation and the normal to the optical circuit. Sagnac also established that the effect does not depend on the shape of the loop or the center of rotation.

Fig. 1. Schematic of Sagnac's interferometer (a) and its implementation in fibre optic technique (b)

It should be noticed that a German graduate student, Harress (1912), performed a very similar experiment for a thesis project a few years before Sagnac did his experiment. Harress used an optical circuit which consisted of a ring of total reflecting prism, but his objective was quite different from Sagnac's. According to Sagnac's data (Sagnac, 1914), for the wavelength of indigo mercury light and a loop area *A*=866 cm2, a fringe shift of 0.07 fringes was clearly detectable for the rate of rotation of 2 rps. However, according to the other data (Post, 1967) the fringe shift detectability at that time was probably of an order of 0.01 of a fringe, so precision of the Sagnac's experiment therefore may have been close to marginal.

A Sagnac experiment of great precision was subsequently performed by Pogany (1926). With a loop area *A=*1178 cm2, =157.43 rad/s, and 0=546 nm, he reproduced within 2% the theoretically expected fringe shift =0.906. Michelson and Gale (1925) succeeded in demonstrating the rotation of the Earth by means of the Sagnac effect, also. To obtain the required sensitivity they had to choose an unusually large size (rectangular 0.4 x 0.2 mile) for the surface area enclosed by the beam. Summarizing, the experiments of Sagnac, Pogany, and Michelson-Gale and the results of Harress, as reinterpreted by Harzer (1914), the following features of the Sagnac effect according to the fringe shift can be given (Post, 1967):


The fibre-optic version of the Sagnac interferometer uses a long length optical fibre *L* coiled in a loop of diameter *D,* as it is shown in Fig. 1b (Vali & Shorthil, 1976). In this approach, instead of the fringe shift *Z*, a phase shift is produced between cw and ccw propagating light, given by

$$
\Delta\phi = \frac{2\pi LD}{\lambda\_0 c\_0} \Omega \tag{2}
$$

Fibre-Optic Sagnac Interferometer as Seismograph for Direct Monitoring of Rotational Events 339

signal, which yields an odd response. The FOG uses a reciprocal phase modulator - PM at the end of the coil, which yields, because of the propagation delay, as a modulation of the phase difference without any residual zero offset (Martin & Winkler, 1978). This was a very important step in the progress of performance, but it was not enough for an ultimate performance which is obtained only if the unbiased response is perfectly even and the biasing modulation has only odd frequencies. For the above reason, the PM being actually a delay line filter, the operation at the so-called proper or eigen frequency (Bergh et al., 1981) - the delay through the coil is half the period of modulation, suppresses the residual even harmonics which are always present because of spurious nonlinearities of the modulation chain. Today the FOG system using also a broadband source has the intensity statistics that happens to cancel the Kerr effect induced phase difference in a Sagnac interferometer (Ezekiel et al., 1982). Such a broadband source is also needed, as it is well-known today, to remove coherence related noise and drift due to backscattering and backreflection as well as lack of rejection of the polarizer (Fredricks & Ulrich, 1984; Lefèvre et al., 1985a; Burns, 1986). Finally, for achieved the high scale factor linearization, FOG utilizes a digital phase step feedback (Lefèvre et al., 1985b) using the same reciprocal PM as the biasing modulation and an all-digital processing scheme where the gyro modulated signal is sampled with an AD convertor and the

demodulation performed by digital subtraction (Auch, 1986; Arditty et al., 1989).

managing as well as device remote control.

part of Fig. 3a.

**3. Autonomous Fibre-Optic Rotational Seismograph** 

Since all-digital processing scheme implemented in the current FOG system is optimized for the presentation of angular changes rather than rotation rate, the same problems exist for its optimized application for measurement of the last phenomena which are interesting for the rotational seismology. For the above reason in the next part of this chapter we have described our experiments in development of the fibre-optic rotational seismograph system. Its construction is based on experiences according to the FOG development described above, but the system is optimized for a direct measurement of the rotation rate only (Jaroszewicz et al., 2003). Such an approach gives a system which through a direct use of the Sagnac effect can limit drift influence on a device operation. Moreover, the special construction of a signal processing unit protects easily its monitoring via Internet including data collecting and

A detailed description of the AFORS system was published previously (Jaroszewicz at al., 2011a, 2011b) hence here we summarized the above data regarding its construction, calibration and management. Now we present two examples of these devices - AFORS-1 located in the Książ (Poland) seismological laboratory for the investigation of the rotational events connected to earthquakes, and AFORS-2 located in Warsaw (Poland) used for initial works connected to the investigation of the irregular engineering construction torsional response and the interstory drift (Jaroszewicz et al., 2011c). Before the end of 2011 the next system AFORS-3 will be available as the replacement to the older version FORS-II mounted

The optical head of the constructed AFORS devices uses a fibre interferometer in a minimum optical gyro configuration (Jaroszewicz et al. 2006a), as it is shown in the upper

The application of the broadband low coherence superluminescent diode – SLD (*EXALOS* - Switzerland with optical power – 20.87 mW, operation wavelength – 1326.9 nm, and spectral radiation band – 31.2 nm,) gives possibility for a minimisation of polarization influence on

in the Ojców (Poland) seismological laboratory (Jaroszewicz & Krajewski, 2008).

where is the rotation component in the axis perpendicular to the fibre-optic loop. In other words, the sensitivity of the Sagnac interferometer in this approach is enhanced not only by increasing the physical sensor loop diameter but also by increasing the totals length of the used fibre. It is easy to see that three such interferometer with loops plane in perpendicular directions give information about a space vector of the rotation rate. This data after an integration in time domain shows the position changes in space – and it is idea of the optical gyroscope.

35-years after the above date its technical application as the FOG is the best recognized interferometric sensor made in the fibre-optic technology. However, because its useful signal is the angular changes, the detected phase shift is integrated in time needed to give it. Moreover, for a desired rotation rate in the range of 10-6 – 10-9 rad/s the Sagnac effect generates a very small phase shift, so needs to be separated from other disturbances and protected so that the Sagnac effect is the unique nonreciprocal effect in the device. For the above reason all FOG uses shown in Fig. 2 the reciprocal configuration (Urlich, 1980) also called the minimum configuration (Arditty & Lefevre, 1981) where a perfect balance between both counter-propagating paths is obtained simply with a truly single-mode (single spatial mode and single polarization) filter at the common input-output port of the interferometer, even if the propagation is not single-mode along the rest of the interferometer.

Fig. 2. The minimum configuration of the FOG

The FOG interferometer using the minimum reciprocal configuration yields a raised cosine response as any interferometer. It is classical to bias such an even response that has a maximum at zero by modulating the abscissa parameter and demodulating the output

d. does not depend on the presence of a commoving refracting medium in the path of the

The fibre-optic version of the Sagnac interferometer uses a long length optical fibre *L* coiled in a loop of diameter *D,* as it is shown in Fig. 1b (Vali & Shorthil, 1976). In this approach,

> 0 0 2 *LD c*

is the rotation component in the axis perpendicular to the fibre-optic loop. In other

words, the sensitivity of the Sagnac interferometer in this approach is enhanced not only by increasing the physical sensor loop diameter but also by increasing the totals length of the used fibre. It is easy to see that three such interferometer with loops plane in perpendicular directions give information about a space vector of the rotation rate. This data after an integration in time domain shows the position changes in space – and it is idea of the optical

35-years after the above date its technical application as the FOG is the best recognized interferometric sensor made in the fibre-optic technology. However, because its useful

it. Moreover, for a desired rotation rate in the range of 10-6 – 10-9 rad/s the Sagnac effect generates a very small phase shift, so needs to be separated from other disturbances and protected so that the Sagnac effect is the unique nonreciprocal effect in the device. For the above reason all FOG uses shown in Fig. 2 the reciprocal configuration (Urlich, 1980) also called the minimum configuration (Arditty & Lefevre, 1981) where a perfect balance between both counter-propagating paths is obtained simply with a truly single-mode (single spatial mode and single polarization) filter at the common input-output port of the interferometer, even if the propagation is not single-mode along the rest of the

The FOG interferometer using the minimum reciprocal configuration yields a raised cosine response as any interferometer. It is classical to bias such an even response that has a maximum at zero by modulating the abscissa parameter and demodulating the output

is produced between cw and ccw propagating

is integrated in time needed to give

(2)

a. obeys formula (1),

instead of the fringe shift

beam.

light, given by

where 

gyroscope.

interferometer.

b. does not depend on the shape of surface area *A*,

signal is the angular changes, the detected phase shift

Fig. 2. The minimum configuration of the FOG

c. does not depend on the location of the center of rotation,

*Z*, a phase shift

signal, which yields an odd response. The FOG uses a reciprocal phase modulator - PM at the end of the coil, which yields, because of the propagation delay, as a modulation of the phase difference without any residual zero offset (Martin & Winkler, 1978). This was a very important step in the progress of performance, but it was not enough for an ultimate performance which is obtained only if the unbiased response is perfectly even and the biasing modulation has only odd frequencies. For the above reason, the PM being actually a delay line filter, the operation at the so-called proper or eigen frequency (Bergh et al., 1981) - the delay through the coil is half the period of modulation, suppresses the residual even harmonics which are always present because of spurious nonlinearities of the modulation chain. Today the FOG system using also a broadband source has the intensity statistics that happens to cancel the Kerr effect induced phase difference in a Sagnac interferometer (Ezekiel et al., 1982). Such a broadband source is also needed, as it is well-known today, to remove coherence related noise and drift due to backscattering and backreflection as well as lack of rejection of the polarizer (Fredricks & Ulrich, 1984; Lefèvre et al., 1985a; Burns, 1986). Finally, for achieved the high scale factor linearization, FOG utilizes a digital phase step feedback (Lefèvre et al., 1985b) using the same reciprocal PM as the biasing modulation and an all-digital processing scheme where the gyro modulated signal is sampled with an AD convertor and the demodulation performed by digital subtraction (Auch, 1986; Arditty et al., 1989).

Since all-digital processing scheme implemented in the current FOG system is optimized for the presentation of angular changes rather than rotation rate, the same problems exist for its optimized application for measurement of the last phenomena which are interesting for the rotational seismology. For the above reason in the next part of this chapter we have described our experiments in development of the fibre-optic rotational seismograph system. Its construction is based on experiences according to the FOG development described above, but the system is optimized for a direct measurement of the rotation rate only (Jaroszewicz et al., 2003). Such an approach gives a system which through a direct use of the Sagnac effect can limit drift influence on a device operation. Moreover, the special construction of a signal processing unit protects easily its monitoring via Internet including data collecting and managing as well as device remote control.
