Evaluation of Systematic Errors in the Compact Absolute Gravimeter TAG-1 for Network Monitoring of Volcanic Activities

Volcanic activities sometimes involve gravity changes, and this research is intended to establish an observation network surrounding an active volcano using compact absolute gravimeters. To simplify the configuration of absolute gravimeters, they are preferably operated with a light source distributed from a telecom band (wavelength of 1.5 μm) laser through optical fibers. To evaluate the accuracy of the absolute gravimeter with the telecom band laser, we conducted observations using a prototype gravimeter (TAG-1) with frequency-stabilized lasers at both 1.5 μm and 633 nm, and compared these results with the expected gravity at the site. Initially, both results showed offsets −187 μGal and −9.6 μGal for the 1.5-μm laser and the 633-nm laser, respectively (1 Gal = 10−8 m/s2). By correcting the systematic errors of the photo detectors measured by the synthetic chirp signal, the obtained absolute gravity was consistent with the expected value for both wavelengths; offsets from the expected gravity were reduced to 6.6 μGal and 5.4 μGal for 1.5 μm and 633 nm, respectively. We also evaluated the errors associated with long-distance transmission of the 1.5-μm laser using a reeled optical fiber (26 km) and an optical amplifier and found no degradation in the gravity data from the case of short transmission (10 m). These results allow networking of compact absolute gravimeters connected by telecom optical fibers that are operated using a common laser and expansion to volcanic areas to monitor the gravity change associated with volcanic activities.

of magma that is monitored for the prediction of volcanic eruptions and to evaluate the transition of volcanic activities. Both types of gravimeters, relative gravimeters and absolute gravimeters, have been used, and the latter can measure longterm gravity changes without any instrumental drift with reference to an accurate wavelength of the frequency-stabilized laser. However, owing to the complex mechanism, large size, and high cost, absolute gravimeters have not commonly been used for volcanic observations. This research is intended to establish a network of compact absolute gravimeters for volcanic observations.
To construct this observation network, absolute gravimeters are preferably operated with telecom band (wavelength of 1.5 m) lasers distributed to each gravimeter via optical fibers because conventional lasers (wavelength of 633 nm) cannot be transmitted to distant sites because of the loss of optical fibers; which is typically 15-30 dB/km for 633nm light, and 0.2-1 dB/km for 1.5-m light. To evaluate the accuracy of the absolute gravimeter with a telecom band laser, we conducted observations using a prototype gravimeter (TAG-1) with frequency-stabilized lasers at both 1.5-m and 633-nm wavelengths, and compared these results with the expected gravity of the site.

Gravity Change Associated with Volcanic Activities
Sakurajima is one of the most active volcanos in Japan. A devastating eruption occurred in 1914, and small eruptions still continue. It has been determined that the amount of magma in the magma chamber beneath the mountain is coming to that of 1914. Okubo et al. (2013) observed gravity changes associated with the volcanic eruption of Sakurajima using an absolute gravimeter. The gravity change was 10 Gal (1 Gal D 10 8 m/s 2 ) at a distance of 2 km from the crater; this is only one factor larger than the background noise level due to local disturbances such as groundwater ). Therefore, observations near the crater and networking with a number of gravimeters surrounding the crater will significantly enhance the detectability of magma motion near the source by averaging the local disturbances using a number of sensors. Araya et al. (2014) developed a compact absolute gravimeter, TAG-1, and we used it for the evaluation of the availability of network monitoring of volcanic activities. To evaluate the accuracy of the absolute gravity with the telecom band laser, we conducted observations using TAG-1 with frequencystabilized lasers at wavelengths of 1.5 m and 633 nm, and compared these results with the expected gravity of the site. Figure 1 shows a picture and a schematic diagram of the TAG-1 gravimeter. It is comprised of a dropper for the free-fall mass and a built-in accelerometer for correction of seismic vibrations. By applying the built-in accelerometer and the small dropper, TAG-1 is compact and transportable for observations. The laser light is introduced into the optical unit through the optical fiber and is incident to vacuum chambers confining the free-fall mass (Free-fall mirror) dropper and a ref-erence pendulum (Reference mirror), both of which include retro reflective mirrors forming an interferometer. The interfered light is guided to photo detectors (PDs) through optical fibers. TAG-1 uses a quadrature interferometer for the displacement measurement of the free-fall mass, and the optical phase is calculated from the detected signals (Heydemann 1981;Svitlov and Araya 2014). From the quadratic dependence of the displacement with respect to time, the absolute gravity can be obtained. Effects of ground vibration acceleration on the gravity are corrected using data from the build-in accelerometer using the reference pendulum.

TAG-1 Gravimeter
TAG-1 can be operated at both wavelengths of 1.5 m and 633 nm by using the PDs and the optical unit designed for each wavelength. InGaAs-type and Si-type PDs are used for the wavelengths of 1.5 m and 633 nm, respectively. Beam verticality can be adjusted so that the measuring laser beam and beam of the auto-collimator reflected on a reference alcohol surface are in parallel. For the vertical adjustment at the invisible 1.5-m wavelength, the measuring laser beam is monitored using an IR (infrared) viewer.

Observation Using a Conventional 633-nm Laser and a Telecom Band (1.5 m) Laser
We performed gravity measurements in a basement room of the main building of the Research Institute of Electrical Communication (RIEC), Tohoku University, using TAG-1 operated with both a conventional iodine-stabilized 633-nm He-Ne laser (wavelength of oe 6 D 632.99081163 nm), and a telecom band (1.5 m) laser (oe 15 D 1,538.803242 nm, Fig.  2) which was frequency-stabilized using the acetylene linear absorption spectrum with a linewidth of 500 MHz (Kasai et al. 2016) and whose frequency accuracy is estimated to be 10 9 (Nakagawa and Onae 2004); the latter may realize the long-distance distribution of the light source and networking of gravimeters. The systematic errors in operation for both wavelengths were evaluated. The free-fall mirror was dropped every 2 min. The obtained data were corrected for seismic noise measured by the build-in accelerometer. Figure 3 shows the measured gravity using the conventional 633-nm laser and the 1.5-m frequency-stabilized laser. The theoretical gravity variation is shown by the red line based on calculated tidal gravity and the absolute gravity measured by the relative measurement from a gravity reference point, as described in the following  section. Slow tidal gravity variations were commonly observed for both cases, while offsets were apparent. The offsets averaged in the periods were 187 Gal for the 1.5-m laser and 9.6 Gal for the 633-nm laser. This may be due to the PDs because mechanical and optical configurations are essentially the same for both cases, and the laser wavelengths are well defined. We evaluated the systematic error of TAG-1 caused by the frequency response of the PDs.

Systematic Error Evaluation of the PDs
Because the frequency of the fringe signal is almost proportional to the velocity of the free-fall mass, the response of the PD causes a systematic error in the gravity measurement (Niebauer et al. 1995). To evaluate the error directly, synthetically modulated laser light that simulates the interferometer fringe was applied to the PD, and the difference in obtained gravity values from the measurement and from calculations could be regarded as estimates of the systematic error. The free-fall mass in gravity, g, generates a chirp interferometer signal with a frequency rate of df /dt D 2 g/oe, where oe is the wavelength of the laser. Therefore, chirp frequency rates of 13.07 MHz/s and 30.96 MHz/s produce g D 9.8 m/s 2 for oe D 1.5 m, and 633 nm, respectively. The laser intensity was modulated using an electro-optic amplitude modulator for the 1.5-m evaluation, while a laser diode was used for the 633 nm light source. In each case, the chirp signal was applied using a function generator whose clock and data sampling clock were both locked to the same Rb time base. In the data processing of TAG-1, the measured displacement of the free-fall mirror from t 0 (time from the release) to t 0 C t was fitted using a quadratic function of time, and the gravity acceleration, g(t 0 ), was obtained from the quadratic coefficient. For small t 0 , just after a short time from release, g(t 0 ) showed disagreement with the theoretical dependence on t 0 because the release of the free-fall mirror induced a slight recoil vibration; although the total free-fall time was approximately 180 ms, the analysis interval was fixed at t D 80 ms, and g(t 0 ) was calculated with changing t 0 to assess the effect of the recoil vibration. The same calculation was applied to the detection of the synthetic chirp signal and the systematic errors of the PDs were estimated by the difference in g(t 0 ) from the calculated gravity (g 15 or g 6 ) obtained from the frequency rate of the chirp signal. Figure  4 shows the observed g(t 0 ) (blue and light blue dots, left axis) and the estimated error of the PDs obtained from the synthetic chirp signal (green dots, right axis). The observed data for t 0 > 60 ms agreed with the error estimation of the PDs. The estimation shows small systematic errors for whole t 0 , and smaller t 0 gives smaller gravity acceleration; the decrease of observed gravity at 1.5 m in Fig. 3, calculated with t 0 D 10 ms and t D 150 ms, is consistent with this estimates of errors of the PDs. The observed data, calculated with t 0 > 60 ms and t D 80 ms, were corrected using the estimated errors, as shown in Fig. 5. Theoretical tides were removed from the data and then averaged. In contrast to Fig. 3, observed data with the 633-nm laser and 1.5-m laser agreed well after the correction; moreover, they were consistent with the expected level (red dashed line) based on the relative measurements using a LaCoste gravimeter referenced to the Aobayama gravity reference point (AOB-B) where the absolute gravity has been determined. The AOB-B is located 2.3 km westward from RIEC (Fig. 6). The mean offsets shown in Fig.  5 were 6.6 Gal for the 1.5-m laser and 5.4 Gal for the 633-nm laser, which were compared with 187 Gal and 9.6 Gal, respectively, without the correction in Fig.  3.
We also evaluated the errors associated with long-distance transmission of the 1.5-m laser through the optical fiber. The laser light at 1.5 m was introduced through short (10 m) or long (26 km) optical fibers. In this experiment, we used a reeled optical fiber in the laboratory. As shown in Fig. 7, the measured absolute gravity did not change and showed no degradation even when the laser was provided through a 26-km-long optical fiber and an optical amplifier. Nevertheless, to estimate errors in a practical system in the field, environmental effects on the optical fibers, such as vibration and thermal disturbances, need to be measured.

Conclusions
The compact absolute gravimeter, TAG-1, was successfully operated with both 633-nm and 1.5-m lasers. By correcting systematic errors of the PDs measured using a synthetic chirp signal, the obtained absolute gravity was consistent with the expected value for both wavelengths; the systematic error of 1.5-m PDs was estimated to be as much as 190 Gal without the correction. These results can lead to networking of compact absolute gravimeters connected via telecom optical fibers operated using a common laser and can be expanded to volcanic areas to monitor the gravity change associated with volcanic activities.