## 7 Experiment
### Vibration Experiment
#### 7.2.1 The Periodic Vibration  
The FOG-based MWD was mounted on the vibration table with its \(Y\)-axis along the vibration direction. The experiment was carried out according to the following steps: first, the vibration table was kept stationary for 15 min, then the vibration table started to vibrate and kept vibrating for 1 h. The frequency of the vibration was 20 Hz, and the amplitude of the vibration is 5 g. Lastly, the vibration table went back to stationary and was kept for 5 min. The experiment time was 80 min in total, which is close to a Schuler Period [34]. The sampling rate of the FOG-based MWD is 100 Hz. Figure 14 shows the original data of the FOG-based MWD. It is can be seen that the fluctuation amplitude of the data in the vibrations is much larger than that is in the stationary. One reason is that the sensors could sense the vibration motion; the other one is that the error performance of the sensors is different from that in the stationary. Though the vibration direction is aligned \(Y\)-axis, the X axial ACC and \(Z\) axial ACC were also influenced greatly. The reason is that the misalignment error is existing in the FOG-based MWD. In addition, the fluctuation amplitude of X-axial ACC and \(Z\)-axial ACC did not line up with the horizontal axis in terms of vibration. The reason is that the bias error changed during the vibration. Therefore, it is important to recognize the vibration error and compensate for them. Figure 14: The original data of the FOG-based MWD in the vibration experiment. Figure 13: Vibration experimental set-up. The error items recognized in Section 7.1 were compensated. Thus, we can obtain three sets of data. One set is the original data. The second set is the data that only compensated the linear error items. The third one is the data that compensated both the linear and nonlinear error items. Then using the inertial navigation algorithm to calculate the position, velocity and attitude of the FOG-based MWD with the three sets of data. The results are illustrated in Figure 15.  
It can be seen that the latitude error and longitude error calculated by the original data is \(8.65\times 10^{4}\) m and \(6.22\times 10^{4}\) m. With the second set of data, the latitude error and longitude error is reduced to \(5.67\times 10^{4}\) m and \(5.38\times 10^{4}\) m. It shows that the linear error items were compensated, and the error of latitude and longitude was only reduced by \(34.45\%\) and \(13.50\%\), respectively. However, with the third set of data, the error of latitude and longitude was reduced to \(2402\) m and \(4089\) m. Compared to the original data, the ratio of the decreased errors was \(97.22\%\) and \(93.42\%\). The conclusion could be made that compensating the nonlinear error items of the FOG-based MWD can improve the measurement accuracy. The FOG-based MWD was mounted on the vibration table with the attitude of inclination \(0.09^{\circ}\), the toolface angle \(-90.05^{\circ}\) and the azimuth \(186.77^{\circ}\). Taking this attitude as a standard, the attitude error of the three sets of data could be obtained. The attitude error is illustrated in Figure 16. It can be seen that without compensating for any sensors error, the attitude error increases over time quickly. At the end of the experiment, the error of inclination, toolface angle and azimuth is \(1.77^{\circ},1.42^{\circ}\) and \(4.53^{\circ}\), respectively. It obviously cannot satisfy the requirement of the drilling operation. When the data was compensated for the linear error items, the error of inclination, toolface angle and azimuth were reduced to \(1.29^{\circ}\), \(1.28^{\circ}\) and \(3.23^{\circ}\), respectively. When the data was compensated, both the linear error items and nonlinear error items, the error of inclination, the toolface angle and azimuth were reduced to \(0.55^{\circ}\), \(0.81^{\circ}\) and \(0.42^{\circ}\). Basically, it can meet the requirement of the drilling operation. Table 5 lists the measurement error of the borehole trajectory.