Tracing of a magnetic anomaly body by using three component magnetic data acquired by randomly placed three component magnetic sensors with random attitudes through quaternion rotation. 
LIM, M. T. (1), PARK, Y. S. (1), JUNG, H. K. (1), SHIN, Y. H. (1), RIM, H. R. (2), and PARK, C. S. (1) 
(1) Korea Institute of Geoscience & Mineral Resources, Daejeon, Korea, (2) Busan National university, Busan, Korea 
Abstract
The possibility to trace the position of a magnetic anomaly body along time is very useful for example in the water. The superiority of the three component or vector data to scalar data is obvious in interpretation and application. But till now the tracing has been done mainly by using only the scalar magnetic data because of the difficulty to acquire the attitude data of the sensor body frame’s coordinate system. If we can attach an attitude acquiring equipment to the common frame on which the sensor and that equipment are installed aligned each other, then we can rotate the acquired vector data around each of the three axes of the common frame’s coordinate system with the amount of the acquired three attitudes, i. e. yaw, pitch, roll. As the result, we can get the components of the vector data as if we have measured the invariant data, for example the magnetic data, with the frame reoriented to coincide to the geographical coordinate system.
If we are in the environment in which 1) we deployed an array of three component magnetic sensor, 2) we can’t attach an attitude acquiring equipment to each sensor’s frame, 3) the sensors’ frames do not move, i. e. the relation between the geographical coordinate system and the sensor frame’s coordinate system does not change, and 4) the measured property for example the magnetic field data is invariant, then we can calculate the relation between the two coordinate systems by using the quaternion multiplication or quaternion rotation.
For this process, we do some absolute magnetic measurement near the deployed sensor array and with the help of continuous three component magnetic data measured from an internationally certified magnetic observatory, in this study, CYG(Cheongyang) Magnetic Observatory one on IMO (InterMagnet Magnetic Observatory) Network.
Once that relation for each sensor of the deployed array has been calculated, we can apply the quaternion rotation to the time series data from each sensor (x(t), y(t), z(t)), and we can get the time series data from each sensor reoriented to the geographical coordinate system (n(t), e(t), d(t)). As we know each of the three baseline data of each sensor through proper processing on the acquired data, we can subtract the baseline data from the reoriented data and we can get time series differential data (δn(t), δe(t), δd(t)) for each sensor.
We deployed a sensor array composed of no. 1 and no. 2 FVM400 fluxgate magnetometer and no. 3 MS17 fluxgate magnetometer, not in line intentionally, in the campus of KIGAM(Korea Institute of Geoscience and Mineral Resources). We got time series magnetic field data for each sensor. We did a set of absolute magnetic measurement near the sensor array with the help of the CYG Observatory’s data.
Put all data together we derived three sets of time series differential data (δn(t), δe(t), δd(t)) of which the positions are known. Using the inversion, we could calculate the position of a moving magnetic anomaly body for some discrete time points. In the future we could do the same calculation continually and we could trace the position of a magnetic anomaly body continually. 
Applications 
oral 
