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,





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



We deployed a sensor array composed of no. 1 and no. 2 FVM-400

fluxgate magnetometer and no. 3 MS-17 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