measurement of the magnetic field vector with moving


Korepanov V., Dudkin F.

Laboratory for Electromagnetic



The geophysical

research of Earth’s crust structure requires measurements of the

Earth's magnetic field vector variations at big areas. Normally, this

is made with flux-gate magnetometers (FGMs) in numerous stationary

positions to cover all the area. To decrease time and money expenses,

recently the attempts are known to do this with the help of moving

carriers. The use of FGM onboard mobile carriers faces a number of

difficulties that limit their implementation in the practice of

geophysical research. This is due to the fact that the measurements of

rather weak magnetic anomalies are executed in the presence of strong

Earth’s magnetic field B0 (the absolute value |B0| can reach 67 000

nT), which creates great interference unavoidably arising when the FGM

rotates during its movement. This interference signal dB at the output

of the FGM sensor is proportional to the derivative of the field

vector projection onto the sensor axis with respect to the angle ζ

between B0 and the sensor axis:

dB=|B_0 |sinζ dζ,

As follows from this formula, for a sensor being at given moment

orthogonal to the vector B0, the change in the rotation angle dζ only

by one thousandth of degree can lead to the appearance of an

additional signal up to 1.2 nT. Therefore, the application of

magnetometers for operation on mobile carriers is limited by the

recording of variations of B0 absolute value. This decreases the

useful information and is characteristic mostly for scalar

magnetometers. The latter, however, are inferior to the FGMs by such

important parameters as weight, size, and price. It is important to

estimate whether FGMs may be competitive with scalar magnetometers

also in the magnetic field measurement precision with acceptable for

practice errors.

So, let us analyze the possible ways to reduce the magnetic field

values collected onboard moving carrier to the values in the

stationary geomagnetic frame with acceptable errors. It is clear that

for this the data about the orientation of the FGM axes during its

motion are necessary. To obtain such information, a promising way is

the use of an additional magnetometer installed on the ground at the

site of work and properly oriented, as well as to use a tiltmeter in

moving FGM. (Data from FGM of nearest geomagnetic observatories are

not considered here because they do not contain magnetic disturbances

of local origin). The axes direction of moving FGM relatively to the

axes of stationary FGM may be then calculated by comparing the

projections of the magnetic field vector in both magnetometers at

every time moment. When calculating the rotations of the coordinate

system, the Euler angles α, β, γ (respectively precession angle,

nutation angle and angle of proper rotation) are most often used.

Euler angles are convenient for physical interpretation of rotations,

since they are intuitively understandable, and also when describing

time-constant rotations. However, the description of random rotation

with the help of Euler angles has a number of significant drawbacks:

rotations are not commutative; interpolation of rotations presents

significant difficulty; and there is a problem of singularity (the

so-called gimbal lock). To avoid them, the efficiency was estimated of

use the quaternion formalism describing rotations with hypercomplex

numbers in 4-dimensional Euclidean space. It is shown that this way

allows obtaining the final results with good resolution, acceptable

for practice. The experimental tests confirmed these calculations and

their results are discussed in the report.

Also a new FGM version the best suitable for onboard light drones use

is described and its parameters are discussed.