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In figure 60 the magnetic field is represented by the green arrows and the magnetometers will only measure the component of that field along their own axis. Now imagine two magnetometers facing in opposite directions at some angle to the magnetic field. Clearly they will read the same magnitude of field but with opposite signs. Hartman realized that if an MWD sensor pack was rotated around the z axis, the x and y magnetometer readings would follow a sine wave which should have an average of zero. If the average was anything else, there must be a component of the observation which is permanent. This will be some combination of a sensor bias or a magnetic field component which is rotating with the sensors and is never going away.
Figure 60: Axis components of magnetometers.
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