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A magnetoelectrical resistivity measurement system is proposed, which combines measurement of the electric potential and the magnetic field due to a current injection into a sample. Measurement of the electric potential, as well as the injected current, is similar to traditional electrical resistivity tomography (ERT) data acquisition. For the magnetic field measurements, 24 sensor modules have been developed using three component anisotropic magnetoresistive (AMR) sensors, mounted on a vertically moving scanning torus. The system is designed to operate in a typical laboratory magnetic noise environment without extensive shielding. To compensate for the effects of the Earth's magnetic field, the AMR sensors are operated with a field feedback circuit. Optimal noise reduction is provided by the use of a lock-in frequency of 25 Hz, with sine wave modulation and measurement cycles of 10 s. The resolution of the system is better then 50 pT and the aimed accuracy is 0.1%. The system provides a data set of magnetic fields complimentary to traditional ERT to determine the internal conductivity distribution of cylindrical samples with the dimension of 0.1-m radius and 0.5-m height.