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Geomagnetic field signals have potential for use in underwater navigation and geophysical surveys. To map underwater geomagnetic fields, we propose a method that exploits an autonomous surface vehicle. In our system, a magnetometer is rigidly attached to the vehicle and not towed by a cable, minimizing the system's size and complexity but requiring a dedicated calibration procedure due to magnetic distortion caused by the vehicle. Conventional 2-D methods can be employed for the calibration by assuming the horizontal movement of the magnetometer, and the proposed 3-D approach can correct for horizontal misalignment of the sensor. Our method does not require a supporting crane system to rotate the vehicle, and calibrates and maps simultaneously by exploiting data obtained from field operation. The proposed method has been verified experimentally in inland waters, generating a magnetic field map of the test area that is of much higher resolution than the public magnetic field data.