The intensity of the magnetic field at a point during our history is possible thanks to a quirk called paramagnetism that occurs in molten rock (amongst other things). Above a certain temperature, rock assumes a magnetic intensity proportional to the magnetic field it's under (almost always the Earth's). As it slowly cools, the configuration becomes 'trapped' in the rock, preserving that magnetism, almost as though it were fossilized. If you can find these tiny magnets and date them, you can get a bearing on what the field was like at a given time.
One problem is that the magnetic field that's recorded may have been that of the solar wind, but the wind is too variable and would have been weaker than that recorded, even taking the greater intensity of the young sun into account. However, the magnetopause, the point beyond which earth's magnetic field could stand up to the Solar wind would have been less than half today, and the holes at the poles (where the field lines rise straight up) would have been three times bigger than today, and the whole field might have been crushed occasional solar ejections.
Yet there's still another problem. Some lines of evidence about the emergence of life place it at 3.85 billion years ago, which would mean it managed to survive even while being pounded by the force of the solar wind. So something's wrong here.
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