Geophysics

First, the continents do not drift! The theory of continental drift was based on observations of how the outlines of different continents appear to fit like pieces of a jigsaw puzzle and that when so fitted various ancient mountain ranges, etc. align from one continent to another. But for them to 'drift' they would have to 'plow' through the solid rock of the ocean floor, which is clearly not happening. The theory of continental drift was long ago discarded and replaced as new evidence was uncovered.

The speculation that continents might have 'drifted' was first put forward by Abraham Ortelius in 1596. The concept was independently and more fully developed by Alfred Wegener in 1912, but his theory was rejected for lack of a mechanism.

Following WW2 the US Navy made a series of observations showing symmetrical bands of magnetic field reversals on opposite sides of the midocean ridges. Because this information had value for military navigation, it was kept classified into the 1960s. When this information was made available to geophysicists, it confirmed key parts of the theory of plate tectonics (originally proposed in 1953).

The idea of continental drift has been subsumed by the theory of plate tectonics, which explains how the continents appear to move. Convection currents in the semisolid mantle rock drag both continental and oceanic plates that float above the mantle around. The light granitic continental plate material tends to float higher, while the denser basaltic oceanic plate material tends to float lower so if they collide the continental plate will override the oceanic plate, causing it to subduct under the continental plate down into the mantle. If identical type plates collide the plates crumple and fold causing mountain ranges to form.

The important thing to realize is the continents are not drifting, the tectonic plates (both continental and oceanic) of the crust are floating on the moving top surface of the mantle.

Short Answer:

Some people would claim that the idea of the map of Earth's magnetic field had to wait until 1600 when William Gilbert published his book, De Magnete and claimed the Earth was a giant magnet. If is more accurate to recognize that a map of the global magnetic field of Earth took petty much a thousand years to assemble and no single person gets credit for the whole thing.

Historical Answer:

The need for a map of the Earth's magnetic field stems from the difference between magnetic north and true north. Magnetic north is defined by the direction a compass points and true north is the direction of the geographical north pole, the point about which earth rotates on it axis. The difference is called the magnetic declination and it naturally varies depending on the location on earth. At minimum, mapping of the earth's magnetic field would consist of a determination of magnetic declination at various points on a map. In much of Asia, this correction is small, a few degrees. In the US -20 to + 20 degrees. Along the equator, it tends to be a few degrees. In more northern areas, e.g. Canada, the variation is very large. The variation is quite irregular globally and can change some degrees per year.

The history of geomagnetism does not record the first map the Earth's magnetic field. It is likely there were no systematic attempts at global mapping until the last century. In 1914 such a map was published in the US for the worlds oceans, but knowledge of the topic is much older. Prior to that there was an accumulation of information, no doubt preserved and valued by travelers and explorers and particularly important for sea going navigation.

There are historical records indicating the the the compass was known in China in the 4th century BC though it may not have been used for navigation quite that early. A compass as an indicator of north-south becomes clear only in 80 AD. It is not until 1088 AD in China that it is recorded that a compass did not point to true north. That 1088 even would be the first data point on a map of the Earth's magnetic field. Local data points have been recorded since then.

While it is agreed that the Chinese record of the compass predates European records by at least 150 years, there is no agreement as to whether the compass was independently developed or if it traveled from east to west. By the 13th century, it is clear that Europe and China and the Arabic world knew of and used the compass. Given the sophistication of navigation at this point is time, it is certain that local determinations of magnetic declination were recorded and hence more data points for a map.

It should be added that mapping of declination is only part of the job. In addition to the variations of a compass towards east or west, there is a vertical variation as well with the field pointing towards or away from the surface of the earth at each location. We do know when those measurements began using the invention of George Hartmann in Germany in 1544.

The full mapping requires the strength as well as the direction of the field. An appreciation of the strength of the field of magnets was known for a thousand years, so when William Gilbert published his book, De Magnete, in 1600 and asserted the Earth was a giant magnet, one can reasonable ascribe the complete set of features to the concept of the map of Earth's magnetic field. The theory that the Earth was a giant loadstone was developed by Gilbert and others before 1600 and a tabulation of the Earth's field based on that idea was published in 1590 by Henry Biggs in London. It, of course, did not fully agree with maps of the declination used for navigation at the time because the actual field of the Earth is more complicated than a simple magnet.

Nonetheless, a progression of more accurate model and maps developed from the to this day where satellite mapping gives a complete picture of the field and the changes that are occurring each year.