A zodiac fixed to the Earth
Most astrology looks at a moment: the planets as they stood when someone was born or something began. Geodetic astrology looks at places instead. It lays the whole zodiac round the Earth like a belt, starting with 0° Aries on the Greenwich meridian and running eastward, one degree of the zodiac for each degree of longitude, until 30° Pisces meets Greenwich again from the west. Every place on Earth then has a fixed Midheaven, its longitude read as a zodiac degree, and from that Midheaven and its latitude, a fixed Ascendant, worked out exactly as in any chart. Unlike a birth chart, this chart never changes: it is the same for everyone who lives in or visits the place.
How a place's geodetic angles are found
The Midheaven needs no calculation beyond counting. Paris, at 2°21′ east of Greenwich, has a geodetic Midheaven of 2°21′ Aries. Moscow, at 37°37′ east, is past the 30° border into Taurus, at 7°37′ Taurus. West of Greenwich you count the long way round: New York, at 74° west, is 286° east, which is 16° into Capricorn. The Ascendant then follows from that Midheaven and the place's latitude by the usual formula for the rising degree, so two cities on the same meridian share a Midheaven but can have different Ascendants. This site computes it with the obliquity of the ecliptic for the year 2000. The two tables below give the band of longitude for each sign and the geodetic angles of 36 big cities.
Sepharial and Johndro
The system is usually traced to two astrologers of the early twentieth century. The British astrologer Sepharial, the pen name of Walter Gorn Old, set out geodetic equivalents in the 1920s, and the Canadian astrologer Edward Johndro published The Earth in the Heavens, a book on the ruling degrees of cities, in 1929. Johndro's version works in right ascension, measured along the celestial equator rather than the ecliptic, so his degrees for a city differ from Sepharial's. The tables here follow Sepharial's simpler scheme, the one most often meant by geodetic astrology today.
How astrologers use it
Geodetic charts were made for mundane astrology, the astrology of places and events. When an eclipse or a slow planet crosses a region's geodetic angles, astrologers read events there as more likely; Johndro himself applied the method to earthquakes. For a person, the usual use is comparison: a place is read as especially marked for you when its geodetic Midheaven or Ascendant falls on a planet in your birth chart. If your Sun is at 16° Capricorn, for example, the geodetic Midheaven of New York falls on it, and a geodetic astrologer would read the city as a place where your Sun is prominent.
Geodetic astrology and astrocartography
The two are cousins, not rivals. Astrocartography lines come from one birth moment and are personal: your Venus line runs where Venus was rising or overhead when you were born. Geodetic angles belong to the Earth itself. Astrologers who use both look for agreement, a city on one of your natal lines whose geodetic angles also touch the same planet. The astrocartography map draws your personal lines, and the relocation chart gives the angles of your own chart in any city. Like the rest of astrology, geodetics is a tradition, not a measurement: read it as another way of asking what a place stands for.