Measuring and Mapping Earth

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MEASURING AND MAPPING EARTH

CONCEPT

Today a sharp distinction exists between the earth sciences and geography, but this has not always been the case. In ancient times, when scientists lacked the theoretical or technological means to study Earth's interior, the two disciplines were linked much more closely. Even in the centuries since these disciplines parted ways, the earth sciences have continued to benefit from a foundation established in part by early geographers, whose work informed the geophysical subdiscipline of geodesy. Like geographers, earth scientists are interested in measuring and mapping Earth, though their interests are quite different. Among the areas of concern to earth scientists are the location of underground resources and the obtaining of data on the planet's gravitational and magnetic fields. In these and other pursuits, earth scientists use a number of techniques and technologies, ranging from the ancient discipline of surveying to the most modern forms of satellite-based remote sensing.

HOW IT WORKS

Geography and Geology

Whereas geology is the study of the solid earth, including its history, structure, and composition, geography is the study of Earth's surface. Geologists are concerned with the grand sweep of the planet's history over more than four billion years, whereas the work of geographers addresses the here and nowor at most, in the case of historical geography, a span of just a few thousand years.

Today the distinctions between these two disciplines are sharp, so much so that most books on the earth sciences barely even mention geography. In a modern university, chances are that the geography and geology/earth sciences departments will not even be located in the same building. Geography, after all, usually is classified among social sciences such as anthropology or archaeology, whereas geology is a "hard science," along with physics or biology.

It is true that the divisions between geography and geology are clear, symbolized by the features that appear or do not appear on the maps used by either discipline. Geography is somewhat concerned with natural features, but its interests include man-made boundaries, points, and such formations as population centers, roads, and so on. Certainly, an atlas may include physical maps, which are dominated by natural features and contain little or no evidence of man-made demarcations or points of interest. Nonetheless, the purpose of a geographical atlas is to identify locations of interest to humans, among them, cities, roads from one place to another, and borders that must be crossed.

By contrast, geologic maps contain detailed information about rock formations and other natural features, with virtually nothing to indicate the presence of humans except as it relates to natural features under study. An exception might be a map designed to be used by paleoarchaeologists, who study the earliest humans and humanoid forms. Their discipline, which combines aspects of the earth sciences and archaeology, is concerned with human settlements, but mostly only prehistoric human settlements.

Despite the depth and breadth of distinctions between them, it is significant that studies in both geography and geology make use of maps. Mapmaking, or cartography, is considered a subdiscipline of geography, yet it is actually an interdisciplinary pursuit (much like many of the earth sciencessee Studying Earth) and combines aspects of science, mathematics, technology, and even art. Although their interests are in most cases quite different from those of geographers, geologists rely heavily on the work of cartographers.

Early Geographic Studies

The history of the sciences has been characterized by the continual specialization and separation of disciplines. Thus, it should not be surprising to discover that to the ancients, the lines were blurred between geography, mathematics, astronomy, and what people today would call earth sciences. Most of the early advances in the study of Earth involved all of those disciplines, an example being the remarkable estimate of Earth's size made by Eratosthenes of Cyrene (ca. 276-ca. 194 b.c.).

A mathematician and librarian at Alexandria, Egypt, Eratosthenes discovered that at Syene, several hundred miles south along the Nile near what is now Aswan, the Sun shone directly into a deep well and upright pillars cast no shadow at noon on the summer solstice (June 21). By using the difference in angles between the Sun's rays in both locations as well as the distance between the two towns, he calculated Earth's circumference at about 24,662 mi. (39,459 km). This figure is amazingly close to the one used today: 24,901.55 mi. (39,842.48 km) at the equator. Eratosthenes published his results in a book whose Greek name, Geographica (Geography), means "writing about Earth." This was the first known use of the term.

PTOLEMY'S GEOGRAPHY.

Unfortunately, the Alexandrian astronomer Ptolemy (ca. a.d. 100-170), one of the most influential figures of the ancient scientific world, rejected Eratosthenes' calculations and performed his own, based on faulty information. The result was a wildly inaccurate estimate of 16,000 mi. (25,600 km). More than thirteen centuries later, Christopher Columbus (1451-1506) relied on Ptolemy's figures rather than those of Eratosthenes, whose work was probably unknown to him. Thinking that the circumference of Earth was two-thirds what it actually is, Columbus set sail westward from Spainsomething he might not have done if he had known about the "extra" 8,000 mi. (12,874 km) that lay to the west of Europe.

Nonetheless, in his Hyphegesis geographike (Guide to geography), Ptolemy did make useful contributions to geographical study. He helped popularize the use of latitude and longitude lines, first conceived by the Greek astronomer and mathematician Hipparchus (fl. 146-127 b.c.), and rejected the widespread belief that a vast ocean, known to the ancients as "the Ocean Sea," surrounded the entire world. He also presented a set of workable mathematical principles for representing the spherical surface of Earth on a flat page, always a problem for cartographers.

In addition, Ptolemy established the practice of orienting maps with north at the top of the page. Today this is taken for granted, but in his time cartographers depicted the direction of the rising Sun, east, at the top of their maps. Ptolemy used a northward orientation because the Mediterranean region that he knew extended twice as far east to west as it did north to south. To represent the area on a scroll, the form in which books appeared during his time, it was easier to make maps with north at the top.

OTHER ANCIENT GEOGRAPHERS.

Most other ancient geographers of note were primarily historians rather than scientists, preeminent examples being the Greek Herodotus (ca. 484-ca. 430-420 b.c.), the father of history, and Strabo (ca. 64 b.c.-ca. a.d. 24), whose work provides some of the earliest Western descriptions of India and Arabia. An exception was Pomponius Mela (fl. ca. a.d. 44), whose work would fit into the subdiscipline known today as physical geography, concerned with the exterior physical features and changes of Earth.

In his three-volume De situ orbis, (A description of the world), Mela introduced a system of five temperature zones: northern frigid, northern temperate, torrid (very hot), southern temperate, and southern frigid. Unlike many scientific works of antiquity, Mela's geography has remained influential well into modern times, and his idea of the five temperature zones remains in use. Mela and Ptolemy, who followed him by about a century, were among the last geographers of note in the West for more than a thousand years.

THE SEPARATION OF GEOGRAPHY AND EARTH SCIENCES.

During the first half of the Middle Ages significant work in cartography took place in the Muslim world and in the Far East, but not in Europe. Only in the course of the Crusades (1095-1291) did Europeans become interested in exploration again, and this interest grew as the Mongol invasions of the thirteenth century opened trade routes from Europe to China for the first time in a thousand years. The crusading and exploring spirits met in Henry the Navigator (1394-1460), the prince who, while he never actually took part in any voyages himself, quite literally launched the Age of Exploration from his navigation school at Sagres, Portugal.

In the two centuries that followed, European mariners and conquerors explored and mapped the continents of the world. Along the way, these nonscientists sometimes added knowledge to what would now be considered the earth sciences, as when the Italian explorer Christopher Columbus (1451-1506) became the first to notice magnetic declination. (See Geomagnetism for more on this subject.) Meanwhile, Columbus's contemporary, the Italian artist and scientist Leonardo da Vinci (1452-1519), as well as Georgius Agricola (1494-1555) of Germany, known as the father of mineralogy, conducted some of the first modern studies in the earth sciences. (See Studying Earth for more about Leonardo's and Agricola's contributions.)

In the sixteenth century, the Flemish cartographer Gerhardus Mercator (1512-1594) greatly advanced the science of mapmaking with his development of the Mercator projection. The latter method, still used in many maps today, provided an effective means of rendering the spherical surface of Earth on a two-dimensional map. By that time, cartography had emerged as a vital subdiscipline, and over the ensuing two centuries the separation between geography and the earth sciences became more and more distinct.

The full separation of disciplines took place in the eighteenth century, when the German geographer Anton Friedrich Büsching (1724-1793) pioneered modern scientific geography. Beginning in 1754, Büsching published the 11-volume Neue Erdbeschreibung (New description of the earth), which established a foundation for the study of geography in statistics rather than descriptive writing. During the same century geology was in the middle of its own paradigm shift. Until the time of the Scottish geologist James Hutton (1726-1797), a near exact contemporary of Büsching, geologists had been concerned primarily with explaining how the world begana topic that almost inevitably led to conflict over religious questions (see Earth, Science, and Nonscience). Hutton, known as the father of geology, was the first to transcend this issue and instead offer a theory about the workings of Earth's internal mechanisms.

Surveying

The era of Büsching and Hutton coincided with that of the English astronomer Charles Mason (1730-1787) and the English surveyor Jeremiah Dixon (d. 1777), who in 1763 began their famous survey of the boundary between Pennsylvania and Maryland. It took them five years to survey the 233-mi. (373-km) Mason-Dixon Line, which eventually became known as the border between the free and slave states before the Civil War. Surveying, a profession practiced by such great Americans as the first president, George Washington (1732-1799), and the mathematician and astronomer Benjamin Banneker (1731-1806), eventually became associated with the United States, but it originated in Egypt as early as 2700 b.c.

Surveying is a realm of applied mathematics devoted to measuring and mapping areas of land. Though it is obviously of value to the earth sciences and geography, it has a great deal of importance economically and politically as well. For this reason, the Romans, who were not nearly as inclined toward theoretical study as the Greeks, became preeminent surveyors whose land parcels still can be seen from the air over parts of western Europe. Owing to its great practical importance, surveyingunlike virtually all other forms of learningcontinued to thrive in Europe during the early Middle Ages. Nonetheless, surveying improved in the Renaissance and thereafter, as the result of the introduction of new tools and mathematical techniques.

Among these tools were the theodolite, used for measuring horizontal and vertical angles, and the transit, a type of theodolite that employs a hanging plumb bob to determine a level sight line. Mathematical techniques included triangulation, whereby the third side of a triangle can be determined from measurements of the other two sides and angles. The German mathematician Karl Friedrich Gauss (1777-1855), regarded as the father of geodesy, introduced the heliotrope, a mechanism that aids in triangulation. Other tools included the compass, level, and measuring tapes; modern surveying benefits from remote sensing. (Both remote sensing and geodesy are discussed later in this essay.)

REAL-LIFE APPLICATIONS

Geologic Maps and Surveys

A geologic map shows the rocks beneath Earth's surface, including their distribution according to type as well as their ages, relationships, and structural features. The first geologic map, made in 1743, depicted subterranean East Kent, England. Its creator, the English physician and geologist Christopher Packe (1686-1749), introduced the technique of hachuring, that is, representing relief (elevation) on a map by shading in short lines in the direction of the slopes.

Three years later, the French geologist Jean-Etienne Guettard (1715-1786) made the first geologic map that crossed national lines, thus illustrating the distinction between geology and geography. As Guettard discovered, the geologic features of the French and English coasts along the English Channel are identical, indicating that the areas are connected. At a time when France and England were still bitter political and military rivals, Guettard's work showed that they literally shared some of the same land.

Geologic mapmaking received a further boost in 1815, when the English geologist William Smith (1769-1839) produced what has been called the first geologic map based on scientific principles. Entitled A Delineation of the Strata of England and Wales with Part of Scotland, the map used different colors to indicate layers of sedimentation. Roughly 6 ft. by 9 ft. (1.8 × 2.7 m), the map linked paleontology with stratigraphy (the study of fossils and the study of rock layers, respectively) and proved to be a milestone in geologic cartography.

MODERN GEOLOGIC MAPMAKING.

Geologic mapmaking changed considerably in the period after World War II. Before that time, geologists did most of their work with the use of topographical maps, or maps that showed only surface features. Following the war, however, aerial photography became much more common, giving rise to the technique of photogeology, the use of aerial photographic data to make determinations regarding the geologic characteristics of an area.

Petroleum companies, which often have taken the lead in developing advanced methods of geologic study, introduced the practice of creating three-dimensional images from the air. They did this by taking pairs of photographs which, when viewed through a stereoscope, provided images that could be studied in great detail for information about all manner of geologic features. Height proved a great advantage, revealing features that would not have been as clear to a geologist working on the ground.

Of course, a great deal of work on the ground was still necessary for confirming the data revealed by aerial surveillance and for other purposes, such as measurement and sample collection. Nonetheless, aerial photography provided an enormous boost to geologic studies, as did the use of satellite imaging from the 1970s onward. Also helpful were such new devices as the handheld magnetometer, which made it relatively easy to separate rocks containing magnetite from other, nonmagnetic samples.

WHY MAKE GEOLOGIC MAPS?

One might wonder why any of this is important, aside from a purely academic interest in the structure of rocks under the ground. In fact, the need for precise geologic data goes far beyond "purely academic interests," as the reference to oil companies suggests. Geologic mapmaking is critical to the location of oil as well as minerals and other valuable natural resourcesincluding the most useful one of all, water.

Likewise it is necessary to have accurate geologic information before undertaking a large engineering project, such as the building of a road or bridge. In such situations, geologic studies can quite literally be a matter of life and death, and eventually such studies may save more lives by aiding in the prediction of earthquakes or volcanoes. Geologic data is also a critical part of studies directed toward environmental protection, both for areas designed to remain natural habitats and for those designated for development. And, finally, there are studies whose purpose is purely, or mostly, academic but that reveal a great deal of useful information about the history of the planet, the forces that shaped it, and perhaps even future events.

GEOLOGIC SURVEYS.

Geologic mapmaking is so vital, in fact, that national governments have undertaken large-scale and ongoing geologic studies since 1835. That was the year that Great Britain became the first country to establish a geologic survey, with the aim of preparing a geologic map of the entire British Isles. The project began with the mapping of Cornwall and southern Wales and has continued ever since, with the addition of new details as they have become available.

In the ensuing years several other countries established their own geologic surveys, including the United States in 1889. (The Web site of the U.S. Geological Survey is listed in the bibliography.) Other important national geologic surveys include those of France, Canada, China, and Russia. The last of these surveys is of particular interest, dating as it does from the "Stone Department," a mineralogical survey established in 1584. Today even much smaller nations, such as Uruguay, Slovakia, and Namibia, have their own national geologic surveys.

Over the years, techniques of information gathering have evolved, particularly with the development of satellite remote-sensing technology. So, too, have the areas under the purview of various national geologic surveys, which since the 1950s have undertaken the mapping of the continental shelves adjacent to their own shorelines. (In addition, the nations claiming territories in Antarctica, including Britain and the United States, have mapped the geologic features of that continent extensively, though mining or other economic development there is forbidden.) The U.S. Geological Survey has also seen its scope extended to include studies on such issues as radioactive waste disposal and prediction of natural hazards, among them, earthquakes in urban areas.

Geophysical Measurements

Geophysics is a branch of the earth sciences that combines aspects of geology and physics. Among the areas it addresses are Earth's physical processes as well as its gravitational, magnetic, and electric properties and the means by which energy is transmitted through its interior. Areas of geophysics with a particular focus on measurement and mapping include the study of geomagnetism, or Earth's magnetic field, and geodesy, which is devoted to the measurement of Earth's shape and gravitational field.

The measurement of gravitational fields involves the use of either weights dropped in a vacuum or mechanical force-balance instruments. The first of these techniques is much older than the other and provides an absolute measure of the gravitational field in a given area. As for force-balance instruments, they are similar in principle to scales and furnish a relative measure of the gravitational field. To compare the gravitational field at different positions, however, it is necessary to establish a frame of reference. This is known as the geoid, a surface of uniform gravitational potential covering the entire earth at a height equal to sea level. (See Gravity and Geodesy for more on these topics.)

GEODETIC MEASUREMENTS OF EARTH'S SURFACE.

As noted, geodesy is concerned not only with Earth's gravitational field but also with its shape, and earth scientists working on this aspect of the subdiscipline employ many of the techniques and equipment described earlier with regard to geography and surveying. Eratosthenes's measurement of Earth's size is thought to be the first geodetic measurement, and in performing geodetic measurements today, earth scientists often employ concepts familiar to surveyors.

Among these concepts is triangulation, which was developed in the sixteenth century by the Dutch mathematician Gemma Frisius (1508-1555). Triangulation remained an important method of geodetic measurement until the development of satellite geodesy made possible simpler and more accurate measurements through remote sensing. Even today triangulation is still used by geologists without access to satellite data. In performing measurements using triangulation, geologists employ the theodolite, and typically at least one triangulation point is highly visiblefor instance, the top of a mountain.

Until the 1950s scientists used a measuring tape of a material called Invar, a nickel-iron alloy noted for its tendency not to expand or contract with changes in temperature. From that time, however, electronic distance measurement (EDM) systems, which employ microwaves or visible light, came into use. EDM helped overcome some of the possibilities for error inherent in using any kind of tape, for example, the likelihood that it would sag and thus render incorrect measurements. Furthermore, EDM tended to reduce errors caused by atmospheric refraction.

With the advent of the United States program in the 1960s, increasingly more sophisticated forms of geodesic remote-sensing technology came into use. Among these techniques is satellite laser ranging, which relies on measurements of the amount of time required for a laser pulse to travel from a ground station to a satellite and back. Before the development of the global positioning system (GPS), discussed later, the use of satellite systems necessitated tracking through the Doppler effect, or the change in the observed frequency of a wave when the source of the wave is moving with respect to the observer. Thanks to GPS, put into operation by the U.S. Department of Defense, satellite tracking is much simpler and more accurate today.

GEOMAGNETIC MEASUREMENTS.

Ever since the ancient Chinese discovered that pieces of lodestone (magnetite) tend to point north, mariners have used the compass for navigation. The compass was augmented by other navigational devices until it was supplanted by the gyroscope in modern times and still later by more sophisticated devices and methods, such as GPS. Yet a compass still works fine for many a hiker, and its use serves to emphasize the importance of Earth's magnetic field.

Earth has an overall geomagnetic field, and specific areas on the planet have their own local magnetic fields. Thanks in large part to the contributions of Gauss, who developed a standardized local magnetic coordinate system in the early nineteenth century, it became possible to perform reasonably accurate measurements of local magnetic data while correcting for the influence of Earth's geomagnetic field. Indeed, one of the challenges in measuring magnetic fields is the fact that the Earth system possesses magnetic force from so many sources: the molten core, from whence originates the preponderance of Earth's magnetic field; external fields, such as the magnetosphere and ionosphere; local materials, such as magnetite, hematite, or pyrrhotite; and even man-made sources of magnetic or electric force.

After making calculations that correct for interfering sources of magnetism, geophysicists study the remaining magnetic anomalies, which can impart extremely valuable information. Classic examples include the discovery that Earth's magnetic polarity has reversed many times, a finding that led to the development of the geophysical subdiscipline known as paleomagnetism. Paleomagnetic studies, in turn, served as a highly significant confirmation of plate tectonics, which originated in the middle of the twentieth century and remains the dominant theory regarding geologic processes. (See Plate Tectonics. For more about geomagnetism, including some of the topics mentioned here, see Geomagnetism.)

Knowing One's Location

In these and other types of studies that involve mapping and measurement, it is important for scientists conducting surveys to be aware of the frame of reference from which they are operatingthat is, the perspective from which they view data. Simply put, one must know first where one is before one can measure and map geophysical or other data for surrounding areas. This requires knowledge of latitude and longitude, or east-west and north-south positions, respectively.

From earliest times, mariners and scientists have been able to ascertain latitude with relative ease, simply by observing the angle of the Sun and other stars. Determination of longitude, however, proved much more difficult, because it required highly accurate timepieces. Only in the late eighteenth century, with the breakthroughs achieved by the British horologist John Harrison (1693-1776) did such calculations become possible. As a result, many a ship's crew was saved from the misfortunes that could result from inaccurate estimates of location.

GLOBAL POSITIONING SYSTEM.

By the latter part of the twentieth century, navigational technology had become vastly more sophisticated than it was in Harrison's day. From the 1957 launch of the Soviet satellite Sputnik 1, the skies over Earth became increasingly populated with satellites, such that within half a century dozens of countries had payloads in space. Aside from governments and scientific research establishments, even cable television companies used satellites to beam programming to homes all over the industrialized world, a fact that in itself says much about the spread of satellite technology.

Among the most impressive uses of satellites is the GPS, developed by the U.S. Department of Defense to assist in surveillance. GPS consists of 24 satellites orbiting at an altitude of 12,500 mi. (20,000 km). They move in orbital paths such that an earthbound receiver can obtain signals from four or more satellites at any given moment. On board are atomic clocks, which provide exact time data with each signal and eliminate the necessity of the receiver's having such an accurate clock. By receiving data from these satellites, persons on the ground can compute their own positions in terms of latitude and longitude as well as altitude. Not all receivers have access to the most accurate data possible: in line with the strategic mission for which it initiated GPS in the first place, the Defense Department ensures that only authorized personnel receive the most precise information.

Thus, GPS has built-in errors so that civilian users can calculate locations with an accuracy of "only" 328-492 ft. (100-150 m). This, of course, is amazingly accurate, but not as accurate as the data available to those authorized to receive normally encrypted information on the P (Precise) code. The latter provides an accuracy of 3.28-16.4 ft. (1-5 m) instantaneously, and more detailed measurements based on GPS data can be used to achieve accuracy of up to 0.2 in. (5 mm).

Remote Sensing

Many of the methods used by geologists and geophysicists to map and measure Earth make use of remote sensing, the gathering of data without actual contact with the materials or objects being studied. Without remote sensing, it would be impossible to discuss many physical phenomena intelligently, because it is unlikely that any technology ever will make it possible to explore many areas underneath the planet's surface directly.

An example of remote sensing is photogeology, described briefly earlier; so, too, is satellite imaging for data collection. The earth scientist of the twenty-first century likewise has other highly sophisticated forms of technology, such as radar systems or infrared imaging, at his or her disposal. As with many other aspects of geologic mapping and measurement, this one has value far beyond the classroom: remote-sensing studies make it possible, for instance, to observe the environmental impact of deforestation in large geographical areas. (For much more about this subject, see Remote Sensing.)

WHERE TO LEARN MORE

Brooks, Susan. The Geography of the Earth. New York: Oxford University Press, 1996.

Erickson, John. Exploring Earth from Space. Blue Ridge Summit, PA: TAB Books, 1989.

Geologic Maps (Web site). <http://http://www.aqd.nps.gov/grd/usgsnps/gmap/gmap1.html>.

Hancock, Paul L., and Brian J. Skinner. The Oxford Companion to the Earth. New York: Oxford University Press, 2000.

Internet Resources for Geography and Geology (Web site). <http://www.uwsp.edu/geo/internet/geog_geol_resources.html>.

Moffitt, Francis H., and Harry Bouchard. Surveying. 8th ed. New York: Harper and Row, 1987.

Remote Sensing Data and Information (Web site). <http://rsd.gsfc.nasa.gov/rsd/RemoteSensing.html>.

U.S. Geological Survey (Web site). <http://www.usgs.gov/>.

Virtual Museum of Surveying (Web site). <http://www.surveyhistory.org/index.htm>.

Wilford, John Noble. The Mapmakers. New York: Knopf, 2000.

KEY TERMS

CARTOGRAPHY:

The creation, production, and study of maps. Cartography is a subdiscipline of geography and involves not only science but also mathematics, technology, and even art.

DOPPLER EFFECT:

The change in the observed frequency of a wave when the source of the wave is moving with respect to the observer.

FIELD:

A region of space in which it is possible to define the physical properties of each point in the region at any given moment in time.

GEODESY:

An area of geophysics devoted to the measurement of Earth's shape and gravitational field.

GEOGRAPHY:

A social science concerned with the description of physical, biological, and cultural aspects of Earth's surface and with the distribution and interaction of these features. Compare with geology.

GEOID:

A surface of uniform gravitational potential covering the entire earth at a height equal to sea level.

GEOLOGIC MAP:

A map showing the rocks beneath Earth's surface, including their distribution according to type as well as their ages, relationships, and structural features.

GEOLOGY:

The study of the solid earth, in particular, its rocks, minerals, fossils, and land formations.

GEOPHYSICS:

A branch of the earth sciences that combines aspects of geology and physics. Geophysics addresses the planet's physical processes as well as its gravitational, magnetic, and electric properties and the means by which energy is transmitted through its interior.

GEOMAGNETISM:

A term referring to the magnetic properties of Earth as a whole, rather than those possessed by a single object or place on Earth.

HACHURING:

A method of representing relief (elevation) on a map by shading in short lines in the direction of the slopes.

MAGNETOSPHERE:

An area surrounding Earth, reaching far beyond the atmosphere, in which ionized particles (i.e., ones that have lost or gained electrons so as to acquire a net electric charge) are affected by Earth's magnetic field.

PALEOMAGNETISM:

An area of historical geology devoted to studying the direction and intensity of magnetic fields in the past, as discerned from the residual magnetization of rocks.

PALEONTOLOGY:

The study of fossilized plants and animals, or flora and fauna.

PHOTOGEOLOGY:

The use of aerial photographic data to make determinations regarding the geologic characteristics of an area.

PHYSICAL GEOGRAPHY:

A subdiscipline of geography concerned with the exterior physical features and changes of Earth.

POTENTIAL:

Position in a field, such as a gravitational force field.

REFRACTION:

The bending of light as it passes at an angle from one transparent material into a second transparent material.

REMOTE SENSING:

The gathering of data without actual contact with the materials or objects being studied.

STRATIGRAPHY:

The study of rock layers, or strata, beneath Earth's surface.

SURVEYING:

An area of applied mathematics devoted to measuring and mapping areas of land.

TRIANGULATION:

A technique in surveying whereby the third side of a triangle can be determined from measurements of the other two sides and angles.