Condensed Notes Lecture Final F07

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LECTURE 18: GLACIERS Glacier ice is a metamorphic rock. As a glacier is nourished by snowfall (deposition of “sediment”), the older buried snow metamorphoses as the delicate snowflakes become more compact and rounded, transforming into “old snow” or firn. With further compaction the trapped air is mostly driven out and the ice crystals continue to coarsen and develop interlocking projections, all of these changes occurring as the material remains solid, a metamorphic process. Whether a glacier is confined by valley walls (an Alpine glacier), or whether it is an overspreading ice sheet, its internal processes are the same. At high elevations there is a zone of  net accumulation, and a glacier in an ideally steady state maintains a constant size and shape as the ice flows to lower elevations, ultimately to disappear in a zone of  net wastage. Wastage can occur by melting or by discharge of icebergs. A water molecule in a snowflake deposited high upon a glacier travels down into the body of the ice (it gets buried by later snowfalls), to emerge again to the surface in the zone of net wastage. Under most circumstances, internal flow is streamline: the pathways of individual particles, whether H 2 O molecules or embedded debris, are parallel. Streamline flow is in contrast with turbulent (chaotic) flow within a river. Under short-term stress, ice acts as a brittle material. It shatters and can develop deep crevasses (open fractures). Under high confining pressure equivalent to a depth in the glacier greater than ~100 meters, and under sustained long-term stress, the ice acts as a ductile material. Deep ice deforms by flowing. Typically, a glacier flows partly as an entire body of ice sliding across the bedrock, but there is also internal deformation, the upper part flowing more rapidly while motion at the base of the glacier, or where it is in contact with valley walls, is retarded by friction against the bedrock. In a Polar ice sheet, which is a “cold” glacier, the atmospheric temperature remains below freezing throughout the year; a snowstorm can occur in winter or summer. The surface temperature of the ice may be -10° or -15°C, and the deeper ice is even colder. (Older ice was precipitated during a colder Ice Age episode.) The temperature increases toward the base of a Polar ice sheet due to geothermal heat that continually rises from the bedrock. In a temperate or “warm” glacier enough melting and transport of heat energy occurs to bring the entire glacier exactly to the m elting (= freezing) point. A temperate glacier is 0°C at the surface, and slightly colder at the base. Ice floats on water; therefore ice is less dense than water. Application of pressure tends to shift H 2 O into the denser state, which is the liquid state. Therefore the base of the glacier, at higher pressure, must be colder than 0°C to remain solid. Pure ice is too weak and easily deformed to be an effective agent of erosion. Ice laden with rock fragments is a highly effective engine of erosion. In contrast to a river, an Alpine glacier fills the valley, attacking both the valley bottom and its walls. A river valley has a characteristic V-shape cross- sectional profile; a glacially modified valley has a U-shape profile. The glacier also develops steep walls at the head of the valley, revealed after the glacier has melted away as a spectacular bowl-shape depression, a cirque. Both a m aster glacier and its smaller tributary glaciers maintain the U-shape profile. After the ice has disappeared the tributaries are left high as hanging valleys, their streams flowing over the precipice of the master valley as waterfalls, as illustrated in Yosemite National Park, California. Action of valley glaciers followed by their retreat has created the world’s most spectacular scenery. 1

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LECTURE 18: GLACIERS

Glacier ice is a metamorphic rock. As a glacier is nourished by snowfall (deposition of “sediment”), theolder buried snow metamorphoses as the delicate snowflakes become more compact and rounded,transforming into “old snow” or firn. With further compaction the trapped air is mostly driven out andthe ice crystals continue to coarsen and develop interlocking projections, all of these changes occurringas the material remains solid, a metamorphic process.

Whether a glacier is confined by valley walls (an Alpine glacier), or whether it is an overspreading icesheet, its internal processes are the same. At high elevations there is a zone of  net accumulation, and aglacier in an ideally steady state maintains a constant size and shape as the ice flows to lower elevations,ultimately to disappear in a zone of  net wastage. Wastage can occur by melting or by discharge of icebergs. A water molecule in a snowflake deposited high upon a glacier travels down into the body of the ice (it gets buried by later snowfalls), to emerge again to the surface in the zone of net wastage.Under most circumstances, internal flow is streamline: the pathways of individual particles, whetherH2O molecules or embedded debris, are parallel. Streamline flow is in contrast with turbulent (chaotic)flow within a river.

Under short-term stress, ice acts as a brittle material. It shatters and can develop deep crevasses (openfractures). Under high confining pressure equivalent to a depth in the glacier greater than ~100 meters,and under sustained long-term stress, the ice acts as a ductile material. Deep ice deforms by flowing.Typically, a glacier flows partly as an entire body of ice sliding across the bedrock, but there is alsointernal deformation, the upper part flowing more rapidly while motion at the base of the glacier, orwhere it is in contact with valley walls, is retarded by friction against the bedrock.

In a Polar ice sheet, which is a “cold” glacier, the atmospheric temperature remains below freezingthroughout the year; a snowstorm can occur in winter or summer. The surface temperature of the icemay be -10° or -15°C, and the deeper ice is even colder. (Older ice was precipitated during a colder IceAge episode.) The temperature increases toward the base of a Polar ice sheet due to geothermal heat

that continually rises from the bedrock.

In a temperate or “warm” glacier enough melting and transport of heat energy occurs to bring the entireglacier exactly to the melting (= freezing) point. A temperate glacier is 0°C at the surface, and slightlycolder at the base. Ice floats on water; therefore ice is less dense than water. Application of pressuretends to shift H2O into the denser state, which is the liquid state. Therefore the base of the glacier, athigher pressure, must be colder than 0°C to remain solid.

Pure ice is too weak and easily deformed to be an effective agent of erosion. Ice laden with rock fragments is a highly effective engine of erosion. In contrast to a river, an Alpine glacier fills the valley,attacking both the valley bottom and its walls. A river valley has a characteristic V-shape cross-sectional profile; a glacially modified valley has a U-shape profile. The glacier also develops steep

walls at the head of the valley, revealed after the glacier has melted away as a spectacular bowl-shapedepression, a cirque. Both a master glacier and its smaller tributary glaciers maintain the U-shapeprofile. After the ice has disappeared the tributaries are left high as hanging valleys, their streamsflowing over the precipice of the master valley as waterfalls, as illustrated in Yosemite National Park,California. Action of valley glaciers followed by their retreat has created the world’s most spectacularscenery.

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Glaciers deposit till, a chaotic, unsorted sediment consisting of all particle sizes from microscopic, toclasts the size of a house. The landform consisting of till is a glacial moraine, which may be depositedbeneath an ice sheet as a ground moraine, or heaped up at the snout of a glacier as an end moraine.Lateral (side) moraines of merging valley glaciers join down-glacier, forming a medial moraine.

In the northern U. S. and much of Canada, landscape that was recently covered by an ice sheet may bemantled by ground moraine, a jumbled heap. Drainages are not yet integrated; there are countlessswamps and lakes whose cavities were scooped by the glacier, or that remained after blocks of strandedice finally melted. In late stages of glacial retreat, pressurized meltwater passes through tunnels locatedwithin or at the base of a glacier. Water-reworked glacial sediment is left behind as ridges that snakeacross the countryside, and may even go up and down over hills.

LECTURE 19: ICE AGES

During most of geologic history the earth was ice-free. The current deepfreeze began some 30 to 40million years ago when Antarctica, and later the Northern Hemisphere, became glaciated. There was aprolonged glacial interval between 0.6 and 0.8 billion years ago, and an earlier Ice Age at 2.4 billion

years has been documented. The evidence suggests that at other times, world climate was warm andequitable from pole to pole in spite of long winter nights in the high latitudes. Geologists refer to a“Greenhouse” Earth (no glaciation), or an “Icehouse” Earth (extensive ice sheets present, as today), andthere is evidence for a former “Snowball” Earth when the entire planet was frozen, the oceans beingcoated with ice a kilometer thick! Snowball Earth was promptly followed by Hothouse Earth, a time of unbearably hot climate worldwide that would have killed all but microscopic life. You don’t want tohave been around during the harshness of Snowball Earth or Hothouse Earth.

The configuration of land and sea helps to explain the appearance and disappearance of glaciations onthe very long time scale. Ocean water transports heat energy efficiently from tropical to polar regions.If a polar region is occupied by a continent (such as present-day Antarctica at the South Pole) or by anocean (such as the present-day Arctic Ocean at the North Pole) whose interchange with the world ocean

is restricted, the polar regions become thermally isolated and an Ice Age results. The positions of waterand landmasses change because of the drift of continents that are embedded in the tectonic plates,themselves in motion. Before breakup, the southern supercontinent (Gondwana) drifted across theSouth Pole. During early Paleozoic time, ice sheets developed in what is today the Sahara Desert; inmid-Paleozoic time the ice centered in what is Brazil today, and even later in what is Antarctica today.

As a moist air mass ascends over a Polar ice sheet, precipitating H2O as it goes, the heavy stable isotopeof oxygen (18O) is precipitated more effectively than the light isotope (16O). This process of partialseparation is called isotope fractionation. As precipitation continues with preferential loss of the heavyisotope, the 18O/ 16O ratio in water vapor in the air mass becomes smaller and smaller, and so does theassociated later precipitation. Consequently rain and snow, which comprise meteoric water (waterprecipitated from the atmosphere) are isotopically “light.” Moreover, the isotope fractionation is more

pronounced at lower temperature. Thus summer snow is isotopically “light” and winter snow is “verylight.”

We can make thousands of isotopic analyses along the length of a core retrieved from the ice sheet inGreenland or Antarctica, and count annual summer and winter layers, somewhat like counting tree rings,and the isotopic compositions also provide information about average annual temperature as far back asabout 250 thousand years in Greenland, and back to ~750 thousand years in Antarctica. (Future drillingin Antarctica may penetrate ice more than a million years old.)

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 Associated changes occur in the ocean, the ultimate source of the H2O in glacier ice. As isotopicallylight ice accumulates on the continents, the heavy oxygen isotope (18O) is left behind preferentially inthe ocean. Foraminifera, single-celled organisms typically about the size of a sand grain, secrete shellsof calcium carbonate. The oxygen isotopic composition changes from heavier during an Ice Age, tolighter during intervals when the ice has melted, returning the light H2O to the ocean. We may retrievea core of deep-ocean sediment and make many analyses of the oxygen in foraminifera going back several million years. (Sedimentary deposition in the mid-ocean is very slow). Data from glacier iceand from deep-ocean cores are complementary, and they spell out details of the Pleistocene Ice Age.

Causes of climatic fluctuation are extraordinarily complex. During the Cenozoic Era, climate becamecooler, culminating within the last 3 or 4 million years in a series of 40-thousand to 100-thousand yearglacial cycles. The overspreading polar ice sheets slowly build, and then melt back catastrophicallyrepeatedly. To a remarkable degree, this behavior seems to be explained by Milankovitch cycles. Themathematician M. Milankovitch noted that the eccentricity of the earth’s orbit around the sun variesfrom a near-perfect circle, to an ellipse, and back again with ~100 thousand year cycle. The precession,or “wobble” of the earth’s spinning motion (~23 thousand year cycle) causes the projection of its spin

axis to draw a circle in the sky. The degree of tilt of the earth’s spin axis with respect to the plane of itsorbit oscillates with a period of ~41 thousand years.

These subtle modulations of the earth’s basic orbit and spin cause the distribution of the sun’s heatenergy to vary within the course of a year. Glaciers grow during prolonged intervals of relatively mildsummers and mild winters (low seasonal contrast). During periods of extremely hot summers and coldwinters (high seasonal contrast), the annual snowfall cannot survive the hot summers, and the glaciersmelt back. Timing of the advances and recessions of polar ice sheets correspond well with climaticcycles that are calculated from Milankovitch theory.

The concentrations of atmospheric greenhouse gases also influence climate. Water vapor, CO2, andCH4 (methane) are examples of greenhouse gases. They permit the sun’s visible light to penetrate to the

earth’s surface. Some of the energy that strikes the ground is returned skyward as longer-wavelengthinfrared radiation, which is blocked by the greenhouse gases. The greater the concentration of greenhouse gases, the more effectively the atmosphere traps the heat energy.

Bubbles in glacier ice trap ancient atmosphere that can be dated by counting summer/winter ice layers asdiscussed above. The ice preserves a record of ancient fluctuating levels of atmospheric CO2 that, whencombined with historical measurements, show a precipitous increase within the past century or so. CO2 is a by-product of combustion, whether of burning of fossil fuels (industrialized nations) or burning of fields and forests (developing nations). World climate is currently warming at a pace that is increasinglyalarming to climatologists (and it should alarm all of us!).

LECTURE 20: GRAVITY AND MOUNTAINS

The force of gravity causes every particle that has mass to attract every other particle. As the amount of mass increases, the gravitational attraction increases. As the distance between the particles increases,the gravitational attraction decreases. To describe the attractive force between bodies composed of many particles (for example, gravitative force between your body and the earth), it is convenient to think of all of the mass to be located at a single point – the object’s “center of gravity.” For example, theearth’s center of gravity lies at its physical center. The mathematical expression is:

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Force of gravity is proportional to m1m2 / r2, where m1 and m2 are two masses, and r is the distancebetween their centers of gravity.

We may describe the shape of the earth by a series of approximations. To a first approximation the earthis a sphere. Even if it had not started out with a spherical shape, it would have become a sphere asevery particle tries to get as close as possible to the center of the earth (its center of gravity). Thisimplies that the shape of the earth can change; the earth can deform, which implies further that rocks inthe deep interior, although solid and under very high pressure, do not have much strength. On a shorttime scale, a rock acts as a brittle material; it shatters when hit by a hammer or it ruptures by faultaction. On a long time scale of thousands of years or longer, rock acts as a ductile material; it flows just as a ball of silly putty flattens under its own weight. (On a short time scale, silly putty also acts as abrittle material. If you abruptly stretch a ball of silly putty it breaks apart.)

Secondly, the spherical earth is rotating, which draws the equatorial region outward into a bulge whilethe polar regions are flattened. A sphere, and the modified shape of a rotating earth, the spheroid, aresmooth surfaces described by simple mathematical expressions.

If you were standing at sea level on the Equator, you would weigh less than if you were standing at theNorth Pole. This is because (i) the earth’s equatorial radius is larger than polar radius (at the Equatorthere is a greater distance between you and the earth’s center), and because (ii) the daily rotation tendsslightly to “levitate” you away from the earth at the Equator, but not at the North Pole.

Thirdly, the spheroid is the basis for a further approximation, an irregular shape with depressions andhumps, the geoid. Sea level describes the shape of the geoid. Because each water molecule is ablefreely to seek the lowest possible elevation, the sea surface is level. (It is not flat ; it wraps around theglobe!) Sea level in the interior of a continent could be determined in principle by digging a slot canalto that spot, and connected to the world ocean at the other end. The ups and downs of the geoid are notwell understood, as they are the result of uneven distribution of mass (and associated gravity field) verydeep within the earth.

Ideas about isostasy—flotational equilibrium amongst large segments of the earth’s crust—began in themid-1800s in India. The occasion was in measurement of distance between a stake in Kaliana, at thefoot of the Himalaya Mountains, and a stake in Kalianpur 600 kilometers due south. Conventionalsurveying techniques gave an answer with a measurement uncertainty of about 0.2 meter, but anindependent astronomical technique that utilizes a plumb bob (a heavy weight dangled on a string) gavean answer that was discrepant by 150 meters from the result of the surveying technique.

The Rev. J. H. Pratt, Archdeacon of Calcutta, correctly identified the astronomical technique to give anincorrect result, and it is because the plumb bob in Kaliana is deflected toward the local towering massof the Himalaya Mountains. Pratt calculated that if the Himalayas were an “extra mass” perched at highelevation, that the plumb bob should not just be deflected; in fact it should be deflected three times more

than is noted by actual observation. He had to scrap the extra-mass hypothesis, and this led to theconcept of isostasy.

Pratt’s computations led him to postulate that mountains originate chiefly through vertical uplift, just asa rising mass of bread dough becomes less dense as it expands into a greater volume. In the Pratt modelof isostasy, high mountains are underlain by least dense crust, low plains by more dense crust, and thedensest crust underlies the ocean floor. All segments of more dense or less dense crust are “floating”upon even more dense material at depth.

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 The British astronomer Airy proposed an alternative model whose analogy is logs of the same densitybut different diameters, floating in a pond. In the Airy model of isostasy, high topography is underlainby thick crust, and low topography is underlain by thin crust of the same density.

To summarize, Airy’s situation of isostasy is accomplished through crust of varying thickness, the baseof the crust being a mirror image of its topographic surface. In Pratt’s model, a dense plate initially of uniform thickness expands upward to various extents, and in doing so, acquiring different densities.

On a very broad scale of continental crust vs. oceanic crust, both hypotheses are valid. Continentalcrust comprised of low-density granitic material stands higher than oceanic crust comprised of high-density basalt (as explained by Pratt’s hypothesis). Thick continental crust (~35-40 km) stands higherthan thin (~7 ± 1 km) oceanic crust (as explained by Airy’s hypothesis). Within a more restrictedregion, such as in the contrast between the Himalaya Mountains in northern India vs. lower country inSouth India, Pratt’s hypothesis does not explain isostatic balance very well. South India is comprised of continental crust, high-grade metamorphic rocks that long ago were mountains perhaps like the modernHimalayas. On a worldwide basis, Airy’s explanation gets credit for at least 2/3 of isostatic balance, and

Pratt’s explanation gets credit for the remainder, but both are valid explanations.

According to Airy, the Himalaya Mountains should be underlain and buoyantly supported by athickened “root zone” of low-density crust, analogous to a big log that both rises higher above and sinksdeeper beneath the pond water level. Seismic evidence brilliantly confirms that the crust beneath theHimalayas and adjacent Tibetan Plateau is of about double normal thickness.

Currently the Himalayas are experiencing rapid erosional attack. Even if the processes that created themountains were no longer active, the Himalayas would respond to erosion by rising vertically asmaterial is removed from the surface. Material of the surrounding mantle flows inward to occupy spacevacated by the ascending crustal root zone, as silly putty would do. Processes of erosion and isostaticuplift continue until both the root zone and mountains have disappeared, resulting finally in a low plain

comprised of strongly deformed metamorphic and intrusive igneous rocks that had originated deepwithin a mountain range. Vast areas, Precambrian shields, are of this origin. Isostatic compensationcauses eroding mountains to be rejuvenated, to persist about three times longer than they would in theabsence of this process.

What is the origin of the world’s greatest mountain chains (Himalayas, Alps, Andes, great ranges inChina, etc.) that are supported by thickened root zones? Mapping of faults and folds in these mountainsindicates that horizontal transport of material has far exceeded the vertical uplift. Pratt’s postulate of vertical uplift is correct, but it is a mere side effect of a larger phenomenon. As forces of compressionhave jammed the crust together, it deformed and thickened, bulging downward into the mantle andupward into the sky.

LECTURE 21: EARTH MAGNETISM

A magnetic field (a volume of space where magnetic force is present) is conveniently described bymagnetic lines of  force. In principle, the lines could be mapped if we were to position a compassneedle at all points of space, and plot its direction of pointing. A magnetic field has a “size” and“shape.” The intensity, or strength of the field is symbolized by the degree to which the lines of forceare crowded together, greater crowding corresponding to a more intense field. Any object that has mass

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responds to the force of gravity, but the magnetic force affects only magnets. We cannot sense magneticforce directly.

Magnetic lines of force can occupy the interior of the earth, and outer space above the earth. Each line,no matter how complexly shaped, is a closed loop. In the field surrounding the earth, which acts as amagnet, one end of the compass needle is attracted toward the North Magnetic Pole, while beingrepelled away from the South Magnetic Pole. Gravity is an attractive force only, but magnetism haspolarity, i.e., both attraction and repulsion.

Magnetism originates by an organized motion of electrically charged particles. One manifestation of motion is electron “spin,” and in most materials the electrons are paired such that two counterpartelectrons are spinning in opposite directions. The effects of their spin cancel out; there is no netorganized motion, and the material is non-magnetic. In a permanent magnet there are unpairedelectrons whose directions of spin are aligned, and in this sense there is an organized motion of electricalcharge. In an electromagnet, the organized motion is an electric current, a flow of electrons through aconductor. The field associated with an electromagnet disappears when the current is shut off.

Could the earth be behaving as a giant permanent magnet? Rocks contain permanently magneticminerals such as magnetite—magnetic iron oxide (Fe3O4). As basalt lava emerges at about 1200°C andcools, it is already fully solid by 900°C, but its grains of magnetite are still too hot to act as magnets.Thermal agitation causes the directions of electron spin to be chaotic and disorganized. Permanentmagnetism begins to develop as cooling drops through the Curie temperature (580°C for magnetite).Temperature increases with depth in the earth such that all rocks deeper than the base of the crust arehotter than the Curie temperature for any magnetic mineral. Permanently magnetized minerals canaccount for only about 2% of earth magnetism.

Moreover, monitoring of the earth’s magnetic field shows that both the directions of the lines of force,and the strength of the field are continually changing in a very impermanent fashion. Currently, thestrength of earth’s magnetic field is rapidly diminishing. Thus, in some sense the earth must act as an

electromagnet. In a dynamo, mechanical motion (spinning of magnets inside the machine) generateselectricity. In an electric motor, electricity causes magnets to spin, producing useful mechanical motion.Thus mechanical motion, an electric current, and a magnetic field are associated. This condition isfulfilled in the earth’s outer core, which is capable of internal motion because it is liquid, and which iscomprised of iron-nickel alloy that can conduct electricity. A magnetic field is created in the core, someof it “leaking” up to the earth’s surface. We postulate that ascending and descending convection cells inthe liquid alloy are what activate the earth’s internal dynamo. As the complex pattern of convection inthe core changes, so do the directionality and strength of the magnetic field observed at the earth’ssurface.

When a basalt flow cools below the Curie temperature for its magnetic minerals, a permanent magneticfield is created whose lines of force are parallel to the earth’s local lines of force. At the earth’s surface

the lines are horizontal at the magnetic equator, and dipping into the earth at steeper and steeper anglesat higher magnetic latitudes, becoming vertical to the surface at the magnetic pole. We may drill out acore of rock and determine the orientation of its magnetic lines of force, and from this information wemay calculate the location of the magnetic pole when the rock formed. For rocks that originatedrecently, determinations of many magnetic pole positions plot as a swarm that is centered upon therotational pole, not the magnetic pole that happens to be located currently in northern Greenland.Conclusion: the position of the magnetic pole, averaged over thousands of years, centers upon the

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rotational pole. Earth magnetism serves as a proxy (an indirect indicator) for locating ancient rotationalpoles, which, as we shall see, may be located very distantly from the modern pole position.

Occasionally, at random times, the magnetic polarity suddenly flips—north becoming south, and viceversa. Thus we have a “normal” magnetic episode in which the North Magnetic Pole is located where itis now, or a “reverse” episode of opposite polarity. By using the K-Ar method to date many basalt flowsof normal or reverse magnetic polarity, we may pinpoint the times of magnetic reversal quiteaccurately. The most recent reversal occurred about 0.78 million years ago, and the field has reverseddozens of times within the past few million years. During any time interval of normal or reversepolarity, the magnetic field strength fluctuates just as it does today. Other than for reversed positions of the magnetic poles, the normal state behaves the same as the reversed state of the magnetic field.Causes of the earth’s magnetic field, its fluctuations and reversal behavior, are not well understood.

LECTURE 22: GEOLOGY OF THE OCEAN FLOOR

The character of the mid-ocean ridge system may be seen in Ohio-size Iceland, an island that sitsastride the Mid-Atlantic Ridge. Iceland is constructed of basalt volcanoes and flood basalt flows, and it

is subject to numerous but not especially destructive shallow earthquakes. As we follow the Mid-Atlantic Ridge to the south, we see that it maintains a midway position between Europe and Africa onthe east, and South and North America on the west. It is severed in many places where the ridge crest isoffset laterally by fracture zones. The ridge system, which occupies approximately the central one-third of the Atlantic Ocean basin, has a symmetrical profile that features a sharp medial valley runningalong the crest of the ridge. Parallelism of the ocean margins and the central ridge makes the Atlanticappear somewhat like a great winding river.

The ridge system runs below Africa, continuing toward the central Indian Ocean where it forks. Onebranch leads northward, thence through the Gulf of Aden, which separates the Arabian Peninsula fromthe Horn of Africa. There it branches again, one arm leading up the axis of the long, narrow Red Sea,thence up the Gulf of Aqaba and through the Dead Sea Rift along the Jordan-Israel border. Another

branch leads down through Ethiopia and African countries farther south where it is manifested as theEast African Rift Valleys. These fault-bounded valleys contain active volcanoes and a series of lakes,some of them with floors well below sea level. These depressions could not have been carved solely byrivers, which cannot erode significantly deeper than sea level; rather, the valleys were down-droppedalong big faults. In places, the ocean ridge system runs onto a continent, East Africa being an example.In size and shape, the profile of the continental rift valley system (for example, in Kenya) closelyresembles the profile of the submerged ridge (as in the mid-Atlantic).

Resuming back at the mid-Indian branching point, we follow the ridge system as it maintains a midwayposition between Australia and Antarctica, thence into the Pacific Ocean. Here the ridge is notsymmetrically positioned, but trends way toward the eastern side where it is known as the East PacificRise. The crest of the Rise trends up the axis of the Gulf of California, which separates mainland

Mexico from a long prong of Mexican territory called Baja California. The ridge system runs agroundup through the western side of the State of California where it is known locally as the San AndreasFault System, thence out into the Pacific just north of San Francisco, and offshore up to its terminationin the Gulf of Alaska. This great underwater mountain range, 75 thousand kilometers long, whichoccupies all of the world’s major ocean basins, was not even known until serious exploration of theocean floor commenced in the mid-1900s.

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Just as the ridge system is a topographic high in the ocean floor, its opposite is the ocean trench system,a topographic low. In contrast to the pattern of the mid-ocean ridge system, almost all of the trenchesare associated with the Pacific Ocean, being located along its margin or in adjoining parts of the Atlanticand Indian Oceans. (One exception is a trench in the distant Mediterranean Sea.) Trenches are long,linear furrows, some deeper below sea level than Mt. Everest, the highest point of land, rises above sealevel. Trenches are sites of violent earthquakes that are shallow beneath the trench floor, defining adipping plane oriented downward toward the neighboring continent. That is, the plane dips down to theeast beneath South and North America, to the north beneath the Aleutian Islands, and to the west along acomplex series of trenches offshore from Asia and Australia. Foci of the deepest of these deep-focus earthquakes approach 650 kilometers below the earth’s surface. Explosive andesite volcanism isassociated with the trenches, either as giant volcanoes perched atop the Andes Mountains (namesake of andesite), or as a string-of-pearls-like series of islands comprising an island arc, of which the AleutianIslands are an example. Andesite composition is midway between that of basalt and granite (or itsextrusive equivalent, rhyolite), and andesite volcanism can be substantially explosive.

LECTURE 23: CONTINENTAL DRIFT

For decades preceding the 1970s, geologists had noted some amazing features about the earth that canbe explained only by postulating that a former supercontinent (or perhaps two supercontinents) hadrifted apart, and the fragments that today are recognized as continents had drifted laterally over the faceof the globe. For example, restoration of the Americas against Europe and Africa reveals an excellentfit if the edges of continental shelves, not coastlines, are used in the fit. (Continental shelves areunderlain by true continental crust.) A possible problem is seen where Africa would overlap thenortheast corner of Brazil if the two landmasses were to be restored. In fact, this is not a problembecause in Africa the overlapping area, the Niger Delta is constructed of new land deposited sincebreakup and drifting apart. The region of Mexico, the Gulf of Mexico, and the Caribbean is verycomplex, consisting of small blocks (called terranes) that presumably have drifted or rotated. Forexample, Yucatan once lay in what is South Texas today.

In ancient rocks we see evidence that local climate differed from today’s climate. For example, glacialdeposits are abundant in the tropical regions of the Southern Hemisphere. Conversely, in islands of theHigh Arctic we see rocks that must have formed in the tropics. There must have been a radicallydifferent relationship among the continents, the poles, and the tropics.

Distribution of fossils provides another line of evidence for continental drift. Even in the 19th centuryit was recognized that fossil organisms of the same species are distributed on landmasses now widelydispersed (for example, South America, Africa, and Antarctica). Many of these organisms could nothave crossed the ocean, as we see from their fossil forms and associated sediments that they adapted tolife in freshwater streams or swamps. Wide dispersal of fossils of an organism that could swim, drift, orfly across the ocean would be consistent with continental drift, but such evidence would present a lessconvincing case for drift.

Yet another line of evidence is seen in the distribution of ancient mountain belts and zones of regionalmetamorphism. For example, a belt of a distinctive age crosses from Brazil out to sea, and resumes inwest Africa. Another such belt consists of the Appalachians in the eastern U.S. and Canada, whichheads out to sea in Newfoundland. It resumes in Ireland and continues through Scandinavia where it isknown as the Caledonian Mountains. In these zones the fossil organisms, rock types, ages, structures,etc. can be correlated nicely across the two sides of the Atlantic. These ancient mountain belts musthave been continuous strands that were broken apart and separated.

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 Yet another piece of evidence is seen in apparent polar wandering curves. We may observe theorientation of magnetic lines of force locked into a rock, and from that information calculate where themagnetic pole must have been when the rock received its magnetic imprint. Another importantassumption is that the magnetic pole and geographic pole (where the earth’s spin axis intersects thesurface) were always located near to one another, just as they are today. If that is so, then magnetic polepositions serve as a proxy for rotational pole positions, which in turn correlate with locations of ancientclimatic zones.

From the viewpoint of rocks in North America, in early Paleozoic times the North Pole appeared to be inwhat is today the southwest Pacific. Analysis of younger and yet younger North American rocks revealsa broadly curved pathway, the “apparent polar wandering curve.” As we come to more recently formedrocks, the Pole appears to approach its modern position. Which moved, the North American continent,the Pole, or both? We can state positively only that there was a relative movement between the Pole andthe continent.

However, if the same analysis is done on rocks from Europe, another polar wandering path appears,

which is not the same as the North American pathway. In principle, the two wandering paths could bereconciled by repositioning these two continents back together. As the continents drifted apart, theirpolar wandering paths also drifted apart, and thus we can state that at least the two continents havemoved apart with respect to one another.

How is continental drift accomplished? For years, geologists were facing the evidence for its reality, butbecause they could not understand the geologic mechanism that would cause drift, many of them feltobligated to declare that continental drift does not occur! They were not stupid; rather, it is a familiarsituation in science that unless you have a theory to explain the observations, then you do not know whatto do with the observations even though you know that existing theory is inadequate. The theory of plate tectonics was to change all this in the 1970s.

LECTURE 24: PLATE TECTONICS

A global map of earthquake epicenters shows them to be generally distributed in long, narrow beltswhose locations we already recognize. Epicenters are narrowly confined to the crest of the mid-oceanridge system. A broader band of epicenters traces the trenches of the Pacific perimeter, and an evenmore diffuse swath of epicenters occupies the world's greatest mountain belt from the Pyrenees on theAtlantic seaboard, through the Alps, Carpathians, mountain ranges of the Middle East, Himalayas, andinto southeast Asia. Throughout the remainder of the globe, earthquake activity is sparse and seldom.

We postulate that the earth's surface is composed of a small number of tectonic plates that are inmotion, chiefly in a horizontal sense. Belts of epicenters and volcanoes mark the margins whereadjacent plates are interacting with one another. Thus "plates" comprise the noun, and "tectonics" is the

verb, referring to these interactions. An analogy is floes of pack ice drifting about, being driven bywater currents underneath. Continents are analogous to ships embedded in the ice, drifting passivelywith the pack. Continental drift is not the most fundamental activity but rather, it is a surfacemanifestation of motions deeper within the earth.

The top of a tectonic plate is simply the land surface in continents, or ocean floor in ocean basins. Theland surface is being eroded while the ocean floor receives deposition of sediment. Plate margins do notpay particular attention to edges of continents and oceans. For example, the African Plate contains the

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entire African continent, the Atlantic Ocean east of the mid-Atlantic Ridge, the western Indian Ocean,the northern part of the Southern Ocean (between Africa and Antarctica), and part of the MediterraneanSea. The northern margin of the Indian Plate slices between the Indian subcontinent and the TibetanPlateau, both within Asia. Thus a plate must be thicker than either continental or oceanic crust, toinclude also some of the earth's mantle.

We identify the bottom of a plate as a narrow zone within the upper mantle where P and S waves slowdown. As we go deeper in the earth it gets hotter, and higher temperature tends to melt materials. Butthe pressure is also greater at depth, a factor that tends to inhibit melting. In this critical zone, called theasthenosphere (Greek: "weak sphere"), the competing factors of high temperature and high pressureare almost in balance such that the mantle is softened, and perhaps a tiny bit melted. In fact, high-frequency S waves, which travel only through solids, almost don’t make it through this zone. Meltedasthenosphere becomes basaltic magma upon ascent to the earth's surface. The asthenosphere acts as aductile "lubricating" layer over which the strong, rigid, brittle plates are in motion. The plates are thelithosphere (Greek: "rock sphere" implying strength and rigidity), comprised of either continental oroceanic crust and uppermost mantle acting coherently as a unit.

Three logical types of interaction among plates are possible at their margins. Plates may be (i) pullingapart from one another, or (ii) colliding head-on, or (iii) slipping sideways past one another. Pull-apartzones are identified with the mid-ocean ridge system, where oceanic crust is being created. Oncontinents, pull-apart zones correspond to rift valleys. Collision zones are equated either with the oceantrench system where oceanic crust is being consumed, or on the continents with compressionalmountain ranges such as the Himalayas. Regions of strike-slip motion are identified with fracture zones.Most of these are submarine, but in places such a zone cuts through a continent, as in the San AndreasFault system. In zones of strike-slip motion, crust is neither created nor consumed, but rather, it isconserved.

Ocean Ridge System: Consider the region of the Arabian Peninsula, Red Sea, adjacent northeastAfrica, and the Gulf of Aden. A few million years ago an unusually warm part of the mantle developed

beneath this region. The mantle expanded and bulged upward, stretching and thinning the continentalcrust overhead, and then causing the crust to rift along faults. The Arabian Peninsula, initiallycontiguous with Africa, began to drift away to the northeast, opening two new, long, narrow seaways:the Gulf of Aden and the Red Sea. A third rift that passes southwestward through Ethiopia has neverwidened and deepened sufficiently to be invaded by a new seaway. In this sense, the East African RiftValleys are a failed arm—one that fell short of its potential to develop into a new ocean basin.

The Mid-Atlantic Ridge illustrates a divergent plate boundary in a more mature stage of development.Under the medial valley at the ridge crest, adjacent plates are pulling apart from one another, openingfractures that are filled with basalt magma ascending from the asthenosphere. The basalt cools andcrystallizes, thus "healing" the fracture which then opens anew. The process of fracture opening andhealing continues such that the two plates not only drift away from one another, but also receive the

addition of new basaltic ocean crust onto their trailing margins.

While this continuous process of seafloor spreading is in progress, the earth's magnetic fieldoccasionally reverses at randomly long and short intervals of time. Basalt that crystallizes during a"normal" episode of magnetic field polarity (in which the magnetic North Pole and South Pole are wherewe see them today) inherits a “normal” magnetic directionality. The magnetic field generated bymagnetic minerals (for example, magnetite) in this basalt is added to the magnetic field currently beinggenerated in the earth's core. The result is a positive magnetic anomaly—a place where the earth's

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magnetic field strength is higher than the regional average. Adjacent to this ocean-floor stripe is anothermagnetic stripe that crystallized in a reverse magnetic field, in which the South and North magneticpoles occupied positions that are the opposite of what we see today. Magnetism in magnetic minerals inthis stripe is oriented in the opposite direction; it partially cancels the magnetism coming from theearth's core, resulting is a negative magnetic anomaly where the field is weaker than the regionalaverage.

These stripes are alternately normally and reversely magnetized, being broad if generated during aprolonged magnetic polarity episode, or narrow if the polarity episode was brief. The stripes are oldergoing away from the ridge crest where they had originated. There is a symmetrical magnetic pattern onthe opposite side of the ridge crest.

Of course, magnetic polarity reversals are experienced worldwide, on land as well as at sea. We maysample basalt flows on land and date them using the potassium-argon (K-Ar) method of agedetermination. As a result of intensive sampling and dating, the times of magnetic field reversal havebecome quite well known, the most recent reversal having occurred about 0.78 million years ago. Thispermits us to assign ages to seafloor magnetic stripes, analogous to a pattern of randomly thick and thin

tree rings of known ages. And since speed = distance/time, referring to the age and the distance of agiven stripe from the ridge crest, we may determine the rate of seafloor spreading.

Rates of spreading are different in the various ocean basins, but a typical value is on the order of an inchper year, about the rate that one's fingernails grow. This rate, sustained since the Atlantic Ocean beganto rift open in the Mesozoic, can nicely account for the observed width of that ocean. Creation of thepattern of ocean-floor magnetic stripes encompasses a process of many millions of year’s duration.Modern technology that utilizes GPS (Global Positioning System) can be used to determine the positionof a point on land within an error of a few millimeters—the distance of continental drift occurring in justa few weeks to months. By making repeated precise measurements we may track the widening gapbetween, say, specified points in New York and London. The instantaneous rate of continental drift(involving Atlantic seafloor spreading in both directions) over a period of a few years is seen to be the

same as the average rate determined from the analysis of magnetic stripes created over periods of millions of years. The spreading process must be extremely constant, continuous, and prolonged on thegeologic time scale. It is remarkable! Moreover the distance, for example from Austin to New York,both cities being located on the same tectonic plate, is shown not to change. This is consistent with thenotion that the internal parts of tectonic plates are quite inert.

Different parts of the world ocean are of different age but the oldest ocean floor, the area that hasmigrated the greatest distance from the ridge crest, is located in the western Pacific off Japan, havingtraveled almost the entire width of the world's largest ocean. Even here the age is Jurassic, about 150million years, representing less than the latest 4% of earth history! Older ocean floor has beenswallowed up, disappeared from view, which brings us to our second type of plate interaction.

Ocean Trench System: Three different possibilities are seen where plates converge in head-oncollision. If one plate contains oceanic crust and the other continental crust, as along the west coast of South America, the oceanic plate heels over and plunges down under the continental plate. This isbecause oceanic crust is relatively thin and dense. The ocean floor is bent downward into a trenchwhere the plate subducts (Latin: "to lead under") into the mantle. Stored elastic energy that is abruptlyreleased as earthquakes traces the progress of the subducting plate down a dipping plane to depthsapproaching 650 kilometers beneath the earth's surface. The plate, containing material formerly on theocean floor, carries H2O down into the mantle. This added H2O lowers the melting point, encouraging

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melting. Andesitic or granitic magma ascends to form surface volcanoes, or granite or granodioritebatholiths are emplaced within the crust.

What happens to the subducting plate at greater depths is a subject on the frontier of scientificinvestigation, and evidence suggests that the plates can descend all the way to the core-mantle boundary.In this sense, oceanic crust has been consumed back into the mantle.

If both plates contain oceanic crust, one of them subducts beneath the other. Sometimes the roles of these plates "flip" such that the formerly overriding plate becomes the subducting plate.

If both plates contain thick, strong, low-density, buoyant continental crust, sustained subduction of suchmaterial into the high-density mantle is not possible. The analogy is of a cork caught in a whirlpool.The cork may be sucked down for a while, but eventually its buoyancy will cause it to pop back to thesurface. In continental collision zones we see one plate thrusting over the other, creating continentalcrust approaching double the normal thickness, consisting of an enormous pile-up of crumpled rocks. Amountain range has been born, the classic example being the greatest of them all, the Himalayas. Thecrust thickens, bulging downward into the mantle and towering high into the sky. Ancient collision

zones, long since beveled by erosion down almost to sea level, are present in Precambrian shields.

Transform Faults: The third type of plate margin experiences strike-slip motion. As one plate slipspast the adjacent plate, lateral transport over vast distances of hundreds to thousands of kilometers canbe accommodated. The vertical component of such motion is relatively trivial. These faults,exemplified by oceanic fracture zones or by the San Andreas, are called transform faults because attheir two ends they transform into some other type of plate tectonic boundary. For example, the ends of an oceanic fracture zone may terminate against offset segments of a mid-ocean ridge. The zigzag offsetsegments of the Mid-Atlantic Ridge apparently were present from the very beginning when thesupercontinent rifted apart.

Hot Spots: The Hawaiian Islands illustrate a hot spot, which in this case is in the middle of the Pacific

plate far from its margins. In a hot spot, ascending heat is concentrated into a relatively small area, notalong an extensive elongated zone such as a mid-ocean ridge. As the Pacific plate rides over thestationary Hawaiian hot spot, the plate is perforated by rising basaltic magma, which builds a linearchain of islands. The analogy is of puffs of smoke ascending from a chimney, then drifting downwind.Currently the volcanically active island is the "Big Island" of Hawaii, the southeasternmost island in thechain. To the northwest, the islands are progressively older and more eroded. There is minor volcanicactivity on the adjacent island, and none further beyond. A giant volcano is building offshore from theBig Island, destined one day to become the next new island in the Hawaiian chain. The offshorevolcano has yet to build up another kilometer before emerging above the waves.

What drives the tectonic plates? We can observe plate processes at the earth's surface but we are onlybeginning to understand the pattern of flow of material at depth in the earth. Plate motion is believed to

be driven thermally. Where a portion of the mantle is abnormally warm it expands, becoming lessdense, and it rises toward the surface. Recall that this is possible because rock has two "personalities."Rock shatters when struck with a hammer, but stress applied to a rock over a prolonged time scalecauses it to flow in a ductile manner, even while remaining solid. (Glacier ice does the same.) Wherethe mantle is relatively cool it contracts, becoming denser, and it sinks. A rising-and-sinking internalmotion, called convection, is established in the mantle.

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Where deep mantle is rising we have the ocean ridge system. This provides an efficient way to transferexcess heat energy up to the earth's surface where it is quickly dissipated. The sense of convectivemotion turns laterally, parallel to the earth's surface as the ocean floor spreads and continents embeddedin the plate drift. Where the convection cell heads back into the depths we have subduction of plates. If the earth maintains a constant volume, the global average rate of creation of new crust in the ridge mustequal the rate of subduction of old crust into trenches.

By tracing seismic waves whose ray paths pass through the deep earth in many directions we mayconstruct a picture of mantle that conducts seismic waves just a little faster in one place, and just a littleslower in another place. “Faster” is equated with “cooler,” and “slower” is equated with “hotter.” Thesezones in the mantle in turn correspond to locations of hotspots (hotter) and old, dead, subducting(sinking) tectonic plates (cooler).

LECTURE 25: PETROLEUM

Petroleum (also known as crude oil) is composed of simple to complex hydrocarbon molecules.Hydrocarbons are molecules composed chiefly of hydrogen (H) and carbon (C). Petroleum is primarily

composed of a simple group of hydrocarbons molecules called the alkanes. Alkanes are composed of chains of carbon bonded to hydrogen and have the chemical formula CnH2n+2, where n refers to thenumber of carbon atoms. Methane (CH4), also called natural gas, is the simplest (shortest C-chain)alkane.

As organic matter is buried, it undergoes diagenesis (any changes to the sediment and fossils that occurafter deposition at relatively low temperature and pressure). As burial temperature and pressureincreases, diagenesis transforms the buried organic matter into kerogen, a waxy solid composed of complex hydrocarbon molecules. At even higher temperature and pressure, kerogen breaks down intosimpler hydrocarbons to make crude oil and natural gas. This breakdown of kerogen into oil and gas iscalled cracking. Crude oil can then be refined by distillation so that the lighter hydrocarbons likegasoline are separated from the heavier hydrocarbons like diesel fuel.

In order to form economical and extractable accumulations of oil and gas, four things are necessary: asource rock, reservoir rock, seal, and trap. First, a seals and prevent the oil and gas from leaving thereservoir rock. A trap is also required in order for oil to be concentrated in a particular part of thereservoir rock. Traps may be geologic structures like anticlines, faults, and salt domes. However, theymay also be stratigraphic traps. In a stratigraphic trap, a reservoir rock body is surrounded by sourceand seal rocks just by the way that sediments with different properties were originally deposited inadjacent environments. Fro example, as a meandering river migrates laterally, point bar sand (apotential reservoir rock) is buried by floodplain mud (a potential source and seal), setting up a potentialstratigraphic trap for oil and gas. In a hydrocarbon reservoir, pore space in the rock may be occupied bywater, oil, and gas. In this situation, water (more dense than oil) will settle to the bottom of thereservoir, while gas (less dense than oil) will rise to the top of the reservoir; oil will accumulate in

between the water and gas.

Drilling a well to pump oil and gas is expensive, so geologists rely on seismic surveys to help themdecide where to drill. Artificially generated seismic waves are blasted into the ground and the seismicwaves are reflected off of different layers below the source rock for the hydrocarbons is required. Thesource rock contains the organic material that is transformed into oil and gas. Shale, which would haveoriginally been deposited as organic-rich mud in a barrier island lagoon, the prodelta, or a meanderingriver floodplain, makes a good source rock. When the source rock is buried and exposed to high

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temperature and pressure, the hydrocarbons will migrate out of the source rock and into overlying strata.A reservoir rock is a rock that will store the oil and gas that gets “squeezed out” of the source rock.Reservoir rocks have high porosity and permeability. Mature, well-sorted sandstone, which would haveoriginally been deposited as sand in the dunes of a barrier island, the point bar of a meandering stream,or the channel of a delta distributary, makes a good reservoir rock. In order for the hydrocarbons to stayin the reservoir, there must be a rock to serve as a seal above the reservoir rock. Impermeable rocks likeshale and evaporites make good earth’s surface. Geophone or hydrophone receivers record the reflectedwaves. Finally, computer-processed seismic data is used to create detailed images of the rock andstructures below the Earth’s surface. Because some oil may stick to mineral grains in the reservoir rock,not all the oil can be pumped out. Secondary recovery techniques, like injecting gas or chemicalsolvents into a well, mobilize the oil so that more oil (up to 50-60% of the oil) can be recovered from thereservoir.

Production of oil is expected to peak world wide in this decade, and world oil reserves will only last afew more decades. U.S. oil production has already peaked. Domestic oil production has been decliningover the last 20 years or so, while consumption has increased. To satisfy this increasing demand, theU.S. has been increasingly relying on imports of foreign oil. A majority of the world’s oil reserves are

located in the Middle East. Production and consumption of this nonrenewable resource (fossil fuelstake millions of years to form) is associated with a variety of economic, political and environmentalconsequences.

LECTURE 26: LIMITATIONS OF THE EARTH FROM A GEOLOGIST’S PERSPECTIVE

Demographers are monitoring worldwide population, which is experiencing a net increase of births morethan deaths of approximately 2.4 persons/second, or about 1.14% increase per year. However, theincrease is "compound interest" in the sense that the previous year also included a population increaseover its preceding year. Compounded at a 1.14% annual increase, population will double in about 50years. Another factor is the technological advantages resulting from the Industrial Revolution, resultingin greater human longevity. Since approximately 1700 AD, the rate of population increase has been 100

times greater than it was before that time. World population currently is 6.6 billion persons, increasingat an alarming rate of 75 million persons/year.

At the same time, we see favorable population trends. Population will remain at a steady state if thestatistical average female fertility rate is 2.1 children per female. In many industrial nations, the femalefertility rate is about 1.6 to as low as 1.2 children—substantially below the steady-state rate of replacement. (U. S. population is currently growing, but more due to a high influx by immigration.)The counterpart of low birth rates in technologically advanced nations are much higher rates in thepoorer nations that ironically are least able to care for their citizens. However, in many of thesecountries the high rates are being dramatically reduced. If human reproduction were to decline instantlyto just the replacement rate, population would still continue to climb to 10 or more billion because somany persons today are young children who are yet to begin families.

The vigorously debated theory proposed by Thomas Malthus (English clergyman, late 1700s) relatespopulation growth to food supply. According to Malthus, population grows in a geometric progression(1 unit, 2, 4, 8, 16, etc.), whereas food supply increases only arithmetically (1 unit, 2, 3, 4, 5, etc.), andthus insufficient food supply will ultimately limit the growth of human population. Those who contestthis theory argue that there is sufficient time for world population to be brought under control beforeMalthusian starvation becomes a serious threat. What seems to be happening is that Malthusian doom is

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actually occurring, but in limited parts of the world such as some countries in sub-Saharan Africa,notably in Somalia.

Studies show a poor correlation between the birth rate in a given country, and certain factors thatadmittedly are difficult to quantify. These include radical methods of birth control, quality of publiceducation, and religious orthodoxy. However, there is a very good anti-correlation between birth rateand per capita usage of energy. To have abundant available energy is the key to averting theconsequences of Malthus.

We needy persons must be sustained by the earth's resources, which may be classified as renewable ornon-renewable. Renewable resources include food, timber, and in some situations groundwater, whichare replenished on a time scale of months (food) to decades (lumber), to centuries (an average forgroundwater). Thus renewable resources have a short time scale of renewal but they are also consumedrapidly such that replenishment must be continuous. In principle, the stockpile of food would sustainworld population for 9 months if production suddenly were to cease.

Natural processes also replenish non-renewable resources but the time scale is vastly longer than a

human lifetime. Hence these resources, which include metals and fossil fuels, are non-renewable inpractical terms. In principle, fossil fuels could be renewed by combining the combustion products, CO2 and H2O, back into hydrocarbons. However, the energy required to make these synthetic fuels would bemore than the energy gained by burning them, and so this procedure is not feasible.

Non-renewable resources are characterized by (i) sporadic distribution, (ii) increasing rate of usageand extent of usage (finding uses for more chemical elements), and (iii) exhaustibility. It is a fact of nature that fossil fuel resources and ore deposits are concentrated into just a few "pinpoint" localities.An ore deposit contains some valuable metal (not groundwater, sand and gravel, or fossil fuel) inconcentrations high enough to make it profitable to mine. Depending upon market fluctuations, amarginal deposit may be an ore one day but not the next. Improved efficiency of extraction of rareconstituents can make a deposit to be an ore that formerly was not an ore with older technology.

Because of sporadic distribution, large nations are more likely to contain somewhere within theirborders the "mix" of resources necessary to sustain modern technological civilization. Small nations aremore likely to contain just a handful of valuable economic deposits, or none at all. Russia is the mostnearly self-sufficient of all nations, but no one country or entire continent is completely so. All nationsmust engage in buying and selling of resources in order to develop. Even abundant resources such ascoal are sporadically distributed. Coal resources are heavily concentrated in the Northern Hemisphere incontrast to the impoverished Southern Hemisphere.

The rate of usage of resources has stepped up enormously. Some of them are currently being used atrates that are tens of thousands of times faster than the rate of usage when records first began to be kept.

Exhaustibility is described by mathematical models based on the history of resource usage. We mayplot the rate of production of a resource (units/year where a unit could be tons of iron, barrels of oil,ounces of gold, etc.) against time (years). The result is a bell-shape curve pertaining to the time spansince the resource first began to be utilized, until its ultimate exhaustion. The area under the curve(height x width, or units/year x years = units) represents the total number of units of resource that onceexisted.

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The area under the curve may be further subdivided. Take petroleum, for example. The sub-areasconsist of oil already produced, oil in proven reserves, and oil postulated yet to be discovered. Analysisof the history of oil production indicates that for domestic U. S. production, the peak of the bell-shapecurve was reached in the 1970s and we have been on the far downslope ever since. On a worldwidebasis, we are today approaching the top of curve. Fortunately, advances in technology have improveddiscovery, and have enabled us to extract oil much more efficiently out of existing fields. The result isto stretch the curve, sustaining its high level farther into the future and giving us several decades of opportunity to develop alternative sources of energy. In regard to domestic coal in the U.S., we havealready used only a small fraction, and supplies at the present rate of consumption will last at least forseveral centuries.

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