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Geologic Time: Concepts and Principles


Chapter 2 Geologic Time: Concepts and Principles PRINCIPLE OF INCLUSIONS The PRINCIPLE OF INCLUSIONS states that inclusions of one kind of rock in another are always ... – PowerPoint PPT presentation

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Title: Geologic Time: Concepts and Principles

Chapter 2
Geologic TimeConcepts and Principles
Horizontally bedded sedimentary strata as seen
from the North Rim of the Grand Canyon
illustrating the immensity of geologic time.  It
took hundreds of millions of years for these
strata to be deposited as layers of sediment that
were eventually converted into rock.  The
geologic history of the Grand Canyon region can
be read from these sedimentary layers. (photo by
E.L. Crisp, May 2002)
Grand Canyon
  • More than 2 billion years of Earth history are
  • like pages of a book,
  • in the rock layers of the Grand Canyon
  • Reading this rock book we learn
  • that the area underwent episodes of
  • mountain building
  • advancing and retreating shallow seas, etc.
  • We know these things by
  • applying the principles of relative dating to the
  • and recognizing that present-day processes
  • have operated throughout Earth history

Concept of Geologic Time
  • Geologists use two different frames of reference
  • when discussing geologic time
  • Relative dating involves placing geologic events
  • in a sequential order as determined
  • from their position in the geologic record
  • It does not tell us how long ago
  • a particular event occurred,
  • only that one event preceded another
  • For over 200 hundred years geologists
  • have been using relative dating
  • to establish a relative geologic time scale

  •      There was very little advancement in geology
    until the middle of the eighteenth century.  This
    dark time (prior to mid-1700's) for all
    scientific and original thought was mostly due to
    a strict interpretation of the Book of Genesis in
    the Bible.  Geologic time was considered to be
    but a few thousand years (and some people today
    still adhere to a young Earth based on a literal
    interpretation of the Bible). 
  • Fossils were regarded as creatures engulfed by
    the Biblical Flood, freaks of nature, inventions
    of the devil, or figured stones.

  •      In 1650, James Ussher (1581-1665),
    Archbishop of Armagh, Ireland, calculated, using
    genealogies described in Genesis, that Earth was
    created on October 22, 4004 B. C.  Thus, Earth is
    only about 6000 years old.  (INTERESTING NOTE 
    Leonardi da Vinci (1452-1519) estimated that it
    took 200,000 years just to deposit the sediments
    in the Po River Valley in Italy.)
  • During the late 1700s and into the early 1800s,
    many naturalists believed that Earth history
    consisted of a series of catastrophic upheavals
    that had shaped the geologic features of the
    earth. Those who believed in this concept of
    catastrophic earth history became known as
    CATASTROPHISTS. Baron Georges Cuvier (1769-1832)
    is credited as the first to propose this concept
    to explain the rock record.  Cuvier proposed that
    the physical and biological history of Earth is
    explained by a series of sudden widespread
    catastrophes.  Each catastrophe killed life forms
    in a portion of the area affected, new life forms
    were created (by Divine Power) or migrated in
    from elsewhere. 

  •  JAMES HUTTON (1727-1797), a Scottish medical
    doctor (and often referred to as the FATHER OF
    GEOLOGY), proposed a concept in the late 1700s
    now referred to as UNIFORMITARIANISM.  Hutton
    never practiced medicine, but was very interested
    in the processes which formed and shaped the
  • By careful observations, he proposed that the
    physical, chemical, and biological laws of nature
    operated the same way in the past as they do
    today thus, the present is the key to the
    past and we can interpret the rock record as
    resulting from the same laws of nature that
    operate today.
  • This is the concept of uniformitarianism.

  • One of Hutton's greatest contributions to geology
    was his concept of UNIFORMITARIANISM. 
  • This concept, meaning "the present is the key to
    the past", states that by studying geologic
    processes in operation today we can safely assume
    that such processes operated in the past and thus
    we can interpret rocks as a response to geologic
  • With modification, this concept is still the
    basis for modern geologic thought. 
  • We now realize that, although the processes
    themselves probably have not changed with time,
    the rates of some geologic processes may have
    varied drastically from time to time.
  • However, the basics laws of nature are still the
    same today as they were in the past.
  • So, by using this principle and others we have
    constructed a relative time scale.  

Relative Geologic Time Scale
  • The relative geologic time scale has a sequence
  • eons
  • eras
  • periods
  • epochs

Concept of Geologic Time
  • The second frame of reference for geologic time
  • is absolute dating
  • Absolute dating results in specific dates
  • for rock units or events
  • expressed in years before the present
  • It tells us how long ago a particular event
  • giving us numerical information about time
  • Radiometric dating is the most common method
  • of obtaining absolute ages
  • Such dates are calculated
  • from the natural rates of decay
  • of various natural radioactive elements
  • present in trace amounts in some rocks

Geologic Time Scale
  • The discovery of radioactivity
  • near the end of the 19th century
  • allowed absolute ages
  • to be accurately applied
  • to the relative geologic time scale
  • The modern geologic time scale is a dual scale
  • a relative scale
  • and an absolute scale

Changes in the Concept of Geologic Time
  • During the 1700s and 1800s Earths age
  • was estimated scientifically
  • Georges Louis de Buffon (1707-1788)
  • calculated how long Earth took to cool gradually
  • from a molten beginning
  • using melted iron balls of various diameters.
  • Extrapolating their cooling rate
  • to an Earth-sized ball,
  • he estimated Earth was 75,000 years old

Changes in the Concept of Geologic Time
  • Others used different techniques
  • Scholars using rates of deposition of various
  • and total thickness of sedimentary rock in the
  • produced estimates of lt1 million
  • to more than 2 billion years.
  • John Joly used the amount of salt carried
  • by rivers to the ocean
  • and the salinity of seawater
  • and obtained a minimum age of 90 million years

Relative-Dating Principles
  • Six fundamental geologic principles are used in
    relative dating
  • Principle of superposition (Steno, 1669)
  • Nicolas Steno (1638-1686)
  • In an undisturbed succession of sedimentary rock
  • the oldest layer is at the bottom
  • and the youngest layer is at the top
  • This method is used for determining the relative
  • of rock layers (strata) and the fossils they

Kaibab Limestone
Toroweap Formation
Coconino Sandstone
Hermit Shale
Supai Group
  • Horizontally bedded sedimentary strata as seen
    from the North Rim of the Grand Canyon
    illustrating the immensity of geologic time.  It
    took hundreds of millions of years for these
    strata to be deposited as layers of sediment that
    were eventually converted into rock.  The
    geologic history of the Grand Canyon region can
    be read from these sedimentary layers. (photo by
    E.L. Crisp, May 2002)

Relative-Dating Principles
  • Principle of original horizontality
  • Nicolas Steno (1669)
  • Sediment is deposited
  • in essentially horizontal layers
  • Therefore, a sequence of sedimentary rock layers
  • that is steeply inclined from horizontal
  • must have been tilted
  • after deposition and lithification

Kaibab Limestone
Toroweap Formation
Coconino Sandstone
Hermit Shale
Supai Group
  • Horizontally bedded sedimentary strata as seen
    from the North Rim of the Grand Canyon
    illustrating the immensity of geologic time.  It
    took hundreds of millions of years for these
    strata to be deposited as layers of sediment that
    were eventually converted into rock.  The
    geologic history of the Grand Canyon region can
    be read from these sedimentary layers. (photo by
    E.L. Crisp, May 2002)

Horizontal beds of the Morrison Formation near
Cleveland, Utah.
  • The Morrison Formation at Dinosaur National
    Monument, Utah. Note that the beds are strongly
    dipping here.

Sidling Hill Syncline on I-68 near Cumberland,
Maryland (Photo by E. L. Crisp, August, 2005)
Relative-Dating Principles
  • Principle of lateral continuity
  • Nicolas Steno (1669)
  • Sediment extends laterally in all direction
  • until it thins and pinches out
  • or terminates against the edges
  • of the depositional basin
  • Principle of cross-cutting relationships
  • James Hutton (1726-1797)
  • An igneous intrusion or a fault
  • must be younger than the rocks
  • it intrudes or displaces

Kaibab Limestone
Toroweap Formation
Coconino Sandstone
Hermit Shale
Supai Group
  • Horizontally bedded sedimentary strata as seen
    from the North Rim of the Grand Canyon
    illustrating the immensity of geologic time.  It
    took hundreds of millions of years for these
    strata to be deposited as layers of sediment that
    were eventually converted into rock.  The
    geologic history of the Grand Canyon region can
    be read from these sedimentary layers. (photo by
    E.L. Crisp, May 2002)

An basalt dike cutting through granite. The
basalt dike is younger than the granite. (Photo
taken on Cadillac Mountain, Bar Harbor, Maine by
E. L. Crisp, August, 2005).
Cross-cutting Relationships
  • This is a small reverse fault in Allegheny Group
    rocks along Schultz Road in Pleasants County,
    West Virginia.  A dashed line represents the
    fault that is probably associated with the
    formation of the Burning Springs Anticline.
     Light colored mudstones are adjacent to the
    asphalt road.  The Lower Freeport continuous coal
    is near the center of the photo with the Upper
    Freeport sandstone at the top.

Relative-Dating Principles
  • Other principles of relative dating
  • Principle of inclusions
  • Principle of fossil succession

    inclusions of one kind of rock in another are
    always representative of the older rock
    material.  For example, if a granitic magma has
    intruded into a sandstone and chunks of sandstone
    have been incorporated into the rising magma, as
    cooling occurs there will be inclusions of
    sandstone in the granite and the inclusions will
    represent the older rock.

  • Correlation is the matching up of rocks in one
    area to those in another area.
  • There are two types of correlation of rock units.
  • Physical Correlation correlation of rock units
    based on physical characteristics of the rocks or
    position in a sequence of rocks. Assumes that
    the rock units were once continuous.
  • Time-rock Correlation correlation of rock units
    that are time equivalent (rock units in different
    areas that are of the same age).

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  • What are fossils?
  • Any remains or evidence of activity of a once
    living organism (usually restricted to
    prehistoric time).
  • Scientists who study fossils are called
    paleontologists (not archeologists!!!).
  • Two major types of fossils Body fossils and
    trace fossils.

Fossils evidence of past life
  • Types of fossils
  • Indirect evidence includes Trace Fossils
  • Tracks
  • Burrows
  • Coprolites fossil dung and stomach contents
  • Gastroliths stomach stones used to grind food
    by some extinct reptiles

A dinosaur footprint
The Formation of Body Fossils
  •      The usual prerequisites for fossilization to
    form body fossils is the possession of hard parts
    (bones, teeth, mineralized exoskeleton, etc.) and
    the rapid burial of the hard parts by sediment
    (this reduces the amount of oxygen present to
    very low levels and slows decomposition of the
    hard parts).  Usually soft parts of an organism
    rot rapidly.  Only rarely are soft parts
    preserved (such as skin impressions for
    dinosaurs), but under some conditions they are
    preserved and give paleontologists valuable
    information that is usually not present in the
    rock record.  After burial some sort of
    mineralization typically occurs.  Unaltered
    remains are very rare.

Altered Remains
  • Permineralization Mineral matter from
    percolating ground waters is added to pores and
    cavities in bones, shell, teeth, etc.  In this
    type of preseravation the original material is
    still present with new mineral matter added to
    the void spaces.  Many dinosaur bones are
    preserved by this method.
  • Replacement Sometimes original hard parts (bone
    in the case of dinosaurs) is replaced (sometimes
    referred to as petrified, which means turned to
    stone) with new mineral matter of a different
    composition than the original mineral matter
    (often at a molecular level, so the
    microstructure of the original mineral matter is
    preserved).  Silica (as microcrystalline quartz,
    SiO2), iron oxide (hematite, Fe2O3), and calcium
    carbonate (calcite, CaCO3) are common replacement
    minerals (they are also common permineralizing
    agents).  Many dinosaur bones are both
    permineralized and partially replaced.

Altered Remains
  • Recrystallization  The recrystalliztion of
    fossils is another common type of preservation in
    which the original mineral present simply
    recrystallizes (the original crystals grow larger
    and fill most of the void space).  This is more
    common in invertebrate fossils (such as bivalves
    clams, brachiopods, gastropods, etc.) than in
    vertebrate fossils. This form of preservation
    usually destroys or partially obscures the
    original microstructure of the skeletal
    material.  An example would be the
    recrystallization of a clam shell originally
    composed of the mineral aragonite (a metastable
    form of calcium carbonate) to calcite (the more
    stable form of calcium carbonate at low

Altered Remains
  • Carbonization Sometimes soft parts and/or hard
    parts of the body of an organism are compressed
    by burial before decomposition is complete such
    that the volatile substances (such as oxygen,
    nitrogen, carbon dioxide, water, etc.) are
    squeezed out leaving behind a film of fairly pure
    carbon.  This is particulary common in the
    preservation plant fossils (such as ferns and
    leaves Look at the fossil leaves and insects
    from the Green River Formation of Utah that are
    present in the Geology Lab at WVUP, these are
    preserved by carbonization) and some
    invertebrates, but also occurs sometimes for
    vertebrates (for example, fifty million year old
    fossil fish of the Eocene Green River Formation
    of Wyoming, Colorado, and Utah).
  • Molds and Casts Sometimes the hard parts (bone
    or other material) (and sometimes even soft
    tissue) of organisms are buried by sediment and
    even may remain until the sediment is lithified
    (by compaction and cementation), but are later
    dissolved by acidic ground waters percolating
    through the pores of the rock (or decomposed by
    other processes).  This will leave an impression
    of the external morphology of the original
    material that was buried.  This is called an
    external mold.  If later the mold is filled in
    with mineral matter or sediment, a cast is formed
    which mimics the external morphology of the
    original material.  Sometimes internal cavities
    of skeletons (from both invertebrates and
    vertebrates) may be filled with sediment or
    mineral matter resulting in a mold of the
    internal morphology of the cavity that was
    filled, this is called an internal mold. Internal
    molds are quite common for some invertebrates
    (such as for clams and gastropods).

Natural casts of shelled invertebrates
  • Although rocks may be correlated based on
    physical correlation and superposition, this can
    only be done in a limited area where beds can be
    traced from one area to another. Also if we are
    correlating over a large area (from region to
    region, or continent to continent), it is
    unlikely that we can use physical correlation
    because rock types will change.
  • To correlate over large regions and to correlate
    age-equivalent strata, geologists must use
    fossils. The use of fossils to correlate
    sedimentary strata is based on the work of
    William Smith (1812), the first to accurately
    state and use the Principle of Fossil Succession.
  • The Principle of Fossil Succession states the
    assemblages of fossils succeed themselves in a
    definite and determinable order and the age of
    sedimentary strata can be determined by their
    contained fossils.
  • To use the Principle of Fossil Succession,
    geologists and paleontologists use Index Fossils
    (Guide Fossils).

  • The Principle of Fossil Succession is based on
    the following
  • Life has varied through time. Of course this
    implies that evolutionary change has occurred
    over time.
  • Because biologic diversity has varied over time,
    fossil assemblages are different in successivly
    younger strata.
  • The relative ages of fossil assemblages can be
    determined by superposition.

  • Index fossils are used to correlate
    age-equivalent strata via the Principle of Fossil
  • Index fossils have the following characteristics
  • Short geologic time range.
  • Wide geographic distribution
  • Abundant
  • Easily recognizable

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Some More History of Geologic Time
  • Neptunism
  • All rocks, including granite and basalt,
  • were precipitated in an orderly sequence
  • from a primeval, worldwide ocean.
  • proposed in 1787 by Abraham Werner (1749-1817)
  • Werner was an excellent mineralogist,
  • but is best remembered
  • for his incorrect interpretation of Earth history

  • Werners geologic column was widely accepted
  • Alluvial rocks
  • unconsolidated sediments, youngest
  • Secondary rocks
  • rocks such as sandstones, limestones, coal,
  • Transition rocks
  • chemical and detrital rocks, some fossiliferous
  • Primitive rocks
  • oldest including igneous and metamorphic

  • Catastrophism
  • concept proposed by Georges Cuvier (1769-1832)
  • dominated European geologic thinking
  • The physical and biological history of Earth
  • resulted from a series of sudden widespread
  • which accounted for significant and rapid changes
    in Earth
  • and exterminated existing life in the affected
  • Six major catastrophes occurred,
  • corresponding to the six days of biblical
  • The last one was the biblical deluge

Neptunism and Catastrophism
  • These hypotheses were abandoned because
  • they were not supported by field evidence
  • Basalt was shown to be of igneous origin
  • Volcanic rocks interbedded with sedimentary
  • and primitive rocks showed that igneous activity
  • had occurred throughout geologic time
  • More than 6 catastrophes were needed
  • to explain field observations
  • The principle of uniformitarianism
  • became the guiding philosophy of geology

  • Principle of uniformitarianism
  • Present-day processes have operated throughout
    geologic time.
  • Developed by James Hutton (1726-1797), advocated
    by Charles Lyell (1797-1875)
  • William Whewell coined the term
    uniformitarianism in 1832
  • Hutton applied the principle of uniformitarianism
  • when interpreting rocks at Siccar Point, Scotland
  • We now call what Hutton observed an unconformity,
  • but he properly interpreted its formation

Unconformity at Siccar Point
  • Hutton explained that
  • the tilted, lower rocks
  • resulted from severe upheavals that formed
  • these were then worn away
  • and covered by younger flat-lying rocks
  • the erosional surface
  • represents a gap in the rock record

  • Hutton viewed Earth history as cyclical

  • He also understood
  • that geologic processes operate over a vast
    amount of time
  • Modern view of uniformitarianism
  • Today, geologists assume that the principles or
    laws of nature are constant
  • but the rates and intensities of change have
    varied through time
  • Some geologists prefer the term actualism

Crisis in Geology
  • Lord Kelvin (1824-1907)
  • knew about high temperatures inside of deep mines
  • and reasoned that Earth
  • was losing heat from its interior
  • Assuming Earth was once molten, he used
  • the melting temperature of rocks
  • the size of Earth
  • and the rate of heat loss
  • to calculate the age of Earth as
  • between 400 and 20 million years

Crisis in Geology
  • This age was too young
  • for the geologic processes envisioned
  • by other geologists at that time,
  • leading to a crisis in geology
  • Kelvin did not know about radioactivity
  • as a heat source within the Earth

Absolute-Dating Methods
  • The discovery of radioactivity
  • destroyed Kelvins argument for the age of Earth
  • and provided a clock to measure Earths age
  • Radioactivity is the spontaneous decay
  • of an atoms nucleus to a more stable form
  • The heat from radioactivity
  • helps explain why the Earth is still warm inside
  • Radioactivity provides geologists
  • with a powerful tool to measure
  • absolute ages of rocks and past geologic events

Atoms A Review
  • Understanding absolute dating requires
  • knowledge of atoms and isotopes
  • All matter is made up of atoms
  • The nucleus of an atom is composed of
  • protons particles with a positive electrical
  • neutrons electrically neutral particles
  • with electrons negatively charged particles
    outside the nucleus
  • The number of protons ( the atomic number)
  • helps determine the atoms chemical properties
  • and the element to which it belongs

Isotopes A Review
  • Atomic mass number
  • number of protons number of neutrons
  • The different forms of an elements atoms
  • with varying numbers of neutrons
  • are called isotopes
  • Different isotopes of the same element
  • have different atomic mass numbers
  • but behave the same chemically
  • Most isotopes are stable,
  • but some are unstable
  • Geologists use decay rates of unstable isotopes
  • to determine absolute ages of rocks

Radioactive Decay
  • Radioactive decay is the process whereby
  • an unstable atomic nucleus spontaneously
  • into an atomic nucleus of a different element
  • Three types of radioactive decay
  • In alpha decay, two protons and two neutrons
  • (alpha particle) are emitted from the nucleus.

Radioactive Decay
  • In beta decay, a neutron emits a fast moving
    electron (beta particle) and becomes a proton.
  • In electron capture decay, a proton captures an
    electron and converts to a neutron.

Uranium 238 decay
  • The half-life of a radioactive isotope
  • is the time it takes for
  • one half of the atoms
  • of the original unstable parent isotope
  • to decay to atoms
  • of a new more stable daughter isotope
  • The half-life of a specific radioactive isotope
  • is constant and can be precisely measured

  • The length of half-lives for different isotopes
  • of different elements
  • can vary from
  • less than one billionth of a second
  • to 49 billion years!
  • Radioactive decay
  • is geometric (or exponential), NOT linear,
  • and produces a curved graph

Uniform Linear Change
  • In this example
  • of uniform linear change,
  • water is dripping into a glass
  • at a constant rate

Geometric Radioactive Decay
  • In radioactive decay,
  • during each equal time unit
  • half-life
  • the proportion of parent atoms
  • decreases by 1/2

Determining Age
  • By measuring the parent/daughter ratio
  • and knowing the half-life of the parent
  • which has been determined in the laboratory
  • geologists can calculate the age of a sample
  • containing the radioactive element
  • The parent/daughter ratio
  • is usually determined by a mass spectrometer
  • an instrument that measures the proportions
  • of atoms with different masses

Determining Age
  • Example
  • If a rock has a parent/daughter ratio of 13
  • or a ratio of (parent)/(parent daughter) 14
    or 25,
  • and the half-life is 57 million years,
  • how old is the rock?
  • 25 means it is 2 half-lives old.
  • the rock is 57my x 2 114 million years old.

What Materials Can Be Dated?
  • Most radiometric dates are obtained
  • from igneous rocks
  • As magma cools and crystallizes,
  • radioactive parent atoms separate
  • from previously formed daughter atoms
  • Because they are the right size
  • some radioactive parents
  • are included in the crystal structure of cooling

What Materials Can Be Dated?
  • The daughter atoms are different elements
  • with different sizes
  • and, therefore, do not generally fit
  • into the same minerals as the parents
  • Geologists can use the crystals containing
  • the parent atoms
  • to date the time of crystallization

Igneous Crystallization
  • Crystallization of magma separates parent atoms
  • from previously formed daughters
  • This resets the radiometric clock to zero.
  • Then the parents gradually decay.

Sedimentary Rocks
  • Generally, sedimentary rocks can NOT be
    radiometrically dated
  • The date obtained would correspond to the time of
    crystallization of the mineral,
  • when it formed in an igneous or metamorphic rock,
  • and NOT the time that it was deposited as a
    sedimentary particle
  • Exception The mineral glauconite can be dated
  • because it forms in certain marine environments
    as a reaction with clay minerals
  • during the formation of the sedimentary rock

Sources of Uncertainty
  • During metamorphism, some of the daughter or
    parent atoms may escape
  • leading to a date that is inaccurate.
  • However, if all of the daughters are forced out
    during metamorphism,
  • then the date obtained would be the time of
    metamorphisma useful piece of information.
  • Dating techniques are always improving.
  • Presently measurement error is typically lt0.5
    of the age, and in some cases, better than 0.1
  • A date of 540 million might have an error of 2.7
    million years, or as low as 0.54 million

Long-Lived Radioactive Isotope Pairs Used in
  • The isotopes used in radiometric dating
  • need to be sufficiently long-lived
  • so the amount of parent material left is
  • Such isotopes include
  • Parents Daughters Half-Life (years)

Most of these are useful for dating older rocks
Uranium 238 Lead 206 4.5 billion Uranium
234 Lead 207 704 million Thorium 232
Lead 208 14 billion Rubidium 87 Strontium
87 48.8 billion Potassium 40 Argon 40 1.3
Radiocarbon Dating Method
  • Carbon is found in all forms of life
  • It has 3 isotopes
  • carbon 12 and 13 are stable, but carbon 14 is not
  • Carbon 14 has a half-life of 5730 years
  • Carbon 14 dating uses the carbon 14/carbon 12
  • of material that was once living
  • The short half-life of carbon 14
  • makes it suitable for dating material
  • lt 70,000 years old
  • It is not useful for most rocks,
  • but is useful for archaeology
  • and young geologic materials

Carbon 14
  • Carbon 14 is constantly forming
  • in the upper atmosphere
  • When cosmic rays
  • strike atoms of upper atmospheric gases,
  • Splitting nuclei into protons and neutons
  • When a neutron strikes a nitrogen 14 atom
  • it may be absorbed
  • by the nucleus and eject a proton
  • changing it to carbon 14

Carbon 14
  • The carbon 14 becomes
  • part of the natural carbon cycle
  • and becomes incorporated into organisms
  • While the organism lives
  • it continues to take in carbon 14,
  • but when it dies
  • the carbon 14 begins to decay
  • without being replenished
  • Thus, carbon 14 dating
  • measures the time of death

Tree-Ring Dating Method
  • The age of a tree can be determined
  • by counting the annual growth rings
  • in lower part of the stem (trunk)
  • The width of the rings are related to climate
  • and can be correlated from tree to tree
  • a procedure called cross-dating
  • The tree-ring time scale
  • now extends back 14,000 years

Tree-Ring Dating Method
  • In cross-dating, tree-ring patterns are used from
    different trees, with overlapping life spans

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