numerical age dating

Dating Rocks

• Relative Age Dating

  • Establishes relative ages of rocks by comparing their sequential order.

• Absolute Age Dating

  • Establishes absolute ages of rocks using numerical methods.

• Geologic Time

  • Defined by geochronologic units (such as Eons, Eras, Periods).

  • Involves time-rock units, known as chronostratigraphic units, referring to all strata deposited during a specific interval of time.

  • Fundamental Unit: System.

  • Eons: Phanerozoic.

  • Eras: Paleozoic.

  • Periods: Devonian (System).

  • Epochs: Lower Devonian (Series).

  • Age: Emsian (Stage).

Geologic Column

• Definition:

  • A composite stratigraphic column representing the entirety of the Earth’s history, correlating stratigraphy from various locations worldwide.

  • Referenced as Figure 9.15.

Historical Development of Geologic Time

• By the end of the 1800s, geologic time was divided into eons, eras, and periods, and the relative ages of many rocks were established.

  • Boundaries recognized through:

  • Faunal changes.

  • Extinctions.

  • Unconformities (erosion surfaces).

  • Absolute ages were still unknown.

Estimates of Age of Earth

• James Hutton

  • Suggested Earth was older than the biblical estimate of approximately 6,000 years, stating, "No vestige of a beginning, no prospect of an end."

• Charles Lyell

  • Proposed that many geological processes were slow, implying Earth's age must be in the hundreds of millions of years.

• Charles Darwin

  • Initially estimated Earth's age at 300 million years but later revised it to 96 million years.

Accumulation of Sediments

• Accumulation time of sediments used to estimate Earth's age based on:

  • Rate of deposition.

  • Thickness of sedimentary strata.

• Estimates range around 100 million years, considered too small due to:

  • Interruption of continuous deposition (bedding planes and erosional unconformities).

  • Some sediments undergoing metamorphism. - This must be too small because deposition not continuous (bedding planes, erosional unconformities, some sediments have been metamorphosed.

Uplift Rates

• Darwin concluded that the Earth must be hundreds of millions of years old based on assumed rates of evolution.

• Acknowledged that uplift occurs sporadically and is accompanied by earthquakes.

• Even in regions with rapid uplift, mountain formation takes hundreds of thousands to millions of years.

  • For example, Mount Everest (8,850 m altitude).

  • Estimates of uplift rates suggest formation times of around 590,000 to 1,770,000 years; more realistic rates of 0.1-0.2 m per century suggest times of 4.42-8.85 million years.

Age Estimation Based on Physics and Chemistry

• Ocean salinity was used to estimate Earth's age by calculating the time for fresh water to reach the current salt content.

  • Jolly (1899) estimated this age at 90 million years, considered too young due to evaporation processes reducing ocean salinity.

Buffon, Newton, and the Origin of Earth's Temperature

• Georges-Louis Leclerc, Comte de Buffon (1778):

  • Proposed that Earth originated as a molten planet cooling to its present state, challenging the young Earth paradigm.

  • Estimated the cooling time from molten to present temperature at 75,000 years but thought it too small.

  • Note that temperatures increase with depth, therefore the earth is cooling.

• Isaac Newton (1687):

  • Agreed with Buffon's premise of the Earth having originated in a molten state, asserting it would take longer than 50,000 years to cool.

Cooling of Earth and Kelvin's Calculations

• William Thomson, Lord Kelvin:

  • Assumed Earth cooled from a molten state, initially estimating its age at 20-400 million years in 1862, which supported geological conclusions.

  • Revised this to less than 100 million years in 1871 and ultimately concluded an age of 20-40 million years in 1897, influencing Darwin's estimates.

• Kelvin's calculations relied on various assumptions, including:

  • Initial cooling temperature.

  • Mode of heat loss (conduction).

  • No internal heat sources within Earth.

  • Notably, one of Kelvin’s students pointed out these assumptions could lead to uncertainties of billions of years in the calculated age.

Radioactivity and Age Estimation

• Henri Becquerel (1896):

  • Discovered radioactivity, which led to a new understanding of heat generation within the Earth.

  • The Curies identified radioactive elements, allowing a new method for dating minerals and rocks via radioactive decay.

• Ernest Rutherford (1902):

  • Discovered that heat is produced by radioactive decay.

  • Established that radioactive decay occurs over time, providing an invaluable means for establishing the age of materials.

First Estimates of Absolute Ages Using Radioactive Decay

• Boltwood (1905):

  • Provided first estimates of the age of Earth using radioactive decay, ranging from 410 million to 2.2 billion years, shortly after Kelvin's much younger estimate.

  • Heat is produced by radioactive decay.

  • Radioactive elements decay as a function of time. 

• Arthur Holmes (1927):

  • Revised estimates further, arriving at a contemporary accepted age of 4.55 billion years.

  • Absolute ages for major divisions of the geologic column established afterward.

Isotopes: Definitions and Properties

• Nucleus of Atoms:

  • Comprised of protons (positively charged) and neutrons (neutral).

• Atoms of an Element:

  • Consistent number of protons but varying numbers of neutrons, leading to different isotopes.

  • Some isotopes remain stable while others undergo decay, transforming into new isotopes over time.

  • Radioactive - taking an atom that is unhappy and turning into an atom that is happy, or in other words, stable.

Modes of Radioactive Decay

• Modes of decay include:

  • Alpha decay:

  • Emission of 2 neutrons and 2 protons (Helium nucleus).

  • Results in a decrease of 4 in atomic weight and 2 in atomic number.

  • Beta emission:

  • Loss of a neutron and gain of a proton, with the emission of a beta particle; results increase in atomic number by 1.

  • Electron capture:

  • Proton combines with a beta particle to create a neutron, emitting an x-ray; decreases atomic number by 1.

• Each decay is accompanied by a release of energy given by the equation $E=mc^2$, leading to the formation of a new elemental isotope.

Radioactive Decay Example: Uranium-Thorium (U-Th)

• Alpha Particle Emission:

  • Parent isotope decays into a daughter isotope through emission of an alpha particle.

Exponential Decay

• Radioactive decay occurs at a constant, exponential rate:

  • The number of nuclei decaying over a period is proportional to the remaining total number of nuclei present.

Rate of Decay

• Decay can be expressed as:

  • Decay constant (
    ) or Half-Life (THL).

  • Decay constants are isotopic-specific, measured independently of external conditions.

  • Unaffected by changes in physical or chemical environment.

• A common assumption in decay calculations is that at the onset (t=0), the material contains no daughter products (ND=0).

Important Equations for Radioactive Decay

• Decay constant:

  • 
    = rac{ ext{ln}(2)}{THL} (approximately 0.69315/THL).

• Remaining Parent Calculation:

  • Np/N0=(1-
    )^t
    Where $N<em>p$ is the remaining parent and $N</em>0$ is the original parent number.

• Elapsed Time Calculation:

  • t= rac{ ext{ln}(Np/N0)}{-
    }.

• Using Calculus:

  • Np=N0e^{(-
    THL)}, where $e ext{(Euler's number)} ext{= } 2.71828$.

Principles of Age Dating

• Method involves measuring the counts of parent isotopes (NP) and daughter isotopes (ND).

• The total amount present at time t=0 is:

  • $N<em>0=N</em>P + N_D$.

• Utilize decay constants or half-lives to calculate ages.

  • Example: If $N<em>P = 250$ and $N</em>D = 750$:
    $rac{250}{1000} = rac{1}{4} ext{ (indicating 2 half-lives)}$.

  • Convert half-lives to years using decay constants as needed.

U-Pb Decay Scheme

• Decay can involve complex processes and multiple decay modes.

• Intermediate isotopes may form throughout the decay process.

Common Isotopic Systems in Dating

• Most Commonly Used Isotopes (with decay modes, half-lives, and minerals):

  • $^{238}U$ to $^{206}Pb$: β + α decay, half-life = 4.5 billion years.

  • $^{235}U$ to $^{207}Pb$: β + α decay, half-life = 704 million years.

  • $^{232}Th$ to $^{208}Pb$: β + α decay, half-life = 14 billion years.

  • $^{40}K$ to $^{40}Ar$: β capture, half-life = 1.25 billion years.

  • $^{40}K$ to $^{40}Ca$: β decay, half-life = 1.25 billion years.

  • $^{87}Rb$ to $^{87}Sr$: β decay, half-life = 48.8 billion years.

  • $^{147}Sm$ to $^{143}Nd$: α decay, half-life = 106 billion years.

  • $^{14}C$ to $^{14}N$: β decay, half-life = 5730 years.

Criteria for Choosing Isotopic Systems in Dating

• Rocks must contain parent isotopes, and daughter isotopes must either be zero or of a known ratio at t=0.

• Important considerations:

  1. Mineral Type: Typically only igneous and metamorphic rocks can be dated, with adjustments for modern methods.

  2. Closure Temperature: Rocks must not have allowed isotopes to escape or new isotopes to enter after formation.

Understanding Isotopic Dates

• Closure Temperature:

  • The temperature below which isotopes can no longer move freely in/out of a crystal.

• Most isotopic dates correspond to the moment of formation, predominantly in igneous and some metamorphic rocks.

• In sedimentary rocks, determining the closure temperature relative to rock creation is complicated; hence relative dating is often utilized as a surrogate for isotopic dating.

Methodology for Mineral Dating

• Igneous Rocks:

  • Dates reflect the time of crystallization due to magma intrusion or extrusion.

• Metamorphic Rocks:

  • Dates indicate the time of metamorphism.

• Sedimentary Rocks:

  • Dates are often inferred from associated ages of igneous or metamorphic rocks.

Overview of Geologic Time Scale

• Eons: Various eons encompass different stages of Earth's history, detailed in a geologic time scale with geological events occurring relative to each eon and era. Basic relationships include:

  • Phanerozoic - Cenozoic - Mesozoic - Paleozoic: Each epoch within associated periods primarily delineates events leading to significant aplastic features in Earth’s geological record.

Absolute Ages of Geological Boundaries

• Geological boundaries defined based on dates acquired from surrounding igneous rocks.

• Noted that these ages are associated with uncertainties and are subject to frequent adjustments.

Carbon Isotopes in Dating

• Carbon-14 ($^{14}C$):

  • Created in the atmosphere from $^{14}N$ through neutron capture and proton emission, becoming integrated into organic materials.

  • Once an organism dies, it stops absorbing $^{14}C$, leading to the decay to $^{14}N$ through β particle emission.

  • The ratio $^{14}C/^{12}C$ assists in determining age.

• Most effective for dating events less than 50,000 years due to the short half-life of 5730 years, permitting up to eight half-lives to be measured safely.

Conformation of Dating Methods

• Following Kelvin's estimates, geologists were cautious regarding early 20th-century radiometric dating validity.

  • Tested using varve counting, a method analyzing sediment deposition rates over seasonal changes, developed in the late 1800s.

• Varves:

  • Rapidly layered sediment deposited in glacial environments; their counting provides resounding correlations between geological history.

Cosmogenic Nuclide Dating

• Cosmic Ray Interaction:

  • Isotopes like $^{21}Ne$ and $^{3}H$ created by cosmic radiation, while unstable isotopes like $^{10}Be$ and $^{26}Al$ found in quartz can date rock exposure at the surface and measure burial ages.

Other Methods of Dating

• Luminescence Dating:

  • Employed for sedimentary rocks to determine the burial time of minerals like quartz and k-spar by counting trapped electrons in crystal lattice defects, reset by light exposure.

• Fission Track Dating:

  • Utilizes damage trails in minerals (like apatite) caused by uranium decay to ascertain ages via density of tracks recorded.

Earth's Magnetic Field and Dating Reversals

• Originates from the molten outer core, behaving like a bar magnet with magnetic north and south close to but not equivalent to geographic north.

• Magnetic polarity periodically reverses, displayed by lava crystallization, providing a record used to create a magnetic time scale for terrestrial rock dating.

• Magnetic time scale established with high accuracy for the last 65 million years (Cenozoic) and reliably over 180 million years.

Age of Oceanic Crust

• Magnetic polarity is frequently utilized to date ocean floor rocks, which aids in determining the rate of plate motion.

Isochron Relations in Dating

• If the original sample (at t=0) contained daughter isotopes (ND≠0), the dating process requires understanding the relation between parent and daughter isotopes through the isochron equation, normalized to $^{86}Sr$.

• Isochron Equation:

  • Defines a linear relation describing how the isotopes evolve over time due to decay; slope of the accumulation provides the age, with intercept correlating initial ratios at formation.

Sm-Nd Isotope System for Geological Dating

• Decay of $^{147}Sm$ to $^{143}Nd$:

  • Offers reliable dating methods, ensuring that daughters (143Nd) could have been present when the minerals formed.

  • Fractionation considerations were necessary for accurate age determination.