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Selected Topics

Geophysics

Abbreviated Course Notes

 

Two major emphases of geophysics:

  1. "pure"
  2. "applied"

1. pure geophysics - study of the physics of the Earth
Examples:

2. applied geophysics (also called exploration geophysics) - to find economic deposits
All methods depend fundamentally on the presence of bodies with contrasting physical properties, such as density, magnetic susceptibility, heat conductivity, elastic constants, etc.


Part 1: Gravity

Assume Earth does not rotate and has uniform density distribution.
Determine acceleration of gravity (usually just called "gravity" by geophysicists) at point on Earth's surface.

Law of Universal Gravitation:

          GMeM
     F = -------
           R2

G = Universal Gravitational Constant = 6.673 x 10-8 dyne cm2/gm2 +/- 0.003 (dyne = 1 gm cm/sec2)

Newton's 2nd Law: F = Ma
for earth, use symbol "g" instead of "a," so F = Mg

                            GMeM           GMe
    Since F = F; then Mg = ------ and g = ----
                             R2             R2

g = approximately 980 cm/sec2 (or 9.8 m/sec2)

1 cm/sec2 is called a gal.
Normally use milligals (1/1000 gal or about 1 millionth g) or gravity units (g. u.; 0.1 mgal)

Complication #1:
Earth rotates
Result: Earth not round but bulges at equator and is flattened at poles.
Equatorial radius is 21 kilometers greater than at poles.

Complication #2:
Earth's mass is not symmetrical about the equatorial plane - Earth is "pear-shaped."

Complication #3:
The equator isn't perfectly spherical but only varies by a few meters.

The regular surface which most nearly approximates the surface of the actual Earth is a surface called the geoid.
The geoid surface is everywhere perpendicular to a plumb bob.
The geoid corresponds to mean sea level.
In land covered areas, the geoid is the surface that would be determined by the level to which water would rise in narrow canals cut through the continents.

Since g depends on distance from center of Earth (radius), g varies with latitude.
International Gravity Formula can be used to determine g at a particular latitude:
g = 9.780318 (1 + .0053024 sin2 - 0.0000059 sin2 2) where is the latitude; units are m/sec2
Calculated value for g "corrected" for latitude is called the theoretical gravity and abbreviated gt

Now measure actual value of gravity at any spot.

1. can use pendulum

(formula from physics: where L is length of pendulum and T is period)

Accuracy = 1.5 mgal; takes about 30 minutes per measurement

2. can experimentally measure acceleration of object dropped at Earth's surface
Accuracy = 0.1 mgal; measuring apparatus not portable (although one of the latest models available is said to be portable because it weighs less than one ton)

3. most commonly measure differences in gravity from place to place by using a "gravity meter" (Mass suspended from spring).
Accuracy = .01 mgal

Average density of Earth is 5.52 gm/cm3.
Average density of surface rocks is much less.
Therefore interior of Earth must be of much higher density than surface rocks.

Can get some idea of Earth's density distribution from study of its angular momentum:
Angular Momentum = Moment of Inertia x Angular Velocity

The moment of inertia of any object depends on its mass distribution.
Examples:

Earth's moment of inertia = 0.3307 MR2
Best fitting model is series of nested ellipsoids of different densities, but generally denser toward center.

Measured value of g (called "actual" value and abbreviated ga) is not usually the same as gt.
Difference in ga and gt called a gravity anomaly.

Actual not same as theoretical because:

  1. actual not measured at sea level where theoretical is calculated
  2. actual not measured on a flat surface
  3. solid Earth has tides of 7-14 cm
  4. density distribution in Earth not uniform

To adjust for difference #1, we apply two "corrections" to the measured value before comparing it to the theoretical value:

To adjust for difference #2, we then add another "correction" to the measured value before comparing it to the theoretical value by removing the influence of nearby mountains and valleys.
called the Topographic or Terrain Correction
Since this correction rarely exceeds 1 mgal except in mountainous areas, it is frequenty ignored.

To adjust for difference #3, formulas are available to determine the necessary correction. This tidal correction is very frequently ignored.

Finally, any difference between the "corrected" values of actual gravity and theoretical gravity should be due to density variations (#4).
Higher than average density rock will cause the measured value of g to be greater than the theoretical value and produces a positive "anomaly" while less dense rock produces a negative anomaly.

Consider a plumb bob hanging near a tall mountain.
The mass of the mountain pulls it sideways.
Knowing the density and volume of the mountain allows us to calculate its mass and enables us to determine how much force it should exert on the plumb bob.
Measurements show mountains exert only about 1/3 of the expected amount.
Question: Why?

Mountain supposedly has low density "roots."
Theory of Isostasy - the total mass of rock (and sea) in any vertical column of unit cross section is constant
Various models have been developed to describe this root (Airy, Pratt, etc.)

Questions:

Large scale gravity anomalies are called regional anomalies.
Usually due to density variations in lower crust or variation in thickness of crust.
Make it hard to recognize small or shallow features.
Often "removed" by various processes.
Process so subjective that I have sometimes thought that "the regional anomaly is what you take out in order to make what's left look like what you want it to."

Small scale anomalies (often called residual anomalies) produced by ore bodies or geologic structures.
Seldom more than a few milligals in size.

Use trial and error to find a body of the right location, shape, size and density to produce the anomaly.

Example of a spherical ore body:
For a sphere, g at a location x

where R is the radius of the sphere, z is the depth to the center of the sphere, x is measured from a point on the surface directly above the center of the sphere to the location, and is the density contrast (difference in densities of body and surrounding material).

There is usually assumed to be a constant density difference between an ore body and its surroundings and a sharp, well- defined boundary separating them.
Neither assumption is likely to be correct.
Finding the density contrast to use in the formula is very difficult if you don't know what lies below ground. (And if you knew what was down there, why bother with exploration methods like gravity surveys?)

Other shapes can be modeled with similar but more complex formulas.
Complex forms can be thought of as combinations of simple forms.
Usually use computers.

Some general rules have been found.

Circular anomalies produced by:

Elongated anomalies produced by:

Negative anomalies:

Positive anomalies:

The deeper the body, the broader and lower in amplitude will be the anomaly profile.

Rapid change in amplitude or gradient should suggest density change in subsurface - such as a fault or edge of a buried basin.

There is no unique answer.
Several models can produce exactly the same anomaly.
Very important to use knowledge of area's geology to limit possible solutions.


Part 2: Radioactivity, Radiometric Dating and Natural Gamma Methods

Geochronology - concerned with determining age and history of geologic materials by studying their isotopes

Radioactivity
Discovered in 1896
Natural change from one element to another by emission of particles from nucleus or addition of particles to nucleus

Particles include:

Decay occurs at constant rate and is not affected by temperature, pressure, chemical combination or any other known thing

Radioactive isotopes - an element capable of spontaneously changing into another element by the emission or addition of particles to its nucleus
Stable isotopes - an isotope which is not radioactive

Radiogenic isotopes - an isotope produced by radioactive decay
Non-radiogenic isotopes - an isotope not produced by radioactive decay

Half-life - time for half of element to decay

Parent - the radioactive element which decays
Daughter - an element formed from another by radioactive decay

T (half life) = ln 2/ = 0.6931/

The equation which represents radioactive decay is (derived in most geophysics texts for those who are interested and know a little calculus):

solved for t (age of rock):

Assumptions made in radiometric dating:


RbSr dating

Rb87 -> Sr87 (could also write 87Rb, etc.)
Rb commonly substitutes for K in minerals; so method used on K-bearing minerals or rocks which contain them

Decay equation reads:

(Subscript m stands for measured, or in other words, now; o stands for original)

It is easier to measure ratios of atoms rather than absolute numbers so expression usually written:

Could solve for t (age of mineral):

Now measure Sr87/Sr86 and Rb87/Sr86 ratios and for reaction ( = 1.39 x 10-11/yr)
Then
estimate (Sr87/Sr86)o (Can measure this ratio in coexisting undisturbed minerals which contain no Rb)

Note: Sr86m = Sr86o since Sr86 is stable and non-radiogenic
Sr
86, Sr84, and Sr88 are all stable and non-radiogenic.
Any could be used; Sr
86 most abundant and therefore most often used.

Easier mathematics and more accurate way of determining (Sr87/Sr86)original:
Equation for straight line is y = ax + b, (where a is slope, b is intercept on y axis)
Equation is in that form (actually y = b + ax) when t is constant (for several minerals in a rock or several rocks of the same age)

If we plot (Sr87/Sr86)m vs (Rb87/Sr86)m, the values should be different for different rocks and minerals because they would have different initial amounts of Rb.
The slope of the line obtained by connecting these points is -1 and the intercept is (Sr
87/Sr86)o
Thus we can
obtain both the age of the suite and the initial strontium ratio.
These plotted lines are called
isochrons.

Isochrons can also be used to determine age of metamorphism.
If whole rock hasn't lost Rb or Sr, but minerals have passed them around during metamorphism, two ages will be obtained - one from dating whole rock and one (metamorphism age) from dating individual minerals in rock.

Another Sr isotope use:
First must know Sr
87/Sr86 in material that made up primitive Earth.
Usually assume it was same as non-Rb
87 bearing meteorites or about 0.699

During differentiation of crust, behavior of Rb and Sr would be different (different charge, different size).
Rb concentrated in crust, Sr evenly distributed between crust and mantle.
Production of Sr
87 should thus be faster in crust than in mantle and Sr87/Sr86 ratios should be higher for crustal material.
Difference in Sr87/Sr86 ratios, then, is a means for distinguishing igneous rocks that have formed by partial melting of crustal rocks from those that have their origin in differentiation or partial melting of mantle material

Present Sr87/Sr86 ratio for mantle rock estimated from analyses of recent basalts and gabbros from oceanic environments (direct origin from mantle assumed and no contamination by continental material)
Value is about 0.704
Extrapolation between 0.699 and 0.704 gives reasonable estimate for ratio in mantle at any time in past.
Look at Sr87/Sr86 ratios for rocks when they formed to determine origin.
(ratio above or consistent with expected mantle ratio?)
(Remember can get Sr
87/Sr86 ratios from isochrons.)


Uranium, Thorium - Lead dating:

U238 -> Pb206

U235 -> Pb207

Th232 -> Pb208

Commonly use ratio with stable Pb204

One equation might be written:

or:

Must determine ratio (Pb206/Pb204)o and .
Can find
original ratio from associated lead minerals (such as galena) or can use mineral for study that wouldn't have had any original lead (zircon, uraninite, sphene, apatite, monazite, etc.)

By using U238, U235, and Th232, theoretically you get three age determinations and they should agree (concordant ages).
If disagreement, ages are said to be
discordant.
This is probably
due to gain or loss of material.

Lead-lead method

If equation for U235 is divided by equation for U238, we get another equation:

Use of this equation called lead-lead method.
Handy because U
235/U238 ratio known, as are decay constants.
Can't solve remaining equation directly for t but ages corresponding to different isotope ratios have been plotted and can be obtained from published graphs or tables

Use of Pb-Pb method is good check on U235, U238, and Th methods because if lead lost, the ratio of isotopes of remaining lead should not be changed and valid age should still be given.

Can also directly use ratio:

These two quantities increase with time at different rates and if plotted against each other, a curved line is formed (called a concordia curve because all points on the curve have concordant U238/Pb206 and U235/Pb207 ages).

If a rock sample has lost no Pb, calculated ages from U238 and U235 would be concordant and a point representing the ratio of the above quantities would lie on the concordia curve.

If Pb has been lost, the ages will be discordant and the point representing the ratio will lie below the curve.

Since lead loss would presumably be different for different areas in the sample, several different analyses from different locations in the sample should give several different ratios and thus several different points below the concordia curve.
It can be determined mathematically that these several points will lie on a straight line (called a
discordia).

If the discordia line is extended to intersect the concordia curve, upper intersection gives age of rock.
Lower intersection supposedly gives time lead lost but almost never accurate since lead almost never lost all at once but gradually over long time.

Technically could use U238 -> He4, U235 -> He4, or Th232 -> He4
But, helium may be lost since a gas.

Assume that any He present when rock was molten escaped
Therefore, any He present now formed from U or Th after solidification.
He ages thus give solidification ages
(Example: how long it takes for granite batholith to solidify).


Other Pb uses

1. Can measure average amounts of U238 and Pb206, or U235 and Pb207 in rocks at the Earth's surface (usually use recent marine sediments).
Assume no radiogenic lead to start with, can calculate
age of Earth's outer portion.

2. Begin with primeval lead (lead present when Earth formed): Pb204, Pb206, Pb207, Pb208 in certain ratios for Earth as whole (usually assume this to be same as ratios in meteorites without U, Th).
With time, radiogenic lead increases, thus higher Pb
206/Pb204, etc., ratios with time.
Can get
age of Earth (4550-4750 my).

3. (variation on 2)
After a time, ore might form (example: galena).
This ore would "sample" the lead at time of formation, which would consist of the primeval lead plus all radioactive lead formed before the time of ore formation (total lead called the common lead).
Thus,
age of ore can be determined by comparing its lead ratios to the ratios which would have existed at various times.

4. Stable nuclei atomic weight about 40 and above are present in about same abundance.
Assume when elements formed, same rule applied to unstable elements.
Now U
238 is 140 times as abundant as U235.
If both once equally abundant, would take 6 billion years to reach present proportion.
Age of Universe? of our part of Universe? of our Solar System nebula?


Fission-track dating:

U238 spontaneously breaks down by fission (splits into two large parts).
This is a rare occurrence.
These fission particles pass through the surrounding material with very high energy and leave tube-shaped
damage tracks.

These tracks can be counted (etch mineral with HFl, look at under microscope) and thus the number of spontaneous fissions may be counted.
This
gives amount of daughter product in sample.

Can determine (generally from measurement of amount of radiation being emitted) current U238 content in sample.
Essentially
have number of daughter atoms and number of remaining parent atoms and can thus determine age.

Useful because can be used on wide variety of substances of wide range of ages.

Disadvantage which turns out to be an advantage:
Fission tracks are "healed" by prolonged heating (millions of years).
Temperature at which healing occurs is different for each mineral.
Each different mineral thus can yield a different age (apparent disadvantage) because each mineral has its clock "restarted" by healing at different temperatures and thus different times.
But
temperature history of sample can be determined by comparing different minerals in sample.


Potassium-Argon dating:

K40 undergoes 2 principal kinds of decay, to Ca40 and to Ar40.
Decay to Ca
40 not useful, because Ca40 most common isotope of Ca and small amount produced radiogenically would be undetectable.
Therefore, use K-Ar.

Since 2 separate decay types are possible, decay equation somewhat more complicated.

Let be total decay constant, Ar be decay constant for K-Ar reaction, and Ca be decay constant for K-Ca reaction.
Then decay equation can be written:

Ar40original = 0 for all but very exotic minerals (original Ar a gas, wouldn't survive formation except under very unusual circumstances, such as enormously high pressures).
Therefore, substituting 0 for original Ar and also substituting decay constants:

     t = 1.88 x 109 ln (1+ 9.07 Ar40/K40)

If metamorphism occurs, Ar40 already formed will probably be lost and clock reset.
K-Ar methods can therefore be
used to date metamorphic events.

Disadvantage to method:

Advantages to method:


Samarium-Neodymium dating:

Techniques same as for Rb-Sr or K-Ar.

Has advantage that both elements are members of rare-earth group and have virtually identical chemical properties.
Both similarly affected by weathering and metamorphic processes.
Sm/Nd ratios would remain unchanged, giving reliable date for original crystallization.


Carbon dating:

Carbon 14 dating (also called radiocarbon dating)

C14 formed in upper atmosphere by reaction of N2 with neutrons produced by cosmic rays.
Reaction is:
0N1 + 7N14 -> 6C14 + 1H1
then C
14 decays -> 7N14 + -10
Thus,
total amount of C14 in atmosphere constant.

Carbon in organism has same C14/C12 ratio as air or water does as long as organism alive.
When organism dies, C
14 not replenished, disappears, and C14/C12 ratio decreases to zero.
C14/C12 ratio thus gives age since death.

Limited to very young samples (less than 70,000 years) because of short half-life (5730 years).

Instead of measuring C14/C12 ratio in material directly, normally we compare C14 in sample to C14 in air by comparing radioactivity of the 2 samples (number of decays per minute per gram of carbon).
A is activity of C
14 in material to be dated and Ao is activity of air.
(Age of sample) t = 19,035 log Ao/A.

Is % C14 really constant?
Known that C14 content of atmosphere increased 10 % in period 6000 to 2000 years ago.
Found by studying tree rings.
Cause not known.
Now changing because of:

possibly through changes in intensity of Earth's magnetic field


Natural Gamma

Concentrations of radioactive substances such as uranium and thorium can be detected by measuring the products of their decay, especially gamma rays. 

Other minerals such as titanium and zirconium are often associated with radioisotopes so radioacivity surveying may also be used in their search. Nonradioactive minerals (especially those formed by mineral replacement processes) are sometimes associated with depletions as well as with concentrations of radioisotopes.

Measurements may be made from the air, along a ground traverse or in boreholes.

Different rocks often have different radioactivity and these differences can be utilized in geologic mapping.

Radioactivity is often concentrated along faults.

Radioactivity lows are sometimes associated with oilfields but the reason is not known.


Part 3: Heat

Heat flows from points of high temperature to points of low temperature.

Methods of heat transfer:

Heat flow due to conduction = K x temperature gradient

where K is coefficient of thermal conductivity of substance and temperature gradient = T/thickness.

The thermal diffusibility of a substance

where is the density and Cp is the specific heat of the substance at constant pressure.

Thermal conductivity determined by:

If K is large, then material is a good conductor of heat.
Quartz is the best conductor of heat among minerals usually encountered.

Heat travels extremely slowly through soil and rocks by conduction.
Typical values would be 15-60 km2 per million years.
If transfer due to conduction alone, a thermal event originating at a depth of 100 km will not be perceptible near the surface for 10 million - 100 million years

Examples:

Temperature at Earth's surface depends mainly on radiation from Sun.
Heat flow from interior is 1/1000 as much as that from Sun.

Temperature in Earth rises with depth.
Temperature gradient near surface is about 10-50 oC/kilometer but decreases with depth.
Can use mantle/core boundary conditions to estimate internal temperature.
Temperature on both sides must be same.
Material at bottom of mantle solid; material at top of core liquid.
Considering all possible materials, maximum is 2700oK.

Some sources of Earth's internal heat:

Heat flow about the same all over the Earth; average heat flow for continents same as that for oceans.
However, continental materials much richer in radioactive materials and thus should give off more heat.
Explanation: Some heat flow in ocean basins due to conduction.
Total surface heat flow:

Interesting speculation: Is it a coincidence that oceanic heat flow equals continental heat flow?

Examples of large scale anomalies:

1. lower than average heat flow:

2. higher than average heat flow

Examples of local heat anomalies useful for prospecting:


Part 4: Magnetism

 

Simplest magnetic structure is called a dipole.
A dipole consists of 2 poles of equal strength and opposite sign separated by a small distance.
Electrons and nuclei are dipoles.

Speculation:
Do poles always exist in pairs?

Earth is a magnet.
North-seeking pole of a magnet (also called positive) is one that is attracted to the Earth's north pole.
Earth's north pole is a south-seeking pole.

The Earth's magnetic field is defined by giving its strength and direction.

The magnetic field strength (H) at a point in the field of a magnet is the force per unit of pole strength which would be exerted on a pole at that point.
Magnetic field strength is also sometimes given in terms of the density of imaginary lines of force representing the field.
1 Oersted = 1 line of force per cm2 (called a gauss)
Typical laboratory magnet has field strength of 10,000 Oersteds
The field strength of the Earth varies from about 0.3 Oersteds at the equator to about 0.6 Oersteds at the poles.

Direction given by specifying declination and inclination.
Declination - deflection of a north-seeking pole from geographical north; positive if toward east
Inclination or dip - deflection of north-seeking pole from horizontal; positive if down

Some terminology:

Component's of the Earth's field:

Internal field can be mostly accounted for by a fictitious magnetic dipole displaced from the center of the Earth about 400 kilometers southward (toward Indonesia) and tilted 11 1/2 degrees with respect to the axis of rotation.

Question: Where does Earth's internal field originate?
Since a uniformly magnetized sphere gives the same magnetic field as a dipole at center; there are two possibilities:

  1. Whole earth is magnetized
  2. Field comes from Earth's center

If #1, Field strength should decrease with depth
If #2, Field strength should increase with depth.
Experimental evidence supports #2

Question: How is Earth's internal field produced?
Two possibilities:

  1. permanently magnetized material (will discuss process later)
  2. electric currents

Problem with possibility #1:
All materials lose their ability to become permanently magnetized at temperatures which are reached in the lower crust.

Support for possibility #2:
Experimental studies show that relatively simple motions of a conducting fluid (such as a nickle-iron alloy) can produce a magnetic field.

Michael Faraday's experiment:
Conducting disk, spinning about an axle in a magnetic field.
Result is voltage difference between axle and rim of disk.
If we connect wire from axle to rim, a current will flow.
The current in the wire generates its own magnetic field which can add to the original.
Now remove original magnetic field.
If disk continues to spin quickly enough, the current keeps flowing through the wire and a magnetic field still exists.
Called a self-exciting dynamo.

Notice 2 things necessary:

Possible initial field for Earth's dynamo?

Source of energy to keep dynamo "spinning"?

Magnetic fields which will spontaneously reverse polarity can be produced by a combination of disk generators.
(Will examine significance of this fact later)

Source of external field is mostly circulating electric currents in the ionosphere.

Earth's magnetic field not constant.
Changes:

  1. magnetic storms
  2. diurnal changes
  3. secular variation
  4. westward drift
  5. reversals

Continuous recordings of changes are called magnetograms.

1. Magnetic storms:

2. Diurnal changes:

3. Secular variation:

4. Westward drift:

5. Magnetic reversals:
North magnetic pole becomes a south pole and vice versa.

There are no reasons why the Earth's field should have a particular polarity and there is no fundamental reason why its polarity should not change.
Magnetic reversals are known to occur in the Sun and have been observed in other stars.

Major groupings of normal and reversed sequences are called magnetic epochs.
Briefer fluctuations in polarity are called events.
Average of three reversals per million years.

Reversals occurred in the preCambrian and have been found in all subsequent periods except the Permian.
Question: Why were there no reversals in the Permian?

The most recent period of reversed polarity was about 8000 - 20000 years ago.

Reversal process takes about 5000 years.
In one area in southeastern Oregon, a gradual transition from normal to reverse magnetization can be observed across a section made up of 6 individual flows.

During a reversal, the dipole field strength decreases to near zero.
The strength is currently dropping 5% per century and has been dropping for the past 2000 years.
We may be approaching a reversal.

Earth's magnetic field shields surface from cosmic radiation.
Cosmic radiation produces mutations.
In general, there is a rough agreement between faunal extinctions and reversals.
The probability of a correlation occurring by chance is 1 in 700.

Other correlations found:

Lenz's law:
When a substance is placed in a magnetic field, little extra currents are generated inside the atoms by a process called induction.
These currents produce a magnetic field opposite in direction to the applied field.
(For details, look up Larmor precessions in a quantum mechanics book.)

This induced field is called the Intensity of Magnetization (I) and is proportional to the applied field: I = kH
k is called the magnetic susceptibility of the substance

Examples of direct uses of magnetic susceptibility measurements:

The total new field in the substance is the applied field plus the induced field.
This is called the Magnetic Induction (B): B = H + I
B is usally given in Tesla (104 Oersteds).
Gamma (or nonotesla, 10-9 Oersteds) are usually used in exploration geophysics.

Motions of electric particles (including electron spin and orbital motion) produce magnetic fields.

Three types of magnetic behavior:

  1. diamagnetic
  2. paramagnetic
  3. ferromagnetic

1. In diamagnetic substances, small magnetic fields produced by particle motions are randomly oriented and cancel each other out, leaving atoms and ions with no net magnetic field.
Examples: salt, gypsum, marble, quartz, graphite

2. In paramagnetic substances (which include most substances), the small fields don't cancel each other out but leave the atoms or ions with net magnetic fields.
However, since the atoms are randomly arranged, the substance as a whole has no net magnetic field.

3. In ferromagnetic substances, the atoms have net magnetic fields and the atoms are arranged in regions called domains in such a way that each domain has a magetic field.
(Domains can only be explained by using quantum theory.)
However, normally the domains are randomly oriented and there is no net magnetic field in the substance.
Examples: iron (which is technically ferrimagnetic), magnetite, hematite (technically canted anti-ferrimagnetic), ilmenite, pyrrhotite, goethite, many other iron compounds

When each of these kinds of substances is placed in an external magnetic field (like the Earth's field, for example), additional small magnetic fields are induced.

1. Diamagnetic substances:
Small induced field produced opposite to applied field.
Thus total field is slightly less than the applied field.
Produces small negative magnetic anomaly.
Remove applied field; induced field disappears.

2. Paramagnetic substances:
Two effects occur:

  1. Small induced field produced opposite to applied field.
  2. Small magnetic fields already existing are partially lined up in same direction as applied field.

Don't line up completely because of thermal agitation; so the lower the temperature, the stronger the effect
Effect 2 is greater.
Net effect is total field larger than applied field.
Produces small positive magnetic anomaly.
Remove applied field; induced field disappears, thermal agitation randomly distributes the atoms

3. Ferromagnetic substances:
Three effects:

  1. Small induced field produced opposite to applied field.
  2. Domains which are oriented in a favorable direction grow larger.
  3. Domains may rotate to a more favorable direction.

Effects 2 and 3 are very large effects.
Result is a total field is considerable larger than applied field.
Remove applied field,

Exceptions:

The effects of an applied external magnetic field on a ferromagnetic substance are usually shown by using a plot called a hysteresis curve.

Magnetism remaining in a rock when the applied field is removed is called natural remanent magnetization (NRM) or paleomagnetism.
Types include:

Example of thermoremanent magnetization (TRM):
when lava cools and freezes, it will acquire a TRM dependent on the strength and orientation of the Earth's field at that time.

Example of depositional remanent magnetization (DRM):
small grains of magnetic minerals, when settling or while a sediment is still wet and unconsolidated, will align themselves with the direction of the Earth's magnetic field.

Example of chemical remanent magnetization (CRM):
acquired during growth or recrystallization of mineral grains; such as iron oxidizing

Example of isothermal remanent magnetization (IRM):
exposure to strong magnetic field for short time at relatively low temperature; such as field from lightning strike

Example of viscous remanent magnetization (VRM):
on exposure to a magnetic field for a long time, thermal fluctuations gradually favor direction of applied field.

One problem in interpreting paleomagnetic data is in deciding how much the magnetization has been altered by later changes.

Examples of uses of paleomagnetism:

1. relative dating
Example: preCambrian dikes in one part of the Canadian Shield all have the same orientations but 3 different remanence directions, indicating that they are of 3 different ages.

2. Did Japan "bend" during Tertiary?
Tertiary and Quaternary declinations for the north and south ends are the same; pre-Tertiary declinations vary.

3. Has Spain rotated with respect to Europe?
Late Paleozoic rocks have a declination 35o different from Europe; less difference with time

4. Paleomagnetic correlation of deep-sea cores

5. Paleomagnetic inclinations allow the determination of past latitudes
Examples:

6. Determine former fit of continents and time of plate break-up by use of "polar wandering" curves which are identical until the time of break-up and then diverge (or convergence of plates if curves merge)

7. Marine anomalies (will examine later)

Earth's magnetic field shows little relationship to broad features of geography and geology;
no obvious relationship to mountains, oceanic ridges, continents or oceans

However, field strength varies from place to place due to magnetization of rocks beneath the surface
Can produce local disturbances of 3 Oersteds or more
(remember, Earth's average is much less)

Anomalies due to:

Magnetic methods involve looking for these anomalies.
More complicated than gravity anomalies because strength and direction must be determined and because they are bipolar (have associated highs and lows).
However, no major "corrections" are made.

Note: sedimentary rocks usually produce no significant magnetic effect.

Examples of use:

1. depth to basement
measurements close to anomalous bodies show sharp anomalies; distant bodies produce smaller, broader and smoother anomalies
On maps, the closer the contours, the shallower the source.

2. (Variation on 1) map structural features on basement
sedimentary basins are characterized by smooth contours and low magnetic relief
uplifted areas have steep gradients and high magnetic relief

3. prospect for magnetic minerals or non-magnetic minerals often found associated with magnetic minerals
(Example: diamonds in kimberlite pipes)
Note: salt (which is diamagnetic) produces negative anomalies

4. Map rock bodies whose magnetic properties are very different from those of surrounding rocks.

5. (Variation on 4) presence of magnetic anomalies generally means lack of sediments

6. Locate faults
A sudden change in spacing of contour lines suggests a discontinuity at depth.
Offsets of magnetic anomalies may indicate strike-slip faults which extend below the sedimentary cover.

Magnetic anomalies are commonly interpreted qualitatively.
Sometimes individual magnetic anomalies are found which stand out so clearly that they can easily be separated from neighboring effects and which are so simple in appearance that they seem to be due to a single, magnetized body.
In these situations, quantitative methods can be used.

Example of sphere studied in profile:
The vertical component of the magnetic field strength (V) at a location x

where R is the radius of the sphere
I is the Intensity of Magnetization
Z is the depth to the center of the sphere
x is measured from a point on the surface directly above the center of the sphere to the location

Other formulas can be used for horizontal cylinders (useful for veins), horizontal sheets (for dikes or layers faulted by vertical faults), etc., but are considerably more complicated.
All the formulas assume susceptibility known, Earth's field is vertical and magnetization is in the directions of Earth's field, none of which is usually true.

Marine anomalies:
Due to thermoremanent magnetization of basalt, which is injected along the central rifts in oceanic ridges, magnetized in the direction of the Earth's field, and then conveyed away in either direction from the ridge.
Reversals result in parallel, linear, alternating positive and negative anomalies which are symmetrical about the ridge axis.
Age of reversals and distance from ridge can be used to determine rate of spreading.
Varies from 1-8 cm/year.


Part 5: Electrical Methods

Most commonly used in searching for metals.
Increasingly used for finding depth to basement, in the study of groundwater, and in geothermal exploration.

Types of methods:

  1. Self Potential Methods
  2. Resistivity Methods
  3. Well Logging
  4. Electromagnetic Methods

1. Self- Potential Methods:
Uses Potential Difference or Voltage - the difference in electrical potential energy between two places. Unit is volt.

Potential differences occur naturally within the Earth and can be measured.

These potential differences are caused by

  1. ore bodies behaving like natural "batteries" with separation of positive and negative charge (called Electrolytic Potential)
    How this works is not understood.
    The most accepted theory for sulfides suggests that the portion of the ore body above the water table is being oxidized (losing electrons) while the portion below is being reduced, setting up a flow of electrons from one end of the ore body to the other.
    This theory cannot explain anomalies where the ore body is completely below the water table, explain why a clay overburden prevents a self-potential from forming, or explain how self-potentials form in poor conductors.
  2. differences in salt concentration in water (called Electrochemical Potential)
  3. solutions flowing through permeable rocks (called Streaming Potential)
  4. electric activity caused by life processes of plants and animals (such as differences between open ground and bush) (called Bioelectric Potential)

2. Resistivity methods:
Make use of the fact that some materials are good conductors of electricity and some are poor conductors

where I is the amount of current flowing through a body
A is the cross sectional area through which the current flows
V is the voltage
L is the distance the current flows
is the conductivity of the material of which the body is made

The reciprocal of the conductivity is the resistivity.
Resistivity is measured in ohm cm or ohm m.
Resistance (Resistivity x L/A), in ohms, is more commonly used by physicists.
Poor conductors have high resistivities.
Note: for inhomogeneous bodies, we actually measure a sort of average resistivity along the path of current flow, called the apparent resistivity.

Good conductors include metals, graphite, most sulfides.
Intermediate conductors (called semi-conductors) include most oxides and porous rocks.
Poor conductors (insulators) include most common rock-forming minerals.

Current in most rocks is carried by ions in fluids in the rock's pores (called electrolytic conduction).
A small change in water content affects resistivity enormously.
Also, the salinity of the water is highly important in determining conductivity.
The shapes and arrangements of the pores can result in greater current flow in some directions than in others.
Faults, joints, etc., can produce "structural" conductors.

Procedure:
Current driven through ground using 2 electrodes
Potential distribution mapped with 2nd set of electrodes to determine potential difference pattern (voltage distribution) and directions of current flow.
Anomalies (conducting bodies, for example) disturb regular patterns that would normally be produced

Common methods look for:

  1. variation of resistivity with depth
  2. variation of resistivity horizontally

1. to measure variation of resitivity with depth:
current penetrates to deeper depths with increasing separation of current electrodes
can determine approximate depths to layers but not thicknesses of layers

problem 1- the deeper you go, the wider the electrodes must be spaced and the more powerful the current supply necessary.
This limits the method to a few hundred feet.

problem 2- a layer with intermediate resistivity between layers of high and low resistivitywill not show up.
Example - looking for groundwater where layer of wet alluvium lies between layer of dry alluvium and layer of shale

Often used for basement depth determinations:
sedimentary section generally has range of resistivities substantially lower than basement rocks, so can be thought of as a 2-layer problem

Quantitative method for first approximations, rough work:
(gives reasonable estimates for shallow depths; does not give good results on thick beds)
sum all apparent resistivity values up to and including present reading and plot vs electrode spacing
Example: If readings are 100, 200, 300 ohm m for spacings of 10, 20, 30 m; plot 100, 300, 600 ohm m vs 10, 20, 30 m
then draw segments of straight lines through as many readings as possible
cross-overs of segments gives depths to interfaces

2. to measure horizontal variations in resistivity
place current electrodes great distance apart and move closely spaced potential electrodes along grid between them
plot resistivity vs. locations of potential electrodes
can use map or profile to display data; profiles are most common.

Interpreting maps:
Can use either current lines or equipotential lines on maps
Lines of current flow always perpendicular to equipotential lines (lines along which potential is constant)
Usually interpret maps qualitatively to simply identify locations of good conductors or good resistors

Interpreting profiles:

3. Well Logging:
In well logging, both potential differences and resistivities are used.

Example:
High resistivity could be due to limestone or oil bearing sand.
A potential difference indicates flow of water into or out of well and/or difference in salt concentration.
Therefore indicates oil bearing sand.

Main value of well logging lies in the possibility of correlation between wells.

4. Electromagnetic Methods:

  1. Telluric methods
  2. Magnetotelluric methods
  3. Electromagnetic Induction methods
  4. Induced Polarization methods

a. Telluric methods:
Faraday's Law of Induction: changing magnetic fields produce alternating currents.
Changes in the Earth's magnetic field produce alternating electric currents just below the Earth's surface called Telluric currents.
The lower the frequency of the current, the greater the depth of penetration.
Telluric methods use these natural currents to detect resistivity differences which are then interpreted using procedures similar to those described earlier under resistivity methods.

b. Magnetotelluric methods:
The changing magnetic fields of the Earth and the telluric currents they produce have different amplitudes.
The ratio of the amplitudes can be used to determine the apparent resistivity to the greatest depth in the Earth to which energy of that frequency penetrates.

Typical equation:

apparent resistivity =

where Ex is the strength of the electric field in the x direction in millivolts
Hy is the strength of the magnetic field in the y direction in gammas
f is the frequency of the currents

Depth of penetration =

This methods is commonly used in determining the thickness of sedimentary basins.

c. Electromagnetic Induction methods:
Changing magnetic fields are produced by passing alternating currents through long wires or coils.
These changing magnetic fields induce electric currents in buried conductors such as ore bodies which then produce their own induced magnetic field.
There are a huge variety of techniques which use either the induced electric currents or the induced magnetic field which these currents in turn produce.
This method is especially important in mineral exploration and surveys are easy to conduct form airplanes.

(Advantages to using an airplane to conduct geophysical surveys:

d. Induced polarization methods:
When a current is applied to a formation containing metallic minerals, each metallic mineral grain has a small voltage produced across it in the direction of current flow.

     ---------> ----------> [ mineral grain ] ---------->
      current    negative                      negative
                 charge                        charge
                 added                         removed

 

When the current is turned off, the separation of charge remains for a short time and the voltage can be measured.
The total voltage for the formation depends on the percentage of metallic minerals it contains.


Part 6: Seismology

Stress - specifies the nature of the internal forces acting within a mineral

Strain - defines the changes of size and shape (deformation) arising from those sources

An elastic substance is one in which stress is proportional to strain (Hooke's Law)
The constants of proportionality are known as the elastic constants and are different for different kinds of stress (twisting, compressing, stretching) and for different materials.
Examples:

In a plastic substance, under a given stress, strain is not constant but is dependent on time.

The Earth is constantly undergoing stress.
The rocks of the Earth sometimes behave elastically and sometimes plastically.

If the stress becomes large enough (the elastic limit is reached), fracturing will occur, suddenly releasing stress and producing elastic waves which travel through the Earth (earthquake)

Five most important types of waves:

P-waves:
usually have the smallest amplitude
Velocity can be calculated from elastic constants of material through which wave is traveling - one formula is:

vp = where is density

S-waves:
If the particles in an S-wave all move in a parallel line, the wave is said to be polarized.
An S-wave with all vertical particle motion is called SV; one with all horizontal motion is SH.

The velocity of S-waves is given by the formula:

Vs =

Question: Why can't S-waves travel through fluids?
In a fluid, rigidity () is zero, therefore Vs must also be zero.

Question: Why are P-waves always faster than S-waves?

Because K and are always positive numbers, the ratio of Vp to Vs will always be greater than 1.

Love waves:
transverse and horizontal
possible only in a low-speed layer overlying a medium in which elastic waves have a higher speed

Rayleigh waves:
particle motion in circles like water waves, but in opposite direction
travel only along the free surface of an elastic solid
amplitude decreases with depth below surface
slower than Love waves

When there is a low speed layer overlying a much thicker layer of material in which the speed of elastic waves is higher, the surface wave velocity varies with wavelength.
This variation of velocity with wavelength is called dispersion.

For deep focus earthquakes, surface waves are either non-existent or have very low amplitudes.

Free Oscillations:
motions of the Earth as a whole

The energy of a seismic wave is proportional to the square of its amplitude.
As a wave spreads out from its source, the energy spreads out over a large area and therefore the amplitude decreases.
There is also a loss of energy due to friction converting the elastic energy into heat, leading to an additional reduction in amplitude.
The loss of amplitude is called attenuation of the wave.

Need many seismographs to completely record motion of ground during an earthquake, including one each to record N-S motion, E-W motion and up-down motion.

The relation between the natural period of a seismograph and the period of the waves being recorded determines whether the instrument will measure the displacement, the velocity or the acceleration associated with the Earth motion.

When a wave meets a surface of discontinuity, part of it will be reflected and part refracted (bent).
Every reflection or refraction generates additional waves, producing an incredibly complex situation and seismograms which are extremely confusing.
The recognition of the several different arrivals is a skill acquired by long practice.

It is often easier to follow reflected and refracted waves by viewing them as rays moving at right angles to the wave front.

Review of physics:

When a wave is reflected, the angle to reflection is equal to the angle of incidence.

When a wave is refracted, Snell's Law applies:

where v1 is the velocity in the 1st medium; v2 is the velocity in the 2nd medium;
is the angle of incidence and ' is the angle of refraction.

A wave which strikes the discontinuity at the particular angle when sin = v1/v2 will not penetrate into the 2nd medium but will travel along the interface. is known as the critical angle of refraction when this occurs.

Some applications of seismology:

  1. determining location of an earthquake
  2. determining magnitude of an earthquake
  3. determining direction of motion along a fault
  4. locating "liquid" layers inside the Earth
  5. determining structure and composition of Earth, both on large scale and small scale (seismic exploration)

1a. determining epicenter:
Since velocity of P and S waves are different, time interval between arrivals increases with increasing distance, allowing the calculation of the distance between epicenter and recording station.
Must have 3 stations to fix location.
Can usually be done to within 15 miles for a moderate earthquake and to within 3 miles in a well-monitored area such as California.

1b. determining depth of focus:
Consider 2 P-waves produced by an earthquake, one traveling directly through the Earth to a recording station on the opposite side, the other first bouncing off the Earth's surface at the epicenter and then traveling to the same recording station.
The "bounced" wave has traveled farther than the direct wave by an amount equal to twice the depth of focus.
Thus the time interval between the arrivals of these 2 waves can be used to calculate the depth of focus.

2. determining magnitude:
The magnitude of an earthquake is a quantitative measure of its size.
Magnitude scales were originally determined from the amplitudes of the elastic waves generated.

The Richter Magnitude Scale can be described by the following formula:
M = log10 (a/T) + f (, h) + C

The Richter Magnitude Scale did not originally specify which wave type used.
Now we commonly use P-waves for deep focus earthquakes and the horizontal component of Rayleigh waves for shallow focus earthquakes.

One big problem with the Richter Magnitude Scale is that it doesn't directly measure anything related to fault mechanics.
A relatively new scale, called the Moment Magnitude Scale, which attempts to address this problem is now becoming widely used.

The seismic moment is defined as: Mo = A u

The Moment Magnitude is: Mw = 2/3 log Mo - 10.7

A formula often used to give the relationship between magnitude and total elastic wave energy of an earthquake is:
log10 E = 12.24 + 1.44 M (E is in ergs)

3. First Motion Studies:
For simplification, we will choose simple horizontal strike-slip motion and choose axes parallel and perpendicular to fault. Other cases more complicated.
In 2 of the quadrants, first motion will be away from the epicenter; in other 2 quadrants, 1st motion will be toward epicenter.
Motion away from the epicenter (and toward the observer) appears as an upward movement on a seismic record.
At right angles to the fault, the motion would be at a minimum, while at small angles to the fault, motion would be maximum.
There will be a reversal in the direction of first motion as one crosses the trend of the fault.
Transform faults were found to be different from regular strike-slip faults by looking at their relative movement as determined by First Motion Studies.

4. locating areas of molten or partially molten rock:
The formulas for the velocities of P and S waves indicate

Major regions:

5a. determining depths to discontinuities
Travel times for P and S waves depend primarily on the distance they travel and therefore the depth to which they penetrate into the Earth.
The velocities of seismic waves depends on rocks' elastic properties and can be determined.
Knowing velocities and timing the arrivals of reflected and refracted waves at known distances from source allows the calculation of the depths to discontinuities.

Within the Earth, major discontinuities occur at depths of 30 to 60 km (the Mohorovicic discontinuity), 2900 km (the Gutenberg discontinuity) and 5000 km.
These discontinuities are used to divide the Earth into the crust, mantle, outer core and inner core.

In addition, there are many minor discontinuties.
Notable ones are:

The Earth can be thought of as being made up of an infinite number of layers, each with greater density than the one above. This results in an infinite number of refractions and is responsible for the general curved nature of the paths of seismic waves through the Earth.

Diagrams which trace the paths of seismic waves through the Earth usually use symbols as follows:

5b. determining compositional variations
Knowing the velocities of seismic waves at different locations allows us to determine densities and elastic properties at those locations.

Exploring the Earth's interior with P and S waves is sometimes called seismic tomography by analogy with CAT scans (Cathode Applied Tomography) which use x-rays to study the interior of a human body.

5c. Seismic prospecting methods:
Explosions, vibrations and dropped objects often used to produce artificial earthquakes.
Basic procedure is to set up seismic waves and time their arrivals at known distances.
The waves may travel along direct paths, or may be refracted or reflected.
Almost always use only the first arrivals of P-waves (regardless of the path taken).

Two commonly used types of methods:

  1. Seismic refraction methods
  2. Seismic reflection methods

1. Seismic refraction:
Can be used to detemine thicknesses and dips of layers and seismic velocities in each layer, making identification of rock types possible.

Example of one layer case:
Plot time of arrival of waves (T) versus distance to detector (x).
Will obtain a straight line with a slope of dT/dx (which is equal to 1/velocity), allowing calculation of velocity of P-waves in layer.
Of limited usefulness, obviously.

Example of two layer case:
Waves can travel from source to the detectors directly or by critical refraction along the boundary between the layers.
Those that travel directly will produce the same type of plot as in the one layer case.
The travel time versus distance plot for refracted waves will also produce a straight line but one which has an intercept on the T axis.
(The mathematical proof for this statement and the associated calculations can be found in any introductory geophysics text, generally occupying a number of pages of manipulations of formulae. Go look it up if you are interested.)

The depth to the boundary,

where Ti is the intercept on the T axis and V2 is the velocity in the lower layer.
The slope of the line is 1/V2.

In reality, since we measure only first arrivals, at distances less than a certain distance (called the critical distance), the direct wave is recorded and at distances beyond the critical distance, the refracted wave is recorded.
The plot we obtain is thus made up of segments of two straight lines and allows us to obtain the velocities in both layers and the depth to the interface.

For multi-layer cases, the procedure is similar but more complicated.
The plot is made up of one line segment for each layer.
Velocities can be read off the graph fairly easily but the equations used to obtain the depths to the interfaces are horrendous and generally impossible without the use of a computer.

Example of a situation where the higher velocity layer is on top (very rare in nature):
No critical refraction occurs
Layer missed and thickness not accounted for
Leads to depth calculation errors

Example where velocity increases continuously with depth:
Basically the same as a multi-layer case with an infinite number of layers.
Plot will look like a curve with the shape of the curve dependant upon how the velocity varies with depth.

Example of case of fault:
If a bed is faulted vertically, the plot obtained perpendicular to the strike of the fault will consist of 2 parallel but displaced linear segments.
The throw (vertical displacement) of the fault can be calculated from the difference between the T intercepts of the the two linear segments.

Example of dipping layers:
If layers are horizontal, the same plot will be obtained by reversing positions of the energy source and the detector.
This will not be true if layers dip.
The apparent dip and velocities in the layers can still be determined but the procedure is extremely complicated. Consult geophysics text if interested.

2. Seismic reflection:
the most widely used and valuable geophysical exploration method and one of the easiest to interpret qualitatively

Seismic waves traveling down from a source are reflected upward from each interface encountered.
Interfaces are not necessarily boundaries between layers but could be any of a number of lithologic changes which cause velocity contrasts.
Reflections from a single shot are usually recorded by groups of geophones - frequently as many as 96.

When several closely spaced detectors are laid out along a line, each will record a reflection from each interface.
If the seismograms from these detectors are recorded parallel to each other, the waves corresponding to a reflection will all line up across the records in such a way that the crests and troughs on adjacent traces will appear more or less to fit into one another.

To make a record easier to analyse, we usually make a dynamic correction (also called normal moveout).
The different geophones were at different distances from the shot point and therefore the waves had longer distances to travel.
The dynamic correction has the effect of mathematically placing all geophones at the same distance from the shot point.

Other corrections might involve:

After reflections have been identified, they are timed, using the trough of the 1st wave.
For horizontal beds, where T is the travel time, x is the distance between the shot point and the receiver, and V is the average velocity in the section above the interface, the depth to the interface is:

The average velocity in an area is often determined by exploding charges of dynamite in a shallow drill hole alongside a deep exploratory borehole and recording the arrival times of waves at detectors at a number of depths in the hole.
The average velocity is simply the total vertical distance divided by the total time.

The difference between the times of a peak or a trough for the same reflection at successive detector positions gives information about the dip of the reflecting interface.

Changing the distance between the shot point and the geophones gives several readings for the same reflecting surfaces.
This results in the same reflection signal being recorded but different "noise" signals, enabling us to remove the noise signals (or at least to minimize them) with the use of various techniques.
Filters used in geophysics can be compared to maps of different scales
One geophysicist's noise is another's music. Rayleigh waves (disparagingly called ground roll) get in the way of exploration geophysics but are very important in crustal studies.
Noises are due to many things and we could devote an entire course to the techniques used to deal with them.

Interpretation:
Know thicknesses and know velocities.
Have at least some knowledge of the geology of the area.
In addition to type of rock, several other factors also affect velocity, including porosity and water content.
Guess a little.


Seismic Tomography

Seismic tomography uses data from hundreds of earthquakes and recording stations to generate a sort of CAT scan of the Earth in a way that is similar to the whole-body scanning method used for medical purposes.

The computer modeling methods are very complex. The end result is a three-dimensional model of the shear-wave velocity within the Earth.

These S-wave variations provide information about temperature conditions and mantle flow.


Earthquake Prediction

Geophysical properties used in earthquake prediction attempts:

1. slowing down of seismic waves

2. rock deformation

3. increase in electrical resistivity

4. local magnetic field changes

5. electromagnetic "noise"

6. "earthquake lights"