Geophysics Notes

7/29/2019 Geophysics Notes

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Geophysics

Abbreviated Course Notes

Two major emphases of geophysics:

1. "pure"2. "applied"

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

Examples:

variations in temperature with depth causes of reversals in Earth's magnetic field

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.

Active methods - stimulate response (ex. - setting off dynamite blast) Passive mehtods - simply measure property (ex. - density)

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:

GMeMF = -------

R2


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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 GMeSince 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 rotatesResult: 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; unitsare m/sec2

Calculated value for g "corrected" for latitude is called the theoretical gravity and

abbreviated gt


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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 ofEarth'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:

solid cylinder revolving about its axis, I = 0.5 MR2; where M is mass and R isradius of cylinder

sphere, I = 0.4 MR2 spherical shell, I = 0.67 MR2

Earth's moment of inertia = 0.3307 MR2Best 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.


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Actual not same as theoretical because:

1. actual not measured at sea level where theoretical is calculated2. actual not measured on a flat surface3. solid Earth has tides of 7-14 cm4. 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:

1st : adjust for elevation (distance from center of Earth, h)called the Free Air Correction; = 0.3086 h when h is in meters

2nd: remove that portion of g due to the mass between sea level and the pointwhere measurement made

called the Bouguer Correction = -0.0419 h ( is density in kg/m3)

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 rockwill 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?


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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:

Are roots permanent features? Why do mountains have roots?

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 andits 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?)


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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:

compact mineral body salt dome (gravity low with small high due to dense cap rock in center)

Elongated anomalies produced by:

graben buried folds buried channels subduction zones oceanic ridges

Negative anomalies:

Less dense rock such as in sedimentary basins, batholiths, subduction zones,oceanic ridges

Positive anomalies:

More dense rock such as ultramafic masses Uplifts of denser rock in structures such as anticlines or reverse faults.

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.


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Part 2: Radioactivity, Radiometric Dating and Natural Gamma Methods

Geochronology - concerned with determining age and history of geologic materials

by studying their isotopes

RadioactivityDiscovered in 1896

Natural change from one element to another by emission of particles from nucleus or

addition of particles to nucleus

Particles include:

helium nuclei (alpha particles) electrons (beta particles) high energy electromagnetic waves (gamma rays)

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 fort (age of rock):


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Assumptions made in radiometric dating:

no loss or gain of parent or daughter decay rate constant half life known can measure amounts of parent and daughter accurately (usually use mass

spectrometer)

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

Sr86, Sr84, and Sr88 are all stable and non-radiogenic.

Any could be used; Sr86 most abundant and therefore most often used.


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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

(Sr87/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 duringmetamorphism, 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 Sr87/Sr86 in material that made up primitive Earth.

Usually assume it was same as non-Rb87 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 Sr87 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 0.704Extrapolation 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 Sr87/Sr86 ratios from isochrons.)


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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:


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Use of this equation called lead-lead method.

Handy because U235/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 leadlost, 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.


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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 Pb206/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 U238 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?


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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:

K40undergoes 2 principal kinds of decay, to Ca40 and to Ar40.

Decay to Ca40 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, Arbe decay constant for K-Ar reaction, and Ca be

decay constant for K-Ca reaction.

Then decay equation can be written:


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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:

Ar is gas and will often escapeAdvantages to method:

can be applied to very common and abundant rocks and minerals, since K oneof major elements in Earth's crust

Glauconite in sedimentary rocks can be used and other methods not generallyuseful for sedimentary rocks

schists and slates can be dated since Rb usually found with K, 2 independent ages can usually be obtained

from same sample and compared wide range of ages because of length of halflife (from age of Earth to about

5000 years old); no other methods allow dating of rocks a few tens of

thousands of years old (important for establishing chronology of recent

magnetic reversals)

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.


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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 C14 decays -> 7N14 + -1 0

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, C14 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 ofshort 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 C14 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:

burning of fossil fuels nuclear explosions

possibly through changes in intensity of Earth's magnetic field


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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 withradioisotopes 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:

radiation (may occur in Earth's core) conduction convection

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.


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Thermal conductivity determined by:

composition (most important) whether saturated with water (open cracks don't conduct) pressure (closes cracks)

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:

50 cm below surface - daily changes are seldom more than 1 degree and are 1/2to 1 day late

few meters down - only seasonal changes detectible and arrive months late few thousand meters down - effects of last ice age still detectible Pliocene and Pleistocene lavas are warmer than the average lava

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:

radioactivity (by far most important) left over potential energy from formation recrystallization heat of fusion if outer core solidifying chemical reactions, including oxidation at surface and exothermic reactions

between sea water and basalt

compression of rocks and friction along fault planes


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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:

Oceans - small amount due to conduction; large amount due to convection Continents - mostly due to conduction

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:

continental shields (1.2 x 10-6 cal/cm2 sec)due to low concentrations of radioactive elements? or cold underlying upper

mantle?

seaward of oceanic trenches2. higher than average heat flow

island arcs (1.8 x 10-6 cal/cm2 sec) oceanic ridges (1.5 x 10-6 cal/cm2 sec) other areas of recent volcanic activity (as high as 7 x 10-6 cal/cm2 sec) young orogenic regions

as a result of crustal thickening?

Examples of local heat anomalies useful for prospecting:

chemical reactions which give off heat (ex. - oxidation of sulfide ores producesdetectable heat)

presence of local radioactive heat sources (ex. - granite intrusions) differences in heat conductivity of rocks (ex. - salt is highly conductive) presence of volcanic and hydrothermal sources


19/46

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:

Magnetic equator - curve around the Earth connecting points whereinclination is horizontal

Magnetic dip poles - points on the Earth's surface where inclination is vertical(several in polar region; also occur where strong local fields exist)

Isomagnetic charts - plots of Earth's magnetic field Isodynamics - contours of equal intensity Isogonics - contours of equal declination Isoclinics - contours of equal inclination


20/46

Component's of the Earth's field:

internally generated (99% of total); called the dipole component externally generated (1% of total); called the non-dipole component

Internal field can be mostly accounted for by a fictitious magnetic dipole displacedfrom 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 magnetized2. 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


21/46

and a magnetic field still exists.

Called a self-exciting dynamo.

Notice 2 things necessary:

must supply energy continually to spin disk must have small initial applied magnetic field

Possible initial field for Earth's dynamo?

some kind of primitive battery action produced by variations in chemicalcomposition and temperature in Earth's interior?

the Sun?Source ofenergy to keep dynamo "spinning"?

thermal convection?If so, source of heat?

Why doesn't the convection disturb the layering of the outer core (called fine

structure)?

solification of inner core? rocking of Earth as it moves around Sun (precession) setting liquid in outer

core in motion

try rocking a bottle of liquid to see similar effect

Magnetic fields which will spontaneously reverse polarity can be produced by acombination 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 storms2. diurnal changes3. secular variation4. westward drift5. reversals

Continuous recordings of changes are called magnetograms.


22/46

1. Magnetic storms:

last several days change of about 1000 gamma (1 gamma = 10-9 Oersteds) produced by charged particles emitted by the Sun.

2. Diurnal changes:

last about a day change of about 25 gamma produced by:

o effect of radiation from Sun on ionosphere (varies with latitude)o tidal pulls of Sun and Moon on atmosphere

3. Secular variation:

regional changes occur over decades or centuries possible cause?

variations in core motions, especially eddies near the core boundary

4. Westward drift:

entire magnetic field "drifts" around Earth in period of about 2000 years possible cause?

core rotates slower than rest of Earth

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?


23/46

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:

Higher magnetic field strengths correlate with colder climates.Question: Could climatic changes cause extinctions?

Reversals correlate with tektite increases in deep sea sediments.Question: Do violent meteorite impacts produce reversals?

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:

maximum in direction of bedding planes and foliation planes earthquake prediction (will discuss later)

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.


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

magnetic fields.

Three types of magnetic behavior:

1. diamagnetic2.paramagnetic3. 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 (technicallycanted 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.


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2. Small magnetic fields already existing are partially lined up in same directionas 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,

effect 1 disappears effect 3 disappears because of thermal agitation effect 2 remains and substance becomes "permanently magnetized"

Exceptions:

When temperature of substance is above the Curie Temperature, domainsbreak down; substance becomes paramagnetic.

Can also remove "permanent" magnetization by reversing applied field.The strength of the reversed field necessary to reduce the magnetization to zero

is called the coercive force.

The effects of an applied external magnetic field on a ferromagnetic substance are

usually shown by using a plot called a hysteresis curve.


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Magnetism remaining in a rock when the applied field is removed is called natural

remanent magnetization (NRM) or paleomagnetism.

Types include:

Thermoremanent magnetization Depositonal remanent magnetization Chemical remanent magnetization Isothermal remanent magnetization Viscous remanent magnetization

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 andunconsolidated, 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 sameorientations 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.


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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:

trace India's path distinguish among terrains

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:

variation in distance to magnetic body (including relief in basement rocks) difference in magnetic susceptibility (how easily rocks magnetized)

Magnetic susceptibility is very low for most materials; only high for

ferromagnetic substances.

Susceptibility of rocks is primarily controlled by the amount of ferromagnetic

minerals in the rock and is extremely variable.

difference in NRMMagnetic 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.


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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 bodiesproduce 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


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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 Methods2. Resistivity Methods3. Well Logging4. 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.


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These potential differences are caused by

a. ore bodies behaving like natural "batteries" with separation of positive andnegative charge (called Electrolytic Potential)

How this works is not understood.

The most accepted theory for sulfides suggests that the portion of the ore body abovethe 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.

b. differences in salt concentration in water (called Electrochemical Potential)c. solutions flowing through permeable rocks (called Streaming Potential)d. 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 voltageL 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.


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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 depth2. 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 forbasement 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


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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 resistivityplace 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 conductorsor good resistors

Interpreting profiles:

Estimate of depth to conducting body (to +/- 100%) can be made bythe shape of the profile - depth is half of the width of the curve at half its

maximum height.

Steep gradients in resistivity curve are characteristic markers of structureswith near-vertical boundaries, such as faults, dikes, veins, stream channels,

etc. A lack of symmetry in the profile implies a dipping body, with steeper slope

and positive tail on the downdip side.

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 ofcorrelation between wells.


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4. Electromagnetic Methods:

a. Telluric methodsb. Magnetotelluric methodsc. Electromagnetic Induction methodsd. 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


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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:

not necessary to get permits from landowners straight, evenly spaced survey grid pattern easier to obtain)

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:

If wire is stretched and becomes thinner, the proportionality constants areE, Young's modulus and , Poisson's ratio.


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If wire twisted, the proportionality constant is , the modulus of rigidityorshear modulus.

If a sphere is compressed, the proportionality constant is K, the bulk modulus.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:

Body waves -o compressional (longitudinal, primary or P-waves)o transverse (shear, secondary or S-waves)

Surface waves (S-waves) -o Love waves (transverse, horizontal)o Rayleigh waves (circular, reverse of water wave motion)

Free oscillationsP-waves:

usually have the smallest amplitudeVelocity 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.


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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 directiontravel 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.

Fordeep focus earthquakes, surface waves are either non-existent or have very low

amplitudes.

Free Oscillations:

motions of the Earth as a whole


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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.

If the natural period of a seismograph is much less than that of the earthvibration (frequency greater), the displacement of the seismograph becomes

proportional to the acceleration of the Earth and the instrument acts as

an accelerometer.

If the two periods are approximately equal, the instrument reading will beproportional to the velocity of the Earth motion.

If the natural period is much greater than the period of Earth vibration, thereading becomes proportional to the actual displacement of the Earth.

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.


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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

thecritical angle of refraction when this occurs.

Some applications of seismology:

1. determining location of an earthquake2. determining magnitude of an earthquake3. determining direction of motion along a fault4. locating "liquid" layers inside the Earth5. 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 theEarth'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.


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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

a is the amplitude of the ground motion for surface waves from a SouthernCalifornia earthquake recorded on a Wood-Anderson seismograph (in microns,

.001 mm)

T is the dominant wave period (in seconds) is the distance (measured as the angle subtended at the center of the Earth)

between the earthquake and the seismometer

h is the depth of focus f ( , h) is a term found from a study of many recordings. It is basically an

expression for the attenuation of the waves and has the effect of reducing all

observations to a standard distance

C is a station correction to adjust for local peculiarities of seismometer siting.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

is the shear modulus A is the area of the fault u is the average displacement on the fault

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)


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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 upwardmovement 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

the lower the rigidity, the lower the velocity S-waves don't travel through fluids.

Major regions:

the molten outer core the partially melted zone in the upper mantle (about 100 km down) called the

Low Velocity Zone orasthenosphere

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 5000km.

These discontinuities are used to divide the Earth into the crust, mantle, outer core

and inner core.


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In addition, there are many minor discontinuties.

Notable ones are:

Crustal layers Low Velocity Zone in upper mantle (discussed previously)

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:

reflection at surface of Earth indicated by succession of chief symbols (ex. PP,PS, SS)

reflection at the outer surface of the core is shown by interposing C (ex. PcP,ScS, PcS)

K is used for a P-wave refracted through the outer core (PKP) and is oftenabbreviated P'

I is used for a P-wave refracted through the inner core. J is used for an S-wave refracted through the inner core. For deep focus earthquakes, a small preceding s or p is used to indicate a wave

moving up from the focus to the surface (ex. pP, pS, pPcP)

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).


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Two commonly used types of methods:

1. Seismic refraction methods2. 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 ofone 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 oftwo 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 toobtain the velocities in both layers and the depth to the interface.


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Formulti-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 offault:

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 ofdipping 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 anumber 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.


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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 (alsocalled 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:

elevation variations removing the effects of the surface layer because it is generally very variable

and not of particular interest

correcting for the fact that we are assuming vertical paths for the incident andreflecting rays and this would not be true for dipping or irregular

surfaces and correcting for diffraction effects (both corrections called seismic

migration)

removing multiple reflections (called deconvolution)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 shotpoint and the receiver, and V is the average velocity in the section above the interface,

thedepth 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.


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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 scalesOne 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 ofCAT 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.


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Earthquake Prediction

Geophysical properties used in earthquake prediction attempts:

1. slowing down of seismic waves

Before an earthquake, the P-wave velocity drops to a minimum and thenreturns to normal.

Quake occurs in about 1/10 time that anomaly lasted. Size of quake correlates to duration of anomaly Possible explanation: When cracks first begin to open, P-waves slow down

because they don't travel as fast through open

space as they do through solid rock. Ground water then seeps in and P-wavevelocity returns to normal; also rocks are lubricated.

Problems:o usually doesn't occuro Sometimes when it occurs, earthquakes don't

2. rock deformation

characterised by tilting or vertical changes3. increase in electrical resistivity

Possible explanation: air in cracks is not a good conductor4. local magnetic field changes

Laboratory experiments show that compression in direction of magnetizationreduces susceptibility and remanence; perpendicular compression increases it.

Effect probably due to rotation of magnetic domains.

Could be related to increase in stress before quake or release of stress at time offaulting.

5. electromagnetic "noise"

6. "earthquake lights"

Documents

Geophysics Notes