This document outlines lecture materials for a course on geophysics. Chapter 1 discusses Newton's derivation of the inverse square law of gravity and its implications for planetary orbits and gravitational force. It also examines how gravitational force depends on mass and distance between objects. Chapter 2 covers isostasy, or equilibrium between the lithosphere and asthenosphere. Subsequent chapters will address seismicity, geomagnetism, heat flow within the Earth, and the general and applied uses of geophysics.
3.1.3 Relate gravitational acceleration, g on the surface of the Earth with the universal gravitational constant, G
3.1.4 Justify the importance of knowing the values of gravitational acceleration of the planets in the Solar System.
3.1.5 Describe the centripetal force in the motion of satellites and planets system.
Centripetal Force, F = 푚푣2푟
3.1.6 Determine the mass of the Earth and the Sun using Newton’s universal law of gravitation and centripetal force.
Law Of Gravitation PPT For All The Students | With Modern Animations and Info...Jay Butani
Law Of Gravitation PPT For All The Students | With Modern Animations and Infographics
All the Students od Class 1,2,3,4,5,6,7,8,9,10,11,12 and all the students of engineering, medical, CBSE, GSEB, U.P from beginner to Top and high level can get used. All The informtion are gathered to help you all the people.
All colleges and School students can use it.
All the people can reuse it by downloading by giving credits.
Copyright @ Jay Butani 2019
DISCLAIMER :- ALL THE INFORMARION ARE NOT EXACT OR 100% CORRECT THERE MAY BE MISTAKE. WE ARE NOT RESPONSIBLE OVER THAT.
3.1.3 Relate gravitational acceleration, g on the surface of the Earth with the universal gravitational constant, G
3.1.4 Justify the importance of knowing the values of gravitational acceleration of the planets in the Solar System.
3.1.5 Describe the centripetal force in the motion of satellites and planets system.
Centripetal Force, F = 푚푣2푟
3.1.6 Determine the mass of the Earth and the Sun using Newton’s universal law of gravitation and centripetal force.
Law Of Gravitation PPT For All The Students | With Modern Animations and Info...Jay Butani
Law Of Gravitation PPT For All The Students | With Modern Animations and Infographics
All the Students od Class 1,2,3,4,5,6,7,8,9,10,11,12 and all the students of engineering, medical, CBSE, GSEB, U.P from beginner to Top and high level can get used. All The informtion are gathered to help you all the people.
All colleges and School students can use it.
All the people can reuse it by downloading by giving credits.
Copyright @ Jay Butani 2019
DISCLAIMER :- ALL THE INFORMARION ARE NOT EXACT OR 100% CORRECT THERE MAY BE MISTAKE. WE ARE NOT RESPONSIBLE OVER THAT.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
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He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
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The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
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1. MTU
College of Natural and Computational
Science
Geology Department
Course: Geophysics(Geol3091)
2. LECTURE OUTLINES
CHAPTER 1 THE EARTH’S GRAVITY
Newton's law, gravity
Gravity potentials and acceleration
Gravity of the Earth
Earth’s shape and composition
Normal gravity and gravity anomalies
Observed gravity and geoid anomalies
Flexure of the lithosphere and the viscosity of the mantle
6/2/2023 2
4. CHAPTER 3. SEISMICITY
Waves through the earth
Earthquake seismology
Refraction and reflection seismology
Seismic tomography
Global seismicity distribution
6/2/2023 4
5. 6/2/2023
CHAPTER 4.
GEOMAGNETISM
Origin of earth’s magnetism and magnetic
field
Magnetism and plate motions
Magnetization of rocks and
paleomagnetism
Magnetic anomalies 5
6. CHAPTER 5
The Sources Of Internal And External Heat And Their
Applications Conductive Heat Flow
Calculation of simple geotherms
Worldwide heat flow: total heat loss from the Earth
Oceanic heat flow
Continental heat flow
The adiabatic and melting in the mantle
Metamorphism: Geotherms in the continental crust
6/2/2023 6
8. Geophysics is the application of physical principles
and methods to problems in Earth Sciences. Essentially, as
the word suggests, geophysics is the application of method
of physics to the study of the Earth. The rocks does not
differ only by their macroscopic or microscopic properties
studied field geologists or petrologists. They also differ by
their chemical and physical properties.
6/2/2023 8
9. Hence as the rocks differ according to their origin,
structure, texture, etc. they also differ by their density,
magnetization, resistivity, etc. The bad news is that the
physical properties do not always clearly correlates with
geological classifications and do not necessarily easily
translates into the geological terms.
What does this mean? Lets take the density as an
example. We have a rock sample and we have
measured the value of density to be 2.60 g/cm3.
6/2/2023 9
10. According to this value we could assume that the rock sample
could be, e. g. a limestone, some shale, compact sand- stone,
rhyolite, phonolite, andesite, granite, possibly some kind of
schist and many others.
The wide range of possible rock types suggests that the physical
properties does not directly refer to the geological classification.
This is a principal problem of geophysics, however, as we will
see later, there are ways to overcome this problem.
6/2/2023 10
11. So, what we can conclude from this
example? The geophysics is a kind of proxy
in our attempts to study the geological
structures.
It does not “talk” to us in geological
terms and we have to interpret obtained
physical parameters in a geological sense.
6/2/2023 11
12. Moreover, the centrifugal force interpretation is not
unique as we have seen in our example. The successful
interpretation is based on experiences of an interpreter and
on the a priori knowledge of the geological environment
studied.
In the terms of our example if we know that we are
working in the crystalline complex we can mostly likely
leave sedimentary rocks out of our interpretation.
6/2/2023 12
13. There is no clear distinction between general and
applied geophysics.
General geophysics methods are typically applied to
solve academic questions, whereas applied geophysics
can be characterized by the application of geophysical
methods for commercial purposes (“making money)
6/2/2023 13
14. Chapter one
Newton's "derivation" of the inverse square law of gravity
From observations of the night sky, it was clear to Newton (and
many before him) that there must be some form of attraction
between the earth and the moon, and the sun and the planets that
caused them to orbit around the Sun.
Yet, it was not at all clear that the same force of attraction could
be responsible for the behavior of falling bodies near the surface
of the earth.
Newton postulated that one force called gravity was responsible
for both motions. His problem, then, was to attempt to determine
the force law.
6/2/2023 14
15. His method involved a comparison of the motions of the moon
around the earth and an object (e.g., apple) falling towards the
earth. Since neither the apple or the moon are moving in a
straight line at constant speed, they must each be undergoing an
acceleration.
Would it be possible to determine the nature of the force
responsible for that acceleration? In order to do so, he must first
determine the accelerations of the moon and the apple.
6/2/2023 15
16. Inertial and Gravitational Mass
There are two kinds of mass define by the m in
their equations:
Inertial (F=ma) and gravitational ( g=Gm/r2 ).
should the two mass (m) be the same ? but we now
know that the two mass kinds are the same
(relativity). a detail is that force, momentum, and
velocity are vectors in 3-space.
17. Inertial mass is define as m = F/a. this mass can be
measured by applying a force to an object and
measuring its acceleration.
This mass is thus a measure of the inertia of an object.
and, inertia is the fact that masses remain at rest or in
straight-line constant velocity motion unless acted upon
by an unbalanced force. and a force is defined as a
change in an object velocity vector (momentum:
p=m*v)
6/2/2023 17
18. gravitational mass is defined as m = g(r)*r2/ g.
this mass can be measured by measuring the
gravity field at a distance r and knowing the
value of big-g. this mass is thus a measure of
the gravitational acceleration field made by all
objects (mass).
6/2/2023 18
19. Newton’s Law of Gravity
1 2
Fg
Fg
M1 = Mass of object 1 (grams)
M2 = Mass of object 2 (grams)
D = Distance between objects (cm)
G = 6.67x10-8 cm3/sec2/gm
D
Fg
GM1M2
D2
6/2/2023 19
21. Newton’s Law of Gravity
Mass = Amount of Material
Weight = Force Due to Gravity
90 kg
200 lbs 200 lbs
Earth
30 lbs 30 lbs
Moon
0 lbs 0 lbs
6/2/2023 21
22. Newton’s Law of Gravity
Orbits - Moon is constantly in free fall, as are all orbiting
objects
- “Always falling to earth, but never getting closer!”
0.14 cm
1 km
6/2/2023 22
23. Newton’s Law of Gravity
Kepler’s 3rd Law
A
S
P
In order for planet P to travel in a circle around the Sun…
Central Force = Gravitational Force
MpVp
2
A
GMS Mp
A2
Vp
2
A
GMS
A2
Vp
2
GMS
A
Velocity depends only on distance,
not on mass of planet
Velocity decreases w. greater distance
23
24. Newton’s Law of Gravity
Kepler’s 3rd Law
Vp
2
GMS
A
Vp
distance
time
2A
P
4 2
A2
P2
GMS
A
4 2
A3
P2
GMS
4 2
A3
GMS P2
4 2
G
A3
MS
P2
P2
4 2
G
1
MS
A3
A
C
P
6/2/2023 24
25. Newton’s Law of Gravity
Kepler’s 3rd Law
P2
4 2
G
1
MS
A3
In general, in units of cm, sec, gms
(1yr)2
4 2
G
1
Mo
(1AU)3
For the Earth
P2
1
MS
A3 In general, in units of AU, years, solar
masses
P2
A3
For objects orbiting the Sun (Mc = 1 Mo)
A
C
P
1 Solar Mass
6/2/2023 25
26. Gravitational force law and Inertial force Law
1 2
2 1
1 2
2 2
1
1 2 1
2 2
2
2 1 2
2 2
( ) ( )
( ) ( )
( ) ( )
on
on
m m
m m
m m m
F r G Newtons kg
r s
m m
g r G F m g
r s
m m
g r G F m g
r s
•The two Forces (F) is the magnitude of the
force applied by mass 1 on mass 2 AND the
force of mass 2 on mass 1.
•The magnitudes of the two force is equal and
opposite in direction.
•This unbalanced force will cause each mass
to accelerate in inverse proportion to its mass:
a = F/m.
•The little mass accelerates much more than
the big mass, but the forces magnitudes are
the same!
So when I drop a ball, the ball
accelerates down at 9.8 m/s*2…yes.
And, the earth accelerates upwards
towards the balls mass….yes.
Why don’t we notice the earth’s upward
acceleration?
27. Result:
The considerable inward directed
force of gravitational attraction
of the earth on the moon
balances the centrifugal force of
the moon orbiting around the
earth. The gravitational force
bends the straight line trajectory
(inertial law) into a circle.
The force also cause the
ocean tides as the earth
spins daily underneath the
moon (moon takes 28 day
to go around the earth).
6/2/2023
27
29. Inverse square laws result from spherical area scaling
The area of a spherically symmetric field increase as the radius squared;
therefore, for the field energy to be conserved (as it must), then the field
energy must decrease as the radius squared: e.g., the gravity law, coulomb
electrical force law.
1/r*2 fall-off
6/2/2023 29
30. Calculate
1 2
2 1
1 2
2
1
1 2 1
2 2
2
2 1 2
2 2
( )
( ) ( )
( ) ( )
on
on
m m
m m
m m
F r G N
r
m m
g r G F m g
r s
m m
g r G F m g
r s
Q. How can the gravity fields for the two masses
be different, BUT the forces on each mass has
the same magnitude (albeit opposite direction) ?
6/2/2023 30
31. Calculating gravity for general shapes
Problem: how to calculate gravity field between a point mass (m2)
and a general mass distribution on left side (i.e., earth, asteroid)?
Easy, divide the general shape into little squares (2-d) or cubes (3-
d) and label them (I and J) and then add up the vector forces
applied by all the little cubes on mass m2.
6/2/2023 31
32. Calculating gravity of perfect spheres
When an object’s geometry can be
approximated as a sphere, we integrate
(add-up) the sphere’s gravity using
spherical shells that extend over a small
radial distance.
In doing this integration, we find that the
symmetry of the sphere makes the sphere’s
gravity field to be the same as if ALL the
mass was concentrated at the center of the
sphere!!
One requirement: the ability to treat a sphere’s
mass distribution as a point is true ONLY IF the
ms mass is outside the radius of the sphere.
This theorem found by Newton greatly simplifies
the mathematics by treating the Me spherical
mass as a point!
Easy to apply to solar system as all the masses are
near spherical. On the other hand, it is the Earth’s
non-spherical ellipsoidal shape that makes the
moon recede from the earth about 3.8 cm/yr and
the earths rotation to slow by 0.002 s a day.
6/2/2023 32
34. Densities of Rocks and liquids
Notice we are not using the MKS mass units of kilo-grams (kg) for
density.
Mass is being calculated in mega-grams which is a thousand (103 )
grams.
Note that in general the substances density increase as follows: liquids,
unconsolidated sediments, sediments, igneous/metamorphic rocks,
minerals/ores. Density is defined by the Greek letter rho as:
mass
volume
6/2/2023 34
35. 6/2/2023 35
Estimates of earth’s
mass and volume give
a whole earth density
of ~5.5 g/cm3
Typical rocks at the
surface of the Earth
have a density of 2.0-
2.5 g/cm3
36. Calculating gravity at different points on surface
To calculate the gravity effect of the
irregular body above at point P1 , the
body is divided into small squares
(parcels) and the many gravity
vectors from all the parcels are
added up to get the total gravity. Do
the same analysis to get the gravity
at the other points.
An important detail. The gravity field is a vector
quantity (has magnitude and direction). When
measuring the gravity of the above situation, both
the ‘pull of rest of Earth’ and the ‘total pull of
excess mass of body’ are measured. Note that with
respect to point P, the Earth and the ‘body’ pull at
different directions. When can ignore this detail,
because the Earth’s pull is so much greater, and just
assume we are measuring the ‘vertical component
of Fb
‘ .
6/2/2023 36
37. Gravity field of a sphere on the 2-d surface
If we measured the gravity at every point in the 45 km square plane
and reduce it to bouguer gravity, this is what the gravity field would
look like for a buried spherical mass.
What is the sign of the mass difference between the spherical mass
anomaly and the background material ?
6/2/2023 37
38. Gravity Anomalies
Gravity interpretation for subsurface density is inherently ambiguous.
Many possible density distributions can lead to identical anomalies.
Geological insight must be applied in gravity interpretation.
39. Gravity anomalies of a sphere & a cylinder
The y-axis is the gravity anomaly (mgal) and the x-axis is distance from the center of the
sphere/cylinder (m). These graphs are cross-section through these 3-d objects. The cylinder
extends to +/- infinite in and out of the page. This is why, for the same depth object and
mass anomaly, the cylinder and sphere anomalies are different.
Important: Note that the peak amplitude reduces and the anomalies ‘half-width’ widens as
the anomaly is placed deeper. This is just a consequence of gravity being an ‘inverse
square law’.
+ 6/2/2023 39
40. Gravity anomalies of dipping narrow mass sheets
Note: three gravity
effects:
As the depth to the top of the
anomalies increases the peak
amplitude of the anomaly
decreases.
As the sheet anomaly dips to one
side, the anomaly’s peak value
moves to that side.
As the sheet anomaly dips to one
side, the anomaly has a long-tail
on that side, and a short tail on the
other side.
From these effects, we can determine
the dip of the sheet anomaly.
What is the sign of the mass anomaly?
6/2/2023 40
41. Gravity effects of half-sheets
Note two effects:
1. The deeper sheet has a smaller
peak anomaly.
2. The deeper sheet has a wider
anomaly half-width.
Figure (a) shows a stratigraphic section with
different layer densities that has be offset by a
vertical fault.
Figure (b) shows the layer densities changed into
density contrasts so that we can easily calculate the
total gravity anomaly associated with the variable
vertical distribution of density. From this the
relative motion of the fault can be determined.
6/2/2023 41
42. Gravitational potential
By virtue of its position in the gravity field g due to mass M, any
mass m has gravitational potential energy. This energy can be
regarded as the work W done on a mass m by the gravitational force
due to M in moving m from ref to r where one often takes ref =
∞.The gravitational potential U is the potential energy in the field
due to M per unit mass. In other words, it’s the work done by the
gravitational force g per unit mass. Negative
sign is
absolutely
essential.
6/2/2023 42
45. Shape of the earth
Terms to know:
•Spherical radius
•Equatorial radius
•Polar radius
•Reference ellipsoid
•Geoid (Gravitational Potential)
Non-spherical shape and centrifugal
force makes the gravity vary as IGF
equation.
Also, the earth rotates once a day
around its spin axis to make forces.
6/2/2023 45
46. Misconceptions about crust, lithosphere, asthenosphere*
(1) Crust (compositional). The crust is the residue from
melting the mantle. Crustal thicknesses is 10 km
(oceans) and 30-80 km (continents).
(2) Mantle (compositional). The mantle +crust+core =
chondrite meteorites.
(3) Core (compositional). Made of liquid/solid iron mostly.
(4) Lithosphere (strength). Also, called a plate. The strong
layer that slides over the asthensophere. The lithosphere
is strong because it is colder.
(5) Asthenosphere (strength). The mantle just below the
lithosphere is often weaker than the deeper mantle due to
pressure and temperature effects.
6/2/2023 46
48. 6/2/2023 48
Normal gravity and gravity anomalies
The mean value of gravity at the surface of the Earth is approximately
9.80m/s2, or 980,000 mgal.
The Earth’s rotation and flattening cause gravity to increase by roughly
5300 mgal from equator to pole, which is a variation of only about
0.5%. Accordingly, measurements of gravity are of two types.
The first corresponds to determination of the absolute magnitude of
gravity at any place; the second consists of measuring the change in
gravity from one place to another.
49.
50. Geoid
Locus (surface) of points with equal gravity
potential approximately at Mean Sea Level.
Every day heights are relative to geoid (MSL)
physically exists.
51. Ellipsoid – a mathematical construct used to approximate
the geoid.
Fit it to the geoid:
A single ellipsoid can’t fit perfectly everywhere due to the
irregular nature of the geoid.