isotacy

2. GEO PHYSICS
Topic
ISOSTASY
DENSITY,SUSCEPTIBILITY AND RESISTIVITY
INSTITUTE OF GEOLOGY
UNIVERSITY OF AZAD JAMMU & KASHMIR MUZAFFARABAD

4. WE PLACED FIRMLY EMBEDDED MOUNTAINS ON
THE EARTH, SO IT WOULD NOT MOVE UNDER THEM
(QUR'AN, 21:31)

5. ISOSTASY

6. ISOSTASY
It refers to the state of
gravitational
equilibrium between
the earth's lithosphere
and asthenosphere
such that the tectonic
plates "float" at an
elevation which
depends on their
thickness and density.

7. WORD ATTRIBUTION
• Isostasy is derived
from two Greek words
ISO and STASIS
• ISO means “same”
and
• STASIS mean
“standstill”.

8. HISTORY
• In 1735, expeditions over the
Andes led by Pierre Bouguer,
a French photometrist studied
the isostasy for the first time.
About a century later, similar
discrepancies were observed
by Sir George Everest,
surveyor general of India, in
surveys south of
the Himalayas, indicating a
lack of compensating mass
beneath the visible mountain
ranges. The general term
'isostasy' was coined in the
year 1889 by the American
geologist Clarence Dutton.

9. ISOSTASTAIC MODELS
• There are three principal models of isostasy:
 THE AIRY MODEL
 THE PRATT MODEL
 THE VENING OR FLEXURAL ISOSTASY MODEL

10. • THE AIRY MODEL
Different topographic heights are accommodated by changes
in crustal thickness, in which the crust has a constant density.
• THE PRATT MODEL
Different topographic heights are accommodated by lateral changes
in rock density.
• THE VENING OR FLEXURAL ISOSTASY MODEL
Where the lithosphere acts as an elastic plate and its inherent rigidity
distributes local topographic loads over a broad region by bending.
Airy and Pratt isostasy are statements of buoyancy, while flexural isostasy
is a statement of buoyancy while deflecting a sheet of finite elastic
strength.

11. The main types of isostatic models. Each model
implies a state of hydrostatic equilibrium such
that the Earth’s outermost layers are in a state of
flotation on their more fluid substrate. (a / 1) The
Airy-Heiskanen Model (b / 2) - The Pratt-Hayford
Model. (c) Vening Meinesz model.

13. Airy isostasy, in which a constant-density crust floats on a higher-density
mantle, and topography is determined by the thickness of the crust.

15. Airy was mostly correct about what supports large
(wide) mountains, but it took until the 1970’s to
prove this with seismic work that measured the
thickness of the crust and lithosphere beneath
mountains.
Pratt was correct in that the difference between
the low standing ocean basins and the high
standing continents is partially due to the fact that
oceans have dense gabbroic composition crust
whereas continents have lighter less dense
‘Andesitic’ composition crust.

17. THE VENING MEINESZ OR FLEXURAL MODEL
• This hypothesis was suggested to explain how large topographic loads
such as seamounts. A seamount is a mountain rising from the ocean
seafloor that does not reach to the water's surface (sea level), and
thus is not an island.(e.g. Hawaiian Islands) could be compensated by
regional rather than local displacement of the lithosphere. This is the
more general solution for lithospheric flexure as it approaches the
locally-compensated models above as the load becomes much larger
than a flexural wavelength or the flexural rigidity of the lithosphere
approaches 0.

18. Regional Or Vening Isostasy - The Lithosphere Flexes Under Its Own Weight And Shields
The Asthenosphere From The Difference In Pressures.

19. WHICH DO YOU THINK WOULD HAVE THE GREATER VOLUME
AND MASS?
WHY?
• 1 kg of feathers
• 1 kg of rock
DENSITY

20. • Density is defined as mass per unit volume. It is a measure of how
tightly packed and how heavy the molecules are in an object. Density
is the amount of matter within a certain volume.

21. UNITS FOR DENSITY
The SI unit of density is kg/m3 , g/cm3.
FORMULA
 M = D x V
 V = M / D
 D = M / V

22. TABLE SHOWING AVERAGE GRAVITY OF VARIOUS
SEDIMENTARY, METAMORPHIC AND IGNEOUS ROCKS
• Density is a property that is proportional to the composition of the rock. The higher the
amount of silica (felsic) the less dense the rock will be. The less amount of silica in the
rock the more dense the rock will be.

23. DENSITIES OF TYPICAL ROCK TYPES AND MINERALS

25. PUMICE
Environment of formation =Extrusive
(Volcanic)
Texture = Glassy, Vesicular
Grain size = Non-Crystalline
Color = Light
Density = Low (1.00 g/cm3 )
Composition = Felsic

26. VESICULAR BASALT
Environment of formation =extrusive
(volcanic)
Texture = Glassy, vesicular
Grain size = non-crystalline
Color = dark
Density = medium (2.74 g/cm3)
Composition = mafic

27. RHYOLITE
Environment of formation =extrusive (volcanic)
Texture = fine
Grain size = less than 1 mm
Color = light
Density = low (2.51 g/cm3)
Composition = felsic

28. ANDESITE
Environment of formation =extrusive
(volcanic)
Texture = fine
Grain size = less than 1 mm
Color = light
Density = medium (2.64 g/cm3)
Composition = intermediate

29. BASALT
Environment of formation =extrusive
(volcanic)
Texture = fine
Grain size = less than 1 mm
Color = dark
Density = high (2.99 g/cm3)
Composition = mafic

30. GRANITE
Environment of formation =intrusive
(plutonic)
Texture = coarse
Grain size = 1 mm to 10mm
Color = light
Density = low (2.667 g/cm3)
Composition = felsic

31. GABBRO
Environment of formation =intrusive
(plutonic)
Texture = coarse
Grain size = 1 mm to 10mm
Color = dark
Density = high ( 3.03 g/cm3)
Composition = mafic

32. METAMORPHIC ROCKS
SLATE (2.79 g/m3) PHYLLITE (2.18 and 3.3 g/m3)

33. SCHIST (2.64 g/cm3)
GNEISS (2.80 g/cm3)

34. MARBLE (2.75 g/cm3) QUARTZITE (2.60 g/cm3)

35. SEDIMENTARY ROCKS
SANDSTONE (2.35 g/cm3)

36. ROCK SALT
(2.17 g/cm3)
SHALE (2.40 g/cm3)

37. GYPSUM (2.31 g/cm3)
LIMESTONE (2.55 g/cm3)

38. IGNEOUS ROCKS
Igneous rocks form when molten rock (magma) cools
and solidifies, with or without crystallization, either
below the surface as intrusive (plutonic) rocks or on
The surface as extrusive (volcanic) rocks.
IGNEOUS ROCK’S DENSITY > METAMORPHIC ROCK’S DENSITY
> SEDIMENTARY ROCK’S DENSITY

39. REASON OF HIGH DENSITY OF IGNEOUS
ROCKS THEN METAMORPHIC AND
SEDIMENTARY ROCKS
 Lack of pore pressure
 Due to mafic minerals
 Due to slow cooling
 Due to close packing or compaction
 Due to impermeable nature
 Number of atoms
 Impurities or Neighboring minerals involvement.
 Due to slow crystallization
 More pressure in the subsurface.

40. SUSCEPTIBILITY

41. SUSCEPTIBILITY (K)
• The degree of magnetization in response to the external magnetic field is
known as susceptibility.
Or
• It is a measure of the ease with which the material can be magnetized.
Mathematically
K= I / H
I= intensity of magnetization
H = Magnetic Field Strength
Definition

42. THE VALUES GIVEN HERE ARE FOR SI,
INTERNATIONAL SYSTEM UNITS.

43. VALUE OF THE MAGNETIC SUSCEPTIBILITY
The value of the magnetic susceptibility can either be
 POSITIVE
 NEGATIVE.

44. POSITIVE VALUE
• Positive value means that the
induced magnetic field, I, is in
the same direction as the
inducing field, H.

45. NEGATIVE VALUE
• Negative value means that the
induced magnetic field is in
the opposite direction as the
inducing field.

46. REMNANT MAGNETIZATION
• If the magnetic material has relatively
large susceptibilities, or if the inducing
field is strong, the magnetic material
will retain a portion of its induced
magnetization even after the induced
field disappears. This remaining
magnetization is called remnant
magnetization.
• The total magnetic field is a sum of the
main magnetic field produced in the
Earth's core, and the remnant field
within the material.

47. MAGNETIC PROPERTIES OF ROCKS
• All rocks contain magnetic properties. Sedimentary and metamorphic
rocks have less magnetic properties as compared to igneous rocks.
Because sedimentary and metamorphic rocks have low susceptibility
and igneous rocks have high susceptibility.
• IGNEOUS ROCK’S SUSCEPTIBILITY > METAMORPHIC ROCK’S
SUSCEPTIBILITY > SEDIMENTARY ROCK’S SUSCEPTIBILITY

48. KINDS OF MAGNETIC MATERIAL
• Magnetic material are of different kinds. Three main types are as
follows:
1. Paramagnetic materials
2. Diamagnetic materials
3. Ferromagnetic materials

49. PARAMAGNETIC MATERIALS
• The magnetic material which have weak positive susceptibility is called
paramagnetic material. Grains of such material tends to line up with their
long dimension in the direction of magnetic field.
EXAMPLE
1. Iron compounds
2. Mica
3. Biotite
4. Garnet
5. Amphibole

50. Examples of paramagnetic minerals
Olivine (Fe,Mg)2SiO4 1.6 · 10-3
Montmorillonite (clay) 0.34 ·10-3
Siderite (FeCO3) 1.3-11.0 · 10-3
Serpentinite 3.1-75.0 · 10-3
(Mg3Si2O5(OH)4)
κ (SI)Mineral

51. DIAMAGNETIC MATERIALS
• The magnetic material which have weak negative susceptibility is known
as diamagnetic material. Grains of such material tends to line up with their
long dimension across the direction of magnetic field.
• EXAMPLE
1. Rock salt
2. Gypsum
3. Anhydrite
4. Quartz

52. Quartz (SiO2) - (13-17) · 10-6
Calcite (CaCO3) - (8-39) · 10-6
Graphite (C) - (80-200) · 10-6
Halite (NaCl) - (10-16) · 10-6
Examples of diamagnetic minerals
κ (SI)Mineral

53. FERROMAGNETIC MATERIALS
• Such material which have high susceptibility is called ferromagnetic material.
Electron coupling is more stronger in these materials. Grains are aligned in the
direction of magnetic field.
• EXAMPLE
1. Iron
2. Cobalt
3. Nickel
4. Hematite
5. Magnetite

54. MAIN REASON OF MAGNETIZATION OF
ROCKS
• The liquid portion in the outer core consist of iron, nickel and cobalt which are
in continues motion because it is high density material and it wants to move
from high density to low density, as a result convectional currents are
produced in the outer core. These convectional currents are also produce in
the upper mantle due to which plate moves. Due to these currents iron, nickel
and cobalt are magnetized and earth behaves as a magnet as a whole.
• Lightening is another factor that magnetized the rocks when it pass through
magnetosphere when the electron pass through magnetosphere current is
produced which results in the magnetization of the earth and this is a rare
case.

55. SUSCEPTIBILITY OF VARIOUS ROCKS

56. TABLE SHOWING SUSCEPTIBILITY OF FEW MATERIALS

57. REASON OF HIGH SUSCEPTIBILITY OF IGNEOUS
ROCKS
• Susceptibility is higher in rocks having magnetic minerals and in igneous
rocks ( mainly mafic and ultramafic ) have more ferromagnetic
minerals, so they have more susceptibility then metamorphic and
sedimentary rocks.
• Igneous rocks have high susceptibility because grains of igneous rocks
align in the direction of external field, also electron coupling is stronger in
these rocks.
• Magnetic susceptibility of rocks is principally controlled by the type and
amount of magnetic minerals contained in a rock.
• The magnetic susceptibility depends also on temperature.
• Outer core’s material.

58. IGNEOUS ROCK’S SUSCEPTIBILITY > METAMORPHIC ROCK’S SUSCEPTIBILITY >
SEDIMENTARY ROCK’S SUSCEPTIBILITY
Volcanic rocks, particularly the young ones (called neo-volcanics ), are often strongly magnetic.

59. RESISTIVITY

60. RESISTIVITY
DEFINITION
• Resistivity is an intrinsic property that quantifies how strongly a given
material opposes the flow of electric current. It Is also called electrical
resistivity, specific electrical resistance, or volume resistivity. A low
resistivity indicates a material that readily allows the movement
of electric charge.
• Resistivity is commonly represented by the Greek letter ρ (rho).
• The SI unit of electrical resistivity is the ohm meter (Ω⋅m)

61. BASIC PHYSICS OF ELECTRIC CURRENT
FLOW
 SIMPLE RESISTOR IN CIRCUIT
Ohm’s Law states that for a resistor, the resistance (in ohms),
R is defined as R = IV
V = voltage (volts);
I = current flow (amps)
 ELECTRIC CURRENT FLOW IN A FINITE VOLUME
Ohm’s Law as written above describes a resistor, which has no dimensions.
In considering the flow of electric current in the Earth, we must consider the
flow of electric current in a finite volume. Consider a cylinder of length L and
cross section A that carries a current I .

62. where ρ is the electrical resistivity of the material (ohm-m). This is the resistance per
unit volume and is an inherent property of the material.
Resistivity is basically opposition to the flow of electron.
R is the electrical resistance of a uniform specimen of the material (measured
in ohms, Ω)
L is the length of the piece of material (measured in meters, m)
A is the cross-sectional area of the specimen (measured in square meters, m2).

63. HOW TO CALCULATE RESISTIVITY OF ROCKS
• Pure materials are rarely found in the Earth and most rocks are a
mixture of two or more phases (solid, liquid or gas). Thus to calculate
the overall electrical resistivity of a rock, we must consider the
individual resistivities and then compute the overall electrical
resistivity.

64. FACTORS THAT WILL INCREASE THE
RESISTIVITY OF A ROCK
Factors that will INCREASE the resistivity of a rock
(a) Minimum pore fluid.
(b) Lower salinity of pore fluid
(c) Compaction - less pathways for electric current flow.
(d) Lithification - block pores by deposition of minerals.
(e)Fluid content constant, but decrease connection between pores.

65. FACTORS THAT WILL DECREASE THE
RESISTIVITY OF A ROCK
Factors that will DECREASE the resistivity of a rock:
(a) More pore fluid
(b) Increase the salinity of the pore fluid - more ions to conduct electricity
(c) Fracture rock to create extra pathways for current flow
(d) Add clay minerals
(e) Fluid content constant, but improve interconnection between
pores.

66. REASON OF HIGH RESISTIVITY OF IGNEOUS
ROCKS
• Compacted rocks
• No pore spaces
• Presence of Magnetic minerals
• No fluids
• Pressure
• Temperature
• Fractures
• Composition

67. IGNEOUS ROCK’S RESISTIVITY >
METAMORPHIC ROCK’S RESISTIVITY >
SEDIMENTARY ROCK’S RESISTIVITY
 Igneous rocks have highest resistivity.
 Sedimentary rocks tend to be the most conductive due to their high
fluid content
 Metamorphic rocks have intermediate but overlapping resistivity.
Age of the rock is also important for the resistivity.
For example:
Young volcanic rock (Quaternary) ≈10−200Ωm
Old volcanic rock (Precambrian) ≈100−2000Ωm

68. RESISTIVITY LEVELS OF VARIOUS ROCKS

69. TABLE SHOWING RESISTIVITY OF FEW
ROCKS

70.  Groundwater exploration.
 Mineral exploration,
detection of cavities.
 Waste site exploration.
 Oil exploration
APPLICATION OF RESISTIVITY

71. REFERENCES
• Archie, G.E., 1942: The electrical resistivity log as an aid in
determining some reservoir characteristics. Tran. AIME, 146, 54-67.
• Lowrie. Fundamentals of Geophysics. Cambridge University Press.
pp. 254–.ISBN 978-1-139-46595-3
• A.B. Watts, Isostasy and flexure of the lithosphere, Cambridge Univ.
Press., 2001
• Altschaeffel, A. G., and Harrison, W., 1959, Estimation of a minimum
depth of burial for a Pennsylvanian under clay: Jour. Sed. Petrology, v.
29, p.178-185
• Hrouda, F. & Rejl, L., 1982. Small-scale magnetic susceptibility
distribution in some plutonic rocks and its geological implications.
Věst. Ústř. Úst.geol., 57-69. Prague.
• Smirnov, V., 1982. Geology of mineral deposits. Nedra. Moscow.