GEO PHYSICS

Topic

ISOSTASYDENSITY,SUSCEPTIBILITY AND RESISTIVITY

INSTITUTE OF GEOLOGYUNIVERSITY OF AZAD JAMMU & KASHMIR MUZAFFARABAD

WE PLACED FIRMLY EMBEDDED MOUNTAINS ON

THE EARTH, SO IT WOULD NOT MOVE UNDER THEM

(QUR'AN, 21:31)

ISOSTASY

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.

WORD ATTRIBUTION

• Isostasy is derived

from two Greek words

ISO and STASIS

• ISO means “same”

and

• STASIS mean

“standstill”.

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.

ISOSTASTAIC MODELS

• There are three principal models of isostasy:

THE AIRY MODEL

THE PRATT MODEL

THE VENING OR FLEXURAL ISOSTASY MODEL

• 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.

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.

Airy isostasy, in which a constant-density crust floats on a higher-density

mantle, and topography is determined by the thickness of the crust.

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.

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.

Regional Or Vening Isostasy - The Lithosphere Flexes Under Its Own Weight And Shields

The Asthenosphere From The Difference In Pressures.

WHICH DO YOU THINK WOULD HAVE THE GREATER VOLUME

AND MASS?

WHY?

• 1 kg of feathers

• 1 kg of rock

DENSITY

• 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.

UNITS FOR DENSITY

The SI unit of density is kg/m3 , g/cm3.

FORMULA

M = D x V

V = M / D

D = M / V

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.

DENSITIES OF TYPICAL ROCK TYPES AND MINERALS

PUMICE

Environment of formation =Extrusive

(Volcanic)

Texture = Glassy, Vesicular

Grain size = Non-Crystalline

Color = Light

Density = Low (1.00 g/cm3 )

Composition = Felsic

VESICULAR BASALT

Environment of formation =extrusive

(volcanic)

Texture = Glassy, vesicular

Grain size = non-crystalline

Color = dark

Density = medium (2.74 g/cm3)

Composition = mafic

RHYOLITE

Environment of formation =extrusive (volcanic)

Texture = fine

Grain size = less than 1 mm

Color = light

Density = low (2.51 g/cm3)

Composition = felsic

ANDESITE

Environment of formation =extrusive

(volcanic)

Texture = fine

Grain size = less than 1 mm

Color = light

Density = medium (2.64 g/cm3)

Composition = intermediate

BASALT

Environment of formation =extrusive

(volcanic)

Texture = fine

Grain size = less than 1 mm

Color = dark

Density = high (2.99 g/cm3)

Composition = mafic

GRANITE

Environment of formation =intrusive

(plutonic)

Texture = coarse

Grain size = 1 mm to 10mm

Color = light

Density = low (2.667 g/cm3)

Composition = felsic

GABBRO

Environment of formation =intrusive

(plutonic)

Texture = coarse

Grain size = 1 mm to 10mm

Color = dark

Density = high ( 3.03 g/cm3)

Composition = mafic

METAMORPHIC ROCKS

SLATE (2.79 g/m3) PHYLLITE (2.18 and 3.3 g/m3)

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

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

SEDIMENTARY ROCKS

SANDSTONE (2.35 g/cm3)

ROCK SALT

(2.17 g/cm3)SHALE (2.40 g/cm3)

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

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

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.

SUSCEPTIBILITY

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

THE VALUES GIVEN HERE ARE FOR SI,

INTERNATIONAL SYSTEM UNITS.

VALUE OF THE MAGNETIC SUSCEPTIBILITY

The value of the magnetic susceptibility can either be

POSITIVE

NEGATIVE.

POSITIVE VALUE

• Positive value means that the

induced magnetic field, I, is in

the same direction as the

inducing field, H.

NEGATIVE VALUE

• Negative value means that the

induced magnetic field is in

the opposite direction as the

inducing field.

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.

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

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

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

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

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

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

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

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.

SUSCEPTIBILITY OF VARIOUS ROCKS

TABLE SHOWING SUSCEPTIBILITY OF FEW MATERIALS

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.

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.

RESISTIVITY

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)

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 .

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).

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.

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.

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.

REASON OF HIGH RESISTIVITY OF IGNEOUS

ROCKS

• Compacted rocks

• No pore spaces

• Presence of Magnetic minerals

• No fluids

• Pressure

• Temperature

• Fractures

• Composition

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

RESISTIVITY LEVELS OF VARIOUS ROCKS

TABLE SHOWING RESISTIVITY OF FEW

ROCKS

Groundwater exploration.

Mineral exploration,

detection of cavities.

Waste site exploration.

Oil exploration

APPLICATION OF RESISTIVITY

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.