The document contains brief discussion on Gravity and magnetic method in geology. It is essetial for Geology students.

1. GRAVITY & MAGNETISM
Gravity methods in Geology and Introduction to
basic magnetism
Md. Asif Hasan

2. Geophysics: Geophysics is the science that applies the principles of physics to the study
of the earth.
Geophysical investigations of the interior of the earth involve taking measurements at or
near the surface of the earth that are influenced by the internal distribution of physical
properties. Analysis of these measurements can reveal how the physical properties of the
earth’s interior vary vertically and laterally.
A wide range of geophysical surveying methods exists, for each of which there is an
operative physical property to which the method is sensitive.The methods are provided in
the table
WHAT ARE THE GEOPHYSICAL TECHNIQUES?
GRAVITY SURVEY
EXAMPLE USES…
 Salt Dome Exploration
 New Basin Reconnaissance
 Estimating Glacial Cover
 Corroborating Seismic Refraction
 Military Applications
 Isostatic Studies of the Earth

3. MAGNETOMETER SURVEY
EXAMPLE USES…
 Estimating Basin Thickness
 Determining Fault Type
 Locating Mining Prospects
 Finding Buried Drums
 Evaluating Ocean-Floor Spreading
ELECTROMAGNETIC SURVEYS
EXAMPLE USES…
 Finding Mineral Prospects
 Locating Contaminant Plumes
 Finding Buried Ordinance
 Locating Utilities & Pipelines
 Shallow Stratigraphy
 Groundwater Exploration
 Locating Mining Prospects
 Environmental Studies
 Estimating Glacial Cover
 Engineering and Construction investigations
Gravity Method
 Gravitation
 The Earth’s Rotation
 Isostasy
 Rheology
Figure of the Earth :-
The expression figure of the Earth has various meanings in geodesy according to the way
it is used and the precision with which the Earth's size and shape is to be defined. The
actual topographic surface is most apparent with its variety of land forms and water areas.
This is, in fact, the surface on which actual Earth measurements are made. It is not
suitable, however, for exact mathematical computations, because the formulas which
would be required to take the irregularities into account would necessitate a prohibitive

4. amount of computations. The topographic surface is generally the concern of
topographers and hydrographers.
The Pythagorean concept of a spherical Earth offers a simple surface which is
mathematically easy to deal with. Many astronomical and navigational computations use it
as a surface representing the Earth. While the sphere is a close approximation of the true
figure of the Earth and satisfactory for many purposes, to the geodesists interested in the
measurement of long distances—spanning continents and oceans—a more exact figure is
necessary. Closer approximations range from modelling the shape of the entire Earth as an
oblate spheroid or an oblate ellipsoid, to the use of spherical harmonics or local
approximations in terms of local reference ellipsoids. The idea of a planar or flat surface
for Earth, however, is still acceptable for surveys of small areas, as local topography is
more important than the curvature. Plane-table surveys are made for relatively small
areas, and no account is taken of the curvature of the Earth. A survey of a city would likely
be computed as though the Earth were a plane surface the size of the city. For such small
areas, exact positions can be determined relative to each other without considering the
size and shape of the total Earth.
A spheroid, or ellipsoid :
 A spheroid, or ellipsoid of revolution is a quadric surface obtained by rotating an
ellipse about one of its principal axes; in other words, an ellipsoid with two equal
semi-diameters.
 If the ellipse is rotated about its major axis, the result is a prolate (elongated)
spheroid, like a rugby ball. If the ellipse is rotated about its minor axis, the result is
an oblate (flattened) spheroid, like a lentil. If the generating ellipse is a circle, the
result is a sphere.
 Because of the combined effects of gravitation and rotation, the Earth's shape is
roughly that of a sphere slightly flattened in the direction of its axis. For that reason,
in cartography the Earth is often approximated by an oblate spheroid instead of a
sphere. The current World Geodetic System model, in particular, uses a spheroid
whose radius is approximately 6,378.137 km at the equator and 6,356.752 km at the
poles (a difference of over 21 km).
o Equation: A spheroid centered at the "y" origin and rotated about the z axis is
defined by the implicit equation
where a is the horizontal,
transverse radius at the equator,
and b is the vertical, conjugate radius

5. Surface area:
o A prolate spheroid has surface area
Where is the angular eccentricity of the prolate spheroid,
and e = sin(α) is its (ordinary) eccentricity.
o An oblate spheroid has surface area
where is the angular eccentricity of the oblate spheroid.
o Volume of a spheroid (of any kind) is .
If A=2a is the equatorial diameter, and
B=2b is the polar diameter, the volume is
GEOID:
 The ellipsoid is a mathematically defined regular surface with specific dimensions.
The geoid, on the other hand, coincides with that surface to which the oceans would
conform over the entire Earth if free to adjust to the combined effect of the Earth's
mass attraction (gravitation) and the centrifugal force of the Earth's rotation. As a
result of the uneven distribution of the Earth's mass, the geoidal surface is irregular
and, since the ellipsoid is a regular surface, the separations between the two,
referred to as geoid undulations, geoid heights, or geoid separations, will be
irregular as well.
 The geoid is a surface along which the gravity potential is everywhere equal and to
which the direction of gravity is always perpendicular. The latter is particularly
important because optical instruments containing gravity-reference leveling devices
are commonly used to make geodetic measurements. When properly adjusted, the
vertical axis of the instrument coincides with the direction of gravity and is,
therefore, perpendicular to the geoid. The angle between the plumb line which is
perpendicular to the geoid (sometimes called "the vertical") and the perpendicular
to the ellipsoid (sometimes called "the ellipsoidal normal") is defined as the
deflection of the vertical. It has two components: an east-west and a north-south
component.
The spheroid and geoid=>
The geoid height (= “geoid anomaly”) varies because
gravity varies from place to place as a result of
variable mass & density distribution

6. What is gravity?
 Gravitation is the force of attraction between two bodies, such as the Earth and our
body. The strength of this attraction depends on the mass of the two bodies and the
distance between them. A mass falls to the ground with increasing velocity, and the
rate of increase is called gravitational acceleration, g, or gravity. The unit of gravity is
the Gal (in honor of Galileo). One Gal equals 1 cm/sec2.
 Gravity is not the same everywhere on Earth, but changes with many known and
measurable factors, such as tidal forces. Gravity surveys exploit the very small
changes in gravity from place to place that are caused by changes in subsurface rock
density. Higher gravity values are found over rocks that are more dense, and lower
gravity values are found over rocks that are less dense.
Why does gravity vary from place to place?
 First, because the Earth is not a sphere ,It is an ellipsoid of revolution
 Second, the mass distribution varies from placeto place
Note that the density contrast is what controls the anomaly, not the absolute density of the
body
Theoretical gravity
 As the Earth's diameter is approximately 21 km smaller from pole to pole than
through the equator, the force of gravity increases the closer we get to the poles. In
addition, the Earth's rotation results in a slightly smaller measured gravity at the
equator than near the poles. In order to isolate the effect of lateral variations in
density within the Earth, the bulk gravity effects of the Earth due to latitude must be
removed.
 The theoretical gravity is given in milligals (10
-5
m·s
-2
) by the International Gravity
Formula :
 gt
= 978032.7(1.0+0.0053024 sin²(θ) - 0.0000058 sin²(2θ)) ,
based on the 1980 Geodetic Reference System, where θ is the latitude in degrees of
any point on the Earth. The effect of latitude is removed by subtracting the
theoretical value of gravity from the observed values.

7. Earth rotation and Earth's interior
 Determining the exact figure of the Earth is not only a geodetic operation or a task of
geometry, but is also related to geophysics. Without any idea of the Earth's interior,
we can state a "constant density" of 5.515 g/cm³ and, according to theoretical
arguments (see Leonhard Euler, Albert Wangerin, etc.), such a body rotating like the
Earth would have a flattening of 1:230.
 In fact the measured flattening is 1:298.25, which is more similar to a sphere and a
strong argument that the Earth's core is very compact. Therefore the density must be
a function of the depth, reaching from about 2.7 g/cm³ at the surface (rock density
of granite, limestone etc. – see regional geology) up to approximately 15 within the
inner core. Modern seismology yields a value of 16 g/cm³ at the center of the earth.
 Global and regional gravity field :-Also with implications for the physical
exploration of the Earth's interior is the gravitational field, which can be measured
very accurately at the surface and remotely by satellites. True vertical generally does
not correspond to theoretical vertical (deflection ranges from 2" to 50") because
topography and all geological masses disturb the gravitational field. Therefore the
gross structure of the earth's crust and mantle can be determined by geodetic-
geophysical models of the subsurface.
 Volume:-Earth's volume is 1,083,210,000,000 km
3
ISOSTASY
Isostasy is the term describing the naturally occurring balance of masses of Earth's
crust that keeps the planet's gravity in equilibrium. Isostasy is not a force or a
process; it is only the term for the phenomenon of adjustments Earth makes to stay
balanced in mass and gravity.
Isostasy (Greek ísos "equal", stásis "standstill") is a term used in geology to refer 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. This concept is invoked to explain how different topographic heights can exist at
the Earth's surface. When a certain area of lithosphere reaches the state of isostasy, it is
said to be in isostatic equilibrium. Isostasy is not a process that upsets equilibrium, but
rather one which restores it (a negative feedback). It is generally accepted that the earth is
a dynamic system that responds to loads in many different ways. However, isostasy
provides an important 'view' of the processes that are happening in areas that are
experiencing vertical movement. Certain areas (such as the Himalayas) are not in isostatic
equilibrium, which has forced researchers to identify other reasons to explain their

8. topographic heights (in the case of the Himalayas, which are still rising), by proposing that
their elevation is being "propped-up" by the force of the impacting Indian plate.
Isostatic models:-
 The Airy-Heiskanen Model :-where different topographic heights are
accommodated by changes in crustal thickness.
 The Pratt-Hayford Model:-where different topographic heights are accommodated
by lateral changes in rock density.
 The Vening Meinesz, or Flexural Model:- where the lithosphere acts as an elastic
plate and its inherent rigidity distributes local topographic loads over a broad region
by bending. This hypothesis was suggested to explain how large topographic loads
such as seamounts (eg. Hawaiian Islands) could be compensated by regional rather
than local displacement of the lithosphere.
Isostasy, a word used to describe how the principle of buoyancy applies to blocks of
the earth's crust as they rest on the mantle. In addition to learning about isostasy, there
are two other purposes :
(1) To trace the development of a theory from observations that
initially could not be explained.
(2) To see how two different models (multiple hypotheses) can
both explain the same observations with equal validity.
DISCOVERY
 OBSERVATIONS:-When British engineers were attempting to make a map on
northern India near the Himalayan foothills during the mid-1800s, they discovered
that their plumb bobs did not ha straight down but were deflected towards the
Himalayas.
 INITIAL HYPOTHESIS:- J. H. Pratt hypothesized that the gravitational attraction the
mountain mass caused the plumb bob to be deflected. However, Pratt's calculations
suggested that the deflection from true vertical was only one third of what it should
be for the size of the mountains involved. Why?

9. 1. AIRY'S MODEL :Airy hypothesized that mountains have "roots" which extend down
into the mantle. Therefore, elevation is proportional the depth of the underlying
"root".
2. PRATT'S MODEL: Pratt hypothesized that elevation is inversely proportional to
density. Therefore, the higher the mountain, the lower is its density (i.e., light rocks
"float" higher).
APPLICATIONS
The principle of isostasy suggests that the earth's crust should adjust to any changes in
mass that occur at the earth's surface (we call these "isostatic adjustments"). There are
basically two types of responses:
1. SUBSIDENCE
 Definition: the slow, sinking of the earth's crust
 Cause: the addition of mass to the crust
 Example: the advance of glacial ice sheets
2. REBOUND:- the slow, vertical rise in earth's crust
3. Isostatic effects of deposition and erosion
4. Isostatic effects of plate tectonics
5. Eustasy and relative sea level change

10. Isostatic effects of ice-sheets:-
 The formation of ice-sheets can cause the Earth's surface to sink. Conversely,
isostatic post-glacial rebound is observed in areas once covered by ice-sheets which
have now melted, such as around the Baltic Sea and Hudson Bay. As the ice retreats,
the load on the lithosphere and asthenosphere is reduced and they rebound back
towards their equilibrium levels. In this way, it is possible to find former sea-cliffs
and associated wave-cut platforms hundreds of metres above present-day sea-level.
The rebound movements are so slow that the uplift caused by the ending of the last
glacial period is still continuing.
 In addition to the vertical movement of the land and sea, isostatic adjustment of the
Earth also involves horizontal movements, changes in the gravitational field, Earth's
rotation rate, polar wander, and can induce earthquakes. For details see Postglacial
rebound.
Isostatic effects of deposition and erosion:-
 When large amounts of sediment are deposited on a particular region, the immense
weight of the new sediment may cause the crust below to sink. Similarly, when large
amounts of material are eroded away from a region, the land may rise to
compensate. Therefore, as a mountain range is eroded down, the (reduced) range
rebounds upwards (to a certain extent) to be eroded further. Some of the rock strata
now visible at the ground surface may have spent much of their history at great
depths below the surface buried under other strata, to be eventually exposed as
those other strata are eroded away and the lower layers rebound upwards again.
 An analogy may be made with an iceberg - it always floats with a certain proportion
of its mass below the surface of the water. If more ice is added to the top of the
iceberg, the iceberg will sink lower in the water. If a layer of ice is somehow sliced off
the top of the iceberg, the remaining iceberg will rise. Similarly, the Earth's
lithosphere "floats" in the asthenosphere.
Isostatic effects of plate tectonics:-
 When continents collide, the continental crust up as with the iceberg analogy. The
idea of continental may thicken at their edges in the collision. If this happens, much
of the thickened crust may move downwards rather than collisions building
mountains "up" is therefore rather a simplification. Instead, the crust thickens and
the upper part of the thickened crust may become a mountain range.
 However, some continental collisions are far more complex than this, and the region
may not be in isostatic equilibrium, so this subject has to be treated with caution.

11. Eustasy and relative sea level change:-
 Eustasy is another cause of relative sea level change quite different from isostatic
causes. The term "eustasy" or "eustatic" refers to changes in the amount of water in
the oceans, usually due to global climatic changes. When the Earth's climate cools, a
greater proportion of the earths water is stored on land masses in the form of
Glaciers, snow, etc. This results in a relative fall in global sea levels (relative to a
stable land mass). The refilling of ocean basins by glacier meltwater at the end of ice
ages is an example of eustatic sea level rise.
 A second significant cause of eustatic sea level rise is thermal expansion of sea
water, when the Earth's mean temperature increases. Current estimates of global
eustatic rise from tide gauge records and satellite altimetry is about +3 mm/a (see
2007 IPCC report). Global sea level is also affected by vertical crustal movements,
changes in the rotational rate of the Earth, (see Postglacial rebound), large scale
changes in continental margin and changes in the spreading rate of the ocean floor.
 When the term "relative" is used in context with "sea level change", the implication is
that both eustasy and isostasy are at work, or that the author does not know which
cause to invoke.
Rheology
Rheology is the science of the deformation and flow of solid materials. The solids
are made up of strongly binded particles and it is rigid and resists any kind of
deformetion. So how can a solid flow?
Actually the behaviour solid to any stress depends on the size of thye stress and the length
of time for which it is applied.
Brittle Deformation:-
 If the applied stress does not exceed the yield stress the short term beahaviour is
elastic, i,e., if the stress is removed the body will completely regain its previous
position. However, if the appliede stress exceeds the yeild stress, the solid may
experience brittle or dutile deformation.
 Brittle deformetion consists of rupture without other distortion. This is an abrupt
processes that causes faulting in rocks and earthquakes accompanied by release of
elestic energy in the form of seismic waves. Brittle fracture occurs at much lower
stresses than the intrinsic strength of the crystal lattice. This is mainly due to the
presence of cracks, that modify the internal stress field of the crystal.

12. Ductile deformation :
 Ductile deformation is a slow process in which a solid aquires a strain over a long
period of time. The time depende3nt deformation is called plastic flow and the
capacity of a material to flow is called its ductality. The ductality of a solid above its
yield stress depends on temperature and confining pressure, and materials that are
brittle under ordinary conditions may be ductile at high temperature and pressure.
The behaviour of rocks and minerals in the deep interior of t5he earth is
characterized by ductile deeformation.
 The transition from the brittle to ductile types from brittle to ductile type of
deformation is thought to occur differently in oceanic and in continental lithosphere.
The depth of the transition depends on several parameters including the
composition of the rocks, the local geothermal gradient, initial crustal thickness and
the strain rate. The oceanic lithosphere has a thin crust and shows a gradual
increase i9n strength with depth, reaching a maximum in the upper mantle at about
30-40km depth. At greater depths the lithospere gradually becomes more ductile,
eventually grading into the low rigidity asthenospere below about 100km depth.
CREEP:
 Many solid materials deform slowly at room temperature when subjected to small
stresses well below their brittle strength for long periods of time. The slow time
dependent deformation is known as crrep. This is also an important mechanism in
the deformation of rocks because of the great interval s of time involved in
geological processes.

13. The earth’s Shape and Gravity:
 The geometrical surface of the earth is very irregular. It is not a suitable reference
level. Let us consider the concept of the GEOID. It is the average level of seas and
oceans. This surface is a equipotential surface. It is everywhere normal to the
vertical. It is not a simple geometric shape. The gravity is also not constant on it.
 The concept of reference spheroid which is a mathematically defined surface but not
quiet a ellipsoid of revolution, but the difference is so small that it can be considered
as ellipsoid.
 The polar flattening of the Earth is given by f = (a – b)/a, = 297, where,
a = 6,378.388m and b = 6,356. 909m, are the equitorial and polar radius of the Earth.
 International gravity formula is (Stockholm, 1930) is given on the basis of the above
Reference Spheroid:
o gt
= 9.78049(1.0+0.0052884 sin²(θ) - 0.0000059 sin²(2θ)) m/s².
How do scientists measure gravity?
 Scientists measure the gravitational acceleration, g, using one of two kinds of gravity
meters. An absolute gravimeter measures the actual value of g by measuring the
speed of a falling mass using a laser beam. Although this meter achieves precisions
of 0.01 to 0.001 mGal (milli Gals, or 1/1000 Gal), they are expensive, heavy, and
bulky.
 A second type of gravity meter measures relative changes in g between two locations.
This instrument uses a mass on the end of a spring that stretches where g is stronger.
This kind of meter can measure g with a precision of 0.01 mGal in about 5 minutes. A
relative gravity measurement is also made at the nearest absolute gravity station,
one of a network of worldwide gravity base stations. The relative gravity
measurements are thereby tied to the absolute gravity network.
Measuring gravity:
Units
 1 Gal (after Galileo) = 1 cm/s2
 thus g (at Earth’s surface) ~ 10
3
Gals
 gravity anomalies measured in milliGals
 1 mGal = 10-3 Gals = 10-5 m/s
2

14. • Gravimeters sensitive to ~ 0.01 mGal,
i.e., 10
-8
of Earth’s field
• Usually relative gravimeters used
Gravity measuring instruments:
On land: Can be done using:
a) relative gravimeters
 stable gravimeters
 unstable gravimeters
b) absolute gravimeters
 pendulums
 falling masses
Stable gravimeters: Work on the principle of a force balancing the force of gravity.
Example: the Gulf gravimeter
Unstable gravimeters:
 Cunning mechanical devices
 increases in g cause extension of spring
 extension magnified by mechanical
geometry
Examples: the Worden and the LaCoste-
Romberg gravimeters
Borehole gravimeter:
 Can be used to obtain density of
formations
 Main problems:
 temperature control
 deviation from vertical
Absolute measurements:
 Pendulums =>First done by Pierre
Bouguer in 1749
 Falling bodies

15. What is rock density?
• Density is a rock property described by the ratio of mass to volume. Rock densities
commonly range between 2.0 and 4.0 grams per cubic centimeter (g/cm3). Pure
water, by comparison, has a density of 1 g/cm3. Each rock type can have a range of
density values, and tables in the scientific literature show the general range of
densities for various rock types.
• Often, the geoscientist will collect samples of exposed rocks in the study area and
measure their densities to estimate the actual density of the rock unit where it is
buried. Various rock types within a study area often contrast enough in density to
cause gravity anomalies. For example, sedimentary rocks that fill basins almost
always have low densities and are characterized by gravity lows on anomaly maps.
Mafic rocks, which contain high-density minerals, often are associated with gravity
highs. The scientist can use these differences to map large regions where rocks are
inaccessible or concealed, to look for faults that juxtapose rocks of difference
densities, or to infer structures such as basins, arches, and buried intrusions.
Reduction of observations:
 Drift - plot graph of measurement of base station
throughout the day
 Meter calibration– provided by manufacturer,
and converts scaleunits to mGal
 Latitude correction – needed because g
increases with latitude because of flattening of
Earth at
poles
 Free-Air correction-

16.  Bouguer correction- accounts for mass of rock between station and sea level
 Terrain corrections- both hills and valleys reduce gravity
 Tidal correction– normally absorbed in drift correction, But necessary for ultra-
accurate surveys
 Eötvös correction– necessary on moving platform
V = speed in knots
α = vehicle heading
φ = latitude
 Isostatic correction-
 The principle of isostasy states that mass excesses, represented by
topographic loads at the surface, are compensated by mass deficiencies at
depth which are referred to as isostatic roots. The effect of these mass
deficiencies are not accounted for in the Bouguer reduction and there exists
an inverse correlation between broad Bouguer anomaly lows and positive
topography. The isostatic correction removes the gravity effect of the isostatic
roots. The depth of the roots can be estimated based on the Airy-Heiskanen
model (Simpson et al., 1986).
 Land areas: The depth of the root is defined for land areas by the formula
d = ds + e (ρt / δρ)
where:
d = depth to the bottom of the root (m)
ds = the depth of compensation for sea level compensations (30 000m)
e = elevation (m)
ρt = density of the topographic load (2670 kg·m-3), and
δρ = density contrast between the root and underlying mantle material (600
kg·m-3).
 Oceanic areas: For oceanic areas, a negative topographic load exists, since
lower density water replaces higher density rock. The depth of the root over
oceanic areas is defined by the formula: d = ds
- dw
((ρt
- ρw
) / δρ)
Where, dw
= depth of water , ρw
= the density of water (1030 kg·m
-3
)

17. Errors
 reading error
 drift error meter
 calibration constant
 subtraction of gφ
 Free-Air & Bouguer corrections - height needed
 Bouguer & Terrain corrections - density needed
 Terrain corrections - topography needed
 Eotvos correction - speed & bearing needed
 satellites - position of satellite
What is a gravity anomaly?
 Gravity meters measure all effects that make up the Earth’s gravity field. Many of
these effects are caused by known sources, such as the Earth’s rotation, distance
from the Earth’s center, topographic relief, and tidal variation. Gravity caused by
these sources can be calculated using realistic Earth models and removed from the
measured data, leaving gravity anomalies caused by unknown sources. To the
geologist, the most important unknown source is the effect of the irregular
underground distribution of rocks having different densities.
 A sequence of gravity corrections are applied to the original gravity reading and
result in various named gravity anomalies. The observed gravity anomaly has been
corrected for Earth rotation, latitude, tidal effects, and gravity meter fluctuations.
 The free air gravity anomaly has been corrected for the gravity effect caused by the
elevation difference between the station and sea level (a correction for distance) and
is a standard for oceanic gravity interpretation.
What is a Bouguer anomaly?
 The Bouguer (pronounced Boo-gay´) gravity anomaly has been further corrected for
the mass that may exist between sea level and the observer (a correction for mass)
and is a standard used in geologic interpretation on land. A simple-Bouguer anomaly
has undergone a simplified removal of topographic effects, which suffices in
relatively flat areas.

18.  A complete-Bouguer anomaly contains a terrain correction that uses a more
complete representation of the local topography, which is necessary for accurate
gravity values in mountainous areas.
 The isostatic (pronounced iso-stat´-ic) gravity anomaly is calculated by subtracting
the gravitational effect of low-density mountain roots below areas of high
topography. Although these roots have never been seen, their isostatic effect has
been measured and models calculated using topography. Isostasy is typified by
floating icebergs that have 90% of their mass of ice below water that supports a
smaller mass of ice projecting above water.
What is a gravity map?
 A gravity map is made using numerous gravity measurements across the area of
interest. Gravity surveying by aircraft is still a new science, so most gravity
measurements are made on the ground at discrete stations. Because access is often a
problem, gravity stations may be randomly spaced, although detailed surveys are
usually made at regular intervals.
 Gravity measurements are often processed to a complete-Bouguer or isostatic
gravity anomaly. These data are then gridded, so that the randomly spaced data are
converted to a representation of the gravity field at equally spaced locations. The
distance chosen between grid points depends on the average distance between
gravity stations. Too large a grid interval would not use all the information from the
original data set, whereas too small a grid interval fragments the continuity of
anomalies across a region—either result is a poor representation of the true gravity
field.
 Gravity anomaly maps can be shown as color figures— with warm colors (reds and
oranges) showing areas of higher gravity values and cool colors (blues and greens)
showing lower values—or as contour line maps, where each contour line follows a
constant gravity value.
What is a derivative gravity map?
 A gravity anomaly map contains information about rock density, and depth and
distribution of anomaly source rocks. Maps can be derived from the original gravity
anomaly grid by using mathematical tools to enhance parts of the gravity field.
Derivative maps can show, for example, anomalies that have been mathematically
filtered for size and that show deeper or shallower sources.

19.  Other derivative techniques can magnify gravity gradients, places where the gravity
field changes from high to low—these places often mark edges of rock units or
faults, or they can mimic a geologic map by converting (or “terracing”) the gravity
anomalies into discrete, bounded units representing rock units. All of these maps
can be used together to make a geologic interpretation.
Theoretical gravity:
 As the Earth's diameter is approximately 20 km smaller from pole to pole than
through the equator, the force of gravity increases the closer we get to the poles. In
addition, the Earth's rotation results in a slightly smaller measured gravity at the
equator than near the poles. In order to isolate the effect of lateral variations in
density within the Earth, the bulk gravity effects of the Earth due to latitude must be
removed.
 The theoretical gravity is given in milligals (10
-5
m·s
-2
) by the International Gravity
Formula :
o gt
= 978032.7(1.0+0.0053024 sin²(θ) - 0.0000058 sin²(2θ))
based on the 1980 Geodetic Reference System, where θ is the latitude in degrees
of any point on the Earth. The effect of latitude is removed by subtracting the
theoretical value of gravity from the observed values.
Free-air anomaly:
 To correct for variations in elevation, the vertical gradient of gravity (vertical rate of
change of the force of gravity, 0.3086 mGal·m
-1
) is multiplied by the elevation of the
station and the result is added, producing the free-air anomaly. The free-air gravity
anomaly is given by the formula: FA = g
o
- g
t
+ (δg/δz) h
where:
g
o
= observed gravity (mGal)
g
t
= theoretical gravity (mGal)
δg/δz = vertical gradient of gravity (0.3086 mGal·m
-1
)
h = elevation above mean sea level (m).
Bouguer anomaly:
 To isolate the effects of lateral variations in density on gravity, it is also necessary to
correct for the gravitational attraction of the slab of material between the
observation point and the mean sea level. This is the Bouguer gravity anomaly,
which is given for static land measurements by the formula :
BA = go
- gt
+ (δg/δz - 2πGρc
) h

20. where:
go
= observed gravity (mGal)
gt
= theoretical gravity (mGal)
δg/δz = vertical gradient of gravity (0.3086 mGal·m
-1
)
G = gravitational constant (6.672 x 10
-11
m³·kg
-1
s
-2
or 6.672 x 10
-6
m²·kg
-1
·mGal
ρc
= density of crustal rock (kg·m
-3
)
h = elevation above mean sea level (m).
Terrain corrections:
 In areas of rough terrain, a correction for the effect of nearby masses above
(mountains) or mass deficiencies below (valleys) the gravity measurement point can
be calculated and applied. The final Bouguer gravity anomaly reflects lateral
variations in rock density.
Gravity Anomaly Separation
1. Regional
2. Residual/Local
Removal of regional trend
 the deeper the body the broader the trend
 we may be interested in the deeper trend, e.g. sedimentary basin thickness
 or the shallower trend, e.g. an ore body
 Depth effect
 the shallower the body, the higher the anomaly amplitude ,the shorter the
wavelength
Methods
a) by eye
b) digitally :(1-dimensional)
c)Griffin’s method:(2-dimensional) - calculate average value of anomaly at surrounding
points, and subtract from gravity value of point
d) Trend surface analysis – fit low-order polynomial

21. DERIVATIVE
1. Taking the vertical derivative (i.e. the gradient)
 gravity falls off as r-2
 1st derivative falls off as r-3
 2nd derivative falls off as r-4
2.Taking the 1st or 2nd derivative:
 enhances shallow bodies and suppresses deep ones
 removes the regional
 can reveal the sense of contacts
 can be used to calculate limiting depths (the “Smith rules”)
 Disadvantage: Enhances noise
Data interpretation
Two basic approaches:
1. Indirect (inverse) interpretation– use the data to draw conclusions about the
causative body
 Excess mass: Gauss theorem.In practice - grid gravity map, calculate area x
anomaly for all boxes, and sum them
 Approximate thickness : rearrange the Slab Formulagives reasonable rough
estimate if anomaly fairly wide
2. Direct (forward) interpretation– erect a model based on geologic knowledge,
calculate the predicted gravity field, compare with observations & iterate the
model to fit
 Buried sphere
 Infinite horizontal cylinder: Imagine the point source extending in and out of
the screen
 Horizontal sheet:
ς = mass/unit area of sheet

22. Geomagnetism and Paleo-magnetism
Introduction: 3 fundamental differences with gravity:
 dealing with vector fields - cannot assume field vertical magnetic poles attractive or
repulsive
 magnetic field dependent on mineralogy, notbulk properties
 simple to make measurements, but very complex to understand & interpret
Magnetism:
 Oldest of all Magnetics techniques
 Has become of minor importance with advent of seismic reflection & other
techniques
 Still most widely used in terms of line-km measured each year
Application:
 oil & minerals
 sedimentary structures
 igneous bodies
 kimberlite pipes
 geothermal
 archaeology
 fire pits
 kilns
 disturbed earth
 hazardous waste
MAGNETIC METHOD:
 The aim of magnetic survey is to investigate subsurface geology on the basis of
anomalies in the earth’s magnetic field resulting from the magnetic properties of the
underlying rocks. Although most of the rock forming minerals are effectively non
magnetic, certain rock types contains sufficient magnetic minerals to produce
significant magnetic anomalies. Similarly, man made ferrous objects also generate
magnetic anomalies. Magnetic surveying thus has a broad range of applications,
from small scale engineering or archeological surveys to detect buried metallic
objects, to large scale surveys carried out to investigate regional geologic structure.
 Magnetic surveys can be performed on land, at sea and in the air. Consequently the
technique is widely employed, and the speed of operation of air borne surveys
makes the method very attractive in the search for types of ore deposits that contain
magnetic mineral.

23. Basic concepts
 Field lines around bar magnet
 “North-seeking” poles are +ve and “south poles” are –ve
 Poles always occur in pairs
 If keep a bar magnet, then magnetic flux develops which flows
from one end of the magnet to the other. The direction of the flux
can be traced by suspending a compass needle within the flux. The points within the
magnet where the flux converges are known as the poles of the magnet. A freely
suspended bar magnet similarly aligns in the flux of the Earth’s magnetic field. The
pole of the magnet which tends to point in the direction of the Earth’s north-seeking
pole is called the north seeking or positive pole, and this is balanced by asouth
seeking pole or negative pole of identical strength at the opposite end of the magnet.
 The force F between two magnetic poles of strength m1 and m2 separated by a
distance r is givenby , F = µ0
m1
m2
/4 π µ0
r
2
Where m and m are constants corresponding to the magnetic permeability of
vacuum and the relative magnetic permeability of the medium separating the poles.
 The force is attractive if the poles are of different sign and repulsive if they are of like
sign.
 The magnetic field strength B due to a pole of strength m at a distance r from the
pole is defined as the force exerted on a unit positive pole at that point
B = µ0
m/4 π µR
r
2
 Magnetic fields can be defined in terms of magnetic potentials in a similar manner to
gravitational fields. For a single pole strength m, the magnetic potential V a distance
r from the pole is given by V = µ0
m/4 π µR
r
 The magnetic field component then in any direction is given by the partial derivative
of the potential in that direction.
Parameters & variables
 Magnetic force (F) = force between two poles
 Intensity of induced magnetisation (I) = strength of field induced when body placed
in an external field
 Magnetic susceptibility (k) = the degree to which abody can be magnetised
Unit of Magnetic Measurements:
• Until recently, all measurements of earth’s magnetic field used the CGS emu system
of units (cm-gram-second, electromagnetic units). In this system the unit of
magnetic field strength is the oersted (Oe). However, there is a strong tradition to
state the magnetic field strength in terms of gauss (G). Unfortunately this is the unit

24. of magnetic induction, though numerically there is no practical difference because
the relative permeabilities of vacuum, air and water practically equal to unity.
• In practice smaller unit is used, namely the gamma (γ) defined as 10
-5
Oe.
1 Oe = 1G
1gamma = 1 γ = 10
-5
Oe, or 1 oe = 10
5
γ
• These are not SI units. The SI unit of magnetic induction is the tesla (T). Practical
unit for the magnetic field strength is nanotesla (nT).
1 nT = 10
-9
T = 1γ
• In SI system, magnetic parameters are defined in parameters in terms flow of
electric current. If a current is passed through a coil consisting of several turns of
wire, a magnetic flux flow through and around the coil annulas which arises from a
magnetizing force H. The magnitude of H, is proportional to the number of turns to
the coil and the strength of current, and inversely proportional to the length of the
wire, so that H is expressed in Am
-1
. The density of the magnetic flux, measured over
an area perpendicular to the direction of flow, is known as the magnetic induction or
magnetic field B of the coil. B is proportional to H and the proportionality constant µ
is known as the magnetic permeability. Lenz’s law of induction relates the rate of
change of magnetic flux in a circuit to the voltage developed within it so that B is
expressed in volts m
-2
(Weber (Wb) m
-2
). The unit of the Wbm
-2
is designated the
tesla (T).
Units
 Magnetic field strength: Newtons/Ampere-metre (N/A-m), known as a Tesla (T)
 For surveying the nanoTesla (nT) is used, also known as a gamma (γ). 1 nT = 10
-9
T
 The average strength of Earth’s field is ~ 50,000 nT
Magnetic Moment
 Common magnets exhibit a pair of poles and are therefore referred to as dipoles.
The magnetic moment M of a dipole with poles strength m, a distance l apart is given
by , M = ml
 The magnetic moment of a current carrying coil is proportional to the number of
turns in the coil, its cross sectional area and the magnitude of the current so that
magnetic moment is expressed in Am
2
.
Induced Magnetization/ magnetic Polarization
 When a material is placed in a magnetic field it may acquire magnetization in the
direction of the field which is lost when the material is removed from the field. This
phenomenon is referred to as induced magnetization or magnetic polarization, and
results from the alignment of elementary dipoles within the material in the direction

25. of the field. As a result of this alignment the material has magnetic poles distributed
over its surface which corresponds to the end of the dipoles.
Intensity of Induced magnetization
 The intensity of induced magnetization Ii
of a material is defined as the dipole
moment of dipole per unit volume of material and is given by ,Ii
= M/LA
Where, M is magnetic moment of a sample of length L and cross sectional area A.
Induced magnetization Ii
is expressed Am. In CGS system induced magnetization is
expressed in emu cm
-3
, where 1 emucm
-3
= 1000Am
-1
.
 The induced intensity of magnetization is proportional to the strength of the
magnetizing force H of the inducing field: Ii
= kH
Where, k is the magnetic susceptibility of the material. Since Ii
and H are both
measured in A m
-1
, susceptibility is dimensionless in SI system. In CGS system
susceptibility is also dimensionless, but a consequence of rationalizing SI system is
that SI susceptibility values are 4π greater than corresponding CGS values.
Magnetic induction
o When magnetic material, e.g. iron, is placed in a magnetic field, the magnetic material
will produce its own magnetization. This is called induced magnetization
o In vacuum the magnetic field strength B and magnetizing force H are related by:
 B = µ0
H
Where, µ0
is the permeability of vacuum (4 π x 10
-7
Hm
-1
). Water and air have very
similar permeabilities to µ0
and so this relationship can be taken to represent the
earth’s magnetic field when it is undisturbed by magnetic materials. When a
magnetic material is placed in this field, the resulting magnetization gives rise to an
additional magnetic field in this region occupied by the material whose strength is
given by µ0
Ii
.
o Within the body total magnetic field, or magnetic induction, B is given by:
 B = µ0
H + µ0
Ii
= µ0
H + µ0
kH = (1+ k) µ0
H = µR
µ0
H
Where, µR
is a dimensionless constant known as relative magnetic permeability. The
magnetic permeability is thus equal to the product of the relative permeability and
the permeability of the vacuum, and has the same dimension as for µ0
.µR
air and
water is thus close to unity.

26. Magnetic hysteresis
 describes behaviour of sample placed in a coil
 magnetisation of sample lags behind that of the inducing
field
Magnetism of Materials
 All materials are magnetic at an atomic scale. Each electron acts as dipole due to the
spin of the electrons and the orbital path of the electrons around the nucleus.
Quantum theory allows two such electrons to exist in the same state (or electron
shell) provided that their spins are in opposite directions. Two such electrons are
called paired electrons and their spin magnetic moments cancel. Depending on the
number of spinning unpaired electrons and their spinning direction the materials
can be of:
 Diamagnetic: All electronic shells are filled and no unpaired electrons are
available. When placed in a magnetic field the orbital paths of the electrons
rotate so as to produce a magnetic field in opposition to the applied field.
Consequently the susceptibility of diamagnetic substances is weak and
negative.
 Paramagnetic: Here the electronic shells are incomplete and a magnetic field
results from the spin of unpaired electrons. When placed in an external
magnetic field the dipoles corresponding to the unpaired electron spins rotate
to produce a field in the direction of the applied field. The susceptibility is
positive but with a relatively weak effect.
 Ferromagnetic: Paramagnetic substances contain atoms of several unpaired
electrons. Dipoles associated with the spin of unpaired electrons couple
magnetically to the adjacent atoms. Such grains are said to constitute a single
magnetic domain. Depending on the degree of overlap of the electron orbits
the coupling may be parallel or antiparallel. In ferromagnetic materials the
dipoles are parallel, giving rise to a very strong spontaneous magnetization
which can exist even in the absence of external magnetic field. They are highly
susceptible and include iron, cobalt and nickel.
 Anti-ferromagnetic: Here the dipole coupling is antiparallel with equal
numbers of dipoles in each direction. The magnetic fields of the dipoles are
self canceling and there is no external magnetic effect. However, defects in
crystal lattice structure may give rise to small net magnetization, called
parasitic anti-ferromagnetism.
 Ferrimagnetic: Materials here also have anti-parallel dipole couplings, but
the number of diploles in each direction is unequal. As a result ferrimagnetic

27. materials may exhibit a strong spontaneous magnetization and a high
susceptibility. Practically all minerals responsible for the magnetic properties
of common rock types fall into this category.
(The strength of magnetization of ferro- and ferromagnetic substances decreases with
increase of temperature and disappears at Curie temperature. Above this temperature
inter-atomic distances are increased to separations which preclude electron coupling, and
the materials behave as ordinary paramagnetic substance.)
Remanent Magnetization
• If any magnetic material is kept in a strong external magnetic field, the material may
be permanently magnetized in the direction of the applied external field. The
inherited magnetization remaining after the removal of the applied field is known as
Remanent, or Permanent Magnetization Ir.
• Primary remanent magnetization may be acquired either as an igneous rock
solidifies and cools through the Curie temperature of its magnetic minerals known
as Thermo Remanent Magnetization (TRM),
• Or as the magnetic particles of sediment align within the earth’s magnetic field
during sedimentation, known as Detrital Remanent Magnetization (DRM).
• Secondary remanent magnetization may be impressed later in the history of a rock
as magnetic minerals recrystallize or grow during diagenesis or metamorphism,
known as Chemical Remanent metamorphism (CRM).
• Remanent magnetization that develops slowly in a rock standing in an ambient
magnetic field as the domain magnetization relax into the direction of the field is
called Viscous Remanent Magnetization.
• Any rock containing magnetic minerals may possess both induced and remanent
magnetizations Ii and Ir. These may be in different directions and may differ
significantly in magnitude. The magnetic effects of such rock arise from the resultant
I of the magnetization vectors. The magnitude of I controls the amplitude of the
magnetic anomaly and the orientation of I determine its shape.
Rock Magnetism
 Rocks owe their magnetic properties to the generally small proportions of
magnetic minerals that they contain. There are only two geochemical of
groups of rocks which contain such minerals. The iron titanium-oxygen group
possesses a solid solution series of magnetic minerals from magnetite to
ulvospinel (FeTiO4
). The other common iron oxide, haematite is
antiferromagnetic and does not give rise to magnetic anomalies unless a
parasitic antiferromagnetism is developed. The iron sulphur group provides

28. the magnetic mineral pyrrhotite. The most common rock forming magnetic
mineral is magnetite (Curie temp. 5780C).
 Rocks magnetic behaviour can be classified according to their magnetite
content.
The Geomagnetic Field
 The existence of the earth’s magnetic field was appreciated and utilized in the
mariner’s compass long before the origin of the field with in the earth was
suspected. In 1180, Alexander Neckam referred to the directional property of
a magnetized needle, although it was not until 1600 that the true nature of the
Magnetic field observed at the earth’s surface was revealed by the
experimental work of William Gilbert, whose famous treatise “De Magnete”
has been described as the first modern scientific work. The intensity and
direction of magnetization not only vary from place to place, but also show
variation with time.
 Magnetic anomalies are due to the localized rock effects superimposed on the
normal magnetic field of the earth. Consequently, knowledge of the behaviour
of the geomagnetic field is necessary. The geomagnetic field is geometrically
more complex than the gravity field of the Earth and exhibits irregular
variation both in orientation and magnitude with latitude, longitude and time.
The
Earth’s
main
field
• 99% internal
• simple dipole approximates 80%
• rest can be modelled as dipoles distributed around CMB (Core Mantle Boundary)
• real source is convection in Earth’s outer core

29. How do we know its origin is in the outer core?
 Curie temperature
o temperature above which materials lose their magnetisation = 578°C for
magnetite
o this is reached at 5-10 km depth under continents
 Before discovered that outer core was liquid (using seismology), Albert Einstein,
described the problem as one of the 5 most important unsolved problems in physics.
• The external 1%
 caused by electric currents inionosphere
 11-year periodicity(sunspot activity)
 diurnal periodicity up to 30γ(due to SUN)
 monthly variation up to 2γ(due to MOON)
 random variations (magnetic storms) up to 1,000γ (due to solar flares )
Kinds of Rock magnetism:
1. Diamagnetism :
 all electron shells full, electrons spin in opposite directions & magnetic effects
cancel.
 in inducing field, opposite induced field produced, i.e., k -ve, e.g., quartzite, salt
2. Paramagnetism
 electron shells incomplete, & magnetic effects don’t fully cancel.
 in inducing field, same-sense induced field produced, i.e., k +ve, e.g., 20Ca – 28Ni
element series
3. Ferromagnetism
 paramagnetic minerals where groups of atoms align to make “domains”
 very large k
 only 3 minerals: Iron, Nickel & Cobalt
3 kinds of ferromagnetism
a) pure ferromagnetism
directions of spin in domains aligned to Earth’s field - very large k.
Fe, Ni, Co only

30. b) Antiferromagnetism
 directions of spin in domains alternate
 very small k, e.g. hematite
c) ferrimagnetism
 domain spin directions alternate, but one direction
 weaker - small but +ve k, e.g. magnetite
Remanent Magnetism
 Chemical remnant magnetization
 Detrital remnant magnetization
 Isothermal remnant magnetization
 Thermoremnant magnetization
 Viscous remnant magnetization
Magnetic susceptibility
 The intensity of magnetization, I, is related to the strength of the inducing field, H,
through a constant of proportionality k – the magnetic susceptibility. I = kH
 analogous to density in gravity surveying
 Highest in basic igneous rocks
 Lowest in sedimentary rocks