ERTH 4121 Gravity and Magnetic Exploration …Applications of gravity method Mineral exploration: direct detection mapping (incl basement depth structure lithology) Petroleum exploration:

ERTH 4121

Gravity and Magnetic Exploration

Session 1

Introduction to gravity - 1

Lecture schedule (subject to change)

Minimum 10 x 3 hour lecture sessions: 1:30pm Tuesdays

Aug 2 : 1. Introduction to gravity method 1

9: 2. Introduction to gravity method 2

16: 3. Introduction to magnetics method 1

23: 4. Introduction to magnetics method 2

Sept 13 : 5. Gravity forward modelling

20: 6. Magnetics forward modelling

[Term break]

Oct 4: 7. Introduction to inversion 1

Oct 7?: 8. Introduction to inversion 2

Oct 11: 9. Gravity inversion

Oct 18: 10. Magnetics inversion

KEA300 Geophysical Mapping – Lecture 1 3

• Applications

• Rock density

• Field and potential

• Gravity units

• Ellipsoid and geoid

• Gravity meters

• Gravity surveys.

• Data reduction

• Regional removal

Topics – Gravity Session 1

KEA230 Lecture G1

Geophysics

Global

Geophysics Exploration

or Applied

Geophysics

These two disciplines rely upon the same basic physical

phenomena but differ mainly in the scale of investigation.

This course will focus on applied geophysics

KEA230 Lecture G2

Gravity of Australia

Applications of gravity method

Mineral exploration: direct detection

mapping (incl basement depth

structure

lithology)

Petroleum exploration: basin architecture

base of salt mapping

Engineering: void detection

Archeology: micro-gravity

KEA230 Lecture G1

Physical Properties of Rocks There are only six main physical properties of rocks that enable

practical geophysical exploration:

Mass (Density) - Gravitational anomaly

Magnetism - Magnetic anomaly

Conductivity - Electrical / EM anomalies

Elastic properties - Seismic “anomalies”

Radiation - radiometric anomalies

Temperature - Heat flow anomalies

KEA230 Lecture G1

Density • The gravity method (on or above the Earth’s surface) is only effective

where there are significant lateral contrasts in density.

• The density of common geological materials ranges from a minimum of

~0 (air), or ~0.7 t/m3 (oil), to a maximum of 7.5 t/m3 (galena).

• The range of densities encountered in most geological environments is

generally much less than this and can be < 0.1 t/m3 .

• Bulk densities range from ~1.3 t/m3 for coal, to ~2 t/m3 for oil shale and

porous unconsolidated sediments, to a maximum of ~3.3 t/m3 for some

ultramafic rocks.

• A larger range of densities may be encountered in prospect-scale

surveys for dense sulphide orebodies or in engineering surveys where

air or water filled voids are detected.

KEA230 Lecture G1

Density • Most common rock types

have a wide range of densities

• Density variation within each

rock suite is related to variations

in mineralogy together with

variations in pore volume.

• In general, despite the wide

variation, igneous rocks are

typically denser than epiclastic

rocks and basic igneous rocks

are denser than felsic rocks.

• Units: true SI unit is kg/m3

1 t/m3 = 1 g/cc = 1000 kg/m3

Constrained 3D Potential Fields Inversion (after Emerson, 1990)

ROCK DENSITY

2.67

Density in practice

Density is bulk property, c.f. magnetic susceptibility

Variation in density is fairly modest, c.f. conductivity

Density in combination with velocity determines acoustic impedance

Density of halite is low (~2.2 g/cc): base of salt mapping

Density of iron and base metal ores is high: ~4 g/cc

Clastic sediment density sensitive to porosity:

Density of kimberlite ~2.5 g/cc

Weathering reduces density

Density critical for resource & reserve modelling

1grainfluid


• An understanding of the gravity method begins with Newton’s

Law of Universal Gravitation.

The Gravity Method

2

21

r

mGmF

G is the universal gravitational constant

G = 6.673x10-11 Nm2kg-2

• Divide this force by the mass of a test object

and substitute the mass of the earth for the

second mass gives: 2

1 r

Gm

m

Fg e

• g is the acceleration of a freely falling object. It is measured in

ms-2 or more commonly in mms-2 or mGal (10 mms-2 = 1 mGal)

• g is a vector quantity with the vector everywhere directed

vertically downwards, perpendicular to an equipotential surface.

KEA205 - Geophysics 2

Potentials • An alternative description of the Earth’s gravitational force

field is in terms of its potential.

• For a particle in a gravitational field the potential describes

the potential energy per unit mass at that point in the field.

• Since energy is a scalar quantity, the gravitational potential

is a scalar field which is characterised by a single value

(magnitude) at all points in space.

• Potentials can be visualised using lines (2D) or surfaces

(3D) of equal potential called equipotentials.

KEA230 Lecture G1

• For the Earth, the radial

gravitational force field lines mark

the trajectory of a small mass

released in the field

• The field lines are everywhere

perpendicular to gravitational

equipotential surfaces.

• The equipotential surface

closest to mean sea level is the

geoid.

Gravitational Acceleration • g is a vector quantity directed along the line connecting two masses

Gravity is a conservative force field:

work is independent of path

P1

P2

dFW

P

P

2

1

Wz

W

y

W

x

WF

,,

A conservative force field can be represented as the

vector gradient of a scalar “work function” or potential

d

Ug

Gravity as a potential field

Potential of a point mass

r

mGrU )(

Poisson’s Equation: applies within dense medium

)(4)(2 rGrU

Laplace’s Equation: applies in free space or air

0)(2 rU

KEA230 Lecture G1

Gravity Units • The observed gravity at the Earth’s surface, g, ranges from ~9.78 ms-2

near the equator to ~9.83 ms-2 near the poles

• In the SI system gravity is typically quoted in mm-2, known as gravity

units (gu)

• However it is still very common to use the older unit, the gal

1000 gal = 10 ms-2

• Anomalies of interest to geology and geophysics typically have

amplitudes of ~10-5 ms-2 and the most commonly used unit is the milligal

(mgal). 1 mgal = 10 mm-2 = 10 gu

• gmgal 6101

KEA270 Gravity and Geodesy 18

6378.1

63

56

.7

~22

Earth – An Oblate Spheroid • Due to its rotation, the Earth is an

oblate spheroid to a first approximation

• The gross form of the Earth can be

simply described mathematically by the

parameters of a spheroid or ellipsoid

major axis

min

or

axis

a

b

f

f

1flattening Inverse

a

b-a Flattening

axisminor -semi b

axismajor -semia


• The Earth closely approximates an oblate spheroid with

inverse flattening, 1/f, of ~298

• The gross form of the earth can be described easily in

terms of the simple mathematical formula for a spheroid but

on a smaller scale the form of the Earth is more complicated

• The gravitational attraction of the Earth is less at the

equator than at the poles for two reasons: what are they?

Ellipsoid


Ellipsoids


The Geoid & The Ellipsoid • An ellipsoid defines the

gross form of the Earth but

subsurface mass variations

cause smooth but irregular

variations in shape.

• These variations are

specified by the geoid which

is defined as the gravitational

equipotential surface that

lies closest to mean sea level

(excluding the dynamic

effects of winds and ocean

currents)

• The geoid extends both above and

below the ellipsoid and is specified

in terms of the geoid-ellipsoid

separation or N value (in metres).


• The form of the geoid can be calculated from detailed measurements

of the Earth’s gravity field.

• The time averaged ocean surface closely approximates the geoid

(within 1 to 2m).

• Before gravity data can be used for geological or geodetic purposes

it must be corrected for a number of factors including: the gross form

of the Earth, elevation, topography and Earth tides.

• The need for elaborate corrections is one of the defining

characteristics of the gravity method

The Geoid and Gravity


The Geoid and Ellipsoid

Geoid Ellipsoid

• In continental areas the geoid would be represented by the

static water level in thin frictionless channels cut through the

continents.

• The geoid undulates either side of the ellipsoid. The geoid-

ellipsoid separation (the N value) varies from -100m to +100m.


Why use the Geoid? • The geoid might at first seem like a theoretical concept of very

little practical value, particularly beneath the continents where it is

not directly accessible but this is not the case.

• Positions of points on

the land surface are

determined by geodetic

levelling where

“horizontal” is defined by

a spirit level which is

aligned tangential to the

local equipotential surface

and hence closely parallel

to the geoid.


Why use the Geoid?

• Heights determined by

traditional surveying are

relative to the geoid rather

than the ellipsoid.

• The orthometric height

is measured perpendicular

to the local equipotential

surfaces and differs from

the ellipsoidal height which

is the perpendicular

distance from the ellipsoid

surface.

equipotentials

ellipsoid

geoid


Describing the Geoid • While it is feasible to specify the global geoid or gravity field in

terms of a grid of values at uniform mesh, it is more common to

describe these quantities in terms of a spherical harmonic expansion.

• Spherical harmonic analysis is in many ways similar to Fourier

analysis but applied to phenomena observed on the surface of a

sphere (or ellipsoid).

Where: and l are the latitude and longitude

n and m are the degree and the order for the coefficients Cnm and Snm

Pnm specify Legendre polynomials

• The description of the field to degree and order 360 involves

~130,000 coefficients


Zonal Harmonic

m=5 n=0

Tesseral Harmonic

m=5 n=3

Sectoral Harmonic

m=5 n=3

Spherical Harmonics • As the degree and/or order of the coefficients increase, the spatial

complexity of the respective component increases

• Low degree and order terms correspond to long wavelength

features and hence to deep-seated sources. Higher order terms

correspond to short-wavelength and hence shallow features.


The Geoid

The geoid components to order 4

show only the effects of deep seated

(mantle) mass anomalies

The geoid components to order 360

show crustal and bathymetric

features as well as mantle features

The geoid is a smooth but irregular surface which is affected

by the mass distribution within the Earth.


The Gravity Field (n=360)


~2000m

• The gravity field corrected

for the reference ellipsoid is

strongly negative over

topographic features which

rise above the geoid.

Effect of topography on the gravity field

• The gravity field corrected for

elevation ( the free air anomaly )

corrects for elevation but does

not account for mass above the

geoid.

• The free-air anomaly over the

topography is strongly positive

>500mGal

~2000m

~200 mGal


• The Bouguer anomaly should

correct for topographic

irregularities superimposed on a

radially symmetric Earth.

• The Bouguer anomaly in this

case should be near zero

Bouguer correction

• In practice the Bouguer

anomaly is seldom near zero in

this case and is generally

strongly negative over a

topographic high.

Why?

~2000m

Theoretical

~2000m

>100mGal

Actual


• Vertical defined by a plumb-bob is perpendicular to the geoid.

• The angle between a plumb line and vertical w.r.t. the ellipsoid (from

astrogeodetic measurements) is called the deflection of the vertical.

• The vertical deflection measures the local slope of the geoid

surface.

Deflection of Vertical

Geoid Ellipsoid

q

Vertical Deflection


• A topographic irregularity

above the ellipsoid results in

upward deflection of the geoid

• The gravitational attraction

of the topography produces a

deflection of vertical

determined using a plumb bob

from astrogeodetic vertical.

Vertical Deflection

q

Vertical (ellipsoid)

Geoid

• If the density of the topography and its shape are known then

it should be possible to predict the vertical deflection.

• Early measurements of the vertical deflection near mountain

ranges conducted in the 1740’s produced results which were less

than the predictions.


• Accurate measurements of the deflection of the vertical were

carried out in northern India by Sir George Everest in the 1840’s.

• Based on measurements of the size of the mountains to the north

and estimates of their density the maximum predicted vertical

deflection was 28”.

The Himalayas

• The maximum recorded

deflection was only 5”.

• The small value of the

vertical deflection clearly

indicated that the excess

mass of the topographic

edifice was compensated by

an underlying mass

deficiency

predicted

observed +

-


• The presence of a mass deficiency beneath topographic

features is supported by the strong negative correlation

between Bouguer gravity and elevation (~ -100mGal per

1000m)

• The observations in northern India led to the development

of the concept of isostasy

• The term isostasy comes from the Greek:

iso = equal, stasis = standing

• Two alternative models were proposed for isostatic

compensation shortly after Everest’s measurements.

• These models form the basis for isostatic models still

employed today.

Isostasy


Pratt’s Model

constant density

depth of compensation

2.6

7

2.6

2

2.5

7

2.5

2

2.5

9

2.6

7

2.7

6

h

• We can derive a simple

expression for the relationship

between height and density:

positive is when Thus

:hence and equal bemust

columneach of masses The

)(2.67t/m level seaat areas below

elithospher theofdensity average

and

100km)(~ level sea torelative

on compensati ofdepth D

0

0

0

3

0

h

hD

D

DhD


Airy’s Model • Shortly after Pratt proposed his isostatic model the

astronomer royal G.B.Airy proposed an alternative model

• In Airy’s model, mountains of constant density float on an

underlying “lava” of higher density like copper floating in

mercury or ice in water.

• In this model mountain ranges are underlain by low density

“roots”

Hg (13.6)

Cu (8.8)


Pratt or Airy Model? • There is a general, but not perfect correlation between

elevation in continental regions and crustal thickness.

• Bouguer gravity data corrected on the basis of the Airy model

( isostatic residual anomaly ) is close to zero (-50 - +50 mGal) in

mountainous regions indicating that most topographic features

are isostatically compensated.

low

density

root

Bouguer

gravity isostatic residual

gravity


Pratt or Airy Model? • Seismic data suggests the Airy model is more applicable in

continental regions but that it does not explain bathymetric variations

• In the deep ocean basin there is little variation crustal thickness (8-

10 km) but there are still significant topographic features.

• Bathymetric image of

the South Atlantic Ocean

showing the major

topographic high flanking

the mid-ocean ridge


Pratt or Airy Model? • A cross-section through an ocean basin across a spreading

centre would look like:

~1500 km

~2 km

~8 km new

hot

“light”

lithosphere

older

cooler

denser

lithosphere

• Thermal expansion of crustal and upper mantle rocks near the

spreading centre produces a lower average lithospheric density.

• The topography of mid-ocean ridge systems is isostatically

compensated by density variations - Pratt model.

Measuring gravity


• Absolute Measurements - directly record the local value of g (ms-2).

These are difficult and time-consuming. Instruments are not suitable

for rapid field use

• Relative Measurements - involve measurement of the difference in g

between two locations with a gravity meter - quick and simple

• Gravity data is acquired using relative

measurements tied to a series of absolute

determinations.

Measuring Gravity

KEA230 Lecture G1

Absolute Measurements

vacuum

corner

reflector

laser

2

2

2

2

1

t

sg

gts

• The laser measures the

displacement of the corner

reflector as a function of

time:

• The most direct method to determine the

gravitational acceleration g at different locations

is by simply dropping an object and timing its

fall.

• Modern weight drop apparatus can make measurements of g to an

accuracy of ~1mm/s2 (0.1 mGal).

• Field measurements take approximately 1 hour to complete.

KEA230 Lecture G1

Absolute Measurements

• Most modern absolute g determinations are

conducted using weight-drop apparatus.

• Older measurements were conducted using

pendulum equipment.

l

2

242

T

lg

g

lT

• The period of a simple pendulum is related

only to its length and g:

KEA230 Lecture G1

Relative Measurements • Apparatus to record relative gravity variations

are called gravimeters or gravity meters.

• There are many types, but all employ the same

basic principle:

m

l

• For a constant mass the change in the length of

the spring is recorded as the meter moves from

place to place.

• Gravity meter readings must be “tied” to one or more absolute g

determinations

• Gravity meters are sensitive to one part in 108 of g


Hobart Gravity Stations

• 10 – 200 gravity stations can be

acquired by a single operator in one

day. Acquisition rate depends on the

station spacing, the difficulty of access

and the desired survey precision.

• The spacing of gravity stations is

primarily determined by the

characteristics of the target. Small,

near-surface features can only be

resolved with closely spaced

measurements.

Measuring Gravity

• Regional and semi-regional data (1-10 km spacing) is generally

acquired on an irregular grid or along roads and tracks. More detailed

data is typically acquired at an even spacing on lines or grids

KEA230 Lecture G1

Gravity Meters

• All modern gravity meters employ

springs made of fused silica because

of its excellent elastic properties, low

thermal coefficient and small rate of

creep.

• Gravity meters must be carefully levelled to

ensure that the axis of the meter is aligned with

the local gravitational vector.

• Most meters record the force required to

restore the proof mass to the equilibrium

position

KEA230 Lecture G1

Gravity Meters • Older gravity meters such as the Worden

meter shown here have their mechanisms in a

vacuum chamber to reduce thermal effects.

• A light beam measuring system is used in

these meters. The operator manually adjusts an

analogue dial to move the light beam to the null

position.

• More modern gravity meters such as the Scintrex

CG3 and L&R instruments house the spring

mechanism in a thermistatically controlled oven

elevated to above ambient temperatures.

• These meters employ digital recording circuitry

and facilities such as averaging to improve the signal

quality.

KEA230 Lecture G1

Gravity - Field Procedure • Slow instrumental drift occurs in all gravity

meters due to changes in the length of the

spring. This is accounted for by periodic repeat

reading of a base station

• Instrumental drift is generally assumed to be

linear with time over short intervals. Loops

should be closed every few hours.

Base

1020

1021 1022

1023 1024

1025

Station Time Reading Terrain

Base 11.00 4230.53

1020 11.16 4234.62 flat 10m

1021 11.34 4235.15 road centre

1022 11.55 4237.24 +3:10 W

1023 12.15 4232.78 +2:10 S -3:10N

1024 12.32 4231.63 flat 10m

1025 12.50 4230.85 flat 10m

Base 13.05 4230.83

• Field notes should also

record the form of the

topography in the vicinity of

the station to assist in the

calculation of terrain effects.

Gravity surveys

KEA230 Lecture G1

Gravity - Drift Correction

• In this plot of gravity

readings as a function of time,

the drift curve is defined by

joining the repeat readings of

station B

• The gravity anomaly is

difference between the

measured value and the drift

curve.

KEA230 Lecture G1

Gravity - Drift Correction • Instrumental drift must be time-distributed around the loop:

Base 1020 1021 1022

1023 1024 1025

4230.53 4234.62 4234.15 4237.11

4232.60 4231.63 4230.85

4230.83

Total Drift: +0.30 in 125 minutes

16 18 21

20

17 18

15

+0.04 +0.04 +0.05

+0.05

+0.04 +0.04

+0.04

0 -0.04 -0.08 -0.13

-0.18 -0.22 -0.26

-0.30

4230.53 4234.58 4235.07 4237.11

4232.60 4231.41 4230.59

4230.53

• Final drift corrected gravity meter values are shown in white

KEA230 Lecture G1

Tares and Calibration • Gravity meters are sensitive instruments and in addition to slow

predictable instrumental drift they may be subject to sudden jumps or

tares if mishandled

• If a gravity meter receives an unexpected bump then the best

procedure is to return immediately and re-occupy the previous station to

assess if there has been a tare.

• Gravity meters are relative instruments which usually record the

relative differences between two stations on an arbitrary scale.

• To convert these values into gravity values in mGal it is necessary to

calibrate the meter.

• This is achieved by repeatedly recording the difference between two

base stations, typically with a large elevation difference, and then

calculating a meter constant that can be used to convert meter readings

to mGal.

KEA230 Lecture G1

Base Stations • Gravity surveys must be tied to base stations with known gravity values

in order to convert meter readings to absolute gravity values.

• A network of first order gravity

stations has been established

and is maintained by Geoscience

Australia

• Most first-order stations are at

airports or airstrips.

• If practical, a gravity survey

should be tied to a first-order

base station if possible.

KEA230 Lecture G1

Tie Stations • Second and third order gravity base stations or tie stations are

established from the first-order stations.

• The intervals between tie stations and first order base stations should

be based on repeated (4-6 times) drift corrected measurements.

• Intervals between tie stations

should also be recorded to help to

more closely tie the absolute

gravity values of the tie network

together.

• For complex networks, least-

squares network adjustment may

be necessary.

KEA230 Lecture G1

Survey Parameters • The spacing and distribution of gravity stations is determined by the

size, depth and density contrast the expected target.

• For a regional survey in a sedimentary basin, a station spacing of 4

km may be sufficient.

• A survey designed to detect a 5Mt sulphide orebody may require a

station spacing of 50m

• A survey to detect a small underground void would need a station

spacing of 1-2m

• The amplitude of the target anomaly also affects survey design as it

may influence the accuracy requirements of the survey.

• Large regional features (>10 mGal) may be adequately resolved in

data with an uncertainty of >0.5 mGal while an engineering survey may

require an accuracy of 0.02 mGal.

KEA230 Lecture G1

Survey Parameters • Lines of closely spaced gravity measurements may be appropriate for

some geological problems but in most cases a two dimensional distribution

of stations is necessary.

• A uniform regular grid of stations is the preferred distribution

• In many cases, particularly in areas of rugged topography, a uniform grid

is not possible or is too expensive.

• The cost of acquiring and processing

a single regional gravity station is ~$70

• In this case data is usually acquired on

an irregular grid using existing access.

• In remote areas regional gravity surveys

are most economically conducted using

helicopter support


• The gravity method is extremely simple in principle but the

observed gravity values are affected by many factors other than the

subsurface variations in density:

observed gravity = attraction of the reference ellipsoid

+ effect of Earth rotation

+ effect of elevation above sea level ( free air )

+ effect of “normal” mass above sea level ( Bouguer )

+ effect of local topography ( terrain )

+ time-variant effects ( tides )

+ effects of moving platforms ( Eotvos )

+ effect of compensating masses ( Isostasy )

+ effect of crustal density variations ( geology )

Gravity Reductions

} latitude


This expression can be rearranged to define the geological variations:

geological effects = observed gravity

- attraction of the reference ellipsoid

- effect of Earth rotation

- effect of elevation above sea level ( free air )

- effect of “normal” mass above sea level ( Bouguer )

- effect of local topography ( terrain )

- time-variant effects ( tides )

- effects of moving platforms ( Eotvos )

- effect of compensating masses ( Isostasy )

Gravity Reductions

} latitude

Airborne Gravity Corrections become even more critical when gravity recorded from an aircraft

Airborne gravity , British Columbia, Canada


Gravity Reductions

980200

980250

980300

980350

980400

980450

Observed Gravity

mainly shows

topographic features

Hobart Gravity

-10

-5

0

5

10

Residual Bouguer Gravity

shows upper crustal

density variations

KEA230 Lecture G2

Hobart Gravity • The gravity field in the Hobart area provides a good example of the factors

involved in the reduction of gravity data due to the large elevation range, the strong

regional gradients and large amplitude geological anomalies.

Digital Elevation Model Gravity Station Spacing

KEA230 Lecture G2

Hobart Gravity

• The observed gravity in the Hobart area clearly has a strong negative correlation

with topography.

• The observed gravity has a range of ~300 mGal

• Anomalies related to geology are not apparent.

Digital Elevation Model

980200

980250

980300

980350

980400

980450

Observed Gravity

KEA230 Lecture G2

“Normal” Gravity • The normal or theoretical gravity formula takes into account both the attraction of

the reference ellipsoid and the effects of Earth rotation.

• Theoretical gravity formulae are defined by international agreement. Three

formulae are in common use, the 1930 International Gravity Formula, the 1967

International Gravity Formula and the 1980 World Geodetic system formula.

• The 1967 formula is the most commonly used:

latitude theis where

2sin0000058.0sin0053024.0178031846.9 22

0

λ

g ll

• The theoretical gravity is a smoothly varying function that depends only on the

latitude of the observation, it is independent of variations in longitude.

• Gravity anomalies are referenced to the ellipsoid but additional gravity corrections

are commonly made with respect to sea level (the geoid). The geoid-ellipsoid

separation (N value) is only taken into account for large scale geodetic studies

since geoid variations are usually broad and smooth.

KEA230 Lecture G2

“Normal” Gravity

KEA230 Lecture G2

Hobart Gravity • The theoretical gravity field for the Hobart area has a range of ~35 mGal and an

absolute value of ~ 980,440 mGal.

980420

980425

980430

980435

980440

980445

980450

980455

Theoretical Gravity

-250

-200

-150

-100

-50

0

50

Gobs - Gtheo

• After subtraction of the theoretical gravity the reduced gravity data still has a

range of ~300 mGal but the gross value (980440 mGal) has been subtracted. The

data still has a strong negative topographic correlation

KEA230 Lecture G2

Free Air Correction • The free air correction accounts for the changes in distance between the centre of

mass of the Earth and the gravity meter.

• The free air correction is:

metresin level sea

aboveheight theish where

mGal 3086.0 hg fa

• The free air anomaly is then:

faoobsfa gggg

• The free air anomaly compensates for

the negative correlation with topography

but does not take into account the extra

mass above the geoid

• Shipboard gravity measurements can be

directly compared to g0 to give free air

anomalies since they are measured on the

geoid

KEA230 Lecture G2

Hobart - Free Air Anomaly • The free air anomaly always shows a strong positive correlation with elevation as it

does not take into account the mass that lies above the ellipsoid.

Digital Elevation Model

-20

0

20

40

60

80

100

120

Free Air Anomaly

• Free air anomaly data is commonly used for marine interpretation but is not

suitable for land gravity data.

KEA230 Lecture G2

Earth Tides • The gravitational effects of the sun and the moon deform the solid Earth,

producing Earth tides which are measured during a gravity survey.

• Earth tides have a period of approximately 12 hours and a maximum

gravitational effect of ~0.3 mGal at low latitudes.

• Formulae exist to predict

the Earth tide effects for any

latitude, longitude, date and

time and hence to correct

gravity data.

• Modern electronic gravity

meters have built-in Earth

tide correction.

• For older meters without tidal correction software the Earth tides can be

effectively absorbed into the instrumental drift correction process as long as the

loop times are short (maximum 2-3 hours)

KEA230 Lecture G2

Bouguer Correction • The Simple Bouguer correction takes into account the additional mass that lies

between the level of observation and sea level (the geiod).

• The Simple Bouguer

correction approximates all

mass above the geoid by a

homogenous infinite slab of

thickness equal to the height

of the observation.

• The attraction of an infinite slab

of this form is given by: density theis andheight theish where

mGal 2

hGg sb

• For a crustal density of 2670 kg/m3 this gives: mGal 1119.0 hg sb

• The sign of the free air and simple Bouguer corrections are opposite. They can

be combined to give: mGal 1967.0 hgg sbfa

KEA230 Lecture G2

sbfaoobssb ggggg

Bouguer Anomaly • The Simple Bouguer anomaly is:

• It reflects anomalous masses with

densities above or below the standard

crustal density (2670 kg/m3) but does not

take into account the shape of the

topography.

• The Complete Bouguer Anomaly

incorporates an additional terrain

correction as the simple Bouguer correction

overcompensates near topographic

features.

tsbfaoobscb gggggg

KEA230 Lecture G2

Bouguer Density

• In most cases the average crustal density

(2670 kg/m3) is used in the simple Bouguer

and terrain corrections.

• In some circumstances where the

identification of small local anomalies is

important it may be appropriate to calculate

the complete Bouguer anomaly using a

density that is more representative of the local

crustal density.

• The “best” density in this case is the

density for which these is the least correlation

between the complete Bouguer anomaly and

topography. This assumes that gross

topographic variations are not related to

variations in density.

KEA230 Lecture G2

Hobart Simple Bouguer

• The simple Bouguer Anomaly for

the Hobart area has a smaller

range and less correlation with

topographic features.

• Low values are still apparent

adjacent to major topographic

features due to overcompensation

in these areas by the Bouguer slab

approximation.

• Despite this problem some

anomalies related to geological

features can be identified in the

image.

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Simple Bouguer Anomaly

KEA230 Lecture G2

Terrain Correction • The simple Bouguer Anomaly does not take into account the local topographic

features.

+

-

• The additional mass of a mountain

adjacent to the observation point acts

to reduce the observed gravity.

• The absence of mass in a valley

below the observation point also acts

to reduce the observed gravity.

• Terrain correction takes the topography into account. The complete Bouguer

anomaly incorporating the terrain correction is always greater than the simple

Bouguer anomaly. The sign of gt is always negative.

• The influence of topography depends on the elevation change and the proximity

to the observation point. The effects of rapid small changes in elevation close to

the observation point may be as significant as the effects of a major mountain

range at a distance of several km.

KEA230 Lecture G2

Terrain Correction • Terrain corrections can be computed manually by

comparing the elevation of the observation point to

the elevation of surrounding topography using a

zone chart.

• The average elevation difference for each sector of

the chart is estimated

• The correction is determined from a table .

KEA230 Lecture G2

Terrain Correction • Terrain corrections can be computed automatically from a digital

elevation model by summation of the gravitational effects of prismatic

elements that approximate the topography.

• Terrain effects are most apparent close to the observation point.

• Digital elevation models are seldom available in sufficient detail to

adequately model the topography in the immediate vicinity of the

observation point.

• Where possible gravity station locations should be chosen so that the

topography is flat (or at least uniformly sloping) for a distance of ~10-15m

from the meter. Detailed notes should also be kept on the form of the local

topography.

• For most mineral exploration surveys, terrain correction to a radius of

~22km is usually sufficient. In mountainous areas correction may be

required to a radius of ~160km. At these distances the effects of Earth

curvature also become significant.

KEA230 Lecture G2

0

2

4

6

8

10

12

14

16

18

20

Terrain Correction

Hobart Terrain Correction • Terrain corrections in the Hobart

area reach a maximum of ~20 mGal

adjacent to the steep flanks of

Mount Wellington

• In this area the terrain effects are

much larger than the anomalies due

to geological features.

• This terrain correction is added

to the simple Bouguer anomaly

(subtracting negative gt) to generate

the complete Bouguer anomaly.

• In areas of flat or subdued topography (much of Australia) the terrain correction

is generally very small (<0.1 mGal) and is ignored for regional surveys.

(mgal)

Complete Bouguer gravity

aka terrain-corrected gravity • The complete Bouguer anomaly

(after terrain correction) in the

Hobart area shows no consistent

correlation with topography.

• High frequency variations are

due to shallow crustal density

variations these are superimposed

on a broad regional trend from low

values in the NW to high values in

the SE.

• This regional trend is due to the

effects of deeper compensating

masses (isostasy)

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35

Hobart Complete Bouguer Anomaly

Gravity data reduction:

topographic elevation corrections

Free Air Gravity (drift, latitude, & free-air

corrected) is appropriate for modelling &

inversion

Bouguer Gravity (drift, latitude, free-air, &

simple Bouguer corrected) is good for

presentation/ qualitative interpretation,

but not appropriate for quantitative modelling

Terrain Correction (of Bouguer gravity) is not

always necessary prior to 3D modelling &

inversion, but detailed terrain correction can be

advantageous

KEA230 Lecture G2

Regional (Isostatic) Effects • The complete Bouguer anomaly corrects

for elevation, mass above the ellipsoid and

topography but does not take into account

the effects of deep lateral density variations

due to isostatic compensation.

• As a result, Bouguer anomalies are

typically strongly negative in mountainous

regions where the crust is thickest.

• Anomalies due to small near-surface

density variations may be complicated or

obscured by these regional effects.

• There are a variety of numerical methods

available to conduct regional - residual

separation.

KEA230 Lecture G2

Tasmanian Gravity Field • Tasmania lies on a narrow southern extension of the Australian

continental crust surrounded on three sides by deep ocean basins.

• The Tasmanian gravity field is characterised by a steep positive gradient

towards the ocean basins.

Bathymetry Bouguer Gravity - 300mGal

Brownfields Exploration Day 3 – Lecture 1 82

Regional and Residual Fields In many cases large anomalies due to regional geological features can

obscure smaller local anomalies that may be due to mineralisation.

Regional – residual separation isolates local responses.

0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000

500

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1500

2000

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3500

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-6 -5.8

-5.6

-5.4

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-4.6

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-3.6

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-2.6

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-1

Granite model with

adjacent 25 Mt

orebody.

granite

orebody

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1000

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2000

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3500

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-5.6

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-4.6

-4.4

-4.2

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-3.6

-3.4

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-2.6

-2.4

-2.2

-2 -1.8

-1.6

-1.4

-1.2

-1

If the regional field is

accurately known then it

can be subtracted from

the I. R. Bouguer

Anomaly.

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The result is a local

residual Bouguer

Anomaly that shows

local shallow sources.


Regional and Residual Fields In real cases the regional field is not known and it has to be estimated

from the Bouguer anomaly by techniques such as filtering, trend

surfaces and modelling.

0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000

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-5.6

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-2.6

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-1.6

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-1

0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000

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-6.5

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-1.7

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-1.1

Granite model with

adjacent 25 Mt

orebody.

4th Order trend

surface.

0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000

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1000

1500

2000

2500

3000

3500

4000

4500

5000

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-0.7

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0 0.1

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“Real” local residual

anomaly.

KEA230 Lecture G2

Hobart Regional Gravity • The regional gravity field in this

case is derived from a second order

polynomial regression.

• The general trend of increasing

gravitational attraction towards the

southwest reflects the decreasing

thickness of low density continental

crust in this direction.

• Subtraction of this regional field

from the complete Bouguer anomaly

yields a Residual Bouguer Anomaly.

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25

Regional Gravity Field

• The regional-residual separation process is always scale-dependent and

generally quite subjective.

KEA230 Lecture G2

Hobart Residual Gravity • The residual Bouguer gravity

image provides a view of the upper

crustal density variation and is the

final product of the gravity reduction

process.

• The image shows density

variations in the upper 5-10 km of

the crust in this case.

• Positive residual anomalies

mainly indicate the distribution of

thick accumulations of Jurassic

dolerite (feeder systems).

• Elongate negative anomalies in

the Derwent and Coal River valleys

mark grabens infilled by low density

Tertiary sediments.

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Residual Bouguer Gravity

KEA230 Lecture G2

Tasmanian Residual Gravity • The residual gravity map

for Tasmania represents

density variations in the

upper crust (~10km)

• Negative residual

anomalies clearly show the

subsurface distribution of

low density granitoid rocks

and thick accumulations of

low density sediments.

• Steep gradients mark the

positions of major structural

features


Net Effect of Gravity Reductions

980200

980250

980300

980350

980400

980450

Observed Gravity

mainly shows

topographic features

Hobart Gravity

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Isostatic Residual Bouguer Gravity

shows upper crustal

density variations


• The gravity reduction process involves many corrections and

errors in each stage can compound to affect the reliability of the final

residual Bouguer anomaly

• Errors occur due to factors such as: incorrect meter reading,

estimation of location (x,y,z), inadequate correction for terrain

effects, and inappropriate regional-residual separation.

• Inaccuracy in the estimation of height is usually the most significant

source of error. Residual Bouguer anomaly varies by ~0.2mGal for

every metre.

• Modern surveys employ differential GPS to give relatively accurate

coordinates (~0.05-0.5m) but most old regional surveys used

barometric levelling and errors of up to 10m in elevation are common

for widely spaced measurements.

Gravity Accuracy

KEA230 Lecture G3

Gravity Data Uncertainty • Elevation errors affect both the free air and Bouguer corrections.

• An error of one metre in height results in an error of 0.3086 mGal in the

free air correction

• An error of one metre in height results in an error of 0.1967 mGal in the

combined free air and Bouguer anomalies.

• The error in the simple Bouguer anomaly due to a variation of 1 metre in

elevation is ~240 times greater than the maximum effect of a 1 metre N-S

displacement

• Terrain correction errors are more difficult to quantify. They may be due to

a combination of factors including: errors in station position, poor

topographic maps and DEMs, errors in position and elevation , failure to

correctly account for inner zone features, and choice of density.

• Terrain correction errors are probably largest in rugged topography.

Assuming an error of ~5 % in the correction process terrain errors may

range from 0 to 1 mGal.

KEA230 Lecture G3

Gravity Data Uncertainty • The uncertainty in a gravity measurement (complete Bouguer anomaly)

depends on a number of factors.

• Meter reading errors may result from, poor leveling and reading of the

meter (older meters), gradual meter tilt in soft ground, wind effects,

microseismic activity and earthquake activity.

• Observation errors of ~0.01 mGal (meter precision) can be achieved by

a skilled observer in good conditions but this value may increase to ~0.05

mGal or even higher in difficult conditions.

• Errors in latitude affect the theoretical gravity calculation. Latitude errors

are most significant for stations at mid latitudes. The effects of latitude

errors on the Bouguer anomaly decrease north and south.

• At a latitude of 42 degrees (Hobart) an error of one second in latitude

(~30m) produces an error of 0.025 mGal (0.81 mGal / km)

KEA230 Lecture G3

Gravity Data Uncertainty

• Relative errors in Isostatic or regional fields typically have long

wavelengths and hence have little effect on local surveys.

• Absolute errors in regional fields act to shift the entire gravity anomaly

either up or downwards. This may have significant implications for

quantitative interpretation but does not affect the form of local features.

• The accuracy required will vary dependent on the nature of the project

(regional vs local).


Acknowledgement

Dr. M. Roach


• Blakely, R.J., 1995, Potential Theory in Gravity & Magnetic

Applications: Cambridge University Press, 441p.

• Emerson, D.W., 1990, Notes on mass properties of rocks - density,

porosity, permeability: Exploration Geophysics, 21, 209-216.

References

KEA230 Lecture G1

Summary • Lateral variations in crustal density result in variations in the Earth’s

gravity field.

• The gravity field is typically measured using a gravity meter which

records relative gravity variations with respect to a network of base stations

with known absolute gravity values.

• Gravity meters are subject to gradual drift and also tares due to rough

handling.

• Meter drift is corrected by loop recording and time-based drift correction.

• The spacing and distribution of gravity stations is determined by the size,

depth and density contrast of the survey target.

• A large station spacing and low accuracy may be appropriate for regional

surveys where anomalies may exceed 10 mGal but a close station spacing

and high accuracy is necessary for prospect scale or engineering surveys.

KEA230 Lecture G2

Summary • The gravity method is simple in principle but gravity measurements

require several stages of reduction before they can be interpreted

geologically.

• The theoretical gravity is the expected gravity value for the rotating

ellipsoidal Earth. It is subtracted from the observed gravity.

• The free air correction accounts for the elevation of the observation

• The simple Bouguer and terrain corrections together correct for the

distribution of mass above the ellipsoid and convert the free air anomaly to

the complete Bouguer anomaly

• The Eotvos Correction accounts for the motion of the observer

• The regional-residual separation process can be applied to remove the

effects of isostatic compensation to produce a residual Bouguer anomaly

map that best represents upper crustal density variations.

Documents

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