Ali Onceloncel@kfupm.edu.sa

Department of Earth SciencesKFUPM

Gravity Modeling 2

Introduction to GeophysicsIn

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Highest peaks on the planet

Previous Lecture

Local Isostasy & Flexure Regional Isostasy & Flexure Flexural Rigidity (D) Flexural Modeling Examples of Lithospheric Flexure

Example from the West Africa (Watts and Stewart, 1998).

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Homework Status, Due to May 17

Use the online tool for making a gravity map from the site http://www.itis-molinari.mi.it/Gravity.htm.

Make your gravity map and compare changes in the gravity to changes through regions of major tectonics? What is the gravity through the areas:

a) Red Sea b) Dead Sea Fault c) Iranian Sea d) Gulf of Aqaba e) Zagros Thrust Fold

33° E 60° E

10° N

37°N

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Red S

ea

Arabian Gulf

DS

F

Arabian

Shield

Gulf of Aden

Zagros SutureGO

AS

MS

OM

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Homework Status, Due to May 20

Given the following exercises of your handout:8.28.38.8Try to use one of those provided Excel Programs if possible in solving your problems from the link:http://www.mtech.edu/clink/Home/Classes/Geop3020/chapter6.htm

Then, e-mail your homework which is solved under Excel to me: oncel@kfupm.edu.sa.

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2D Gravity Modeling

1> 2

1

2

1< 2

12

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Analogy between the gravitational attraction of the Earth from space and a sphere of anomalous mass buried beneath Earth’s surface.

Earth’s gravitational acceleration (g) at a distant observation point depends on the mass of earth (M) and the distance R (from the center of mass to the observation point.

Analogy between masses

2R

GMg

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The change in gravity (Δg) due to a buried sphere depends on the difference in mass (Δ m, relative to the surrounding material), and the distance ( R ) from the sphere to an observation point on Earth’s surface.

Analogy between masses

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2R

GMg

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Gravitational effect of a buried sphere

The distance ( r ) to the center of the sphere can be broken into components as:

a) horizontal (x) and

b) vertical (z).

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The magnitude of the gravitational attraction vector can be broken into horizontal and vertical components.

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See pages 245-246 to see how that equation is derived since final equation is given here as:

)(

1

3 22

)(4 3

zxg

GR

zx ggg

Horizontal

component

Vertical

component

Following the substitutions in page 246, the vertical component of the gravitational attraction, in which the gravimeter only can measure, is given as:

)()(02794.0

22

3

zx

zRgz

Vertical component of gravitational attraction (mGal)

Difference in density (g/cm3)

Radius of the sphere (m)

Horizontal distance from the observation point

Vertical distance from the distance (m)

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Gravity anomaly profile (Δgz):

Buried Sphere Model

Mass excess (+Δm, implying +Δρ): causes an increase in gravity +Δgz),

Mass deficit (-Δm, implying -Δρ): results in a gravity decrease (-

Δgz)

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The more massive the sphere (larger Δρ/or larger R), the greater the amplitude (l-Δgzl) of the gravity anomaly

Gravity anomaly profile (Δgz):

Buried Sphere Model

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The anomaly is attenuated ( smaller lΔgzl) as the sphere is buried more deeply within the Earth

The width of gravity anomaly increases as the sphere is buried more deeply.

Gravity anomaly profile (Δgz):

Buried Sphere Model

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(see more page 248 of Lillie’s book).

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)()(02794.0

223

zx

zRg z