Gravity Modeling 3

Ali [email protected]

Department of Earth SciencesKFUPM

Gravity Modeling 3

Introduction to GeophysicsIn

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Highest peaks on the planet

Quiz of the Week

What does a positive Bouguer anomaly indicate? How about a negative Bouguer anomaly?

10 minutes

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Previous Lecture

Regional Gravity due to dipping plane Sources of the Local and Regional Gravity Anomalies Wavelength Changes of Anomaly regarding the burial depth of material Factors effecting the Gravity Anomalies

Density Contrast Depth to anomaly Source Geometry

Gravity Effect of Sphere Depth Estimates

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Bouguer Anomaly Map of Anatolia

www.mta.gov.tr

Gravity stations in Saudi Arabia508397 points

Saudi Geological SurveyIntr

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Bouguer gravityDensity 2.3 gm cm-3

Bouguer Anomaly Map of Saudi Arabia

Saudi Geological Survey

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Half Width Depth Estimates

• The depth to the top of a gravity source can be determined approximately from half-width x½ of anomaly x½ is half distance from the centre of anomaly at which amplitude has decreased to half its peak value Z is depth for spherical object z = 1.305x½

z = 1.305x½

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Other Objects

Effects of various bodies can be written by inserting term for object volume and density contrast into gravity equation

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Gradient-Amplitude Method

• Z is depth which also can be estimated to source based on the gradient of the anomaly side slopes •depth found from ratio of maximum amplitude to

gradient z < 0.86 Δg max / Δ g‘ max

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Ambiguity in Gravity Interpretation

Gravity interpretations are ‘non-unique’• infinite number of combinations of object geometry, depth and density contrast can yield the same anomaly

There are two approached to the interpretation of Bouguer anomaly data. One is direct where the original data are analysed to produce an interpretation. The other is indirect, where models are constructed to

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An infinite slab adds or subtracts a constant amount to the gravity field, depending on whether the slab represent a positive (+Δm) or negative (-Δm) mass anomaly.

Gravity variation due to Infinite Slab

+Δm = +Δgz

-Δm = -Δgz

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1. No significant gravity effect in regions far from the slab;

Gravity variation due to semi-infinite Slab

3. The full (positive or negative) gravity effect in regions over the slab but far from the edge

The gravity effect of a semi-infinite slab changes gradually as the edge of the slab is crossed as in the following:

2. An increase or decrease in gravity crossing the edge of the slab;

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An infinite slab produces exactly the same gravity as the slab used for the Bouguer correction as:

Δgz =0.0419ΔρΔh

Estimating Δgz for an infinite slab

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1. The gravity effect of a semi-infinite slab is equal to the Bouguer slab approximation far out over the slab (right),

Estimating Δgz for an infinite slabGravity effect of a semi-infinite slab changes

according to position relative to the slab’s edge.

2. ½ of that value directly over the slab’s edge, and zero far away from the edge (left). In

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Δgz versus Slab’s positionIn

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The angle Ф can be expressed: Ф = π/2 + tan -1 (x/z)

Ф=90 (Away from the slab) Ф > π/2 (Over the slab)

Griffiths and King (1981) develop an equation for the anomaly caused by a semi-infinite slab:

Δgz= G (Δρ) (Δh) (2Ф)

Ф= angle (in radians) from the observation point, between the horizontal surface and a line drawn to the central plane at the slab’s edge

Gravity for Semi-Infinite Slab

G=Universal Gravitational Constant (6.67x10-11 Nm2/kg2).

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Gravity for Semi-Infinite Slab

1. X=- ∞ Δgz=zero Δgz=0 (41.9 Δρ Δh)

2. X=- z Δgz=¼ its full value Δgz=¼ (41.9 Δρ Δh)

3. X= 0 Δgz=½ its full value Δgz=½ (41.9 Δρ Δh)

4. X=+ z Δgz=¾ its full value Δgz=¾ (41.9 Δρ Δh)

5. X=+ ∞ Δgz=its full value Δgz=1 (41.9 Δρ Δh)

Δgz= 13.34 (Δρ) (Δh) (π/2 + tan-1 [x/z]

Units are:Δgz in g/cm3 Δρ in g/cm3 Δh, x, z in km

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Fundamentals of gravity anomalies

1. Amplitude of Δgz : reflecting either the excess (+Δm) or deficit (-Δm) of mass , which depends on density contrast (Δρ) and thickness (Δh).

2. The gradient of Δgz : reflecting the depth of –Δm or +Δm below the surface (z).In

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