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# Gravity Modeling 3

## on Dec 21, 2009

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## Gravity Modeling 3Presentation Transcript

• Ali Oncel [email_address] Department of Earth Sciences KFUPM Gravity Modeling 3 Introduction to Geophysics Introduction to Geophysics-KFUPM Highest peaks on the planet
• Quiz of the Week
• What does a positive Bouguer anomaly indicate? How about a negative Bouguer anomaly?
• 10 minutes
Introduction to Geophysics-KFUPM
• 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
Introduction to Geophysics-KFUPM
• Introduction to Geophysics-KFUPM Bouguer Anomaly Map of Anatolia www.mta.gov.tr
• Gravity stations in Saudi Arabia 508397 points Saudi Geological Survey Introduction to Geophysics-KFUPM
• Bouguer gravity Density 2.3 gm cm -3 Bouguer Anomaly Map of Saudi Arabia Saudi Geological Survey Introduction to Geophysics-KFUPM
• Half Width Depth Estimates • The depth to the top of a gravity source can be determined approximately from half-width x ½ of anomaly x ½ 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 = 1.305x ½ Introduction to Geophysics-KFUPM
• Other Objects Effects of various bodies can be written by inserting term for object volume and density contrast into gravity equation Introduction to Geophysics-KFUPM
• • 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 Δ g max / Δ g‘ max
Introduction to Geophysics-KFUPM
• 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 Introduction to Geophysics-KFUPM
• An infinite slab adds or subtracts a constant amount to the gravity field, depending on whether the slab represent a positive (+ Δ m ) or negative (- Δ m ) mass anomaly. Gravity variation due to Infinite Slab + Δ m = + Δ g z - Δ m = - Δ g z Introduction to Geophysics-KFUPM
• No significant gravity effect in regions far from the slab ;
Gravity variation due to semi-infinite Slab
• 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:
• An increase or decrease in gravity crossing the edge of the slab;
Introduction to Geophysics-KFUPM
• An infinite slab produces exactly the same gravity as the slab used for the Bouguer correction as: Δ g z =0.0419 ΔρΔ h Estimating Δ g z for an infinite slab Introduction to Geophysics-KFUPM
• The gravity effect of a semi-infinite slab is equal to the Bouguer slab approximation far out over the slab (right),
Estimating Δ g z for an infinite slab Gravity effect of a semi-infinite slab changes according to position relative to the slab’s edge.
• ½ of that value directly over the slab’s edge , and zero far away from the edge (left).
Introduction to Geophysics-KFUPM
• Δ g z versus Slab’s position Introduction to Geophysics-KFUPM
• 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: Δ g z = G ( Δρ ) ( Δ h) (2 Ф ) 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/kg 2 ). Introduction to Geophysics-KFUPM
• Gravity for Semi-Infinite Slab
• X=- ∞ Δ g z =zero Δ g z =0 (41.9 Δρ Δ h)
• X=- z Δ g z = ¼ its full value Δ g z =¼ (41.9 Δρ Δ h)
• X=- ∞ Δ g z = ½ its full value Δ g z =½ (41.9 Δρ Δ h)
• X=+ z Δ g z = ¾ its full value Δ g z =¾ (41.9 Δρ Δ h)
• X=+ ∞ Δ g z =its full value Δ g z =1 (41.9 Δρ Δ h)
Δ g z = 13.34 ( Δρ ) ( Δ h) ( π /2 + tan -1 [x/z] Units are: Δ g z in g/cm3 Δρ in g/cm3 Δ h, x, z in km Introduction to Geophysics-KFUPM
• Fundamentals of gravity anomalies
• Amplitude of Δ g z : reflecting either the excess (+ Δ m) or deficit (- Δ m) of mass , which depends on density contrast ( Δρ ) and thickness ( Δ h) .
• The gradient of Δ g z : reflecting the depth of – Δ m or + Δ m below the surface ( z ).
Introduction to Geophysics-KFUPM
• Passive continental margin ρ water = 1.03 g/cm 3 ρ crust = 2.67 g/cm 3 ρ mantle = 3.1 g/cm 3 Thickness for the ocean side: h w = water column = 5 km (h c ) o =crust column = 8km h mantle column = ? Thickness for the continent side (h c ) c = thickness of the continental crust=? km Introduction to Geophysics-KFUPM
• Passive continental margin Mass excess of mantle (+ Δ m): exerting a force onto oceanic crust to pull downward. Equal Pressure: ρ c (h c ) c = ρ w (h w ) + ρ c (h c ) o + ρ m (h m ) Equal Thickness : (h c ) c = (h w ) + (h c ) o + (h m ) Solving the two equations for the unknown parameters: (h c ) c =31.84 km h m =18.84 km Mass deficit due to subsided ocean basin (- Δ m): it has been filled by enough water to establish an isostatic equilibrium by airy model . Introduction to Geophysics-KFUPM
• Water contribution on Gravity The negative contribution to the gravity anomaly is an abrupt change, along a steep gradient where the water deepens. Δρ = ρ w - ρ c Introduction to Geophysics-KFUPM
• The mass excess ( Δ m) that compensates the shallow water relates to the amount of shallowing of the mantle (h m ) times difference between mantle and the crustal densities ( Δ ρ = ρ m - ρ c =0.43 g/cm 3 ). Introduction to Geophysics-KFUPM
• Δ g FA anomaly for the passive margin model is the sum of the contributions from the shallow (water) and deep mantle effects .
• The anomaly through the interiors of the continent and ocean is near zero but a maximum over the continental edge and a minimum over the edge of ocean is shown up.
This gravity coupling as positive/negative is known as edge effect, since the contributions due to the shallow and deep source have different gradient. Free Air Gravity Anomaly Introduction to Geophysics-KFUPM
• Introduction to Geophysics-KFUPM
• Free air/ Bouguer Gravity anomalies Isostatic equilibrium means the absolute value of excess (+ Δ m) mass equals the absolute value of deficient mass (- Δ m). Bouguer anomaly after applied Bouguer correction to Free Air anomaly. Introduction to Geophysics-KFUPM