Gravity - Geoscientific Measure: The variations in the Earth s gravitational field due to changes in density of materials within the Earth.
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1 Gravity - Geoscientific Measure: The variations in the Earth s gravitational field due to changes in density of materials within the Earth. Objective Map variation in gravitational field associated with distribution of densities in different materials (rock types) Note: Critical to this is not the absolute values of density but rather the contrast in density between materials Measurement of Gravity Falling body - measure falling object to calculate acceleration due to gravity Pendulum - measure period of oscillation of a pendulum to determine acceleration due to gravity Mass on Spring - suspending a mass and observing deflection of spring under force of gravity. This is the most commonly used principle in instrument manufacture for the exploration geophysics industry.
2 Galileo Galilei Father of Gravity velocity is out, acceleration is in objects fall with same acceleration under force of gravity at same place on the Earth
3 Distribution of Mass within the Earth How is mass distributed within the earth? inside plum pudding outside Moment of Inertia/distribution of mass
4 Fundamental Principles - Newton s Universal Law of Gravitation The mutual attractive force (F) between two point masses, m1 and m2 is proportional to the square of the distance between them. F? Gm m r m 1 m 2 The constant of proportionality is G the gravitational constant. r
5 Newton s Second Law of Gravitation (motion) However, when measuring the Earth s gravity we measure the acceleration (g) resulting from the gravitational attraction. Newton s Second Law Force is proportional to acceleration F m g? 2 Thus from 1) and 2) and Gravitational Potential U g? Gm r 2 1 U? GM r Units of gravity are gu or micrometer per second per second. The c.g.s. units are milligal where 1milligal = 10gu G=6.67x10-11 Nm 2 kg -2
6 Gravitational Attraction From Newton s Laws, the gravitational acceleration on a mass m2 can be shown to be equal to the mass of attracting object m1 over the squared distance between the centre of the two masses. Further, that the attracting mass is related to the density of that mass and that an increase in density will result in an increase in gravitational acceleration. Taken from T. Boyd at CSM m1 m2
7 The attractiveness of a body!!!! M??? v F? Gm m r more dense, greater the attraction greater the gravitational pull or anomaly
8 from Bouguer to Airy Pierre Bouguer 1735 Established height of Andes with plumb bob Noticed deflection not what it should be Postulated that density very different Sir George Airy, 1855 Postulated that mountains had huge roots to support weight These roots very very less dense than surrounding mantle Floated on Mantle experience replicated in Himalayas by George Everest
9 Factors Influencing Gravity Shape The Geoid and Continental Scale Effects Ellipse The Geoid - an equipotential surface - the sealevel surface if no tidal or wind action These long wave length effects can all be measured by satellite The Geoid and Local Effects Geoid - an equipotential surface These short wave length anomalies measured using airborne, land and sea techniques Mass
10 Corrections for Gravity Measurements (noise) A number of corrections must be made to gravity measurements but these are beyond the scope of this introduction and will be covered during the Honours modules. These corrections are to account for: Instrument Drift - the variations in spring property with time Tidal affects - the variation in observed gravity resulting from the attraction of the moon and sun. Latitude - shape and rotation of the Earth Elevation - Free-Air corrections so all readings taken as if from the same elevation Mass - variations due to excess mass - Bouguer Slab Correction Topography - Terrain Corrections Note: precise surveying of station position (x, y, and z) is essential for gravity and especially micro gravity Note: field observations only estimate relative changes in gravity
11 Rock Properties and Gravity Measurements Density of Common Materials Material Density (Mg m -3) Clay Silt Sand Peat Gravel Sandstone Chalk Shale Granite Basalt
12 Other Factors Influencing Gravity (density) Factor and Approximate % change in density (after Reynolds, 1997) Composition - 35 Cementation - 10 Age and depth of Burial - 25 Tectonic Processes - 10 Porosity and Pore fluids - 10
13 Stable (static) Gravimeters Boliden Gulf Unstable (astatic) gravimeters LaCoste - Romberg Worden Instrumentation Examples Initial Equipment Cost Productivity Maintenance Operation budget Experience 10K to 30K Low Low but expensive when it goes wrong Low Low for survey, high for interpretation
14 Convergent - Destructive Margins Ocean-Continent
15 Gravity Anomalies at Ocean-Continent Collision
16 Gravity in the Wind River Basin
17 Gravity and the Wildcat discoveries in the Gulf of Mexico Salt less dense at depth than surrounding sediments
18 Gravity Anomalies over Sink holes
19 Gravity anomalies over abandoned mine shafts
20 What caused the extinction of the dinosaurs?
21 Meteor impact theory the Chiczulub Crater, Mexico
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25 Terralog solution feature mapping
26 Interpretation of Gravity Anomalies there is no unique solution therefore other geologic knowledge is essential to determine the correct solution Removal of Regional Anomalies regional observed Residual
27 Field Interpretation of Gravity Anomalies / 2? g max 2 x half width (x ½ ) Total Anomaly (g max ) Bouguer anomaly (gu) For a Sphere depth to centre of sphere z? 1.3 x 1/ 2 For a Horizontal Cylinder depth to centre z? x 1 / 2 Note: because a body has a finite size and its mass is not concentrated at the centre, any depth estimate will be an over calculation
28 Gravitational Attraction Sphere? g? G 4 3??? a h 3 a h Horizontal Cylinder? g? G2??? a h 2 h Vertical Cylinder k? g? G??? a k 2 Horizontal Slab? g? 2? G?? t t
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