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Esci 203, Earthquakes & Earth Structure Gravity and isostasy

Esci 203, Earthquakes & Earth Structure Gravity and isostasy. John Townend EQC Fellow in Seismic Studies john.townend@vuw.ac.nz. Lumpy Earth. Image courtesy of GRACE, U. Texas. Overview. Galileo Galilei (1564 –1642. Newton’s Law of Gravitation Factors that influence gravity The geoid

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Esci 203, Earthquakes & Earth Structure Gravity and isostasy

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  1. Esci 203, Earthquakes & Earth StructureGravity and isostasy John Townend EQC Fellow in Seismic Studies john.townend@vuw.ac.nz

  2. LumpyEarth • Image courtesy of GRACE, U. Texas

  3. Overview Galileo Galilei (1564–1642 • Newton’s Law of Gravitation • Factors that influence gravity • The geoid • Measuring gravity • Gravity anomalies • Isostasy and ice-sheet loading

  4. Newton’s law of gravitation m2 r • Force exerted by m1 on m2, and vice versa • Gravitational acceleration of a mass due to m1 m1

  5. True shape Gravity on an oblate spheroid rpole < req, gpole > geq • Latitude effect due to Earth’s rotation rpole~6357 km req~6378 km Exaggerated shape!

  6. Reference gravity formula • The coefficients a and b are related to the Earth’s ellipticity and rate of rotation • About 40% of the variation in gravity with latitude is due to the Earth’s shape, and 60% is due to its rotation • In geophysics, we’re interested in departures from reference gravity g(l) = geq (1 + a sin2 l + b sin4 l)

  7. Describing the Earth’s shape Ellipsoid • Ellipsoid (“oblate spheroid of revolution”) • An idealised representation of the Earth’s shape, obtained by revolving an ellipse about the Earth’s rotation pole • Geoid (“equipotential surface”) • A surface of equal gravitational potential, equivalent to mean sea level over oceans Earth’s surface Geoid

  8. The geoid • The geoid is a gravitational equipotential surface: what is shown are differences between the geoid height (in metres) and the ellipsoid, which is an idealised model of the Earth’s shape

  9. Why measure gravity? • Measurements of gravitational acceleration (“gravity”) provide information about density • Exploration geophysics • Reconnaissance in sedimentary basins • Characterisation of ore bodies or groundwater aquifers • Solid earth geophysics • Determination of crustal/lithospheric structure • Measurement of the shape of the Earth • Investigations of glacial rebound and mantle viscosity

  10. Measuring gravity We usually measure relative differences in gravity LaCoste & Romberg Model “G” Could also use a pendulum: (T2/T1)2 = g2/g1 Zero-length spring L = mg/k

  11. Relative gravity meter’s response to density variations gravity high gravity low High density Low density Local gravity high can be related to a high-density body within the crust, while a gravity low can be related to a lower than average density.

  12. Typical densities

  13. Gravity reduction • Latitude • Temporal changes Tidal and drift corrections • Effect of elevation “Free-air correction” dgFA = gSL– gh = 2h/RgSL • Mass of intervening rocks “Bouguer correction” dgBouguer = 2GrBouguerh • Effect of topography “Terrain correction” Measurement point h rBouguer Datum (sea level)

  14. Tidal and drift corrections gobs Base station Drift curve time gobs • By resurveying several times at a base station, we can correct for tidal and instrumental drift time

  15. Bouguer anomaly BA = gobs– g(l)– dgFA– dgBouguer + dgterrain = gravity data corrected for latitude, elevation, mass beneath the measuring point and surrounding topography • Usually given in mgal (after Galileo) or “gravity units”: 1 g.u. = 0.1 mgal = 10–6 m s–2 • To obtain 0.1 g.u. accuracy (~10–8 times the gravitational acceleration at the Earth’s surface), you must know your latitude to within ~10 m and height to within ~10 mm!

  16. GRACE Gravity Recovery And Climate Experiment

  17. Local anomalies and models • Subtract a regional gravity field to obtain a local anomaly Skridulaitis (1997) B.Sc. Hons. Thesis Wellington fault … which we model in terms of subsurface density contrasts Alluvium Dr = –440 kg m–3 Basement

  18. h h d d rc r1 rd D rc t r’ r rm rm Archimedes and isostasy Airy’s hypothesis Variations in thickness Pratt’s hypothesis Variations in density

  19. Gravity profile in isostatic equilibrium High relief topography is compensated with a low density crustal root. First observed in India by Everest in the 1850’s.

  20. Non-isostatically compensated profile

  21. Non-isostatically compensated profile

  22. CW from TL: Bouguer Residual Model Gradient

  23. Using gravity to measure fault slip rates Davy et al., NZJGG, 2013

  24. Reading material • Mussett and Khan • Chapter 8: Sections 8.1–8.7 • Chapter 9: Sections 9.1 and 9.5 • Fowler (1992) • Chapter 5, especially sections 5.3–5.6

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