Gravity 4 Gravity Modeling

Gravity Corrections/Anomalies 1. Measurements of the gravity (absolute or relative)  2. Calculation of the theoretical gravity (reference formula)  3. Gravity corrections  4. Gravity anomalies 5. Interpretation of the results

2-D approach Developed by Talwani et al. (1959): Gravity anomaly can be computed as a sum of contribution of individual bodies, each with given density and volume. The 2-D bodies are approximated , in cross-section as polygons.

Gravity anomaly of sphere Analogy with the gravitational attraction of the Earth: g  g (change in gravity) M  m (change in mass relative to the surrounding material) R  r

Gravity anomaly of a sphere Total attraction at the observation point due to m

Gravity anomaly of sphere - Total attraction (vector) Horizontal component of the total attraction (vector) Vertical component of the total attraction (vector) Horizontal component Vertical component Angle between a vertical component and g direction

Gravity anomaly of sphere gravimeter measures only this component - distance between the centre of the sphere and the measurement point R – radius of the sphere  - difference in density

Gravity anomaly of sphere

Gravity anomaly of a semi-infinite slab 1. No gravity effects far away from truncation. 2. Increasing/decreasing of gravity crossing the edge of the slab. 3. Full (positive/negative) effects over the slab but far from the edge. Increase or decrease of gravity

Gravity anomaly of semi-infinite slab Gravity effect of infinite slab: gz = 2()G(h) = 0.0419 ()(h) Gravity effect of semi-infinite slab (depends on the position defined by ): gz = ()G(h) (2) =/2 + tan-1(x/z) (~ Bouguer correction) gz = 13.34 ()(h) (/2 + tan-1(x/z))

Gravity anomaly of semi-infinite slab

Gravity anomaly of semi-infinite slab Fundamental properties of gravity anomalies: The amplitude of the anomaly reflects the mass excess or deficit (m=()V). 2. The gradient of the anomaly reflects the depth of the excess or deficient mass below the surface (z): Body close to the surface – steep gradient Body away deep in the Earth - gentle gradient.

Gravity anomaly of semi-infinite slab (models using this approximation) Passive continental margins ? ? Airy (local) isostatic equilibrium

Gravity anomaly of semi-infinite slab (models using this approximation) Passive continental margins (only water contribution) (only mantle contribution) Water – mass deficit – (-m)  = w - c = -1.64 g/cm3 Mantle effects – mass excess – (+m)  = m - c = +0.43 g/cm3 FA gravity anomaly – sum of the contributions from the shallow (water) and deep (mantle) effects max Edge effect min

Gravity anomaly of semi-infinite slab (models using this approximation) Passive continental margins Free Air anomaly: Values are near zero (except for edge effects) (+m) = (-m) 2. The area under the gravity anomaly equals zero  isostatic equilibrium Bouguer anomaly (corrected for mass deficit of the water ~ upper crust) 1. Near zero over continental crust 2. Mimics the Moho – parallel to the mantle topography 3. Mirror image of the topography (bathimetry) over the water – increasing the anomaly – deepening of the water

Gravity anomaly of semi-infinite slab (models using this approximation) Passive continental margins (Atlantic coast of the United States) Free Air anomaly: Values are near zero (except for edge effects) (+m) = (-m) 2. The area under the gravity anomaly equals zero  isostatic equilibrium

Gravity anomaly of semi-infinite slab (models using this approximation) Mountain Range ? ?

Gravity anomaly of semi-infinite slab (models using this approximation) Mountain Range (only topo contribution) (only root contribution) =c- m = -0.43 g/cm3 =c- a = +2.67 g/cm3 gentle gradient “Batman” anomaly

Bouguer Gravity Anomaly/Correction For land gB = gfa – BC in BC must be assumed (reduction density) For a typical  = 2.67 g/cm3 (density of granite): BC = 0.0419 x 2.67 x h = = (0.112 mGal/m) x h gB = gfa – (0.112 mGal/m) x h

Gravity anomaly of semi-infinite slab (models using this approximation) Free Air anomaly: Values are near zero (mass excess of the topography equals the mass deficit of the crustal roots (+m) = (-m) 2. Significant edge effects occur because shallow and deep contributions have different gradients 3. The area under the gravity anomaly equals zero  isostatic equilibrium Bouguer anomaly (corrected for mass deficit of the water ~ upper crust) 1. Near zero over continental crust 2. Mimics the root contribution 3. Mirror image of the topography – the anomaly increases where the topography of the mountains rises Mountain Range

Gravity anomaly of semi-infinite slab (models using this approximation) Mountain Range (Andes Mountains) Non-Typical anomaly Typical mountain anomaly

Local Isostasy (Pratt vs Airy Model) Pratt Model Block of different density The same pressure from all blocks at the depth of compensation (crust/mantle boundary) Airy Model Blocks of the same density but different thickness The base of the crust is exaggerated, mirror image of the topography

Gravity anomalies - example Airy type 100% isostatic compensation Airy type 75% isostatic compensation Pratt type isostatic compensation Airy type – totally uncompensated Isostatic anomaly – the actual Bouguer anomaly minus the computed Bouguer anomaly for the proposed density model

Gravity Corrections/Anomalies 1. Measurements of the gravity (absolute or relative)  2. Calculation of the theoretical gravity (reference formula)  3. Gravity corrections  4. Gravity anomalies  5. Interpretation of the results 

- Examples of application Gravity Anomalies - Examples of application

Exploration of salt domes Bouguer anomaly Map of the Mors salt dome Jutland, Denmark Reynolds, 1997 Feasibility study for safe disposal of radioactive waste in the salt dome 24 20 16 12 8 4

Exploration of salt domes Bouguer anomaly profile across the Mors salt dome, Jutland, Denmark Reynolds, 1997 Modeling of the anomaly using a cylindrical body (fine details are not resolvable unambiguously)

Exploration of salt domes Notice the axis direction Bouguer anomaly profile compared with the corresponding sub-surface geology (Zechstein, northern Germany) Hydrocarbon study Reynolds, 1997

Mineral Exploration Some useful applications: Discovery of Faro lead-zinc deposit in Yukon Gravity was the best geophysical method to delimit the ore body Tonnage estimated (44.7 million tonnes) with the tonnage proven by drilling (46.7 million tonnes) Reynolds, 1997

Mineral Exploration Some not very useful applications: The scale of mineralization, was of the order of only a few meters wide The sensitivity of the gravimeter was insufficient to resolve the small density contrast between the sulphide mineralization and the surrounding rocks Gravimeter with better accuracy ~ Gals and smaller station intervals the zone of mineralization would be detectable No effect Bouguer anomaly profile across mineralized zones in chert at Sourton Tors, north-west Dartmoor (SW England) Reynolds, 1997

Glacier Thickness Determination Some useful applications: Gravity survey to ascertain the glacier’s basal profile prior to excavating a road tunnel beneath it – anomaly 40 mGal Error in the initial estimate for the rock density  10% error in the depth Gravity measurements over large ice sheets can have considerably less accuracy than other methods because of uncertainties in the sub-ice topography. Residual gravity profile across Salmon Glacier, British Columbia Reynolds, 1997

Engineering applications To determine the extend of disturbed ground where other geophysical methods can’t work: Detection of back-filled quarries Detection of massive ice in permafrost terrain Detection of underground cavities – natural or artificial Hydrogeological applications (e.g. for buried valleys, monitoring of ground water levels Volcanic hazards – monitor small changes in the elevation of the flanks of active volcanoes and predict next eruption

Texts Lillie, p. 223 – 261 Fowler, p.193- 228 (appropriate sections only) Reynolds (1997) An introduction to applied and environmental geophysics, p.92 – 115 (this is only additional material about the applications)