ISOSTASY AND GRAVITY CORRECTIONS

  • Isostasy is the gravitational equilibrium between earth’s crust and mantle

  • gravitational balance


AIRY’S THEORY

  • Equal density and unequal thickness

  • It is based on root and anti-root theory

  • Root : in case of high elevation (mountain)

  • Anti-root : in case of low elevation (ocean)


Root = ρch/(ρm-ρc)

Anti-root = (ρc-ρw)z / (ρm-ρc)

h= height of mountain

z = depth of ocean


PRATT’S THEORY

  • Unequal density at uniform depth

  • Not based on root and anti-root


ρ = ρcD/(D+h)

ρ = (ρcD - ρwZ)/(D-z)

D= thickness of crust

z=depth of ocean


VENING MEINESZ

  • The upper layer behaves like an elastic plate overlying a weak fluid.

  • It accounts for regional isostatic compensation

  • Depends on elastic properties of the lithosphere


  • Local compensation : Airy’s and Pratt’s theory

  • Regional compensation : Vening meinesz theory


ISOSTATIC COMPENSATION

  • Gravity anamoly = (observed - calculated) gravity value

  • Isostatic gravity anamoly = Bouguer anamoly - Computed anamoly of root zone


1) OVERCOMPENSATION

  • Occurs when a land-high is reduced (as by erosion)

  • Root of overcompensated landmass will readjust and shift upward w.r.t root zone

  • Computed root is smaller than real root

  • Isostatic gravity anamoly is negative

  • Bouguer anamoly is also negative


2) FULL COMPENSATION

  • Computed root is in hydrostatic equilibrium with its root zone

  • Bouguer anamoly and Computed anamoly are equal in magnitude but opposite sign

  • Isostatic gravity anamoly will be zero (as opposite in algebraic sign giving zero-value)

  • Bouguer anamoly is negative


3) UNDERCOMPENSATION

  • Computed root is larger than real root

  • Isostatic gravity anamoly is positive

  • Bouguer anamoly is negative



GRAVITY CORRECTIONS

1) FREE AIR CORRECTION

  • Corrects for the change in gravity due to change in the height


  • Positive : if station is above sea level

  • Negative : if station is below sea level


  • FAC = 0.3086h mgal (when h is in meter)

  • Free air anamoly = g0 - gλ + 0.3086h



2) BOUGUER CORRECTION

  • Corrects for the change in gravity due to lateral change in density

  • Bouguer correction and free air correction act opposite to each other


  • Positive : if station is below sea level

  • Negative : if station is above sea level


  • BC = 2πGρh = 0.0419ρh (h in meter and ρ in gm/cc)

  • Bouguer anamoly = g0 - gλ + FAC - BC + TC


3) TERRAIN CORRECTION

  • Terrain correction is always added

  • Used to nullify the effects of terrain features using ‘Hammer chart’

  • It tend to lower down the gravity value at a station point


4) LATITUDE CORRECTION

  • Gravity value increases with latitude i.e from Equator to Pole but decreases with radius

  • Difference in gravity value = 5186 gals (1 gal= 1cm/s2)

  • Maximum : At Poles = 9.83 m/s2

  • Minimum : At Equator = 9.78 m/s2

  • Gravity value varries 57 mgal with 10 latitude


5) TIDAL CORRECTION

  • The period of tide correction is known as drift correction

  • Amplitude variation in g due to tidal effect is 0.3 gal


6) EOTVO’S CORRECTION

  • Required in Airborne and shipborne gravity survey

  • Can be made in marine gravity survey and areogravimetry