GRAVITY

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GRAVITY
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EARTHS GRAVITY FIELD
ELLIPSOID
983 Gals
978 Gals
1 Gal 1 cm/sec²
North-South change 1 mGals/km 1.5 mGals/mile 1
?Gals/m .3 ?Gals/ft
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MEASURING GRAVITYABSOLUTE VS RELATIVE
FG-5
A-10

• Absolute
• Pendulum
• Weight Drop
• Rise and Fall

Rise Fall
Weight Drop
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GRAVIMETERS

• Relative
• Stable
• Astatic
• Worden
• La Coste Romberg
• Scintrix Auto Grav

Worden Gravity Meter
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• La Coste Romberg
• Zero length spring
• T proportional L

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GRAVITY FIELD METHODS

• Planning a Survey
• Previous data quality and quantity targer vs
  station density vs dollar.
• Instrumentation and field procedures
• Acquiring permits, field preparations, low
  profile
• Locations
• Base ties, recoccupations, calibration, drift
  tares and tides
• Special considerations in microgal surveys
• Typical field procedures
• Pitfalls and disasters (ignoring the above)

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COMPUTING OBSERVED GRAVITY (MEASURED)

• CORRECT METER READINGS FOR TIDES.
• Earth Tides.
• Caused by pull of sun and moon
• Maximum change 360?Gals/6 hours 1?Gal/minute
• Correction from recording gravimeter ,
  tidetables (obsolete), computer program
• Computer Tide Corrections (Examples)

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SAGE 2009 TIDE CORRECTIONS
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SAGE 2004 TIDE CORRECTIONS
NOTE MAXIMUM AMPLITUDE OF 320?GALS
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COMPUTING OBSERVED GRAVITYTIDE AND DRIFT
CORRECTIONS
DRIFT CORRECTION CAUSED BY LONG TERM
RELAXATION ASSUMED TO BE SMOOTH, SLOW AND
LINEAR ESTIMATE BY REOCCUPATION OF BASE CHECK FOR
QUALITY CONTROL ON REOCC.
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SAGE 2004 TIDE CORRECTIONS
NOTE MAXIMUM AMPLITUDE OF 320?GALS
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COMPUTING OBSERVED GRAVITY

• OBSG (SCGR BCGR)GRCAL ABGV
• Where
• OBSG Observed gravity
• SCGR Station corrected meter reading
• BCGR Base corrected gravity reading
• ABGV Absolute base gravity value
• GRCAL Gravimeter calibration

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GRAVITY REDUCTION (MODEL)
ELLIPSOID
TOPO SURFACE
GEOID

• GEOID Theoretical sea level surface.
• ELLIPSOID Mathematical model of the earth
• (from satellites)
• SPHEROID Clark spheroid 1866
• (from land surveys)

GEOID HEIGHT
EARTHS SURFACE
GEOID
ELLIPSOID
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THEORETICAL GRAVITY (MODEL)

• Geodetic Reference System (GRS) formulae refer
  to theoretical estimates of the Earths shape.
• From these GRS formulae we obtain International
  Gravity Formulae (IGF)
• Several different formulae have been adopted over
  the years
• 1930 First internationally accepted IGF (Geoid
  based)
• THEOG33 978049.0(10.0052884 sin²?-0.0000059
  sin² 2?)
• 1967 Correction for Potsdam (Geoid based)
• THEOG67 978031.846(10.005278895
  sin²?-0.000023462 sin4?)
• 1984 Based on GRS 1980 World Geodetic System
  (WGS84)
• THEOG84 978032.67714 (10.00193185138639sin²?)
• 
  (?1-0.00669437999013sin²?)
• Requires correction for atmosphere (ATMCR).
• ATMCR 0.87e-0.116h1.047 (SL 0.87, 5 km
  0.47, 10 km 0.23 mGals)

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GRAVITY ANOMALIES MEASURED-MODEL

• Free Air Anomaly (FAAyy)
• FAAyy OBSG-THEOGyyFACu x SELEVu
• FACu Free air correction in feet or meters
• SELEVu Station elevation in feet or meters
• FACf (0.094112-0.000134sin?²-0.0000000134SELEVf)
  0.09412SELEVf
• FACm (0.308768-0.000440sin?²-0.0000001442SELEVm)
  
• SELEVf Station elevation in feet
• SELEVm Station elevation in meters
• Simple Bouguer Anomaly (SBAyy)
• SBAyy FAAyy-BSCu
• BSCu Bouguer Slab Correction in feet or meters
• BSCf (2p6.672?0.3048/1000.0)SELEVf
  0.03412SELEVf
• BSCm (2p6.672?/1000.0)SELEVm 0.04192SELEVm
• Note (FACu - BSCu) 0.06 mGals/ft 0.20
  mGals/meter
• Complete Bouguer Anomaly (CBAyy)
• CBAyy SBAyy TC
• TC Terrain Correction (usually calculated in
  two parts)

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COMPLETE BOUGUER ANOMALIES OF THE UNITED STATES
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ISOSTATIC ANOMALIES (PRATT AIRY)
?cdensity of crust ?wdensity of sea
water ?sdensity of substratum ?hdensity of
crust mountains ?odensity of crust-oceans ?rden
sity of crust-ridge
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100 COMPENSATION
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75 COMPENSATION
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0 COMPENSATION
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GEOLOGICAL CORRECTED ANOMALY

• EXAMPLES
• IMPERIAL VALLEY
• RIO GRANDE RIFT
• LOS ANGELES BASIN

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REGIONAL- RESIDUAL GRAVITY ANOMALIES

• DEFINITION
• RESIDUAL REGIONAL COMPLETE BOUGUER
• REGIONAL ANOMALY IS DETERMINE BY SCALE OF THE
  TARGET. (NON UNIQUE)
• SEPARATION METHODS
• LINEAR SEPARATION (PROFILE METHOD 1D)
• MAP SEPARATION (2D)
• LEAST SQUARES FIT OF GRAVITY ANOMALIES

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LINEAR SEPARATION
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MAP SEPARATION
COMPLETE BOUGUER ANOMALY
REGIONAL ANOMALY
-24
-24
-
-32
- 32
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RESIDUAL BOUGUER ANOMALY
0
5
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LEAST SQUARES FIT OF STATION GRAVITY

• PROBLEM PRODUCE A REGULAR GRID OF GRAVITY VALUES
  FROM A RANDOMNLY DISTRIBUTED DATA SET.

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GRAVITY MODELING

• DENSITY-DEPTH-RELATIONSHIP.

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GRAVITY MODELING

• VELOCITY-DENSITY RELATIONSHIP
• NAFE-DRAKE CURVE

VELOCITY km/sec
DENSITY gm/cm³
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GRAVITY MODELING

• VELOCITY-DENSITY RELATIONSHIP

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GRAVITY MODELING

• EFFECTIVE DENSITY

LAYERED MODEL CONTINUOUS MODEL
??(h) CAN BE CONSTANT LINEAR,EXPONENTIAL, OR
HYPERBOLIC WITH DEPTH
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DENSITY-DEPTH RELATIONS

• EXPONENTIAL DENSITY-DEPTH
• ? ?max ??oe-bh
• ?? ?-?max ??oe-bh
• ?? ??o(1 - e-bH)/bh
• HYPERBOLIC DENSITY-DEPTH
• ? ??o( ß²/(hß)²) ?max
• ?? ??o ß²/(hß)²
• ?? ??o ß/(Hß)

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CALCULATING ß

• From the infinite slab formula
• ?g 2p???oßH/(H ß)
• ?g 41.92 ??oßH/(H ß)
• H - ?gß/(?g 41.92??oß)
• ß ?gH/(41.92 ??oH- ?g)
• If we know the residual anomaly (?g) at a point
  and the depth of the basin (H) and the surface
  density contrast (??o) we can calculate ß.

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GRAVITY MODELING

• FORWARD INVERSE MODELING USING RESIDUAL
• SIMPLE SHAPES
• SLAB
• SPHERE
• HORIZONTAL CYLINDER
• TALWANI - BOTT (2D)
• CADY (2 ½D)
• TALWANI CORDELL BIEHLER (3D)

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GRAVITATIONAL FIELD OF A SPHERE AND CYLINDER
SPHERE
CYLINDER
Gz 4/3 p ?R3?(z/(x² z²)3/2
Gz 2p?R²?(z/x² z²)
Gmax
Gmax/2
x½
x½
Z X½
Z1.305X½
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REGIONAL RESIDUAL SEPARATION
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