GRAVITY. EARTH’S GRAVITY FIELD 978 Gals 983 Gals 1 Gal = 1 cm/sec² ELLIPSOID North-South change...
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![Page 1: GRAVITY. EARTH’S GRAVITY FIELD 978 Gals 983 Gals 1 Gal = 1 cm/sec² ELLIPSOID North-South change ~1 mGals/km ~1.5 mGals/mile ~1 Gals/m ~.3 Gals/ft.](https://reader038.fdocuments.us/reader038/viewer/2022102818/56649e155503460f94aff2de/html5/thumbnails/1.jpg)
GRAVITY
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EARTH’S GRAVITY FIELD
978 Gals
983 Gals
1 Gal = 1 cm/sec²
ELLIPSOID
North-South change~1 mGals/km
~1.5 mGals/mile~1 Gals/m~.3 Gals/ft
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MEASURING GRAVITYABSOLUTE VS RELATIVE
• Absolute – Pendulum– Weight Drop– Rise and Fall
A-10 FG-5
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 ~360Gals/6 hours = 1Gal/minute• Correction from recording gravimeter $, tidetables (obsolete),
computer program• Computer Tide Corrections (Examples)
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SAGE 2004 TIDE CORRECTIONS
NOTE: MAXIMUMAMPLITUDE OF
~320GALS
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SAGE 2010 TIDE CORRECTIONS
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COMPUTING OBSERVED GRAVITYTIDE AND DRIFT CORRECTIONS
DRIFT CORRECTION CAUSED BY LONG TERM RELAXATION
ASSUMED TO BE SMOOTH, SLOW AND LINEARESTIMATE BY REOCCUPATION OF BASE
CHECK FOR QUALITY CONTROL ON REOCC.
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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)
• GEOID – Theoretical sea level surface.
• ELLIPSOID – Mathematical model of the earth– (from satellites)
• SPHEROID – Clark spheroid ~ 1866– (from land surveys)
GEOIDELLIPSOID TOPO SURFACE
GEOIDHEIGHT
EARTH’SSURFACE
GEOID
ELLIPSOID
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THEORETICAL GRAVITY (MODEL)
• Geodetic Reference System (GRS) formulae refer to theoretical estimates of the Earth’s 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(1+0.0052884 sin²θ-0.0000059 sin² 2θ)
• 1967 – Correction for Potsdam (Geoid based)– THEOG67 = 978031.846(1+0.005278895 sin²θ-0.000023462 sin4θ)
• 1984 – Based on GRS 1980 – World Geodetic System (WGS84)– THEOG84 = 978032.67714 (1+0.00193185138639sin²θ)
– (1-0.00669437999013sin²θ)
– 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-THEOGyy+FACu x SELEVu– FACu = Free air correction in feet or meters– SELEVu = Station elevation in feet or meters
• FACf = (0.094112-0.000134sinθ²-0.0000000134SELEVf) = ~0.09412SELEVf• FACm = (0.308768-0.000440sinθ²-0.0000001442SELEVm)• 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 = (2π6.6720.3048/1000.0)SELEVf = 0.03412SELEVf• BSCm = (2π6.672/1000.0)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)
c=density of crustw=density of sea waters=density of substratum
h=density of crust –mountainso=density of crust-oceansr=density 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
- 32
-24-24
-
-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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LEAST SQUARES FIT OF STATION GRAVITY
• General quadric function of form:
• F(x,y) = Ax² +By² +Cxy +Dx + Ey +F
• Weighting function of form:
• W = ((R-di)/di)n
•
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DOMAIN RADIUS (R)
• + + + + + + + + + + + + +• + + + + + + • +• + + +• + + + + + + +• + + + + + + +• + + + + + + + + + + + +
+ + + + ++++++• + + + + + +
• + + R
• + + + + +• + + + + +• +• + + + + + +• + + +
• + di
• +++ + + + + • + • + + + • + • + + + + + + +• • +• + + + + + + + + + • + +• + + + + + +• +• + + + + + + +• +• + + + + + + + + • + • + + + + + +
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GRAVITY MODELING• DENSITY-DEPTH-
RELATIONSHIP.
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GRAVITY MODELING
• VELOCITY-DENSITY RELATIONSHIP
• NAFE-DRAKE CURVE
VE
LOC
ITY
km
/sec
DENSITY gm/cm³
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GRAVITY MODELING• VELOCITY-DENSITY RELATIONSHIP
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GRAVITY MODELING
• EFFECTIVE DENSITY
LAYEREDMODEL
CONTINUOUSMODEL
Δρ(h) CAN BE CONSTANTLINEAR,EXPONENTIAL,OR HYPERBOLIC WITH
DEPTH
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DENSITY-DEPTH RELATIONS
• EXPONENTIAL DENSITY-DEPTH = max +Δoe-bh
• Δ = -max = Δoe-bh
• Δ = Δo(1 - e-bH)/bh
• HYPERBOLIC DENSITY-DEPTH = Δo( β²/(h+β)²) + max
• Δ = Δo β²/(h+β)²
• Δ = Δo β/(H+β)
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CALCULATING β
• From the infinite slab formula:
• Δg = 2πγΔoβH/(H + β)• Δg = 41.92 ΔoβH/(H + β)• H = - Δgβ/(Δg – 41.92Δoβ)• β = ΔgH/(41.92 ΔoH- Δg)
• If we know the residual anomaly (Δg) at a point and the depth of the basin (H) and the surface density contrast (Δo) we can calculate β.
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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
Z = X½Z=1.305X½
Gmax
Gmax/2
x½ x½
Gz= 4/3 π γR3(z/(x² + z²)3/2 Gz = 2πγR²(z/x² + z²)
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REGIONAL – RESIDUAL SEPARATION
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