SAGE 2010 – REU LECTURE-DENSITY-SUSCEPTIBILITIES
INTRODUCTION TO GRAVITY METHODS
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The mathematical problem of gravity interpretation.
The inherent ambiguities of solving the inverse problem.
The law of gravitational attraction.
The gravitational constant.
Cavindish’s experiment – weighing the earth.
Earth’s regional gravity field (Figure 1 – 2)
FACTORS WHICH INFLUENCE DENSITY
1) Sedimentary rocks (Figure 3 – Average densities from laboratory measurements)
a. Composition
wet bulk density
i. Soils, alluvium
1.7-2.2 gm/cc
ii. Salt, anhydrites
1.9-2.1
iii. Sandstone
2.1-2.6
iv. Shale and clays
2.0-2.7
v. Calcareous rocks
2.4-2.8
b. Age and depth of burial
i. Shales and clays show greatest effect of compaction.
ii. (Figure 4 – Density vs Depth – Garber County, OK)
2) Igneous rocks
a. Composition
i. Density is inversely proportional to the silica content.
ii. Granite (2.67) --------- Diorite (2.76)--------Gabbro (2.98)
iii. Texture (holocrystalline---------aphanitic) <10%
iv. Mineralization (only locally important)
v. Porosity – weathering – fracturing (can be >30%)
3) Metamorphic rocks
a. Density increases as degree of metamorphism increases.
b. Gneiss (2.7)--------Diorite -----------------Eclogite (3.4)
4) Sampling rock densities
a. Well cores
b. In situ – borehole gravimeter
c. Nettleton’s method (Figure 5 – Nettleton method of density estimation)
d. Velocity – Density relationship (Figure 6-7 – Nafe-Drake/Woolard curves)
5) Average densities
a. All surface rocks = 2.67 gm/cc
b. All basement rocks = 2.74 gm/cc
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SAGE 2010 – REU LECTURE-DENSITY-SUSCEPTIBILITIES
FACTORS WHICH INFLUENCE SUSCEPTIBILITY
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Average susceptibilities from laboratory measurements (Figure 8)
Basic igneous rocks – highest (3000 x 106 c.g.s)
Acidic igneous rocks
(650 x 106 c.g.s)
Metamorphic rocks
(350 x 106 c.g.s)
Sedimentary rocks – magnetically transparent ~ 0
A few percent of magnetite accounts for most susceptibility
Remnant magnetization – serious problem in modeling
DENSITY VERSUS SUSCEPTIBILITY OF ROCKS
1) Compare Figure 3 and Figure 8
2) Variation in susceptibility is over 1,000 times greater then density.
3) Effects on appearance of anomaly maps
REFERENCE
An excellent reference: Grant F.S. and West G.F., Interpretation Theory in
Applied Geophysics, 1965, McGraw-Hill, pp. 189-209.
Figure 1. Bouguer anomaly map of the contemporaneous United States.
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SAGE 2010 – REU LECTURE-DENSITY-SUSCEPTIBILITIES
Figure 2. Generalized Complete Bouguer anomalies over continents and oceans.
Figure 3. Average densities of surface samples and cores based on
laboratory measurements (Mobil Oil Co.).
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SAGE 2010 – REU LECTURE-DENSITY-SUSCEPTIBILITIES
Figure 4. Wet-bulk densities of core samples taken from wells in Garber
County, Oklahoma (after Athy).
Figure 5. Graph illustrating the Nettleton method of density estimation.
Dashed curves show Bouguer gravity calculated for several trial values of
density.
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SAGE 2010 – REU LECTURE-DENSITY-SUSCEPTIBILITIES
Figure 6. A plot of seismic P-wave velocity versus bulk density. (Courtesy of C. Drake)
P wave velocity:
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Vp = ( k+4/3)/
Where: Vp = P wave velocity
k = Bulk Modulus
 = Modulus of Rigidity
 = Density
Note: P wave velocity is inversely proportional to density but empirically Vp increases
with increasing  because k and  increase more rapidly.
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SAGE 2010 – REU LECTURE-DENSITY-SUSCEPTIBILITIES
Figure 7. Composite Velocity – Density curves for sedimentary and crystalline rocks
(after G. P. Woollard).
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SAGE 2010 – REU LECTURE-DENSITY-SUSCEPTIBILITIES
Figure 8. Average magnetic susceptibilities of surface rocks and cores as measured in the
laboratory. (Compiled by J.W. Peters, Mobil Oil Corp.)
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