4-gravity - isostacy and density

7/27/2019 4-Gravity - Isostacy and Density

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isostasyequilibrium of adjacent blocks of brittle crust

floating on underlying upper mantle

outer layers of Earth divided into 2 based on their strength lithosphere : rigid, solid outer layer (brittle) --strong

crust and uppermost mantle

DO NOT CONFUSE WITH

CRUST AND MANTLEWHICH ARE BASEDON COMPOSITION

asthenosphere : underlying denser, heat-softened,

partially melted (plastic) -- weakupper mantle

transition from lithosphere to asthenosphere reflectstemperature and rocks response to increased temperature


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isostasyequilibrium of adjacent blocks of brittle crust

floating on underlying upper mantle i.e. mass above a certain depth must be the same

think of wood blocks in water block that sticks up higher

also extends farther in water density of wood < density of water

for masses to be the same above the isostatic compensation depth:compensation depth

mass in column 1 = mass in column 2masses in both columns in 2 dimensions equal (density wood x thickness wood) + (density water x thickness water)

density water > density woodwood that replaces water in the column

must be thicker than water it replaces


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isostasy

continental crust isless dense than

oceanic crust

mass in column 1 = mass in column 2 = mass in column 3density mantle > density oceanic crust > density continental crust

crust isless dense than

mantle

same concept as wood blocks applies to lithosphere blocks(crust and uppermost mantle)

floating on asthenosphere above the compensation depth

compensation depth

if more mantle in column -- column will be thinner if more continental crust in column -- column will be thicker

implication is that mountains have roots -- crust is thicker below them


4/11

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isostasya more detailed view of density differences

includesea water

&sediments


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isostasyleads to isostatic adjustment if mass is redistributed

erosion redistributes rockfrom mountain (high)

to sediment depositedin basin (low)

less mass on mountaincauses uplift of

crust below mountain(thins and rises)

andsubsidence of basin

as mass of sediment is added

note mountain andcrustal root below it

as mountain erodes,column becomes shorter thus,

mantle mass in columnincreases over time

(mass A = mass B = mass C)

A B C

A

B

C

Xmantle

crust

AX

effect on mass columns


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isostasysee isostatic adjustment today from load of glaciers on crust during last glaciation and unloading from melting

(possible because response of asthenosphere is slow)

process is called post-glacial rebound


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Density Variations of Earth MaterialsThus far it sounds like a fairly simple proposition to estimate the variation indensity of the earth due to local changes in geology. There are, however, severalsignificant complications. The first has to do with the density contrasts measuredfor various earth materials.The densities associated with various earth materials are shown in Table 1. Noticethat the relative variation in rock density is quite small, = 0: 8 gm=cm 3, and thereis considerable overlap in the measured densities. Hence, a knowledge of rock density alone will not be sufficient to determine rock type. This small variation inrock density also implies that the spatial variations in the observed gravitationalacceleration caused by geologic structures will be quite small and thus difficult todetect.


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Factors Influencing the Density of Rocks: Density (p) is defined as the mass (m) of a body per unit volume (V):

p= m / VThe unit for density is kg/m 3, but g/cm 3 is commonly used. Three factors control the

density of rocks (Nettleton, 1971):1-The grain density of the particles forming the rock mass , controlled by theirelemental composition and by the internal bonding within the structure (Sch n,1996).2-The porosity , determined by the size and abundance of cavities or pores betweenthe mineral grains making up the rock. Porosity, , is defined as the ratio of the

volume of pore space, Vp, to the bulk volume, V, of the rock: = Vp / V = 1 - Vm / V, where Vm is the volume of solid matrix substance (Sch n, 1996). Porosity is adimensionless quantity, being expressed as either a decimal fraction or apercentage.3-The fluid in the pore space. Porous sediments are readily compressible, which results in a dependence of density

on pressure (i.e. depth of burial). Igneous rocks are typically denser thansedimentary rocks because their minerals are more mafic (higher percentages of Feand Mg compared to Si, the principal component of sedimentary rocks), and theirporosity is generally lower (Sch n, 1996). The porosity of igneous rocks is generallyso small it can be ignored. However, weathering processes may decrease the densityof igneous rocks by altering the minerals to less dense varieties, and indirectlyincreasing their porosity.


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The most important geologic parameter is the density contrast:

Density contrast = Density of the target Ambient density

ContrastDensitysolutionRe

G

r a v

i t y

Distance

HighGravity

2.72.1

Distance

2.42.1

Distance

2.22.1

Density contrast = 0.6 Density contrast = 0.3 Density contrast = 0.1


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The geoids:Represent a surface over which the gravitational field has equal value and it is calledan equipotential surface.

Note : The sea level surface if undisturbed by winds or tides is known as Geoids.It is characterize by:1- Always horizontal.2- Normal to the direction of gravity.3- The irregular distribution of mass especially near the surface will warps the geoids

so that it is not coincides to the ellipse of rotation.

3.1 Excess mass

warpingGeoids

Sphere

Ellipse of rotation Ellipse of rotation

ocean

Continent


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The actual shape of the earth

4-gravity - isostacy and density

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