Exercise- Isostasy and surface elevation 1: The aim of the exercise is to derive the
mathematical expression for the the total Ridge-Push using the concept of gravitational
potential energy.
A Mid-Oceanic-Ridge (MOR) standing zmor meter below sea level is in isostatic
equilibrium with an oceanic lithosphere in near thermal equilibrium whose surface
stands zb meter below sea level.
In the MOR column, decompression melting occurs down to a depth that corresponds to
that of the base of the thermally equilibrated oceanic lithosphere. The density of the
MOR column depends on the density of melt and on the average melt fraction in the
MOR column (we assume here a melt fraction of 4%). The density of the restite is
assumed to be that of the asthenospheric mantle. The oceanic lithosphere is made of an
oceanic crust overlying the lithospheric mantle colder and therefore denser than the
asthenospheric mantle. T is the difference between the average temperature of the
lithospheric mantle ((Tasthenosphere + TMoho)/2) and that of the asthenosphere. Convection
makes the temperature in the asthenosphere rather homogeneous (0.3ºC k.m -1). The
increase in average density over T is given by: .  T, with  the coefficient of
thermal expansion.
a/ Using the theory of isostasy, derive the expression for the depth zb of the oceanic
lithosphere as a function of other relevant parameters.
b/ Determine the gravitational potential energy of both the MOR and the oceanic
column in near thermal equilibrium.
c/ Using the concept of gravitational potential energy determine the Ridge-Push force
acting between the MOR and the oceanic plate in near equilibrium.
Parameter values
zmor: depth of the MOR=3600 m;
zl: thickness of the oceanic lithosphere near thermal equilibrium=85000 m;
zco: Thickness of the oceanic crust=5000 m;
g: gravitational acceleration=10 m.s-2;
w: density of sea water=1030 kg.m-3;
co: density of the oceanic crust=2950 kg.m-3;
: coefficient of thermal expansion=3.10-5;
TMoho: Temperature of the base of the oceanic crust = 200ºC;
lm: density of the lithospheric mantle at room temperature =3395 kg.m-3;
am: density of the asthenospheric mantle =density of the lithospheric mantle at at
1330ºC;
melt: density of the melt=2600 kg.m-3;
mor: density of the MOR;
ol: Average density of the oceanic lithosphere.