1 Practical 3: Isostasy, ridge-­push and gravitational force... Aim: The purpose of this practical to get up close and personal with the theory of isostasy and the concept of gravitational force. • Outcomes: To develop a deeper understanding of the theory of isostasy and how it controls the surface elevation of plates. To develop a deeper understanding of the dynamic of mid-­‐
oceanic-­‐ridges. • To be able to evaluate the magnitude of the Ridge-­‐Push force and that any other gravitational forces acting between two lithospheric columns of contrasted elevations and/or density structures. • Generic skills: Problem solving ability, computational skills, and analytical skills. • Assumed background knowledge: Basic knowledge on isostasy, lithostatic pressure and gravitational potential energy (check out your lecture notes) and Year 12 Mathematics. • Tools you may want/need to use: MatLab or LiveMath, calculator... • Reading: Turcotte & Schubert: Geodynamics Submission details: Individual report due next Wednesday Some fundamentals: On the theory of isostasy: The theory of isostasy assumes that there is a depth called "the compensation level" under which the stress is lithostatic (isotropic stress) therefore only related to the weight of the rock column above. In other terms, there is no lateral variation of lithostatic pressure (also called confining pressure) along a given gravitational equipotential surface. It is isostasy that dictates the elevation of lithospheric plates. On the gravitational potential energy and the gravitational force: Above the compensation level, lateral variations of density produce lateral contrasts in Gravitational Potential Energy (GPE) responsible for an horizontal force called the gravitational force (Fg, a volume force). The gravitational potential energy of a column of lithosphere corresponds to vertical integration, down to the compensation level, of the lithostatic pressure profile. The gravitational force per unit length (Nm-­‐1) that two lithospheric columns apply to each other is equal to the difference in their GPE 2 Exercise 1-­ 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. ΔT 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 ΔT is given by: ρ . α . ΔT, with α 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; ρw: density of sea water=1030 kg.m-­‐3; ρco: density of the oceanic crust=2950 kg.m-­‐3; α: coefficient of thermal expansion=3.10-­‐5; TMoho: Temperature of the base of the oceanic crust = 200ºC; ρlm: density of the lithospheric mantle at room temperature =3395 kg.m-­‐3; ρam: density of the asthenospheric mantle =density of the lithospheric mantle at at 1330ºC; ρmelt: density of the melt=2600 kg.m-­‐3; 3 ρmor: density of the MOR; ρol: Average density of the oceanic lithosphere. Exercise 2-­ Gravitational force-­ A reference lithosphere is zl km thick and includes a zc km thick continental crust. This reference lithosphere is in isostatic and mechanical equilibrium and has a surface elevation hc at sea level (hc=0 m). A phase of lithospheric deformation changes the thickness of the crust and that of the entire lithosphere. a/ Give the surface elevation h of the deformed lithosphere as a function of the densities and thicknesses of the crust and lithospheric mantle of the reference lithosphere, fc the thickening/thinning factor of the crust, fl the thickening/thinning factor of the entire lithosphere, and any other relevant parameters . NB: The thickening/thinning factor of the crust is defined by fc the ratio between the thickness of the crust after deformation over zc the thickness of the initial crust. The thickening/thinning factor of the entire lithosphere is defined by fl and follows a similar definition. b/ Numerical applications (Use the parameter values given below): Calculate h, ΔGPE, and Fg for the three following cases: • fc = fl =2; (Homogeneous thickness doubling the thickness of the crust and that of the entire lithosphere) • fc = 2; fl =1; (Here only the thickness of the crust is changed) • fc = fl =0.5. (Homogeneous thinning). c/ Assuming lithospheric rocks have a depth independent strength of 70 MPa, would the gravitational forces determined in b/ produce any lithospheric deformation? Parameter values: hc: elevation of the initial lithosphere=0 m; zl: thickness of the continental lithosphere near thermal equilibrium=120 km; zc: Thickness of the continental crust = 40 km; g: gravitational acceleration=10 m.s-­‐2; ρw: density of sea water=1000 kg.m-­‐3; ρco: density of the continental crust=2700 kg.m-­‐3; ρlm: density of the lithospheric mantle =3330 kg.m-­‐3; ρam: density of the asthenospheric mantle =3310 kg.m-­‐3; nb: We assume here that densities are temperature independent. 4