Page 300 - Physical Principles of Sedimentary Basin Analysis

9

Flexure of the lithosphere

The lithosphere acts as a rigid plate that floats on a ductile mantle (asthenosphere), and
we have seen how (Airy) isostasy can be used to predict how deep the lithosphere floats
under the weight of a load. Isostasy is a simplification that ignores the possible bending
of the lithospheric plate due to lateral variations in the surface load. Isostasy applies for
loads of large lateral extent, like for instance a mountain range or a continent. On the other
hand, “small” scale features like a valley or a mountain peak do not lead to any isostatic
uplift or subsidence because they are completely supported by the elastic strength of the
lithosphere. There is a length scale in between where surface loads are partly supported
by the lithosphere, and partly supported by the buoyancy of the displaced mantle. This
length scale can be estimated assuming that the lithosphere acts like a thin linear elastic
plate floating on the mantle. The Hawaiian islands, which are piles of volcanic rock on the
oceanic plate, are good examples of loads that bend the lithosphere. The flexure is in this
case reproduced by simple solutions of the equation for the deflection of a thin elastic plate.
The solutions also predict uplift in the form of a flexural bulge, a feature that isostasy alone
cannot predict. Furthermore, observation of flexure allows for estimations of the thickness
of the elastic part of the lithosphere.
In this chapter we will first derive the equation for the deflection of a thin elastic plate
under loads that are only x-dependent. Some simple solutions for the deflection of a plate
are presented and discussed. The elastic plate model is extended to a viscoelastic model of
flexure, and both the viscoelastic and the viscous behavior of a plate are studied by simple
solutions.

9.1 Equation for flexure of a plate
Loads on the lithospheric plate, like for instance mountain ranges or volcanic islands, may
bend the lithosphere. An equation for the flexure of an elastic plate is needed to study how
such loads may deflect the lithosphere. It turns out that the torque (or the bending moment)
caused by the load is an important quantity that controls the flexure. The terms torque and
bending moment mean the same thing here, and they are used interchangeably. A torque
is the cause of rotation. If an object can rotate around an axis its rotation accelerates as

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