Deep controls on intraplate basin inversion - Intraplate Earthquakes - page 261

(Stein and Stein, 1992 ) .The space between the reference depth (250 km) and the base of
the lithosphere is filled with asthenosphere with a temperature that decreases upward along
the adiabatic gradient of 0.6

C (e.g.,
McKenzie et al ., 2005 ) . This determines the temperature at the base of the lithosphere, the
a-priori depth of which is obtained from a seismologically based model (Gung et al ., 2003 ) .
The CRUST2.0 model includes suggestions for the thicknesses and densities of sediment,
upper crust, middle crust, and lower crust, and densities of the upper mantle although these
values are not perfectly known. Furthermore, the pressure and temperature variations at
the compensation depth are unknowns for which additional data in the form of topogra-
phy and heat flow (Pollack and Chapman, 1977 ) are required to constrain the system. We
consider this as an inverse problem and take the parameters of the lithospheric units as
given by CRUST2.0 as tightly constrained inversion variables, the lithospheric thickness,
the radiogenic heat production rate of the crust and the basal pressure as less constrained
variables, and invoke a fixed coupling between basal pressure and temperature. By allowing
the latter to exhibit up to

° C/km at a reference potential temperature of 1315 °

C variations around the reference potential temperature, this
inverse problem is sufficiently constrained by topography and heat flow. The basal pressure
variation is parameterised using a spherical harmonic polynomial of degree 16 with a total
of 153 variable parameters. The resulting model satisfies topography and (largely) heat flow
by means of isostatically compensated lithospheric columns of almost known structure and
basal pressure (and temperature) variations. This in turn determines the global lithospheric
potential energy in the presence of a basal pressure, i.e., the source terms of Eq. ( 10.2 ) .
To obtain the stresses of Eq. ( 10.2 ) we use a three-dimensional, spherical, global finite
element mesh of flat, thick, elastic triangles each with 15 degrees of freedom. Each triangle
has three corner nodes, each with three spatial coordinates, yielding 9 degrees of freedom.
Each node is furthermore bestowed with a vertical axis with 2 angular degrees of freedom,
pointing initially towards the centre of the sphere, but which upon loading can deviate
slightly from the vertical by pivoting around the mid plane of the element as measured by
the (small) angles. This accounts for the remaining 6 degrees of freedom. The relationship
between strains and stresses for this thick element is given by Zienkiewicz ( 1977 , Chapter
16). Each element furthermore has material parameters in the form of Young's modulus,
Poisson's ratio and thickness, h .

± 50 °

10.2.2 Predicted lithospheric stress from potential energy variations in the
Europe-North Atlantic area

The results of the global three-dimensional stress calculation ( Figure 10.2 a ) are presented in
terms of principal horizontal stress directions and magnitudes at the centre of the triangles.
Effective stress, which is the square root of the second invariant of the deviatoric stress
tensor, is also displayed. Our computed principal stresses compare favourably to previous
models (e.g., Lithgow-Bertelloni and Guynn, 2004 ; Bird et al ., 2008 ) even though we
have not considered plate velocities, shear tractions, and plate boundary processes. The