Deep controls on intraplate basin inversion - Intraplate Earthquakes - page 260

the resulting “swell push force” (Sandwell et al ., 1997 ) , F s , is proportional to the vertical
integral of the first moment of the anomalous density, and given by

g D
0

F s = ρ ( z ) zdz 10.1

In Eq. ( 10.1 ) , g is the gravitational acceleration at the Earth's surface, ρ is the deviatoric
lithospheric density with regard to a reference density at depth z , and D is the depth of
isostatic compensation.
Jones et al .( 1996 ) presented the classical derivation of how the fundamental entities
of vertical density profiles and lithospheric potential energy lead to a vertically averaged,
horizontal stress balance equation where horizontal gradients of the potential energy and
the basal pressure become sources of stress in the lithosphere. For the vertically averaged
deviatoric stresses the set of equations reads

∂E
∂x +

∂τ xx
∂x +

∂τ yx
∂y

1
L

L ∂τ zz
∂x

=

∂E
∂y +

∂τ xy
∂x +

∂τ yy
∂y

1
L

L ∂τ zz
∂y

= 10.2

In Eq. ( 10.2 ) , x and y are local horizontal coordinates, τ xx , τ yy , and τ xy are the horizontal
deviatoric stresses, E is the potential energy of the lithosphere of thickness L , and τ zz is
the average vertical deviatoric stress caused by deviations of the mantle pressure from a
reference pressure.
A number of studies with different focuses on the major stress sources have investigated
lithospheric stresses. Gosh et al .( 2009 ) calculated the geopotential stress field of a mainly
crustal model (based on CRUST2.0) in different isostatic states. Lithgow-Bertelloni and
Guynn ( 2004 ) took a similar approach to the crustal contribution to the geopotential stresses
and introduced vertical and horizontal mantle tractions. The approach of Bird et al . ( 2008 )
included geopotential, plate boundary, and basal stresses. They compared their results to
observed seafloor spreading rates, plate velocities, anisotropy measurements, and principal
stress directions. In general, the main conclusion of all these approaches was that one main
driving force is not sufficient to explain the observations. A geopotential stress component is
as important as basal mantle tractions and boundary forces to form the Earth's lithospheric
stress field.
The present approach is similar but not identical to Jones et al .( 1996 ) and differs from
that of Lithgow-Bertelloni and Guynn ( 2004 ) and Bird et al .( 2008 ) by considering only
lithospheric potential energy and radial tractions. Plate velocities, shear tractions, and plate
boundary forces are not considered.
Using CRUST2.0 (Bassin et al ., 2000 ; http://igppweb.ucsd.edu/ ∼ gabi/rem.html ) we
determine the potential energy of the lithosphere by isostatically balancing one-dimensional
lithospheric columns in the presence of lateral pressure variations causing dynamic topog-
raphy. In other words, we transfer some of the isostatic imbalance of the CRUST2.0 model
to a basal pressure that supports topography. In the oceans we use the standard plate model