P. Wessel, ANALYTICAL SOLUTIONS FOR 3-D FLEXURAL DEFORMATION OF SEMIINFINITE ELASTIC PLATES, Geophysical journal international, 124(3), 1996, pp. 907-918
The theory of elastic-plate flexure has played a prominent role in iso
static studies and investigations of lithospheric deformation caused b
y vertical tectonism. Simple analytical, axisymmetrical solutions exis
t when the boundaries of the plate are far removed from the area where
the load is applied. When deformation is driven by end loads (i.e. be
nding moments and shear forces) the problem is usually simplified to y
ield a 2-D solution that approximates a cross-section of the 3-D solut
ion. We present analytical Green's functions for the point-force respo
nse of semi-infinite elastic plates resting on an inviscid substratum
and being acted upon by constant in-plane forces and arbitrary end loa
ds. This solution may be used to study deformation and stresses caused
by loads close to a free geological boundary (e.g. a trench or weak f
racture zone). We also present Green's functions for the case when two
semi-infinite plates of different rigidities are mechanically coupled
and subject to a point load. This solution may be useful when studyin
g deformation near mechanically strong fracture zones or at ocean-cont
inent transitions. The analytical solutions provide simple alternative
s to (and calibration of) complex numerical finite-element or finite-d
ifference solutions, and furthermore give additional physical insight
into the geological process to be examined. The analytical methods are
used to demonstrate the different stress patterns that may arise near
weak and strong geological boundaries. We also illustrate how the obs
erved scatter in 2-D determinations of elastic thickness at subduction
zones may partly have its origin in 3-D effects.