Next: Oneway Riemannian wavefield extrapolation
Up: REFERENCES
Previous: REFERENCES
Geometry in a generalized 3D Riemannian space is described by a symmetric
metric tensor, g_{ij}=g_{ji}, that relates the geometry in a
nonorthogonal coordinate system, , to an underlying
Cartesian mesh, Guggenheimer (1977). In
matrix form, the metric tensor is written
 
(15) 
where g_{11}, g_{12}, g_{22}, g_{13}, g_{23} and are functions
linking the two coordinate systems through
 

 (16) 
(Summation notation  g_{ii} = g_{11}+g_{22}+g_{33}  is used in
equations throughout this paper.) The associated (or inverse) metric
tensor, g^{ij}, is defined by , where
is metric tensor matrix determinant. The associated
metric tensor is given by
 
(17) 
and with the following metric determinant
 
(18) 
Weighted metric tensor, , is another useful
definition for the following development.
B
Next: Oneway Riemannian wavefield extrapolation
Up: REFERENCES
Previous: REFERENCES
Stanford Exploration Project
1/16/2007