where I assumed .
The matrix representation of this operator is the same as equation(4) except that the size of each matrix is now larger than the corresponding matrix in equation(4) because I need to express the two-dimensional wavefield with an abstract vector form. For a space of (z,x)=(5,6), the matrix becomes a block tridiagonal matrix as follows :
The matrix represents a tri-diagonal matrix :
The conjugate operator can easily be obtained by substitution of the transposed form of the new matrix into the equation(7). The code for 2-D algorithm, which has passed dot-product test, can be found in the CD-rom version of this report.