After preprocessing for multiple reflections, the monochromatic 2-D forward model for a seismic shot record can be written as follows Berkhout (1985):
In equation () source vector and measurement vector refer to one seismic experiment at the surface z=z0 with source location at x=xj. In equation (), propagation operators W(zn,z0) and W(z0,zn) quantify the full propagation effects (down and up, respectively) between depth levels z0 and zn, and reflection matrix R(zn) defines the elastic angle-dependent reflection properties caused by inhomogeneities at depth level zn. All matrices and vectors refer to one temporal Fourier component. Equations () and () are valid for single-component as well as for multi-component measurement of 2-D as well as 3-D data.