The shape of the operator

Deregowski 1981 thoroughly described the elliptic DMO operator; I include Figure (1) only for the sake of introducing the terminology used throughout this paper.

 

Shape
Figure 1 The DMO operator (bold line) is geometrically constructed from the elliptical reflector corresponding to an impulse in a (time, midpoint) section. Notice that in the (t₀,x) space, the maximum slope is 2/v.

The operator is a dip-limited ellipse whose support is given by the equation  

$$\frac{t_0^2}{t_n^2} + \frac{x^2}{h^2} = 1 .$$ (1)

Because it is kinematically impossible to have reflectors dipping more than the slope 2/v in a zero-offset constant-velocity time section, the DMO operator is dip-limited.