The point response

Another simple geometry is a reflecting point within the earth. A wave incident on the point from any direction reflects waves in all directions. This geometry is particularly important because any model is a superposition of such point scatterers. Figure 16 shows an example.

 

twopoint
Figure 16 Response of two point scatterers. Note the flat spots.

The curves in Figure 16 include flat spots for the same reasons that some of the curves in figures12 and 13 were straight lines.

The point-scatterer geometry for a point located at (x,z) is shown in Figure 17.

 

pgeometry
Figure 17 Geometry of a point scatterer.

The equation for travel time t is the sum of the two travel paths  

$$t\,v\ \eq \ \sqrt { z^2\ +\ {( s \ -\ x ) }^2} \ +\ \sqrt { z^2 \ +\ {( g \ -\ x )}^2}$$ (5)