Apparent Velocity

We are almost ready to begin processing the CSG data to achieve the goal of obtaining the ideal ZO section. But first we explain the useful idea of an event's moveout velocity. A moveout velocity can be used to distinguish reflection events from coherent noise such as surface waves or multiples.

Figure 1.9 depicts arrivals that moveout from the source position with offset. The apparent velocity v_xin the x direction of an arrival can be computed by measuring the slope v_x=dx/dt of that event's arrival time curve t(x), as shown on the RHS of Figure 1.8. Arrivals with a large apparent velocity and having a hyperbolic moveout curve are usually reflection events. For example, a 2-layer flat medium with a first layer velocity of v and an interface depth of dwould see the traveltime equation for the primary reflections as

 

$$\sqrt{4 d^2 + x^2 }/v$$ t(x) =

$$\sqrt{t(0)^2 + x^2/v^2 }$$ = (1.3)

where t(0)=2d/v is the 2-way vertical traveltime to the reflector at depth d. This equation describes a hyperbolic curve and characterizes the hyperbolic trajectory of reflection events seen in Figure 1.8 or 1.9.

Check out the html movie to see how plane waves propagate with different apparent velocities for different incidence angles.