Assume you have a code for computing the transfer function p.r;z;!/ for the reflection which you want to use together with Fourier synthesis to model the transient response on a horizontal receiver array 100 m above the interface. The array has 11 elements at a spacing of 50 m, with the first element at r D 0.

a. Which array elements will record the head wave?

b. If you use a fixed time window starting at time t = 0, determine the minimum length Tf of the time window necessary to avoid wrap-around of the response of any of the receivers.

c. Similarly, determine the minimum length Tr of the time window if you allow the starting time tmin to be receiver-dependent (running time window).

d. In general, the computation time for the Fourier synthesis is insignificant compared to that associated with the computation of the transfer functions. Determine in relative terms the computational advantage of using the running time window for this problem.

e. Would there be any computational advantage in using a receiver-dependent length of the window as well?