When to FFT

FFT (Fast Fourier Transform) is used as a decision-supporting tool - it indeed helps identify features near the top that create a periodic vibration

See Figure 1, a trace of a pile constructed with a short casing that created a "step" at 1.8m

 Figure 1 - A trace of a pile constructed with a short casing that created a "step" at 1.8m

In a simplistic way, the FFT is a vector of amplitude vs. frequency (Simple because FFT really produces complex numbers that not only give the frequency but also the phase but let's ignore that for simplicity).

Each frequency f  represents a period T where f = 1/T.  For example, 1KHz frequency is equal to a 1mSec period.

In PET, we transform the period time to length (using the wave speed you define), so (assuming 4000m/sec) 1Khz -> 1mSec -> 4m travel distance, back and forth ==> 2m on the scale.

Note that the reflectogram is also transformed from a time scale (which is what the PET sensor actually measures) to a length scale—so both time and frequency are converted to length.

This dual conversion to the same scale helps you identify peaks on the time curve and associate them with the FFT plot.

Note: The FFT curve is only effective at the top 2-3m of the pile since deeper features hardly ever create a periodic vibration that would be translated by the FFT algorithm to a core frequency.

Note: The FFT curve may show the reflector's location (Depending on the reflections' magnitude) but not its character—bulging or necking.

In your report, consider mentioning this as a flaw (Figure 2): "...A reflector at 1.9m..."

Figure 2 - Typical case drilling reflector 

 About using the FFT function with PET, Read more here.