The examples in this thesis could be done in the (f,x) domain, using about the same theory, but somewhat faster. Aside from simply being cavalier about computational cost, there are some arguments in favor of the time domain. In particular, Abma 1995 argues that time domain filters are more resistant to noise. Abma develops the point that filters calculated in the domain are effectively long in the time domain, because there is a separate filter for each frequency. The extra degrees of freedom make the frequency domain filters more likely to predict the noise. This leads to interpolation of ostensibly incoherent noise.
As noise makes data harder to predict, and thus interpolate, so does irregular acquisition. In the marine case, motivation to interpolate comes largely from the multiple suppression problem. In the land case, the expense and difficulty of data acquisition provides a more general motivation. However, the land problem is also harder. While marine geometry tends to be very regular, land data often has jagged, discontinuous arrangements of shots and receivers, where the survey is forced to work around and over surface features. Land data also tends to be much noisier than marine data. Slow variations in geometry and relative lack of noise mean that a given trace or shot gather in a marine survey is similar to (and thus predictable from) its neighboring shot gathers. Land data is less predictable, so it is harder to interpolate.
In Chapter 4, I discuss the effects of noise and erratic geometry on the interpolation method. I show some land data interpolation results, and compare (f,x) and (t,x) interpolation results on noisy data.