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Radon transforms are simple summations along predefined trajectories of the input data. These trajectories are controlled by a single parameter that defines the geometry of the summation trajectory. Various trajectories are chosen based on the input data with the most
popular being the linear radon transform, the parabolic
radon transform, or the hyperbolic radon transform.
The choice of transform depends exclusively on the data to be processed. For instance, parabolic radon transforms are chosen for multiple attenuation of common mid-point gathers after normal move-out
Foster and Mosher (1992). Hyperbolic radon transforms are most commonly used for producing velocity
panels from seismic reflections following hyperbolic moveout Taner and Koehler (1969) but they can also be used for noise attenuation Foster and Mosher (1992) and data interpolation
Hindriks and Duijndam (1998); Trad et al. (2002). In the teleseismic case, the plane wave nature of the data makes the use of linear radon transform a natural choice to process the data.
With the application of the linear radon transform we hope to extract the signal from the total wavefield and to interpolate the wavefield on return to the data domain. First, we intend to separate the signal and source wavefields from diffracted and ambient noise wavefields based on differences in slowness and wavefield curvature. Arrivals with a planar moveout will map well into the linear radon domain (see Figures and ). However, the diffuse ambient noise wavefield and diffracted arrivals will have near zero amplitude after transformation because they are not represented well as plane waves. In the radon domain, coherent plane wave arrivals that do not follow the expected moveout of specularly scattered waves (e.g. P to Rg scattering from the surface and basin bottom topography) are assumed to be noise and muted. On return to the data domain, we will automatically interpolate the wavefield to a regularly sampled grid because of the plane wave representation of the wavefield and the loss of spatial reference in the radon domain.