Using the Directional Derivative Trace Transform for Seismic Wavefield Separation

We address the directional derivative trace transform (DDTT) for seismic wavefield separation. The goal is to separate the different seismic waves, which is a practical requirement for seismic exploration and geophysics. The DDTT is based on the trace transform, which is a generalization of the Radon transform (RT). It calculates the integral of a directional derivative along the trace line. The directional derivative is the pointwise rate of change of a function in a certain direction. Therefore, the DDTT better reflects the property of linear wavefields and other wavefields than the F-K filtering and RT methods. The DDTT domain consists of two parts: One part mostly represents linear wavefields such as surface waves, and the other part mostly represents the reflection signals. Based on this property, a parametric method is proposed for separating the ground roll better. In order to return data to the time-offset domain, we derive the inverse DDTT using the properties of the Fourier transform and the Hilbert transform. We show the potential of our method for the removal of ground roll on synthetic and real data examples.