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.

The time-frequency peak filtering (TFPF) is an effective method for seismic random noise reduction. To achieve a higher level of noise suppression in seismic records, we propose a novel approach in which we apply the TFPF method in Radon domain. This method, called spatiotemporal TFPF, can be applied with different types of Radon transforms (linear, parabolic, etc.) depending on the geometry of the reflection. The new method is similar to the principle of ridgelet, which is doing 1-D wavelet in linear Radon domain so that there is a parameter representing direction brought in the filtering process. Although the ridgelet has the wonderful ability to process reflection events with linearly changing characteristics, for curving events, it shows lack of effectiveness. With this in mind, and taking the superiority of TFPF into consideration, the new method as mentioned previously is proposed. Thus, it breaks the limitation of doing filtering in linear Radon domain to make the filtering more flexible and plays the advantage of TFPF in denoising. Using both synthetic and real seismic data, we show the better performance of the new method in random noise reduction and higher continuity and clarity of reflection events compared to the conventional TFPF.