Wavefield separation and enhancement using sparse linear radon transform

Summary Radon transform is a useful tool in seismic data processing with lots of applications. However, incomplete information decreases its resolution and limits its applicability. Sparseness is a valid criterion to overcome this problem. In this paper, a forward-backward splitting algorithm is used to solve an l1-norm regularized Radon transform in order to obtain a high resolution linear Radon transform (LRT). Then, it is applied on down-up going wavefield separation in vertical seismic profiling (VSP) data and also seismic interference (SI) noise attenuation. It is also shown that a sparse LRT can be used to enhance the quality of teleseismic data.
Introduction Overlapping wavefields in time-space domain can be separated in Radon domain, however, different reasons cause resolution problems and aliasing in Radon transform. Obtaining a sparse Radon panel enables us to separate coefficients of each event without harming the others. Using sparsity promoting methods results in a high resolution Radon domain with minimum non-zero elements. An l2-l1 norm cost function is constructed and a forward-backward splitting algorithm is employed to obtain a sparse model, which can be used for different purposes among which VSP wavefield separation, SI noise attenuation and wavefield enhancement are dealt with here. Both down- and upgoing wavefields of VSP data contains information of subsurface but they need to be separated. Mapping their coefficients to separable regions using a sparse linear Radon transform is an efficient solution. One other application could be SI noise attenuation. This kind of marine noise is originated by other surveys in the same area and overpowers reflections. According to their linear characteristics and the use of sparse LRT, they can be subtracted from the data. Moreover, it is shown that injecting sparsity to Radon domain eliminates random noise and also non-linear events. Furthermore, low quality traces can be replaced by interpolated new reconstructed traces applying a mask on misfit term in the cost function. This can be used to enhance the quality of teleseismic data with linear wavefields.
Methodology and Approaches The ability of separating coefficients in Radon domain relies on the resolution of Radon transform. Least square regularization results in a smooth solution, which causes the application limitation. Here, a sparse LRT is developed by applying an l1-norm constraint on Radon model. This transformation can be applied on VSP data to map upgoing and downgoing wavefields to negative and positive slowness regions, respectively. Then, each of them can be reconstructed separately using inverse Radon operator. High amplitude seismic interference noise is harmful to many processing steps and they need to be attenuated beforehand. Their linear coherency in shot gathers makes LRT an appropriate tool to eliminate them. Using a sparse LRT converges SI plane waves energy, however, attenuates reflections coefficients. Thus, only SI noise can be reconstructed, and then, subtracted from marine shot gathers. Sparse data acquisition in teleseismic data, and also, the presence of random noise reduce the quality of the data and make arrival time picking difficult. Sparsity in Radon panel and interpolation increases the resolution of the reconstructed data so that the P- and S-wave arrival times can be determined with more accuracy.
Results and Conclusions Synthetic and real numerical examples demonstrated the efficiency of applying a forward-backward splitting algorithm to solve an l2-l1 cost function for obtaining a sparse Radon panel in which even linear wavefields with very close slopes can be identified. This method is a feasible and effective way to separate overlapping upgoing and downgoing VSP wavefields, and to attenuate the seismic interference noise and to enhance teleseismic wavefield.