A causal imaging condition for reverse time migration using the Discrete Hilbert transform and its efficient implementation on GPU

Reverse time migration (RTM) has shown a significant advantage over other imaging algorithms for imaging complex subsurface structures. However, low-wavenumber noise severely contaminates the image, which is one of the main issues in the RTM algorithm. To attenuate the undesired low-wavenumber noise, the causal imaging condition based on wavefield decomposition has been proposed. First, wavefield decompositions are performed to separate the wavefields as up-going and down-going wave components, respectively. Then, to preserve causality, it constructs images by correlating wave components that propagate in different directions. We build a causal imaging condition in this paper. Not only does it consider the up/down wavefield decomposition, but it also applies the decomposition on the horizontal direction to enhance the image quality especially for steeply dipping structures. The wavefield decomposition is conventionally achieved by the frequency-wavenumber (F-K) transform that is very computationally intensive compared with the wave propagation process of the RTM algorithm. To improve the efficiency of the algorithm, we propose a fast implementation to perform wavefield separation using the discrete Hilbert transform via the Graphics Processing Unit. Numerical tests on both the synthetic models and a real data example demonstrate the effectiveness of the proposed method and the efficiency of the optimized implementation scheme. This new imaging condition shows its ability to produce high image quality when applied to both the RTM stack image and also the angle domain common image gathers. The comparison of the total elapsed time for different methods verifies the efficiency of the optimized algorithm.