Ground roll is coherent noise in land seismic data that contaminates seismic reflections. Therefore, it is essential to find efficient ways that remove this noise and still preserve reflections. To this end, we have developed a signal and noise separation framework that uses a hyperbolic moveout assumption on reflections, coupled with the synthesis of coherent ground roll. This framework yields a least-squares problem, which we solve using a sparsity-promoting program that gives coefficients capable of modeling the signal and noise. Subtraction of the predicted noise from the observed data produces data with amplitude-preserved reflections. We develop this technique on synthetic and field data contaminated by weak and strong ground roll noise. Compared to conventional Fourier filtering techniques, our method accurately removes the ground roll while preserving the amplitude of the signal.

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