Ground rolls attenuation via gradient flow regularization

We propose a novel method for seismic ground rolls attenuation by employing the dips differences between ground rolls and reflective signals. The dips differences are modeled by gradient-direction differences, and the overall gradient directions are termed gradient flow. Typically, there are frequency overlap between the ground rolls and reflective signals. But, the gradient flow of a signal needs only the direction information of the gradients, not the exact scale information, and thus, can be extracted using only part of the signal. Firstly, gradient flows for the desired ground rolls and reflective signals are calculated according to the low-frequency part of the ground rolls and high-frequency part of the reflective signals via the structure tensor method. Then, an optimization model is built, which regularizes the separated ground rolls and reflective signals to have the desired gradient flows. An efficient algorithm is designed by employing the specific structure of the finite difference matrices, which are used for calculating the gradients. The optimization problem is strictly convex, and is guaranteed to converge with arbitrary initialization. The method we propose is easy to use, as only two weighting parameters of the regularization terms are set manually to tune the energy distribution of the ground rolls and reflective signals. We demonstrate effectiveness of the proposed method with two field data tests. Compared with the traditional high-pass filtering method and two improved methods, the method we propose attenuates more ground rolls and eliminates less reflective signals, and increases the lateral coherence of the restored reflective signals at the same time.