Coherent noise generated by surface waves or ground roll within a heterogeneous near surface is a major problem in land seismic data. Array forming based on single-sensor recordings might reduce such noise more robustly than conventional hardwired arrays. We use the minimum-variance distortionless-response (MVDR) beamformer to remove (aliased) surface-wave energy from single-sensor data. This beamformer is data adaptive and robust when the presumed and actual desired signals are mismatched. We compute the intertrace covariance for the desired signal, and then for the total signal (desired signal+noise) to obtain optimal weights. We use the raw data of only one array for the covariance of the total signal, and the wavenumber-filtered version of a full seismic single-sensor record for the covariance of the desired signal. In the determination of optimal weights, a parameter that controls the robustness of the beamformer against an arbitrary desired signal mismatch has to be chosen so that the results are optimal. This is similar to stabilization in deconvolution problems. This parameter needs to be smaller than the largest eigenvalue provided by the singular value decomposition of the presumed desired signal covariance. We compare results of MVDR beamforming with standard array forming on single-sensor synthetic and field seismic data. We apply 2D and 3D beamforming and show prestack and poststack results. MVDR beamformers are superior to conventional hardwired arrays for all examples.
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