Wavefield separation using densely deployed three‐component single‐sensor groups in land surface‐seismic recordings

Abstract

Surface seismic data are usually acquired by placing receivers on the earth's free surface. This is exactly the surface at which all up‐coming wave energy is reflecting and converting into down‐going energy, so the wavefield recorded is the sum of up‐coming, down‐going reflected, and down‐going converted waves. In order to anaylze up‐coming (from the reservoir) energy only (e.g., for “true” amplitude analysis), it is necessary to separate and remove all down‐going waves from the recorded data. We present a new approach for wavefield separation of land surface‐seismic data based on receiver groups with densely deployed single‐sensor recordings. By converting vertical spatial derivatives to horizontal derivatives using the free‐surface condition, the methodology only requires locally dense measurements of the wavefield at the free surface to calculate all spatial derivatives of the wavefield. These can in turn be used to compute divergence (giving P‐wave potential) and curl (giving S‐wave potential) of the wavefield at the free surface. The effects of the free surface are removed through an up/down separation step using the elastodynamic representation theorem. This results in infinite spatial‐filter expressions that are appropriate for homogeneous media. The filter for P‐waves depends on both P‐ and S‐velocity at the receivers, whereas the S‐wave filters only depend on the S‐velocity. These velocities can be estimated using the techniques in the companion paper by Curtis and Robertsson in this issue. Spatially compact filters are chosen to approximate the analytical filter expressions. The filters are designed so that they can be applied within a densely deployed, spatially limited group of three‐component (3C) receivers. By assuming that the earth is locally homogeneous (no significant variations within the near‐surface region of the group), wavefield separation can be carried out also in areas with significant statics variations over the survey area. In particular, the simplest approximate expression for P‐waves consists of two terms. The first term corresponds to divergence in the presence of the free surface scaled by a material constant. The second term is a time derivative of the recorded vertical component scaled by a material constant. Hence, the first term is a correction that is added to the “traditional” P‐interpretation—the second term—which improves accuracy for incidence angles other than normal incidence. The proposed methodology is tested on synthetic data. By comparing “traditional” P‐sections to those obtained using the new methodology, we demonstrate that a significant improvement in amplitudes and phases of arrivals is obtained using the new methodology. By using the simplest possible filter which only involves first‐order derivatives in time and space, we obtained sufficiently accurate results up to incidence angles of around 30° away from normal incidence.