Elastic interferometry can be used to retrieve only the surface waves propagating between two re- ceivers, in addition to the full-wavefield pseudo- source records reconstructed by the method. This can be accomplished by both correlation and decon- volution interferometry. Here, we present three dis- tinct approaches for isolating ground-roll using in- terferometry, and for its subsequent adaptive sub- traction from the elastic full-wavefield response. We illustrate our discussion with examples for both ho- mogeneous and highly laterally heterogeneous near- surface models.
The proper representation of the surface-wave re- sponse is a major issue for the processing of onshore seismic data, both in terms of noise attenuation and in characterizing near-surface velocity fields. The exploration-scale interferometric reconstruction and suppression of ground-roll was pioneered by Halliday et al. (2007), and later also treated by van Wijk et al. (2007) and Xue and Schuster (2007). Apart from being useful in suppressing coherent noise, surface- waves retrieved by interferometry could in in prin- ciple be used to infer near-surface properties (e.g., van Wijk et al., 2007; Calderón-MacÍas et al., 2008). In this paper, we extend the methodology originally proposed by Halliday et al. (2007), discuss the use of deconvolution (Vasconcelos and Snieder, 2008a,b) for surface-wave interferometry and propose other al- ternatives for the subtraction of surface waves. We illustrate our ideas with synthetic data from models with different degrees of near-surface complexity. Surface-wave interferometry Interferometry by correlation. Following Wapenaar and Fokkema (2006), elastic interferometry can be accomplished by cross-correlations.
In our examples, we use the models in Figures 2a and 2b. While the deeper subsurface properties of both models are equal, these models differ in that the near-surface properties are either laterally homo- geneous (Figure 2a), or present strong lateral vari- ations (Figure 2b). When modeling data for either model, a line of sources is placed horizontally at the surface with a source spacing of 4 m. We modeled the responses of both vertical and in-plane horizontal point forces. Although we conducted our analysis for all components and source types, here we show only the results pertaining to the vertical response due to vertical point-forces. The data were modeled by a staggered-grid elastic finite difference routine. Figure 3 shows examples of correlation and deconvo- lution gathers for a given pair of receivers. These gathers portray the integrands such as in equa- tions 1, 3 and 4 (i.e., Figures 3a, 3c and 3b, respec- tively). Aimed at reconstructing all possible arrivals in the pseudo-shot, Figures 3a and 3c illustrate all three of the cases schematically represented in Fig- ure 1. The contribution of the sources in Figure 1a can be seen in Figures 3a and 3c for x <0.3 km and x >0.8 km. Their contribution can seen as the strong-amplitude flat events that give rise to surface- wave energy in the pseudo-shots. The body-wave contributions (Figure 1b) can be identified in Fig- ures 3a and 3c as "V"-shaped arrivals at x =0.3 km or by characteristic "?" -like shapes at x =0.8 km.