FD-injection-based elastic wavefield separation for open and closed configurations

An important step in the processing of seismic data that are recorded at the free surface is the isolation of the primary incident wavefield from the total recorded wavefield (which is contaminated with the immediate reflections off the free surface). We present a 3-D wavefield reconstruction technique, based on numerical wavefield injection along a closed boundary, that allows us to isolate this primary wavefield from measurements at the free surface. The technique consists of injecting only the three-component particle velocity recordings acquired at the free surface into a numerical wavefield simulation, and additionally requires information about the medium properties. The result of our proposed procedure is the separation of elastic waves into their first-order incident and reflected constituents, even when the recording or injection surface has sharp corners. With the use of synthetic data it is shown that the method achieves close to numerically exact wavefield separation, provided that the true elastic model in the interior is used. In practice, the parameters for a homogeneous elastic model can be determined efficiently from the surface data itself using an optimization scheme. Finally, the wavefield separation technique is successfully applied to experimental data, with particle velocity recordings acquired along five faces of a cubic granite rock volume. In addition to characterizing materials in laboratories, the presented technique has applications in numerical modelling and in so-called immersive experimentation, where the incident field is required to immerse an elastic object in an arbitrary larger, virtual elastic environment.