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

Abstract

Summary 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 optimisation 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 characterising 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.

Elastic immersive wave experimentation

“…This wavefield injection radiates the outgoing (incident) constituents of the recorded data outward and their ingoing (reflected) constituents inward away from the injection surface 𝑆 sep (the former with opposite polarity), resulting in the incident wavefield being retrieved outside the surface 𝑆 sep with opposite polarity. However, wavefield separation by injection along a closed surface is limited by an important observation: only the primary incident wavefield can be reconstructed and propagated away from the wavefield injection surface 𝑆 sep (Thomsen et al, 2021). This can be understood from the fact that the separated ingoing waves that propagate across the interior of the numerical domain destructively interfere with the separated outgoing waves, injected with opposite polarity, along the other sides of the numerical wavefield injection surface 𝑆 sep , thereby preventing the reconstruction of the higher-order outgoing waves at the surface 𝑆 sep [e.g., ray path 3 in Figs.…”

“…In this paper, we employ a finite-difference (FD) simulation that is second-order accurate in time and space (Virieux, 1986). This FD method is implemented on staggered velocity and stress grids, and the wavefield injection along surface 𝑆 sep is implemented with a method of multiple point sources (MPS) (Li et al, 2022a;Thomsen et al, 2021). In the FD simulation, the grid spacing is chosen to be 25 points (25 • ∆𝑥) per dominant S wavelength (>20 is a rule of thumb), and the time step ∆𝑡 satisfies the Courant-Friedrichs-Lewy (CFL) criterion (Igel, 2017).…”

“…The experimental setup used to study 3D elastic wave propagation in solids is shown in Fig. 3.4(a) (Thomsen et al, 2019;Thomsen et al, 2021;Masfara et al, 2020). A scanning laser Doppler vibrometer (LDV) is used to acquire the three-component particle velocity vector across all accessible surfaces of a target object (Blum et al, 2010;Pouet et al, 2012;Zaccherini et al, 2020), in this case a cubic granitic block.…”

“…However, for a closed-aperture recording geometry it was found that this injection-based wavefield decomposition does not isolate all outgoing energy present in the recorded data (Thomsen et al, 2021): only primary outgoing waves (wave energy that did not previously interact with the free-surface) are isolated. Furthermore, a practical limitation exists with this approach: the elastic model used in the FD simulation has to match the (unknown) physical experimental domain inside the wavefield injection surface 𝑆 sep exactly (Thomsen et al, 2021). As explained below, these limitations can be overcome using a straightforward strategy: prevent the synthetically reconstructed ingoing waves from propagating across the interior such that they do not reach the other sides of the injection surface.…”

“…This methodology works very well for data that are acquired on a single side of the experimental domain (Vasmel & Robertsson, 2016). However, for a closed-aperture recording geometry it was found that this injection-based wavefield decomposition does not isolate all outgoing energy present in the recorded data (Thomsen et al, 2021): only primary outgoing waves (wave energy that did not previously interact with the free-surface) are isolated. Furthermore, a practical limitation exists with this approach: the elastic model used in the FD simulation has to match the (unknown) physical experimental domain inside the wavefield injection surface 𝑆 sep exactly (Thomsen et al, 2021).…”