Elastic imaging with exact wavefield extrapolation for application to ocean-bottom 4C seismic data

Abstract

A central component of imaging methods is receiver-side wavefield backpropagation or extrapolation in which the wavefield from a physical source scattered at any point in the subsurface is estimated from data recorded by receivers located near or at the Earth's surface. Elastic reverse-time migration usually accomplishes wavefield extrapolation by simultaneous reversed-time 'injection' of the particle displacements (or velocities) recorded at each receiver location into a wavefield modeling code. Here, we formulate an exact integral expression based on reciprocity theory that uses a combination of velocity-stress recordings and quadrupole-dipole backpropagating sources, rather than the commonly used approximate formula involving only particle velocity data and dipole backpropagating sources. The latter approximation results in two types of nonphysical waves in the scattered wavefield estimate: First, each arrival contained in the data is injected upward and downward rather than unidirectionally as in the true time-reversed experiment; second, all injected energy emits compressional and shear propagating modes in the model simulation (e.g., if a recorded P-wave is injected, both P and S propagating waves result). These artifacts vanish if the exact wavefield extrapolation integral is used. Finally, we show that such a formula is suitable for extrapolation of ocean-bottom 4C data: Due to the fluid-solid boundary conditions at the seabed, the data recorded in standard surveys are sufficient to perform backpropagation using the exact equations. Synthetic examples provide numerical evidence of the importance of correcting such errors.

Finite-difference modelling of wavefield constituents

“…Furthermore, these intuitive results are not entirely surprising as Masson et al (2014) have established the equivalence between the FD-injection methodology and time-reversal mirrors for tomographic imaging. The results presented by are therefore conceptually equivalent with similar observations presented by Blanch (2012), Ravasi & Curtis (2013) and Vasconcelos (2013) where wavefields are introduced by injecting recordings as 'multiple point sources' using representation theorems (Fokkema & van den Berg 1993).…”

“…Recently it has been recognized that proper injection of multicomponent seismic data on FD grids propagates recorded super-imposed up-and downgoing wavefields with their correct propagation directions (e.g. Blanch 2012;Ravasi & Curtis 2013;Vasconcelos 2013;. However, the full implication of these results for FD modelling has not been realized so far.…”

Elastic P- and S-wave autofocus imaging with primaries and internal multiples

“…Kirchhoff methods, for example, use ray-tracing to perform the extrapolation (Schneider, 1978;Kuo and Dai, 1984;Bleistein, 1987), while elastic reverse-time migration (RTM) (Baysal et al, 1983;Cunha, 1992;Chang and McMechan, 1994;Yan and Sava, 2008;Ravasi and Curtis, 2013) This means that in both imaging methods, we approximate the down-going field in equation 29 with…”

“…The tensorial approach is equivalent to dynamically correct elastic RTM (Ravasi and Curtis, 2013), where the extrapolation is performed using velocity and stress recordings and force and deformation sources.…”

“…These images are of fundamental importance to aid our understanding of the limitations of the single-component approximation. Since they require stress recordings they are currently only practically applicable where stress can be related to strain and where that strain can be measured, for example when using ocean-bottom cables (e.g., Ravasi and Curtis, 2013). However, they also show the potential improvements that could be realized if such stress or strain measurements were to become more generally available.…”