Fast imaging with surface-related multiples by sparse inversion

Abstract

In marine exploration seismology, surface-related multiples are usually treated as noise mainly because subsequent processing steps, such as migration velocity analysis and imaging, require multiple-free data. Failure to remove these wavefield components from the data may lead to erroneous estimates for migration velocity or result in strong coherent artifacts that interfere with the imaged reflectors. However, multiples can carry complementary information compared to primaries, as they interact with the free surface and are therefore exposed more to the subsurface. Recent work has shown that when processed correctly multiples can improve seismic illumination. Given a sufficiently accurate background velocity model and an estimate for the source signature, we propose a new and computationally efficient two-way wave-equation based linearized inversion procedure that produces accurate images of the subsurface from the total upgoing wavefield including surface-related multiples. Modelling of the surface-related multiples in the proposed method derives from the well-known surface-related multiple elimination method. We incur a minimal overhead from incorporating the multiples by having the wave-equation solver carry out 2 Tu and Herrmann the multiple predictions via the inclusion of an areal source instead of expensive dense matrix-matrix multiplications. By using subsampling techniques, we obtain high-quality true-amplitude least-squares migrated images at computational costs of roughly a single reverse-time migration with all the data. These images are virtually free of coherent artifacts from multiples. Proper inversion of the multiples would be computationally infeasible without using these techniques that significantly brings down the cost. By promoting sparsity in the curvelet domain and using rerandomization, out method gains improved robustness to errors in the background velocity model, and errors incurred in the linearization of the wave-equation with respect to the model. We demonstrate the superior performance of the proposed method compared to the conventional reverse-time migration using realistic synthetic examples.

Target-enclosed seismic imaging

“…In this paper, least-squares inversion is implemented by the LSQR algorithm (Paige and Saunders, 1982). Alternative solvers can also be used, for instance, solvers that promote sparsity of the reference Green's functions in an appropriate transform domain (Tu and Herrmann, 2015). The latter strategy can be beneficial in case of low signal-to-noise levels and incomplete data (Lin and Herrmann, 2016).…”

Fast least-squares imaging with surface-related multiples: Application to a North Sea data set

“…(3) We remove cross talk between multiples by promoting curvelet-domain sparsity in the model space. (4) Finally, we reduce the number of wave-equation solves to approximately the same number of a single RTM using all shots (Tu and Herrmann, 2015).…”

“…To demonstrate the possible advantages of our joint imaging (i.e., using both primaries and multiples), we apply this method (Tu and Herrmann, 2015) to a North Sea field data set. In particular, we are interested in specific benefits of imaging primaries and multiples together instead of separately and in how inversion suppresses the interferences associated with multiples.…”

“…In addition, the proposed formalism uses wave-equation solvers to carry out the multidimensional convolutions implicitly (Tu and Herrmann, 2015), which can lead to considerable computational savings. However, as in REPSI, our approach is based on an iterative inversion procedure that requires multiple linearized Born scatterings and migrations, which can be prohibitively expensive for large models.…”

“…To obtain a reasonable estimate for this total upgoing wavefield, the direct waves and the downgoing wavefield at the surface (i.e., receiver ghosts) need to be removed, and the upgoing wavefield needs to be extrapolated from the receiver level to the free surface (Verschuur et al, 1992). The source-side ghosts, on the other hand, should be left intact so that we mimic a dipole source, as required by the theory (Verschuur et al, 1992;Tu and Herrmann, 2015).…”