Full‐waveform inversion from compressively recovered model updates

Abstract

SUMMARYFull-waveform inversion relies on the collection of large multiexperiment data volumes in combination with a sophisticated back-end to create high-fidelity inversion results. While improvements in acquisition and inversion have been extremely successful, the current trend of incessantly pushing for higher quality models in increasingly complicated regions of the Earth reveals fundamental shortcomings in our ability to handle increasing problem size numerically. Two main culprits can be identified. First, there is the so-called "curse of dimensionality" exemplified by Nyquist's sampling criterion, which puts disproportionate strain on current acquisition and processing systems as the size and desired resolution increases. Secondly, there is the recent "departure from Moore's law" that forces us to lower our expectations to compute ourselves out of this. In this paper, we address this situation by randomized dimensionality reduction, which we adapt from the field of compressive sensing. In this approach, we combine deliberate randomized subsampling with structure-exploiting transform-domain sparsity promotion. Our approach is successful because it reduces the size of seismic data volumes without loss of information. With this reduction, we compute Newton-like updates at the cost of roughly one gradient update for the fully-sampled wavefield.

Efficient least‐squares imaging with sparsity promotion and compressive sensing

“…Ill-conditioning, in conjunction with extreme high costs of applying imaging operators, challenges iterative solution methods for least-squares imaging problems. To address this issue, we combine ideas from stochastic optimization (Bertsekas and Tsitsiklis 1996;Shapiro, Dentcheva and Ruszczynski 2009;Nemirovski et al 2009;Haber, Chung and Herrmann 2010) and compressive sensing (CS in short throughout this paper, Candès, Romberg and Tao 2006;Donoho 2006;Mallat 2009), yielding a formulation where we invert the large linearized system by solving a sequence of much smaller subproblems that act on source-encoded 'supershots' (Li and Herrmann 2010).…”

Attenuating crosstalk noise with simultaneous source full waveform inversion★

“…This approach is related to stochastic optimization (van Leeuwen, Aravkin and Herrmann 2011). Alternatively, Li and Herrmann (2010) proposed a sparsity promoting formulation in the curvelet domain.…”

A modified, sparsity-promoting, Gauss-Newton algorithm for seismic waveform inversion

“…In earlier developments in seismic acquisition and imaging, several authors have proposed reducing the computational cost of FWI by randomly combining sources Krebs et al (2009); Moghaddam and Herrmann (2010); Boonyasiriwat and Schuster (2010); Li and Herrmann (2010); Haber et al (2010). We follow the same approach, but focus the exposition on the Gauss-Newton subproblem, setting the stage for further modifications.…”