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

Felix J. Herrmann; Xiang Li; Aleksandr Y. Aravkin; Tristan van Leeuwen

doi:10.1117/12.893861

27 September 2011 A modified, sparsity-promoting, Gauss-Newton algorithm for seismic waveform inversion

Felix J. Herrmann, Xiang Li, Aleksandr Y. Aravkin, Tristan van Leeuwen

Proceedings Volume 8138, Wavelets and Sparsity XIV; 81380V (2011) https://doi.org/10.1117/12.893861
Event: SPIE Optical Engineering + Applications, 2011, San Diego, California, United States

Abstract

Images obtained from seismic data are used by the oil and gas industry for geophysical exploration. Cutting-edge methods for transforming the data into interpretable images are moving away from linear approximations and high-frequency asymptotics towards Full Waveform Inversion (FWI), a nonlinear data-fitting procedure based on full data modeling using the wave-equation. The size of the problem, the nonlinearity of the forward model, and ill-posedness of the formulation all contribute to a pressing need for fast algorithms and novel regularization techniques to speed up and improve inversion results. In this paper, we design a modified Gauss-Newton algorithm to solve the PDE-constrained optimization problem using ideas from stochastic optimization and compressive sensing. More specifically, we replace the Gauss-Newton subproblems by randomly subsampled, ℓ₁ regularized subproblems. This allows us us significantly reduce the computational cost of calculating the updates and exploit the compressibility of wavefields in Curvelets. We explain the relationships and connections between the new method and stochastic optimization and compressive sensing (CS), and demonstrate the efficacy of the new method on a large-scale synthetic seismic example.

Citation Download Citation

Felix J. Herrmann, Xiang Li, Aleksandr Y. Aravkin, and Tristan van Leeuwen "A modified, sparsity-promoting, Gauss-Newton algorithm for seismic waveform inversion", Proc. SPIE 8138, Wavelets and Sparsity XIV, 81380V (27 September 2011); https://doi.org/10.1117/12.893861

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available