Seismic waveform inversion best practices: Regional, global and exploration test cases

Ryan Modrak, Jeroen Tromp

Research output: Contribution to journalArticlepeer-review

75 Scopus citations


Reaching the global minimum of a waveformmisfit function requires careful choices about the nonlinear optimization, preconditioning and regularization methods underlying an inversion. Because waveform inversion problems are susceptible to erratic convergence associated with strong nonlinearity, one or two test cases are not enough to reliably inform such decisions.We identify best practices, instead, using four seismic near-surface problems, one regional problem and two global problems. To make meaningful quantitative comparisons between methods, we carry out hundreds of inversions, varying one aspect of the implementation at a time. Comparing nonlinear optimization algorithms, we find that limited-memory BFGS provides computational savings over nonlinear conjugate gradient methods in a wide range of test cases. Comparing preconditioners, we show that a new diagonal scaling derived from the adjoint of the forward operator provides better performance than two conventional preconditioning schemes. Comparing regularization strategies, we find that projection, convolution, Tikhonov regularization and total variation regularization are effective in different contexts. Besides questions of one strategy or another, reliability and efficiency in waveform inversion depend on close numerical attention and care. Implementation details involving the line search and restart conditions have a strong effect on computational cost, regardless of the chosen nonlinear optimization algorithm.

Original languageEnglish (US)
Pages (from-to)1864-1889
Number of pages26
JournalGeophysical Journal International
Issue number3
StatePublished - Sep 1 2016

All Science Journal Classification (ASJC) codes

  • Geophysics
  • Geochemistry and Petrology


  • Computational seismology
  • Inverse theory
  • Numerical approximations and analysis


Dive into the research topics of 'Seismic waveform inversion best practices: Regional, global and exploration test cases'. Together they form a unique fingerprint.

Cite this