# Modified gauss-newton full-waveform inversion

This application is available only in the software release for members of SINBAD consortium.

This software release includes an parallel framework in Matlab for modified gauss-newton (GN) full-waveform inversion [1,2], which based on the ideas from compressive-sensing and stochastic optimization, where the GN updates are computed from random subsets of the data via curvelet-domain sparsity-promotion. There are two different subset sampling strategies are considered in this package: randomized source encoding, and drawing sequential shots firing at random source locations from marine data with missing near and far offsets. In both cases, we obtain excellent inversion results compared to conventional methods at reduced computational costs. There is also a small example based on Camembert example which can allow users to test the algorithm in a short time

Author: Xiang Li Date : March, 2012

## Contents

## Downloading & Dependencies

The code can be found in the SLIM sofware release under `/applications/WaveformInversion/2DModGaussNewton`.

The code has been tested with *Matlab R2012b* and requires the Parallel Computing Toolbox.

This code uses the following packages, also found in the `tools` part of the SLIM software release.

*utilities/SPOT*- object oriented framework for matrix-free linear algebra.*utilities/pSPOT*- parallel extension of SPOT.*algorithms/2DFreqModeling*- 2D constant-density acoustic modeling*operators/misc*- Misc. operators such as interpolation, smoothing and splines*functions/misc*- Misc. functions.

## Running & Parallelism

All the examples and results are produced by the scripts found in this software release under `applications/WaveformInversion/2DModGaussNewton/`. Start matlab from that directory or run `startup` in that directory to add the appropriate paths.

To run the scripts follow the instrictions in the README file enclosed with the code. The scripts can be run in serial mode but parallel mode is advised.

Read more about SLIM's approach to parallel computing in Matlab.

## Examples and results

Scripts to reproduce the famous Camembert example [7], as well as results from sevaral papers can be foundin the `scripts` directory. The results are shown here.

## References

[1] Felix J. Herrmann, Xiang Li, Aleksandr Y. Aravkin, and Tristan van Leeuwen, A modified, sparsity promoting, Gauss-Newton algorithm for seismic waveform inversion, in Proc. SPIE, 2011, vol. 2011.

[2] Xiang Li, Aleksandr Y. Aravkin, Tristan van Leeuwen, and Felix J. Herrmann, Fast randomized full-waveform inversion with compressive sensing. 2011. Geophysics, accepted.

[3] O. Gauthier, J. Virieux, and A. Tarantola. Two-dimensional nonlinear inversion of seismic waveforms: Numerical results. Geophysics 51, 1387-1403 (1986)

## Acknowledgements

The synthetic Compass model was provided by the BG-GROUP, see also the disclaimer.