Fast Robust Waveform inversion
This software release includes a demonstration of the parallel waveform inversion framework in Matlab that has been developed at SLIM. In particular, it includes implementations of waveform inversion using robust penalties and source estimation [1,2] in conjunction with an optimization strategy that works with only a few sources at each iteration [3-6]. Updated to conform to the new waveform inversion software framework [8].
Author: Tristan van Leeuwen, Aleksandr Aravkin Date : March, 2012
Updated : Curt Da Silva Date : May, 2016
Contents
Downloading & Dependencies
The code can be found in the SLIM sofware release under /applications/WaveformInversion/2DRobustBatching.
The code has been tested with Matlab R2015b 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
- _algorithms/CommonFreqModeling - baseline acoustic modeling components
- _solvers/QuasiNewton - quasi newton optimization algorithms
- 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/2DRobustBatching/. 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.
Functions
The functions specific to this package can be found in the mbin directory.
- twonorms - the two-norm and its derivative.
- hubers - the Huber misfit and its derivative.
- hybrid - the hybrid misfit and its derivative.
- students - the Students t misfit and its derivative.
- mylbfgs - standard L-BFGS with Wolfe linesearch
- minfunc_batch - stochastic optimization with bound constraints
More detailed descriptions and some basic tests are described here.
Examples and results
Scripts to reproduce the famous Camembert example [7], as well as results from several papers can be found in the scripts directory. The results are shown here.
References
[1] A.Y. Aravkin, T. van Leeuwen and F.J. Herrmann - Source estimation for frequency-domain FWI with robust penalties, EAGE Expanded abstracts 2012.
[2] A.Y. Aravkin, T. van Leeuwen, and F.J. Herrmann, 2011. Robust full-waveform inversion using the Student's t-distribution. SEG Technical Program Expanded Abstracts 30, 2669-2673.
[3] M.P. Friedlander, M.Schmidt, 2011. Hybrid Deterministic-Stochastic Methods for Data Fitting. arXiv:1104.2373.
[4] T. van Leeuwen, F.J. Herrmann, M. Schmidt, M.P. Friedlander, 2011. A hybrid stochastic-deterministic optimization method for waveform inversion. EAGE Expanded Abstracts.
[5] T. van Leeuwen and F.J. Herrmann - Fast Waveform inversion without source-encoding, Geophysical Prospecting, submitted
[6] A.Y. Aravkin, M.P. Friedlander, F.J. Herrmann, and T. van Leeuwen, 2011. Robust inversion, dimensionality reduction, and randomized sampling. Mathematical Programming, accepted.
[7] O. Gauthier, J. Virieux, and A. Tarantola. Two-dimensional nonlinear inversion of seismic waveforms: Numerical results. Geophysics 51, 1387-1403 (1986)
[8] C. Da Silva, F.J. Herrmann - A unified 2D/3D software environment for large scale time-harmonic full waveform inversion.
Acknowledgements
The synthetic Compass model was provided by the BG-GROUP, see also the disclaimer.