Material used at the 10 November 2008 Meeting
Igel, H., Sigloch, K., Fichtner, A., The seismic inverse problem (pdf [378 KB]
). This file contains the links to the pdf s listed below.
Igel, H. et al, Seismic inverse problem: introduction (Powerpoint) (pdf [1.438 KB]
)
Igel, H., probabilistic inversion (Powerpoint) (pdf [1.335 KB]
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Sigloch, K., Finite frequency tomography(pdf [2.211 KB]
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Fichtner, A., Waveform tomography (pdf)
The seismic inverse problem in the adjoint formulation:
Inversion of Seismic Reflection Data in the Acoustic Approximation. Albert Tarantola, Geophysics, Vol. 49, No. 8, p 1259-1266, 1984. (pdf). One of the first papers on the application of adjoint methods to seismic wave propagation.
Fichtner, A., H.-P. Bunge, and H. Igel (2006), The adjoint method in seismology: I - Theory, Physics of The Earth and Planetary Interiors, 157(1-2), 86-104, doi:10.1016/j.pepi.2006.03.016. (pdf). A mathematically more general formulation of the seismic waveform inversion problem.
Fichtner, A., P. Bunge, and H. Igel (2006), The adjoint method in seismology: II - Applications: traveltimes and sensitivity functionals, Phys. Earth Planet. Int., 157(1-2), 105-123, doi:10.1016/j.pepi.2006.03.018. (pdf) Paper with illustration of sensitivity kernels for seismic travel times
Fichtner, Andreas, Brian L. N. Kennett, Heiner Igel, Hans-Peter Bunge, DOI:Theoretical background for continental- and global-scale full-waveform inversion in the time–frequency domain (p 665-685) 10.1111/j.1365-246X.2008.03923.x (pdf) Some thoughts and applications of a new misfit criterion based on a time-frequency representation of waveform misfits, separation of travel-time effects and amplitude effects.
Probabilistic description of the inverse problem, uncertainties, visualization:
Popper, Bayes and the inverse problem, by Albert Tarantola, Nature Physics, Vol. 2, August 2006, p 492-494, 2006. (pdf) A qualitative description of the probabilistic approach to geophysical inverse problems stressing the necessity to sample a probability distribution descriptive of prior knowledge.
How do we understand and visualize uncertainty ? Sambridge, M. Beghein, C. Simons, F. and Snieder, R., The Leading Edge, 25,542-546, 2006. (pdf) Description of the problem faced when inverting seismograms and attempting to visualize resolution, and uncertainties in multidimensional model space.
Monte Carlo Sampling of Solutions to Inverse Problems, by Klaus Mosegaard and Albert Tarantola. Journal of Geophysical Research , Vol. 10, No B7, p 12,431-12,447, 1995. (pdf) Basic ideas on how to efficiently sample prior and posterior distributions of probability density functions describing solutions to geophysical inverse problems.
Probabilistic Approach to Inverse Problems, by Klaus Mosegaard and Albert Tarantola, International Handbook of Earthquake & Engineering Seismology, Part A., p 237-265, Academic Press, 2002. (pdf) More extensive than the previous publication, very instructive examples, and introduction of the concept of volumetric probabilities.
(Geo-) Scientfic relevance of seismic inversion:
Sigloch, Karin, Nadine McQuarrie, and Guust Nolet (2008), Two-stage subduction history under North America inferred from multiple-frequency tomography, Nature Geoscience, doi:10.1038/ngeo231. (pdf) An example of the relevance of tomography for questions on the dynamics of Earth’s interior.
More papers on parametrization issues, probabilistic inversion etc. can be found on the pages by Malcolm Sambridge and Albert Tarantola:
http://rses.anu.edu.au/~malcolm/index.php?p=pubs http://www.ipgp.jussieu.fr/~tarantola/
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