Abstract
Many nonlinear inverse problems can be cast into the form of determining the minimum of a misfit function between observations and theoretical predictions, subject to a regularisation condition on the form of the model. For large scale problems, linearised techniques involving inversion of a Hessian matrix rapidly become difficult to handle as the size of the problem increases. It can therefore be computationally advantageous to use techniques which can achieve convergence without the inversion of large matrices. In this class are descent algorithms or modifications thereto, the simplest approach is to use a single direction of search at each step (usually related to the gradient of the misfit function). The efficiency of the search for a minimum can be improved by the introduction of a second search direction at each stage, e.g. the rate of change of the gradient, or the gradient of the regularisation term.
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References
Aki, K. and Richards P.G., 1980. Quantitative Seismology, W.H. Freeman, San Francisco.
Backus, G.E. and Gilbert, F., 1970. Uniqueness in the inversion of inaccurate gross earth data, Phil. Trans. R. Soc. Lond., 266A, 123–192.
Bryan, R. and Skilling, J., 1980. Deconvolution by maximum entropy, as illustrated by application to jet of M87, Mon. Not. R. Astr. Soc., 191, 69–76.
Chapman, C.H. and Orcutt, J., 1985. Least-squares fitting of marine seismic refraction data, Geophys. J. R. Astr. Soc, 82, 339–374.
Harding, A J., 1984. Slowness Methods in Seismology, Ph.D. Thesis, University of Cambridge.
Kennett, B.L.N., 1978. Some aspects of nonlinearity in inversion, Geophys. J. R. Astr. Soc, 55, 373–391.
Menke, W., 1984. Geophysical Data Analysis: Discrete Inverse Theory, Academic Press, New York.
Nolet, G., 1981. Linearised inversion of teleseismic data, in The solution of the inverse problem in geophysical interpretation, 9–37, ed. R. Cassinis, Plenum Press, New York.
Nolet, G., 1985. Solving or resolving inadequate and noisy tomographic systems, J. Comp. Phys., 61, 463–482.
Nolet, G., van Trier, J. and Huisman, R., 1986. A formalism for nonlinear inversion of seismic surface waves, Geophys. Res. Letters, 13, 26–29.
Sambridge, M. and Kennett, B.L.N., 1986. A novel method of hypocentre location, Geophys. J. R. Astr. Soc, 87, 679–697.
Williamson, P.R., 1986. Tomographic inversion of travel time data in reflection seismology, Ph.D. Thesis, University of Cambridge.
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© 1988 D. Reidel Publishing Company
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Kennett, B.L.N., Williamson, P.R. (1988). Subspace methods for large-scale nonlinear inversion. In: Vlaar, N.J., Nolet, G., Wortel, M.J.R., Cloetingh, S.A.P.L. (eds) Mathematical Geophysics. Modern Approaches in Geophysics, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2857-2_7
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DOI: https://doi.org/10.1007/978-94-009-2857-2_7
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