By Mrinal Sen and Paul L. Stoffa (Eds.)
One of many significant ambitions of geophysical inversion is to discover earth types that designate the geophysical observations. therefore the department of arithmetic referred to as optimization has discovered major use in lots of geophysical applications.Both neighborhood and international optimization equipment are utilized in the estimation of fabric homes from geophysical information. because the name of the ebook indicates, the purpose of this ebook is to explain the applying of numerous lately constructed international optimization the way to geophysical difficulties. • the well-known linear and gradient dependent optimization tools were summarized with a view to clarify their benefits and barriers• the idea of simulated annealing and genetic algorithms were defined in adequate element for the readers to appreciate the underlying primary rules upon which those algorithms are dependent• The algorithms were defined utilizing basic circulation charts (the algorithms are normal and will be utilized to a large choice of problemsStudents, researchers and practitioners might be in a position to layout useful algorithms to resolve their particular geophysical inversion difficulties. The ebook is almost self-contained in order that there aren't any must haves, with the exception of a primary mathematical history that features a easy figuring out of linear algebra and calculus.
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Extra resources for Global Optimization Methods in Geophysical Inversion
However, as we will see in Chapter 6, the problem of migration velocity estimation can also be posed as an inverse problem. , 1989]. , 1989] medium. In a medium in which the elastic properties vary only with depth, the elastic wave equation can be transformed into the frequencywavenumber (c0,k) or into the frequency-ray parameter (c0,p) domain by the application of Fourier-Hankel transforms. This transformation reduces the wave equation into an ordinary differential equation in depth, z, that can be solved in either the (c0,k)or (c0,p) domain by propagator matrix methods.
1989] medium. In a medium in which the elastic properties vary only with depth, the elastic wave equation can be transformed into the frequencywavenumber (c0,k) or into the frequency-ray parameter (c0,p) domain by the application of Fourier-Hankel transforms. This transformation reduces the wave equation into an ordinary differential equation in depth, z, that can be solved in either the (c0,k)or (c0,p) domain by propagator matrix methods. Forward modeling methods such as Thompson-Haskell or the reflectivity method [Fuchs and Miiller, 1971; Kennett, 1983] are based on such principles.
This is the situation when we have as many data as the number of model parameters (ND=NM) such that these data contain information on all the model parameters. Such a problem is called an evendetermined problem. , there are fewer data than the number of model parameters. This would usually be the case with geophysical inversion if we attempt to estimate earth model parameters that are continuous (or infinite) from a finite set of measurements. The problem can be reduced to an e v e n - d e t e r m i n e d or even an o v e r d e t e r m i n e d case by discretization which reduces the number of model parameters.
Global Optimization Methods in Geophysical Inversion by Mrinal Sen and Paul L. Stoffa (Eds.)