By Renata Dmowska (Eds.)
The severely acclaimed serialized evaluation magazine for over 50 years, Advances in Geophysics is a hugely revered ebook within the box of geophysics. due to the fact 1952, each one quantity has been eagerly awaited, often consulted, and praised by way of researchers and reviewers alike. Now in its 52nd quantity, it includes a lot fabric nonetheless correct today--truly a necessary book for researchers in all fields of geophysics.
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Extra resources for Advances in Geophysics
2. The Nonlinear Forward Problem In this example (Fig. 6) the theoretical predictions are also assumed to be exact so the t(m, d) distribution is represented by Dirac’s function. However, this time the theoretical relation d = G(m) is strongly nonlinear. The a posteriori PDF which is the marginal of j(m, d) now has two maxima, which makes the solution nonunique in terms of the “optimum” model (the model best fitting to data). Such nonuniqueness is a very typical feature of inverse problems. Note that an attempt to use the covariance matrix to describe the a posteriori errors is meaningless now.
On the other hand, complex theories with a larger number of “free parameters” can better fit a large range of data leading to “lower probability” on average. Secondly, as it has been noted by Gallagher et al. (2009), the a priori PDFs will naturally penalize more complex models as the a priori PDF will tend to have smaller maximum values. 7. Illustration of Probabilistic Inference Solving the inverse problem defined as an optimization task is quite obvious and intuitive. Unfortunately, this is not the case with the probabilistic approach.
This integration can be visualized as the projection (stacking) of pos(m, d) onto the M axis. The side panels contain, if necessary, plots of the a priori PDF apr(m) plotted as a dashed line. If the a priori PDF plot is missing, then apr(Á) = const. is assumed, which means that no a priori information is used for the inversion. The units and scales of M and D and the probability distribution values are arbitrary and have been omitted. Following the previous discussion, the standard solution to the inverse problem consists in inspecting the a posteriori PDF m(m) and involves three steps.