By Renata Dmowska (Eds.)
The significantly acclaimed serialized evaluation magazine for over 50 years, Advances in Geophysics is a hugely revered e-book within the box of geophysics. on the grounds that 1952, each one quantity has been eagerly awaited, often consulted, and praised by means of researchers and reviewers alike. Now in its 52nd quantity, it comprises a lot fabric nonetheless proper today--truly a vital ebook for researchers in all fields of geophysics.
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Approximate Forward Modeling Previous theoretical predictions were supposed to be exact. The example shown in Fig. 8 corresponds to a weakly nonlinear and imprecise forward problem. In this example, theoretical and observational errors are superimposed by an inversion procedure and together determine the a posteriori errors. This type of inverse problem is probably the most common in geophysics and can be solved efficiently by any optimiza tion technique. The a posteriori error analysis should, if possible, include the inspection of the corresponding PDFs as the shape of the confidence region may significantly differ from a simple ellipsoid described by the covariance matrix.
The joint PDF in the central panel which, according to Eq. (59), is proportional to t(m, d) is nonvanishing only along the “regression line” due to the form t(m, d). However, for the clarity of the plot it has been plotted as a “wider” distribution. No a priori information was used and the corresponding PDF is represented by the homogeneous (noninformative) distribution a (m) = const. DE¸BSKI Probability 46 de vi E M�D nc e M D FIG. 11. Example of a complex, ambiguous theory or a few different forward modeling schemes.
From a mathematical point of view, the symmetric treatment of m and d is a consequence of the commutativity of the AND operator. The way in which σpos(Á) is used to solve the inverse problem in hand depends on the task and can be classified into one of the three following categories. ● The most general way of using σpos(Á) is its direct examination—sampling. This provides the most comprehensive insight into the problem under study and the relation between the data and the model parameters. This approach allows to analyze problems which cannot be treated by any other approaches like, for example, compatibility of the a priori information with the experimental data, adequateness of the theory in description of the data, and so on.
Advances in Geophysics by Renata Dmowska (Eds.)