By Renata Dmowska (Eds.)
The severely acclaimed serialized evaluation magazine for over 50 years, Advances in Geophysics is a hugely revered e-book within the box of geophysics. on account that 1952, each one quantity has been eagerly awaited, usually consulted, and praised by way of researchers and reviewers alike. Now in its 52nd quantity, it comprises a lot fabric nonetheless appropriate today--truly a necessary e-book for researchers in all fields of geophysics.
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Extra resources for Advances in Geophysics
Inspection of the joint PDF in the M Â D space can now be used to evaluate the forward modeling relations. Alternatively, inspection of the evidence terms (see Eq. (70)) shown as bars on the right side can be used to select the best theory. 7. Using the probabilistic approach to solve such inverse problems makes sense only if the observational errors have unusual statistics. If they can be described by a Gaussianlike function, the algebraic solution method is the most appropriate approach (Menke, 1989; Parker, 1994).
45 Probability PROBABILISTIC INVERSE THEORY M D M�D FIG. 10. Example of a non-resolved parameter due to an inconsistency between data and theoretical predictions. 7. In the presented examples, inspection of the a posteriori PDF is achieved by plotting the appropriate functions. In real cases, however, when the number of parameters and data disables such an approach, the inspection is usually reduced to searching for the (global) maximum of the a posteriori PDF or plotting 1D or 2D marginal a posteriori PDFs if this is possible (Tarantola, 1987; De¸bski, 1997a).
A Posteriori PDF—Special Cases Now, let us discuss a few special examples of the a posteriori PDF. 1. No Data or No Forward Modeling Let us check first a situation when we have no experimental data, so � � exp d; dobs ¼ d ðdÞ: ð91Þ Then the integral in Eq. (64) evolves to a constant, independent of m, as the forward modeling always predicts some d for any m and consequently m m pos ðmÞ ¼ apr ðmÞ: ð92Þ The a posteriori PDF equals the a priori, as was to be expected since neither theoretical nor a priori information on d is available to constrain m with respect to the a priori knowledge expressed by m apr (m).
Advances in Geophysics by Renata Dmowska (Eds.)
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