By Renata Dmowska (Eds.)
The severely acclaimed serialized evaluation magazine for over 50 years, Advances in Geophysics is a hugely revered book within the box of geophysics. due to the fact that 1952, every one quantity has been eagerly awaited, usually consulted, and praised by way of researchers and reviewers alike. Now in its 52nd quantity, it includes a lot fabric nonetheless correct today--truly an important book for researchers in all fields of geophysics.
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Additional resources for Advances in Geophysics
From the numerical (computational) point of view the main purpose of introducing the a priori information is regularization of the inversion procedure. Consequently, the regularized inverse problem can now be safely 48 DE¸BSKI linearized around the a priori model, and the a posteriori errors can be reliably estimated by the covariance matrix. The use of the probabilistic approach in cases like this does not bring essentially new advantages with respect to the linearized algebraic method. The only possible advantage is the possibility of verifying the influence of nonlinearity and a priori information on the solution.
The right-hand panels in Figs. 5–12 show the PDFs describing observational data. Finally, the left-hand panels show the marginal, a posteriori PDFs which are obtained by integrating pos(m, d) over d. 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.
Following the previous discussion, the standard solution to the inverse problem consists in inspecting the a posteriori PDF m(m) and involves three steps. First, the joint PDF pos(m, d) is constructed from available information. This step is accomplished by choosing the PDFs describing observational, forward modeling and a priori informa tion and joining them. In the next step, the marginal a posteriori PDF m(m) is con structed by integration of pos (m, d) over d. The final (main) stage of the probabilistic inversion consists of an inspection of m(m).