By Renata Dmowska (Eds.)
The significantly acclaimed serialized assessment magazine for over 50 years, Advances in Geophysics is a hugely revered e-book within the box of geophysics. for the reason that 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 comprises a lot fabric nonetheless appropriate today--truly a necessary booklet for researchers in all fields of geophysics.
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Extra info for Advances in Geophysics
43) or Eq. 3. A Posteriori PDF Apply the described mathematical formalism to construct the a posteriori PDF which will describe the joint a priori, theoretical, and observational information. Such a 28 DE¸BSKI distribution provides the most comprehensive answer to any inverse problem, as it contains all the available information (Tarantola, 1987; De¸bski, 1997a). In particular, all the numerical estimators can be drawn from it by calculation of the appropriate statistical moments (Van Kampen, 1992; Lehmann and Casella, 1998).
In particular, it contains information about measurement and theoretical uncertainties and how they are mapped onto the model space. Let us consider this point in more depth. Assuming that d are experimental errors described by the PDF distribution d() = d obs ρ (d – dtrue) and that theoretical (modeling) errors m = dtrue – G(m) are described by the statistics m(m), and finally that d and m are independent of d and m, respectively, the likelihood function reads Z � � ð84Þ LðmÞ ¼ d dobs À d m ðd À GðmÞÞdd: D If the forward modeling does not depend on d, which is usually the case, Eq.
The importance sampling technique relies on the introduction of an additional, easy-to-sample importance distribution q(x) (so-called proposal distribution), which includes the support of (x) so that Eq. 120 can be rewritten as Z ¼ F ðxÞωðxÞqðxÞdx; F ð124Þ where w(x) (x)/q(x).