Download Advances in Geophysics by Renata Dmowska (Eds.) PDF

By Renata Dmowska (Eds.)

The significantly acclaimed serialized assessment magazine for over 50 years, Advances in Geophysics is a hugely revered booklet within the box of geophysics. on account that 1952, every 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 suitable today--truly a necessary ebook for researchers in all fields of geophysics.

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A problem appears, however, when we try to find a way to make a more objective choice of the structural model than only an a priori guess. In fact such questions as, for example, whether the 1D model is appropriate or a more complex 2D or even 3D models are required are quite important for a proper interpretation of the obtained results. , 2002) according to which the simplest models are preferable should be applied, but actually to obtain more quantitative estimates, a systematic method of evaluation and quantitative comparison of different theories—different forward modeling relations—is required.

As the forward problem does not depend on m in some ranges, even accurate data cannot resolve m. In order to be used in situations like this, an algebraic approach has to be regularized because the GTÁ G matrix is singular. Also, the optimization approach does not provide a reliable result—the obtained “optimum” model is usually very unstable with respect to changes of optimiza­ tion parameters. Only inspection of the a posteriori distribution can reliably detect situations like this, especially in cases when the forward modeling operator does not have a null space but only a “region of insensitivity” to m.

53) provides the most general formula for the a posteriori PDF distribution, it can be further simplified in most practical applications, as the following conditions are usually met: 1. m and d are intrinsically independent and the homogeneous PDF factorizes μðm; dÞ ¼ μm ðmÞμd ðdÞ; ð56Þ 2. a priori information about m and d is independent so σapr(Á) can be represented as the product m d σ apr ðm; mapr ; d; dapr Þ ¼ σ apr ðm; mapr Þσ apr ðd; dapr Þ; ð57Þ 3. if m and d are independent physical parameters, then the results of measurement of d are statistically independent of m (Tarantola, 1987; Cook, 1994) and σ exp ðm; d; dobs Þ ¼ μm ðmÞσ exp ðd; dobs Þ: ð58Þ After taking these postulates into account, the a posteriori PDF is simplified and reads obs apr apr d pos ðm; dÞ ¼ m apr ðm; m Þapr ðd; d Þexp ðd; d Þth ðm; dÞ ðm dÞd ðdÞ ; ð59Þ where the dependence of pos(m, d) on mapr, dapr, and dobs has been omitted for the sake of clarity.

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