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Since the initial model is not the result of an inversion but an assembly of independent models, a consistent prior p 0 m was not available and thus had to be designed. For simplicity, we set p 0 m to be uniform. This common choice prevents the appearance of artifacts that are unlikely to be resolved. In all cases, we did not include correlations between physical model parameters. Within the lower mantle, the CSEM is practically isotropic, though this has not been enforced explicitly.
A more comprehensive gallery is shown in the supporting information Figures S5 to S Since a geologic interpretation is not among the objectives of this work, these are mostly intended to provide an impression of the multiscale nature of the CSEM. The SV velocity distribution is marked by the outline of the continents and the smooth lateral variations of the initial crustal model Meier et al.
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Instead, it is designed as a framework for successive refinements on all scales and for the consistent use of prior knowledge. As such, it primarily tries to respond to current data and computing challenges, without claiming to be the only possible solution. The updating scheme from section 2. Its generality makes it translatable to other domains, for example, the inversion of multiscale gravity, electromagnetic, or Global Positioning System GPS data. The current need to simplify suggests future improvements, especially in uncertainty quantification.
Though the framework enables the incorporation of prior knowledge already at the level of the initial model, we decided not to do so, because previously constructed models usually have different parameterizations or lack sufficiently complete uncertainty information. Thus, the ability of the CSEM to take advantage of prior knowledge is to be understood in the sense of an update using information from all previous updates. With the exception of the global update, the regional updates included in the current CSEM are sufficiently independent in coverage and frequency content to avoid the need for reiterations or the application of the scheme from section 2.
In this context, we note that the iterative refinement of the CSEM, including potential reiterations, constitutes an implementation of a stochastic gradient method.
Since convergence of stochastic descent has been shown theoretically and empirically e. To facilitate the participation of an increasing number of collaborators, the addition of refinements requires further automation. While multiscale tomography has been applied for at least two decades e. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries other than missing content should be directed to the corresponding author for the article. Volume 45 , Issue 9. If you do not receive an email within 10 minutes, your email address may not be registered, and you may need to create a new Wiley Online Library account.
If the address matches an existing account you will receive an email with instructions to retrieve your username. Open access. Geophysical Research Letters Volume 45, Issue 9. Research Letter Open Access. Andreas Fichtner Corresponding Author E-mail address: andreas. Fichtner, E-mail address: andreas.
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Tools Request permission Export citation Add to favorites Track citation. Share Give access Share full text access. Share full text access. Please review our Terms and Conditions of Use and check box below to share full-text version of article. Figure 1 Open in figure viewer PowerPoint. Technical implementation and updating of the CSEM. Each update is treated as a new item in an ordered library, keeping the parametrization used during its construction. Different updates may be parametrized differently, that is, have different types of basis functions. Figure 2 Open in figure viewer PowerPoint.
Data coverage proxy. Gray scale represents the minimum period, T , of the waveform data used within a refinement region. The total number of distinct sources earthquakes plus virtual sources from noise correlations is Figure 3 Open in figure viewer PowerPoint. MM: Menderes Massif; b b. This is a preview of subscription content, log in to check access. Aanonsen, S.
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