Perturbations: Astronomical and Geophysical Applications is the third installment of a series of four self-contained English translations of the classic and definitive treatment of rigid body motion.
ICGEM International Center for Global Gravity Field Models
The Theory of the Top was originally presented by Felix Klein as an lecture at Gottingen University that was broadened in scope and clarified as a result of collaboration with Arnold Sommerfeld. Graduate students and researchers interested in theoretical and applied mechanics will find this a thorough and insightful account. Help Centre. Track My Order. My Wishlist Sign In Join. Nagem Translator , Guido Sandri Translator. Be the first to write a review. Add to Wishlist. Ships in 15 business days.
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The Theory of the Top Volume III
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It is shown in Fig. The aim of our analysis is to assess the influence of the local conditioning of structural constraints on inversion through comparison with the non-conditioned case, all other things remaining constant. Prior to examination of the inverted models, we analyse geophysical data misfit after inversion. This enables us to ensure that the inversion results we compare produce, in our case, similar gravity anomalies.
Our study of inverted models focuses on results obtained through usage of non-conditioned Fig. In addition to departures from the prior model, variations between the two cases are studied by visual comparison of Figs. Our interpretation of inversion results is complemented by metrics quantifying the differences between models. We give particular attention to model cells where the probability of mafic greenstone is larger than zero.
For these cells, we classify lithologies by identifying cells with a density contrast corresponding to mafic greenstone.
This similarity illustrates that, as in many other studies, most changes related to holistic data integration in geophysical inversion occur primarily in model space, hence reducing the effect of non-uniqueness Abtahi et al. All voxels are coloured as a function of density contrast.
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Qualitatively, comparison of Fig. This suggests that local regularization conditioning allows inversion to update the model preferentially in geologically uncertain areas. In turn, differences with the prior model in more geologically certain areas are reduced compared to the non-conditioned case. This effect of conditioning is corroborated by Fig. This also translates into a higher difference between model updates of the two cases in Fig. In addition, we observe that local conditioning produces stronger density contrasts in Fig.
Furthermore, structures in the inverted model are easier to identify when local conditioning is used. More specifically, as shown by Fig. The recovered greenstone belts are shown in Fig. In Fig.
Note that it is larger in Fig. As discussed in the next subsection, these differences have a signification impact on the interpretation of inversion results and are important to understand the influence of local conditioning on inversion. This shows that locally conditioned regularization does not enforce changes in the inverted model in all places where geological uncertainty is high, as uncertainty is only a reflection of potential errors.
This also confirms that geophysical data are the main driver of the model updates in geologically uncertain areas. Instead of smooth departures from the prior model to match geophysical data regardless of geological considerations, local regularization constraints allow inversion to account for the probabilistic geological modelling of the area and for geological uncertainty. It can therefore provide results that conform better to known geology.
In consequence, by confronting a probabilistic geological model encapsulating all MCUE realizations with geophysical measurements in an inversion scheme favouring model updates in the most geologically uncertain areas, inversion complements probabilistic geological modelling in that it guides and refines the interpretation of other geoscientific data in the area. Geophysical inversion using geological uncertainty information Fig.
We have introduced a new integration scheme for the inversion of gravity data that utilizes a measure of geological uncertainty to calculate locally conditioned gradient regularization constraints. This approach enables the integration of probabilistic geological modeling in geophysical inversion in the absence of petrophysical information sufficient to the calculation of petrophysical constraints. It uses geophysical measurements to optimize the inverse problem by updating the physical property model preferably in geologically uncertain parts of the studied area during what we called uncertainty-guided inversion.
This therefore partly mitigates the non-uniqueness of the inversion through the addition of constraints encouraging inversion to produce models that account for geological uncertainty across the entire inverted volume. We have demonstrated that it can be used collaboratively with geological modelling efficiently through field application in the Yerrida Basin. Inversion results show that our integration methodology has the capability to refine the recovered physical property model and interpretations in portions of the model where geological uncertainty is high.
Another advantage of the proposed technique is that it is time- and cost-effective as our workflow utilizes the PGM resulting from standalone probabilistic geological modelling and requires the same parameterization as non-conditioned inversion.