Velocity estimation via registration-guided least-squares inversion

This paper introduces an iterative scheme for acoustic model inversion where the notion of proximity of two traces is not the usual least-squares distance, but instead involves registration as in image processing. Observed data are matched to predicted waveforms via piecewise-polynomial warpings, obtained by solving a nonconvex optimization problem in a multiscale fashion from low to high frequencies. This multiscale process requires defining low-frequency augmented signals in order to seed the frequency sweep at zero frequency. Custom adjoint sources are then defined from the warped waveforms. The proposed velocity updates are obtained as the migration of these adjoint sources, and cannot be interpreted as the negative gradient of any given objective function. The new method, referred to as RGLS, is successfully applied to a few scenarios of model velocity estimation in the transmission setting. We show that the new method can converge to the correct model in situations where conventional least-squares inversion suffers from cycle-skipping and converges to a spurious model.Comment: 20 pages, 13 figures, 1 tabl

Bubble number in a caviting flow

Cavitation is a general phenomenon of the fluid flows with obstacles. It appears in the cooling conduits of the fast nuclear engines. A model of this phenomenon using the theory of Laplace and a common non-convex energy for the liquid and vapour bulks is proposed. This model makes it possible to determine a higher limit of the density of bubbles (a number of bubbles per unit of volume in the flow). The maximum intensity of cavitation is associated with the mechanical and thermal characteristics of the fluid flow.Comment: 9 page

Matrix probing: a randomized preconditioner for the wave-equation Hessian

This paper considers the problem of approximating the inverse of the wave-equation Hessian, also called normal operator, in seismology and other types of wave-based imaging. An expansion scheme for the pseudodifferential symbol of the inverse Hessian is set up. The coefficients in this expansion are found via least-squares fitting from a certain number of applications of the normal operator on adequate randomized trial functions built in curvelet space. It is found that the number of parameters that can be fitted increases with the amount of information present in the trial functions, with high probability. Once an approximate inverse Hessian is available, application to an image of the model can be done in very low complexity. Numerical experiments show that randomized operator fitting offers a compelling preconditioner for the linearized seismic inversion problem.Comment: 21 pages, 6 figure

The failure mode of correlation focusing for model velocity estimation

We analyze the correlation focusing objective functional introduced by van Leeuwen and Mulder to avoid the cycle-skipping problem in full waveform inversion. While some encouraging numerical experiments were reported in the transmission setting, we explain why the method cannot be expected to work for general reflection data. We characterize the form that the adjoint source needs to take for model velocity updates to generate a time delay or a time advance. We show that the adjoint source of correlation focusing takes this desired form in the case of a single primary reflection, but not otherwise. Ultimately, failure owes to the specific form of the normalization present in the correlation focusing objective

Sen, Sraffa and the revival of classical political economy

Copyright © 2012 Taylor & Francis.In his new book The Idea of Justice, Amartya Sen argues that political theory should not consist only in the characterisation of ideal situations of perfect justice. In so doing, Sen is making, within the context of political theory, a similar argument to another he also made in economic theory, when crtiticising what he called the ‘rational fool’ of mainstream economics. Sen criticised the ideal and fictitious agent of mainstream economics, while advocating for a return to an integrated view of ethics and economics, which characterised many classical political economists who inspired Sen's theory of justice, from Adam Smith to Karl Marx. I will examine Sen's revival of classical political economy, and argue that a revival of classical political economy, which was undertaken earlier by Piero Sraffa, has much potential for bringing a more plural and realist perspective to economics

Implicative and conjunctive fuzzy rules: A tool for reasoning from knowledge and examples

Fuzzy rule-based systems have been mainly used as a convenient tool for synthesizing control laws from data. Recently, in a knowledge representation-oriented perspective, a typology of fuzzy rules has been laid bare, by emphasizing the distinction between implicative and conjunctive fuzzy rules. The former describe pieces of generic knowledge either tainted with uncertainty or tolerant to similarity, while the latter encode examples-originated information expressing either mere possibilities or how typical situations can be extrapolated. The different types of fuzzy rules are first contrasted, and their representation discussed in the framework of possibility theory. Then, the paper studies the conjoint use of fuzzy rules expressing knowledge (as fuzzy constraints which restrict the possible states of the world), or gathering examples (which testify the possibility of appearance of some states). Coherence and inference issues are briefly addressed

Analogical proportions and the factorization of information in distributive lattices

International audienceAnalogical proportions are statements involving four enti- ties, of the form 'A is to B as C is to D'. They play an important role in analogical reasoning. Their formalization has received much attention from different researchers in the last decade, in particular in a proposi- tional logic setting. Analogical proportions have also been algebraically defined in terms of factorization, as a generalization of geometric nu- merical proportions (that equate ratios). In this paper, we define and study analogical proportions in the general setting of lattices, and more particularly of distributive lattices. The decomposition of analogical pro- portions in canonical proportions is discussed in details, as well as the resolution of analogical proportion equations, which plays a crucial role in reasoning. The case of Boolean lattices, which reflects the logical mod- eling, and the case corresponding to entities described in terms of gradual properties, are especially considered for illustration purposes

Registration-guided least-squares waveform inversion

Full waveform inversion with frequency sweeping cannot start from zero frequency because of the lack of low-frequency data, requiring a good starting model. We study a di fferent iterative scheme where the notion of proximity of two traces is not the usual least-squares distance, but instead involves registration as in image processing. In order to create transported data, we introduce a nonconvex optimization problem and solve it in a multiscale fashion from low to high frequencies. This process requires defining low-frequency augmented signals in order to seed the frequency sweep at zero frequency. Successful registrations of noisy data, and application of the new method to model velocity estimation are demonstrated. In a crosshole seismic inversion example (transmission setting), we show that the new method decreases the model velocity error while conventional least-squares inversion converges to a spurious model

Experimental Evidence of Mixture Segregation by Particle Size Distribution

International audienceIn this study, we discuss experimental segregation results obtained for two industrial cases, namely, ammonium perchlorate and a polymeric resin. These results show a segregation effect due to particle size distribution rather than particle size itself. We used a heap-pouring device as a tester, for which a visual knowledge of the segregation state was observed. The analysis of segregation is based on various coefficients of variations related to the size fractions or particle size distribution's global characteristics, indicating heterogeneities in the heaps formed. Both cases indicate that wide particle size distributions, as opposed to narrow ones, are limiting segregation risks. This collective, and maybe astonishing, effect is extremely marked for the cases studied, and demonstrates again the mesoscopic nature of granular media