Adaptive waveform inversion: theory

Conventional full-waveform seismic inversion attempts to find a model of the subsurface that is able to predict observed seismic waveforms exactly; it proceeds by minimizing the difference between the observed and predicted data directly, iterating in a series of linearized steps from an assumed starting model. If this starting model is too far removed from the true model, then this approach leads to a spurious model in which the predicted data are cycle skipped with respect to the observed data. Adaptive waveform inversion (AWI) provides a new form of full-waveform inversion (FWI) that appears to be immune to the problems otherwise generated by cycle skipping. In this method, least-squares convolutional filters are designed that transform the predicted data into the observed data. The inversion problem is formulated such that the subsurface model is iteratively updated to force these Wiener filters toward zero-lag delta functions. As that is achieved, the predicted data evolve toward the observed data and the assumed model evolves toward the true model. This new method is able to invert synthetic data successfully, beginning from starting models and under conditions for which conventional FWI fails entirely. AWI has a similar computational cost to conventional FWI per iteration, and it appears to converge at a similar rate. The principal advantages of this new method are that it allows waveform inversion to begin from less-accurate starting models, does not require the presence of low frequencies in the field data, and appears to provide a better balance between the influence of refracted and reflected arrivals upon the final-velocity model. The AWI is also able to invert successfully when the assumed source wavelet is severely in error

Linear hydrodynamics and viscoelasticity of nematic elastomers

We develop a continuum theory of linear viscoelastic response in oriented monodomain nematic elastomers. The expression for dissipation function is analogous to the Leslie-Ericksen version of anisotropic nematic viscosity; we propose the relations between the anisotropic rubber moduli and new viscous coefficients. A new dimensionless number is introduced, which describes the relative magnitude of viscous and rubber-elastic torques. In an elastic medium with an independently mobile internal degree of freedom, the nematic director with its own relaxation dynamics, the model shows a dramatic decrease in the dynamic modulus in certain deformation geometries. The degree to which the storage modulus does not altogether drop to zero is shown to be both dependent on frequency and to be proportional to the semi-softness, the non-ideality of a nematic network. We consider the most interesting geometry for the implementation of the theory, calculating the dynamic response to an imposed simple shear and making predictions for effective moduli and (exceptionally high) loss factors.Comment: Latex 2e or PDFlatex (4 EPS or JPG figures) - to appear in Euro.Phys.J.

Reflectivity of cholesteric liquid crystals with spatially varying pitch

Solids with spatially varying photonic structure offer gaps to light of a wider range of frequencies than do simple photonic systems. We solve numerically the field distribution in a solid cholesteric with a linearly varying inverse pitch (helical wavevector) using equations we derive for the general case. The simple idea that the position where the Bragg condition is locally satisfied is where reflection takes place is only true in part. Here, reflection is due to a region where the waves are forced to become evanescent, and the rate of variation of structure determines over which distance the waves decay and therefore how complete reflection is. The approximate local Bragg-de Vries schemes are shown to break down in detail at the edges of the gap, and an analytical estimate is given for the transmission coefficient.Comment: 8 pages, accepted by EPJ E, corrections for publication implemente

Creating a Common Market for Fraud and Corruption in the European Union: an Institutional Accident, or a Deliberate Strategy?

governance; agency theory; policy networks

Did the debt crisis or declining oil prices cause Mexico's investment collapse?

The author proposes and estimates a microeconomic investment model to determine the relative importance of three explanations for Mexico's investment decline in the early 1980s: the decline in oil prices; the termination of capital inflows; and the effects of debt overhang and uncertainty. He uses investment data for private industries between 1981 and 1985, which have yet to be used in addressing the question under discussion. The data indicate that the main microeconomic mechanism driving the decline in investment was a rise in the relative price of investment goods - especially the relative price of machinery (a traded good in Mexico). Moreover, the decline in trade (driven by falling world oil prices) explains much of the increase in this relative price. The decline in Mexico's international terms of trade was probably the most important ultimate cause of the increased relative cost of machinery, but the reversal in net capital inflows to Mexico probably also played a role in increasing this relative price. On this point, the evidence is not as clear. After controlling for these effects, the author finds little evidence that the effects of debt overhang and uncertainty had much to do with the investment decline. The author points out that investment in Texas and Louisiana (which were also riding the oil boom of 1973-81) also fell in 1981-86, and adverse commodity price shocks also affected many other heavily indebted countries. At the very least, commodity price shocks (such as Mexico's decline in oil prices) as a direct cause of declining investment levels in the 1980s have been insufficiently emphasized in the literature on the effects of the international debt crisis.Banks&Banking Reform,International Terrorism&Counterterrorism,Economic Theory&Research,Environmental Economics&Policies,Financial Intermediation

Uniaxial and biaxial soft deformations of nematic elastomers

We give a geometric interpretation of the soft elastic deformation modes of nematic elastomers, with explicit examples, for both uniaxial and biaxial nematic order. We show the importance of body rotations in this non-classical elasticity and how the invariance under rotations of the reference and target states gives soft elasticity (the Golubovic and Lubensky theorem). The role of rotations makes the Polar Decomposition Theorem vital for decomposing general deformations into body rotations and symmetric strains. The role of the square roots of tensors is discussed in this context and that of finding explicit forms for soft deformations (the approach of Olmsted).Comment: 10 pages, 10 figures, RevTex, AmsTe

Achieving Rapid Growth in the Transition Economies of Central Europe

This paper describes ways that the CEEs can speed their convergence with the EU by emulating the growth strategies of the very fast growing economies. In Section II, we introduce the VFGEs, and discuss some of the sources of their superior growth performance. In Section III, we demonstrate the role of key policy variables in the context of cross-country growth equations. In Section IV, we examine how the CEEs can emulate key aspects of the economic policies of the VFGEs, in order to raise their growth in the coming years.economic transition, Central Eastern Europe, economic growth