Anisotropic seismic inversion using a multigrid Monte Carlo approach

We propose a new approach for the inversion of anisotropic P-wave data based on Monte Carlo methods combined with a multigrid approach. Simulated annealing facilitates objective minimization of the functional characterizing the misfit between observed and predicted traveltimes, as controlled by the Thomsen anisotropy parameters (epsilon, delta). Cycling between finer and coarser grids enhances the computational efficiency of the inversion process, thus accelerating the convergence of the solution while acting as a regularization technique of the inverse problem. Multigrid perturbation samples the probability density function without the requirements for the user to adjust tuning parameters. This increases the probability that the preferred global, rather than a poor local, minimum is attained. Undertaking multigrid refinement and Monte Carlo search in parallel produces more robust convergence than does the initially more intuitive approach of completing them sequentially. We demonstrate the usefulness of the new multigrid Monte Carlo (MGMC) scheme by applying it to (a) synthetic, noise-contaminated data reflecting an isotropic subsurface of constant slowness, horizontally layered geologic media and discrete subsurface anomalies; and (b) a crosshole seismic data set acquired by previous authors at the Reskajeage test site in Cornwall, UK. Inverted distributions of slowness (s) and the Thomson anisotropy parameters (epsilon, delta) compare favourably with those obtained previously using a popular matrix-based method. Reconstruction of the Thomsen epsilon parameter is particularly robust compared to that of slowness and the Thomsen delta parameter, even in the face of complex subsurface anomalies. The Thomsen epsilon and delta parameters have enhanced sensitivities to bulk-fabric and fracture-based anisotropies in the TI medium at Reskajeage. Because reconstruction of slowness (s) is intimately linked to that epsilon and delta in the MGMC scheme, inverted images of phase velocity reflect the integrated effects of these two modes of anisotropy. The new MGMC technique thus promises to facilitate rapid inversion of crosshole P-wave data for seismic slownesses and the Thomsen anisotropy parameters, with minimal user input in the inversion process.

Convergence of the iterative algorithm for a general Hammerstein system identification

The convergence of the iterative identification algorithm for a general Hammerstein system has been an open problem for a long time. In this paper, it is shown that the convergence can be achieved by incorporating a regularization procedure on the nonlinearity in addition to a normalization step on the parameters.

Simultaneous optical and X-ray observations of flares and rotational modulation on the RS CVn binary HR 1099 (V711 Tau) from the MUSICOS 1998 campaign

We present simultaneous and continuous observations of the Halpha, Hbeta, He I D-3, Na I D-1,D-2 doublet and the Ca II H&K lines for the RS CVn system HR 1099. The spectroscopic observations were obtained during the MUSICOS 1998 campaign involving several observatories and instruments, both echelle and long-slit spectrographs. During this campaign, HR 1099 was observed almost continuously for more than 8 orbits of 2.(d)8. Two large optical flares were observed, both showing an increase in the emission of Halpha, Ca II H K, Hbeta and He I D-3 and a strong filling-in of the Na I D-1, D-2 doublet. Contemporary photometric observations were carried out with the robotic telescopes APT-80 of Catania and Phoenix-25 of Fairborn Observatories. Maps of the distribution of the spotted regions on the photosphere of the binary components were derived using the Maximum Entropy and Tikhonov photometric regularization criteria. Rotational modulation was observed in Halpha and He I D-3 in anti-correlation with the photometric light curves. Both flares occurred at the same binary phase (0.85), suggesting that these events took place in the same active region. Simultaneous X-ray observations, performed by ASM on board RXTE, show several flare-like events, some of which correlate well with the observed optical flares. Rotational modulation in the X-ray light curve has been detected with minimum flux when the less active G5 V star was in front. A possible periodicity in the X-ray flare-like events was also found.

Regularized Online Mixture of Gaussians for Background Subtraction

Mixture of Gaussians (MoG) modelling [13] is a popular approach to background subtraction in video sequences. Although the algorithm shows good empirical performance, it lacks theoretical justification. In this paper, we give a justification for it from an online stochastic expectation maximization (EM) viewpoint and extend it to a general framework of regularized online classification EM for MoG with guaranteed convergence. By choosing a special regularization function, l1 norm, we derived a new set of updating equations for l1 regularized online MoG. It is shown empirically that l1 regularized online MoG converge faster than the original online MoG .

Virtual metrology enabled early stage prediction for enhanced control of multi-stage fabrication processes

Semiconductor fabrication involves several sequential processing steps with the result that critical production variables are often affected by a superposition of affects over multiple steps. In this paper a Virtual Metrology (VM) system for early stage measurement of such variables is presented; the VM system seeks to express the contribution to the output variability that is due to a defined observable part of the production line. The outputs of the processed system may be used for process monitoring and control purposes. A second contribution of this work is the introduction of Elastic Nets, a regularization and variable selection technique for the modelling of highly-correlated datasets, as a technique for the development of VM models. Elastic Nets and the proposed VM system are illustrated using real data from a multi-stage etch process used in the fabrication of disk drive read/write heads. © 2013 IEEE.

Root Cause Analysis by a Combined Sparse Classification and Monte Carlo Approach

Classification methods with embedded feature selection capability are very appealing for the analysis of complex processes since they allow the analysis of root causes even when the number of input variables is high. In this work, we investigate the performance of three techniques for classification within a Monte Carlo strategy with the aim of root cause analysis. We consider the naive bayes classifier and the logistic regression model with two different implementations for controlling model complexity, namely, a LASSO-like implementation with a L1 norm regularization and a fully Bayesian implementation of the logistic model, the so called relevance vector machine. Several challenges can arise when estimating such models mainly linked to the characteristics of the data: a large number of input variables, high correlation among subsets of variables, the situation where the number of variables is higher than the number of available data points and the case of unbalanced datasets. Using an ecological and a semiconductor manufacturing dataset, we show advantages and drawbacks of each method, highlighting the superior performance in term of classification accuracy for the relevance vector machine with respect to the other classifiers. Moreover, we show how the combination of the proposed techniques and the Monte Carlo approach can be used to get more robust insights into the problem under analysis when faced with challenging modelling conditions.

Solutions of fourth-order parabolic equation modeling thin film growth

In this paper we study the well-posedness for a fourth-order parabolic equation modeling epitaxial thin film growth. Using Kato's Method [1], [2] and [3] we establish existence, uniqueness and regularity of the solution to the model, in suitable spaces, namelyC⁰([0,T];L^p(Ω)) where  with 1<α<2, n∈N and n≥2. We also show the global existence solution to the nonlinear parabolic equations for small initial data. Our main tools are L_p–L_q-estimates, regularization property of the linear part of e^−tΔ2 and successive approximations. Furthermore, we illustrate the qualitative behavior of the approximate solution through some numerical simulations. The approximate solutions exhibit some favorable absorption properties of the model, which highlight the stabilizing effect of our specific formulation of the source term associated with the upward hopping of atoms. Consequently, the solutions describe well some experimentally observed phenomena, which characterize the growth of thin film such as grain coarsening, island formation and thickness growth.

Time-lapse monitoring of climate effects on earthworks using surface waves

The UK’s transportation network is supported by critical geotechnical assets (cuttings/embankments/dams) that require sustainable, cost-effective management, while maintaining an appropriate service level to meet social, economic, and environmental needs. Recent effects of extreme weather on these geotechnical assets have highlighted their vulnerability to climate variations. We have assessed the potential of surface wave data to portray the climate-related variations in mechanical properties of a clay-filled railway embankment. Seismic data were acquired bimonthly from July 2013 to November 2014 along the crest of a heritage railway embankment in southwest England. For each acquisition, the collected data were first processed to obtain a set of Rayleigh-wave dispersion and attenuation curves, referenced to the same spatial locations. These data were then analyzed to identify a coherent trend in their spatial and temporal variability. The relevance of the observed temporal variations was also verified with respect to the experimental data uncertainties. Finally, the surface wave dispersion data sets were inverted to reconstruct a time-lapse model of S-wave velocity for the embankment structure, using a least-squares laterally constrained inversion scheme. A key point of the inversion process was constituted by the estimation of a suitable initial model and the selection of adequate levels of spatial regularization. The initial model and the strength of spatial smoothing were then kept constant throughout the processing of all available data sets to ensure homogeneity of the procedure and comparability among the obtained VS sections. A continuous and coherent temporal pattern of surface wave data, and consequently of the reconstructed VS models, was identified. This pattern is related to the seasonal distribution of precipitation and soil water content measured on site.

Time-lapse monitoring of fluid induced geophysical property variations within an unstable earthwork using P-wave refraction

A significant portion of the UK’s transportation system relies on a network of geotechnical earthworks (cuttings and embankments) that were constructed more than 100 years ago, whose stability is affected by the change in precipitation patterns experienced over the past few decades. The vulnerability of these structures requires a reliable, cost- and time-effective monitoring of their geomechanical condition. We have assessed the potential application of P-wave refraction for tracking the seasonal variations of seismic properties within an aged clay-filled railway embankment, located in southwest England. Seismic data were acquired repeatedly along the crest of the earthwork at regular time intervals, for a total period of 16 months. P-wave first-break times were picked from all available recorded traces, to obtain a set of hodocrones referenced to the same spatial locations, for various dates along the surveyed period of time. Traveltimes extracted from each acquisition were then compared to track the pattern of their temporal variability. The relevance of such variations over time was compared with the data experimental uncertainty. The multiple set of hodocrones was subsequently inverted using a tomographic approach, to retrieve a time-lapse model of VPVP for the embankment structure. To directly compare the reconstructed VPVP sections, identical initial models and spatial regularization were used for the inversion of all available data sets. A consistent temporal trend for P-wave traveltimes, and consequently for the reconstructed VPVP models, was identified. This pattern could be related to the seasonal distribution of precipitation and soil-water content measured on site.

Application of Volterra Equations to Solve Unit Commitment Problem of Optimised Energy Storage and Generation

Development of reliable methods for optimised energy storage and generation is one of the most imminent challenges in modern power systems. In this paper an adaptive approach to load leveling problem using novel dynamic models based on the Volterra integral equations of the first kind with piecewise continuous kernels. These integral equations efficiently solve such inverse problem taking into account both the time dependent efficiencies and the availability of generation/storage of each energy storage technology. In this analysis a direct numerical method is employed to find the least-cost dispatch of available storages. The proposed collocation type numerical method has second order accuracy and enjoys self-regularization properties, which is associated with confidence levels of system demand. This adaptive approach is suitable for energy storage optimisation in real time. The efficiency of the proposed methodology is demonstrated on the Single Electricity Market of Republic of Ireland and Northern Ireland.