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Inversion Scheme (inversion + scheme)
Selected AbstractsJoint full-waveform analysis of off-ground zero-offset ground penetrating radar and electromagnetic induction synthetic data for estimating soil electrical propertiesGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2010D. Moghadas SUMMARY A joint analysis of full-waveform information content in ground penetrating radar (GPR) and electromagnetic induction (EMI) synthetic data was investigated to reconstruct the electrical properties of multilayered media. The GPR and EMI systems operate in zero-offset, off-ground mode and are designed using vector network analyser technology. The inverse problem is formulated in the least-squares sense. We compared four approaches for GPR and EMI data fusion. The two first techniques consisted of defining a single objective function, applying different weighting methods. As a first approach, we weighted the EMI and GPR data using the inverse of the data variance. The ideal point method was also employed as a second weighting scenario. The third approach is the naive Bayesian method and the fourth technique corresponds to GPR,EMI and EMI,GPR sequential inversions. Synthetic GPR and EMI data were generated for the particular case of a two-layered medium. Analysis of the objective function response surfaces from the two first approaches demonstrated the benefit of combining the two sources of information. However, due to the variations of the GPR and EMI model sensitivities with respect to the medium electrical properties, the formulation of an optimal objective function based on the weighting methods is not straightforward. While the Bayesian method relies on assumptions with respect to the statistical distribution of the parameters, it may constitute a relevant alternative for GPR and EMI data fusion. Sequential inversions of different configurations for a two layered medium show that in the case of high conductivity or permittivity for the first layer, the inversion scheme can not fully retrieve the soil hydrogeophysical parameters. But in the case of low permittivity and conductivity for the first layer, GPR,EMI inversion provides proper estimation of values compared to the EMI,GPR inversion. [source] Full waveform inversion of seismic waves reflected in a stratified porous mediumGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2010Louis De Barros SUMMARY In reservoir geophysics applications, seismic imaging techniques are expected to provide as much information as possible on fluid-filled reservoir rocks. Since seismograms are, to some degree, sensitive to the mechanical parameters and fluid properties of porous media, inversion methods can be devised to directly estimate these quantities from the waveforms obtained in seismic reflection experiments. An inversion algorithm that uses a generalized least-squares, quasi-Newton approach is described to determine the porosity, permeability, interstitial fluid properties and mechanical parameters of porous media. The proposed algorithm proceeds by iteratively minimizing a misfit function between observed data and synthetic wavefields computed with the Biot theory. Simple models consisting of plane-layered, fluid-saturated and poro-elastic media are considered to demonstrate the concept and evaluate the performance of such a full waveform inversion scheme. Numerical experiments show that, when applied to synthetic data, the inversion procedure can accurately reconstruct the vertical distribution of a single model parameter, if all other parameters are perfectly known. However, the coupling between some of the model parameters does not permit the reconstruction of several model parameters at the same time. To get around this problem, we consider composite parameters defined from the original model properties and from a priori information, such as the fluid saturation rate or the lithology, to reduce the number of unknowns. Another possibility is to apply this inversion algorithm to time-lapse surveys carried out for fluid substitution problems, such as CO2 injection, since in this case only a few parameters may vary as a function of time. We define a two-step differential inversion approach which allows us to reconstruct the fluid saturation rate in reservoir layers, even though the medium properties are poorly known. [source] Energy Group optimization for forward and inverse problems in nuclear engineering: application to downwell-logging problemsGEOPHYSICAL PROSPECTING, Issue 2 2006Elsa Aristodemou ABSTRACT Simulating radiation transport of neutral particles (neutrons and ,-ray photons) within subsurface formations has been an area of research in the nuclear well-logging community since the 1960s, with many researchers exploiting existing computational tools already available within the nuclear reactor community. Deterministic codes became a popular tool, with the radiation transport equation being solved using a discretization of phase-space of the problem (energy, angle, space and time). The energy discretization in such codes is based on the multigroup approximation, or equivalently the discrete finite-difference energy approximation. One of the uncertainties, therefore, of simulating radiation transport problems, has become the multigroup energy structure. The nuclear reactor community has tackled the problem by optimizing existing nuclear cross-sectional libraries using a variety of group-collapsing codes, whilst the nuclear well-logging community has relied, until now, on libraries used in the nuclear reactor community. However, although the utilization of such libraries has been extremely useful in the past, it has also become clear that a larger number of energy groups were available than was necessary for the well-logging problems. It was obvious, therefore, that a multigroup energy structure specific to the needs of the nuclear well-logging community needed to be established. This would have the benefit of reducing computational time (the ultimate aim of this work) for both the stochastic and deterministic calculations since computational time increases with the number of energy groups. We, therefore, present in this study two methodologies that enable the optimization of any multigroup neutron,, energy structure. Although we test our theoretical approaches on nuclear well-logging synthetic data, the methodologies can be applied to other radiation transport problems that use the multigroup energy approximation. The first approach considers the effect of collapsing the neutron groups by solving the forward transport problem directly using the deterministic code EVENT, and obtaining neutron and ,-ray fluxes deterministically for the different group-collapsing options. The best collapsing option is chosen as the one which minimizes the effect on the ,-ray spectrum. During this methodology, parallel processing is implemented to reduce computational times. The second approach uses the uncollapsed output from neural network simulations in order to estimate the new, collapsed fluxes for the different collapsing cases. Subsequently, an inversion technique is used which calculates the properties of the subsurface, based on the collapsed fluxes. The best collapsing option is chosen as the one that predicts the subsurface properties with a minimal error. The fundamental difference between the two methodologies relates to their effect on the generated ,-rays. The first methodology takes the generation of ,-rays fully into account by solving the transport equation directly. The second methodology assumes that the reduction of the neutron groups has no effect on the ,-ray fluxes. It does, however, utilize an inversion scheme to predict the subsurface properties reliably, and it looks at the effect of collapsing the neutron groups on these predictions. Although the second procedure is favoured because of (a) the speed with which a solution can be obtained and (b) the application of an inversion scheme, its results need to be validated against a physically more stringent methodology. A comparison of the two methodologies is therefore given. [source] Reconstruction of an atmospheric tracer source using the principle of maximum entropy.THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 610 2005I: Theory Abstract Over recent years, tracing back sources of chemical species dispersed through the atmosphere has been of considerable importance, with an emphasis on increasing the precision of the source resolution. This need stems from many problems: being able to estimate the emissions of pollutants; spotting the source of radionuclides; evaluating diffuse gas fluxes; etc. We study the high-resolution retrieval on a continental scale of the source of a passive atmospheric tracer, given a set of concentration measurements. In the first of this two-part paper, we lay out and develop theoretical grounds for the reconstruction. Our approach is based on the principle of maximum entropy on the mean. It offers a general framework in which the information input prior to the inversion is used in a flexible and controlled way. The inversion is shown to be equivalent to the minimization of an optimal cost function, expressed in the dual space of observations. Examples of such cost functions are given for different priors of interest to the retrieval of an atmospheric tracer. In this respect, variational assimilation (4D-Var), as well as projection techniques, are obtained as biproducts of the method. The framework is enlarged to incorporate noisy data in the inversion scheme. Part II of this paper is devoted to the application and testing of these methods. Copyright © 2005 Royal Meteorological Society [source] A Bayesian approach to inverse modelling of stratigraphy, part 1: methodBASIN RESEARCH, Issue 1 2009Karl Charvin ABSTRACT The inference of ancient environmental conditions from their preserved response in the sedimentary record still remains an outstanding issue in stratigraphy. Since the 1970s, conceptual stratigraphic models (e.g. sequence stratigraphy) based on the underlying assumption that accommodation space is the critical control on stratigraphic architecture have been widely used. Although these methods considered more recently other possible parameters such as sediment supply and transport efficiency, they still lack in taking into account the full range of possible parameters, processes, and their complex interactions that control stratigraphic architecture. In this contribution, we present a new quantitative method for the inference of key environmental parameters (specifically sediment supply and relative sea level) that control stratigraphy. The approach combines a fully non-linear inversion scheme with a ,process,response' forward model of stratigraphy. We formulate the inverse problem using a Bayesian framework in order to sample the full range of possible solutions and explicitly build in prior geological knowledge. Our methodology combines Reversible Jump Markov chain Monte Carlo and Simulated Tempering algorithms which are able to deal with variable-dimensional inverse problems and multi-modal posterior probability distributions, respectively. The inverse scheme has been linked to a forward stratigraphic model, BARSIM (developed by Joep Storms, University of Delft), which simulates shallow-marine wave/storm-dominated systems over geological timescales. This link requires the construction of a likelihood function to quantify the agreement between simulated and observed data of different types (e.g. sediment age and thickness, grain size distributions). The technique has been tested and validated with synthetic data, in which all the parameters are specified to produce a ,perfect' simulation, although we add noise to these synthetic data for subsequent testing of the inverse modelling approach. These tests addressed convergence and computational-overhead issues, and highlight the robustness of the inverse scheme, which is able to assess the full range of uncertainties on the inferred environmental parameters and facies distributions. [source] Inversion and interpretation of two-dimensional geoelectrical measurements for detecting permafrost in mountainous regionsPERMAFROST AND PERIGLACIAL PROCESSES, Issue 4 2003Christian Hauck Abstract The use of tomographic geoelectrical measurements for the detection of ground ice occurrences in mountainous regions is evaluated. Because isolated ground ice occurrences in a warming climate may be subject to rapid thawing, they present a future hazard in the context of thawing-permafrost-induced landslides and rockfalls. Isolated permafrost occurrences are difficult to detect with commonly used one-dimensional sounding techniques, as plane-layer approximations for the inversion are often invalid. Therefore, recently developed two-dimensional tomographic inversion schemes are used to yield realistic near-surface geological models. The method is applied to various types of permafrost occurrences in the European Alps. The influence of topography, measurement geometry and different inversion parameters are discussed. In addition, complimentary seismic survey results are used to exclude the possibility of air-filled cavities, which exhibit similarly high resistivities as ground ice occurrences. The results show a large variety of influencing parameters which have to be considered in resistivity inversion and interpretation. Copyright © 2003 John Wiley & Sons, Ltd. [source] Agradient velocity, vortical motion and gravity waves in a rotating shallow-water modelTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 601 2004Georgi G. Sutyrin Abstract A new approach to modelling slow vortical motion and fast inertia-gravity waves is suggested within the rotating shallow-water primitive equations with arbitrary topography. The velocity is exactly expressed as a sum of the gradient wind, described by the Bernoulli function, B, and the remaining agradient part, proportional to the velocity tendency. Then the equation for inverse potential vorticity, Q, as well as momentum equations for agradient velocity include the same source of intrinsic flow evolution expressed as a single term J(B, Q), where J is the Jacobian operator (for any steady state J(B,Q)=0). Two components of agradient velocity are responsible for the fast inertia-gravity wave propagation similar to the traditionally used divergence and ageostrophic vorticity. This approach allows for the construction of balance relations for vortical dynamics and potential vorticity inversion schemes even for moderate Rossby and Froude numbers assuming the characteristic value of |J(B,Q)|=, to be small. The components of agradient velocity are used as the fast variables slaved to potential vorticity that allows for diagnostic estimates of the velocity tendency, the direct potential vorticity inversion with the accuracy of ,2 and the corresponding potential vorticity-conserving agradient velocity balance model (AVBM). The ultimate limitations of constructing the balance are revealed in the form of the ellipticity condition for balanced tendency of the Bernoulli function which incorporates both known criteria of the formal stability: the gradient wind modified by the characteristic vortical Rossby wave phase speed should be subcritical. The accuracy of the AVBM is illustrated by considering the linear normal modes and coastal Kelvin waves in the f -plane channel with topography. Copyright © 2004 Royal Meteorological Society [source] | ||||||||||