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Model Parametrization (model + parametrization)

Distribution by Scientific Domains

Earth and Environmental Science	100%

Selected Abstracts

Joint inversion of multiple data types with the use of multiobjective optimization: problem formulation and application to the seismic anisotropy investigations

GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2007
E. Kozlovskaya
SUMMARY In geophysical studies the problem of joint inversion of multiple experimental data sets obtained by different methods is conventionally considered as a scalar one. Namely, a solution is found by minimization of linear combination of functions describing the fit of the values predicted from the model to each set of data. In the present paper we demonstrate that this standard approach is not always justified and propose to consider a joint inversion problem as a multiobjective optimization problem (MOP), for which the misfit function is a vector. The method is based on analysis of two types of solutions to MOP considered in the space of misfit functions (objective space). The first one is a set of complete optimal solutions that minimize all the components of a vector misfit function simultaneously. The second one is a set of Pareto optimal solutions, or trade-off solutions, for which it is not possible to decrease any component of the vector misfit function without increasing at least one other. We investigate connection between the standard formulation of a joint inversion problem and the multiobjective formulation and demonstrate that the standard formulation is a particular case of scalarization of a multiobjective problem using a weighted sum of component misfit functions (objectives). We illustrate the multiobjective approach with a non-linear problem of the joint inversion of shear wave splitting parameters and longitudinal wave residuals. Using synthetic data and real data from three passive seismic experiments, we demonstrate that random noise in the data and inexact model parametrization destroy the complete optimal solution, which degenerates into a fairly large Pareto set. As a result, non-uniqueness of the problem of joint inversion increases. If the random noise in the data is the only source of uncertainty, the Pareto set expands around the true solution in the objective space. In this case the ,ideal point' method of scalarization of multiobjective problems can be used. If the uncertainty is due to inexact model parametrization, the Pareto set in the objective space deviates strongly from the true solution. In this case all scalarization methods fail to find the solution close to the true one and a change of model parametrization is necessary. [source]

Artificial neural networks for parameter estimation in geophysics

GEOPHYSICAL PROSPECTING, Issue 1 2000
Carlos Calderón-Macías
Artificial neural systems have been used in a variety of problems in the fields of science and engineering. Here we describe a study of the applicability of neural networks to solving some geophysical inverse problems. In particular, we study the problem of obtaining formation resistivities and layer thicknesses from vertical electrical sounding (VES) data and that of obtaining 1D velocity models from seismic waveform data. We use a two-layer feedforward neural network (FNN) that is trained to predict earth models from measured data. Part of the interest in using FNNs for geophysical inversion is that they are adaptive systems that perform a non-linear mapping between two sets of data from a given domain. In both of our applications, we train FNNs using synthetic data as input to the networks and a layer parametrization of the models as the network output. The earth models used for network training are drawn from an ensemble of random models within some prespecified parameter limits. For network training we use the back-propagation algorithm and a hybrid back-propagation,simulated-annealing method for the VES and seismic inverse problems, respectively. Other fundamental issues for obtaining accurate model parameter estimates using trained FNNs are the size of the training data, the network configuration, the description of the data and the model parametrization. Our simulations indicate that FNNs, if adequately trained, produce reasonably accurate earth models when observed data are input to the FNNs. [source]

Turbulent length-scales in the marine atmospheric mixed layer

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 566 2000
P. Durand
Abstract The spectra of turbulence signals can be characterized by several independent scales. To provide a parametrization of these spectra requires knowledge of the relationships between these scales. This paper focuses on three independent scales: the integral scale (which is influenced by the low-frequency behaviour of the spectra); the wavelength of the spectrum peak (which characterizes the energy-containing domain); and the dissipation scale (which is relevant for the inertial subrange). First, we present definitions of these various scales, and the possible relationships between them. The profiles of the scales were computed from airborne measurements made in the atmospheric mixed layer over the open ocean, in a region where horizontal homogeneity can be assumed, at least for several tens of km. Furthermore, the diurnal cycle being very weak in this oceanic area, and aircraft moving at high speed through the air mass, stationarity is well verified on the runs, and Taylor's hypothesis may be used. The meteorological conditions correspond to a slightly unstable mixed layer, with weak to moderate winds. In a first part, we analyse the integral scales of various parameters on a 180-km run and demonstrate that these parameters cannot be computed with any soundness from horizontal-wind, temperature and moisture signals, because of the continuous increase in the spectral energy when moving towards lower frequencies. For the same reasons, the spectrum peak and the corresponding wavelength cannot be determined for these parameters. The computation of the integral and energy-containing scale is therefore restricted to the vertical velocity, and to the various covariances. The turbulence field is characterized by a stretching of the eddies along the mean wind direction which results in greater integral and energy-containing scales (but not in greater dissipation scales) when computed for along-wind runs than for the cross-wind runs. The profiles of the various scales increase with altitude and are well defined in the lower half of the mixed layer, but are much more scattered in the upper half. This behaviour is related to the source of turbulence, which lies in the surface buoyancy flux in the lower half of the mixed layer, and comes from higher altitude sources in the upper half. The integral scales have values comparable with those found in previous work, except for parameters related to temperature fluctuations, which have lower values. The ratio of the energy-containing scale to the integral scale, which determines the sharpness of the ,spectral knee', varies considerably from one parameter to another, and sometimes with altitude. This demonstrates that a single unique parametrization cannot be defined for turbulence spectra. As a consequence, the eddy-exchange coefficients, which depend on a characteristic length-scale, should vary from one parameter to another. This would then have to be taken into account in model parametrization based on mixing length-scales. [source]

Opportunities for enhanced collaboration within the data assimilation community

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 613 2005
Dennis McLaughlin
Abstract Recent advances in sensor technology, telecommunications and computation open up new possibilities for the application of data assimilation concepts across the Earth sciences. As a result, the data assimilation community is expanding beyond meteorology and oceanography to include representatives from climatology, hydrology, atmospheric chemistry, ecology and other disciplines. This development offers new opportunities for collaboration between the operational and research sides of the community. Opportunities exist not only in traditional forecasting applications, but also in areas such as reanalysis, model diagnosis, development of new model parametrizations, and observing-system design. Disciplinary scientists from outside the traditional data assimilation community are starting to appreciate that data assimilation can provide an integrated view of earth processes over a range of time and space scales. Operational data assimilation groups have special expertise and capabilities that are needed by newcomers to the field. If the scope of the operational community expands to include a wider range of applications, the entire field will likely benefit from new ideas, new resources, and increased visibility and recognition. Copyright © 2005 Royal Meteorological Society [source]