3-D CSEM inversion for the complex model with topography using an efficient dual parallel approach

2021 ◽  
Author(s):  
Zhengguang Liu ◽  
Zhengyong Ren ◽  
Jingtian Tang ◽  
Huang Chen
Keyword(s):  
Linear Equations ◽  
Forward Modeling ◽  
Complex Model ◽  
Computational Grids ◽  
Dipole Source ◽  
Model Parameters ◽  
Sensitivity Matrix ◽  
Parallel Methods ◽  
Electric Dipoles ◽  
Edge Based

<p>    There is a significant interest in improving the efficiency of 3-D CSEM inversion and obtaining more reliable inversion results. A 3-D CSEM inversion code using unstructured tetrahedral elements has been developed in order to consider the topographic effect by directly incorporating it into computational grids. In the forward modeling, the electric dipole source is divided into a set of short electric dipoles to simulate its practical shape, size and attitude. We adopt the edge-based finite-element method to discretize the electric field equation. In the inversion, the inversion grids are entirely independent of the forward grids. The lower and upper bounding constraints on model parameters are used to improve the reliability of the inversion result further. We use the Gauss-Newton algorithm to minimize the inversion objective function and obtain the underground conductivity model. The calculation of the forward modeling and the sensitivity matrix spends most of the time in the inversion. At present, most inversion codes use frequency-based parallel methods to accelerate the inversion, to further improve the efficiency of 3D CSEM inversion, except for the frequency-based parallel methods, we use the open-source software METIS to divide the model into several parts and then use the MPI-based parallel toolkits (such as PETSc and MUMPS) to solve the forward linear equations. The same parallel scheme can also be used to calculate the sensitivity matrix. Finally, we can further improve the efficiency of 3-D CSEM inversion by the dual parallel strategy based on the frequency and domain decomposition.</p>

scholarly journals Optimal Calibration of Evaporation Models against Penman–Monteith Equation

Water ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 1484
Author(s):  
Dagmar Dlouhá ◽  
Viktor Dubovský ◽  
Lukáš Pospíšil
Keyword(s):  
Model Calibration ◽  
Heat Storage ◽  
Free Water ◽  
Complex Model ◽  
Model Parameters ◽  
Net Radiation ◽  
Statistical Measures ◽  
Pit Lakes ◽  
Evaporation Models ◽  
Monteith Equation

We present an approach for the calibration of simplified evaporation model parameters based on the optimization of parameters against the most complex model for evaporation estimation, i.e., the Penman–Monteith equation. This model computes the evaporation from several input quantities, such as air temperature, wind speed, heat storage, net radiation etc. However, sometimes all these values are not available, therefore we must use simplified models. Our interest in free water surface evaporation is given by the need for ongoing hydric reclamation of the former Ležáky–Most quarry, i.e., the ongoing restoration of the land that has been mined to a natural and economically usable state. For emerging pit lakes, the prediction of evaporation and the level of water plays a crucial role. We examine the methodology on several popular models and standard statistical measures. The presented approach can be applied in a general model calibration process subject to any theoretical or measured evaporation.

scholarly journals Incremental model breakdown to assess the multi-hypotheses problem

2018 ◽  
Vol 22 (8) ◽  
pp. 4565-4581 ◽  
Author(s):  
Florian U. Jehn ◽  
Lutz Breuer ◽  
Tobias Houska ◽  
Konrad Bestian ◽  
Philipp Kraft
Keyword(s):  
Hydrological Modeling ◽  
Model Performance ◽  
Complex Model ◽  
Model Parameters ◽  
Objective Functions ◽  
Final Model ◽  
Incremental Model ◽  
Model Efficiency ◽  
Improved Model ◽  
Model Structures

Abstract. The ambiguous representation of hydrological processes has led to the formulation of the multiple hypotheses approach in hydrological modeling, which requires new ways of model construction. However, most recent studies focus only on the comparison of predefined model structures or building a model step by step. This study tackles the problem the other way around: we start with one complex model structure, which includes all processes deemed to be important for the catchment. Next, we create 13 additional simplified models, where some of the processes from the starting structure are disabled. The performance of those models is evaluated using three objective functions (logarithmic Nash–Sutcliffe; percentage bias, PBIAS; and the ratio between the root mean square error and the standard deviation of the measured data). Through this incremental breakdown, we identify the most important processes and detect the restraining ones. This procedure allows constructing a more streamlined, subsequent 15th model with improved model performance, less uncertainty and higher model efficiency. We benchmark the original Model 1 and the final Model 15 with HBV Light. The final model is not able to outperform HBV Light, but we find that the incremental model breakdown leads to a structure with good model performance, fewer but more relevant processes and fewer model parameters.

scholarly journals CALCULATION OF MULTI-BLADE CUTTING TOOL RELIABILITY

2019 ◽  
Vol 2019 (6) ◽  
pp. 30-37
Author(s):  
Александр Анцев ◽  
Aleksandr Ancev
Keyword(s):  
Cutting Tool ◽  
Complex Model ◽  
Model Parameters ◽  
Average Period ◽  
Blade Number ◽  
Blade Cutting ◽  
Cutting Processes ◽  
Period Decrease ◽  
Tool Durability ◽  
Average Durability

The process effectiveness of blade cutting is defined considerably with the prediction accuracy of cutting tool durability term. But, in spite of that cutting processes have a probabilistic character, in modern mechanical engineering there are used durability de-pendences describing only the dependence of an average period of blade cutting tool durability upon cutting modes without taking into account a stochastic nature of tool wear depending upon many factors. For ac-counting cutting process variability there are offered stochastic models of cutting tool failure, but they hold good for a cutting tool with one cutting edge and in the case with a multi-blade cutting tool they must be speci-fied. In the paper it is defined that at a fan wear model with the increase of the blade number the period of cutting tool durability decreases, as failure likelihood of even one blade increases because of the blade properties spread of one tool. The factor of a durability period variation decreases with the growth of the blade number because of the decrease of an average durability period decrease. In the case of a wear accumulation model the multi-blade tool reliability does not depend upon the blade number. The dependences of an average period of durability and a factor of variation at a complex model of wear are similar to the case with the fan model of wear, but their values will be higher. In the case of a destruction model the factor of multi-blade tool durability variation does not depend upon the blade number, but an average durability depends considerably upon the blade number, but the dependence appearance corresponds to the dependence of an average durability at a fan model of wear. The type of the dependence of durability average period upon on the blade number at a generalized model of failures is similar to the cases considered previously, and a kind of the dependence of a variation factor changes depending on model parameters

scholarly journals Optimizing models of the North Atlantic spring bloom using physical, chemical and bio-optical observations from a Lagrangian float

2010 ◽  
Vol 7 (6) ◽  
pp. 8477-8520 ◽  
Author(s):  
W. Bagniewski ◽  
K. Fennel ◽  
M. J. Perry ◽  
E. A. D'Asaro
Keyword(s):  
North Atlantic ◽  
Spring Bloom ◽  
Deep Ocean ◽  
Complex Model ◽  
Optical Observations ◽  
Model Parameters ◽  
Carbon Export ◽  
The North ◽  
Chemical Measurements ◽  
The North Atlantic

Abstract. The North Atlantic spring bloom is one of the main events that lead to carbon export to the deep ocean and drive oceanic uptake of CO2 from the atmosphere. Here we use a suite of physical, bio-optical and chemical measurements made during the 2008 spring bloom to optimize and compare three different models of biological carbon export. The observations are from a Lagrangian float that operated south of Iceland from early April to late June, and were calibrated with ship-based measurements. The simplest model is representative of typical NPZD models used for the North Atlantic, while the most complex model explicitly includes diatoms and the formation of fast sinking diatom aggregates and cysts under silicate limitation. We carried out a variational optimization and error analysis for the biological parameters of all three models, and compared their ability to replicate the observations. The observations were sufficient to constrain most phytoplankton-related model parameters to accuracies of better than 15%. However, the lack of zooplankton observations leads to large uncertainties in model parameters for grazing. The simulated vertical carbon flux at 100 m depth is similar between models and agrees well with available observations, but at 600 m the simulated flux is much larger for the model with diatom aggregation. While none of the models can be formally rejected based on their misfit with the available observations, the model that includes export by diatom aggregation has slightly better fit to the observations and more accurately represents the mechanisms and timing of carbon export based on observations not included in the optimization. Thus models that accurately simulate the upper 100 m do not necessarily accurately simulate export to deeper depths.

Fast 3D magnetic inversion of a surface relief in the space domain

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. J57-J67 ◽  
Author(s):  
Marlon C. Hidalgo-Gato ◽  
Valéria C. F. Barbosa
Keyword(s):  
Hessian Matrix ◽  
Computational Cost ◽  
Magnetization Vector ◽  
Forward Modeling ◽  
Magnetic Data ◽  
Total Field ◽  
Inversion Algorithm ◽  
Sensitivity Matrix ◽  
Magnetic Inversion ◽  
Magnetic Basement

We have developed a fast 3D regularized magnetic inversion algorithm for depth-to-basement estimation based on an efficient way to compute the total-field anomaly produced by an arbitrary interface separating nonmagnetic sediments from a magnetic basement. We approximate the basement layer by a grid of 3D vertical prisms juxtaposed in the horizontal directions, in which the prisms’ tops represent the depths to the magnetic basement. To compute the total-field anomaly produced by the basement relief, the 3D integral of the total-field anomaly of a prism is simplified by a 1D integral along the prism thickness, which in turn is multiplied by the horizontal area of the prism. The 1D integral is calculated numerically using the Gauss-Legendre quadrature produced by dipoles located along the vertical axis passing through the prism center. This new magnetic forward modeling overcomes one of the main drawbacks of the nonlinear inverse problem for estimating the basement depths from magnetic data: the intense computational cost to calculate the total-field anomaly of prisms. The new sensitivity matrix is simpler and computationally faster than the one using classic magnetic forward modeling based on the 3D integrals of a set of prisms that parameterize the earth’s subsurface. To speed up the inversion at each iteration, we used the Gauss-Newton approximation for the Hessian matrix keeping the main diagonal only and adding the first-order Tikhonov regularization function. The large sparseness of the Hessian matrix allows us to construct and solve a linear system iteratively that is faster and demands less memory than the classic nonlinear inversion with prism-based modeling using 3D integrals. We successfully inverted the total-field anomaly of a simulated smoothing basement relief with a constant magnetization vector. Tests on field data from a portion of the Pará-Maranhão Basin, Brazil, retrieved a first depth-to-basement estimate that was geologically plausible.

scholarly journals Application and evaluation of the dendroclimatic process-based model MAIDEN during the last century in Canada and Europe

2020 ◽  
Vol 16 (3) ◽  
pp. 1043-1059
Author(s):  
Jeanne Rezsöhazy ◽  
Hugues Goosse ◽  
Joël Guiot ◽  
Fabio Gennaretti ◽  
Etienne Boucher ◽  
...  
Keyword(s):  
Tree Ring ◽  
Tree Growth ◽  
Meteorological Data ◽  
Ring Width ◽  
Complex Model ◽  
Added Value ◽  
Model Parameters ◽  
Sources Of Information ◽  
Calibration And Validation

Abstract. Tree-ring archives are one of the main sources of information to reconstruct climate variations over the last millennium with annual resolution. The links between tree-ring proxies and climate have usually been estimated using statistical approaches, assuming linear and stationary relationships. Both assumptions may be inadequate, but this issue can be overcome by ecophysiological modelling based on mechanistic understanding. In this respect, the model MAIDEN (Modeling and Analysis In DENdroecology) simulating tree-ring growth from daily temperature and precipitation, considering carbon assimilation and allocation in forest stands, may constitute a valuable tool. However, the lack of local meteorological data and the limited characterization of tree species traits can complicate the calibration and validation of such a complex model, which may hamper palaeoclimate applications. The goal of this study is to test the applicability of the MAIDEN model in a palaeoclimate context using as a test case tree-ring observations covering the 20th century from 21 Eastern Canadian taiga sites and 3 European sites. More specifically, we investigate the model sensitivity to parameter calibration and to the quality of climatic inputs, and we evaluate the model performance using a validation procedure. We also examine the added value of using MAIDEN in palaeoclimate applications compared to a simpler tree-growth model, i.e. VS-Lite. A Bayesian calibration of the most sensitive model parameters provides good results at most of the selected sites with high correlations between simulated and observed tree growth. Although MAIDEN is found to be sensitive to the quality of the climatic inputs, simple bias correction and downscaling techniques of these data improve significantly the performance of the model. The split-sample validation of MAIDEN gives encouraging results but requires long tree ring and meteorological series to give robust results. We also highlight a risk of overfitting in the calibration of model parameters that increases with short series. Finally, MAIDEN has shown higher calibration and validation correlations in most cases compared to VS-Lite. Nevertheless, this latter model turns out to be more stable over calibration and validation periods. Our results provide a protocol for the application of MAIDEN to potentially any site with tree-ring width data in the extratropical region.

Quasi‐analytical approximations and series in electromagnetic modeling

Geophysics ◽  
2000 ◽  
Vol 65 (6) ◽  
pp. 1746-1757 ◽  
Author(s):  
Michael S. Zhdanov ◽  
Vladimir I. Dmitriev ◽  
Sheng Fang ◽  
Gábor Hursán
Keyword(s):  
Integral Equation ◽  
Linear Approximation ◽  
Linear Equations ◽  
Integral Equation Method ◽  
Forward Modeling ◽  
Computational Effort ◽  
Correct Result ◽  
Electromagnetic Modeling ◽  
Analytical Approximations ◽  
Analytical Series

The quasi‐linear approximation for electromagnetic forward modeling is based on the assumption that the anomalous electrical field within an inhomogeneous domain is linearly proportional to the background (normal) field through an electrical reflectivity tensor λ⁁. In the original formulation of the quasi‐linear approximation, λ⁁ was determined by solving a minimization problem based on an integral equation for the scattering currents. This approach is much less time‐consuming than the full integral equation method; however, it still requires solution of the corresponding system of linear equations. In this paper, we present a new approach to the approximate solution of the integral equation using λ⁁ through construction of quasi‐analytical expressions for the anomalous electromagnetic field for 3-D and 2-D models. Quasi‐analytical solutions reduce dramatically the computational effort related to forward electromagnetic modeling of inhomogeneous geoelectrical structures. In the last sections of this paper, we extend the quasi‐analytical method using iterations and develop higher order approximations resulting in quasi‐analytical series which provide improved accuracy. Computation of these series is based on repetitive application of the given integral contraction operator, which insures rapid convergence to the correct result. Numerical studies demonstrate that quasi‐analytical series can be treated as a new powerful method of fast but rigorous forward modeling solution.

The Hammerstein Predict Model of Control Valve Based on Least Square Support Vector Machine

2014 ◽  
Vol 472 ◽  
pp. 164-170
Author(s):  
Ai Qin Huang ◽  
Yong Wang
Keyword(s):  
Linear Equations ◽  
Control Valve ◽  
Least Square ◽  
Hammerstein Model ◽  
Support Vector ◽  
Model Parameters ◽  
Chemistry Industry ◽  
Single Output ◽  
Controlling System ◽  
Value Decomposition

Control valve is a kind of essential terminal control component controlling the parameters of fluid such as flow and pressure in process-control. However it is a complex nonlinear, multi-input and single-output (MISO) system that is hard to model by traditional methodologies. To establish the pressure model of control valve, this paper presents a Hammerstein modeling method based on the least squares support vector machines (LS-SVM). The linear model parameters and the static nonlinearity of Hammerstein model can be obtained simultaneously by solving a set of linear equations followed by the singular value decomposition (SVD). As an example, a set of actual production data from a controlling system of chlorine in the salt chemistry industry were applied. The simulation results demonstrate that the obtained LS-SVM Hammerstein model can efficiently approximate the pressure of a control valve. Furthermore, the proposed LS-SVM Hammerstein model can be used in artificial intelligent control and the default diagnosis.

Approximate solution of nonlinear double-scattering inversion for true amplitude imaging

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. R43-R55 ◽  
Author(s):  
Wei Ouyang ◽  
Weijian Mao ◽  
Xuelei Li
Keyword(s):  
Scattered Field ◽  
Born Approximation ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Single Scattering ◽  
Complex Model ◽  
Earth Model ◽  
Model Parameters ◽  
Double Scattering ◽  
Integral Equation Formulation

Linearized inversion algorithms are the main techniques in seismic imaging that apply the single-scattering (Born) approximation to the scattered field, and therefore, have difficulty handling the strong perturbation of model parameters and nonlinear multiple-scattering effects. To theoretically overcome these drawbacks in the linearization of the inverse scattering problem, we have developed an approach to deal with nonlinear double-scattering inversion. We first used an integral equation formulation associated with the scattered field consisting of single and double scattering in an acoustic earth model based on the second-order Born approximation, and we found that the approximation of the scattered field can be naturally related to the generalized Radon transform (GRT). We then adopted the inverse GRT to obtain the corresponding quadratic approximate inversion solution. Our inversion scheme can appropriately handle the first-order transmission effects from double scattering in a local area, which gives a significant amplitude correction for the inversion results and ultimately results in a more accurate image with true amplitude. We conducted numerical experiments that showed the conventional single-scattering inversion was good in amplitude only for perturbation up to 10% of the background medium, but our approach can work for up to 40% or more. Test results indicated that our inversion scheme can effectively relax the requirement of the weak perturbation of the model parameter in the Born approximation and can deal with the complex model directly. The computational complexity of our new scheme is almost the same as conventional linear scattering inversion processing. Therefore, the cost of our approach is at a similar level to that of linear scattering inversion.

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