Non linear inversion of gravity gradients and the GGI gradiometer

2011 ◽  
Vol 3 (4) ◽  
Author(s):  
Manik Talwani
Keyword(s):  
Iterative Procedure ◽  
Least Square ◽  
Inversion Method ◽  
Gravity Gradients ◽  
Linear Inversion ◽  
Non Linear ◽  
Best Fitting ◽  
The Difference ◽  
Differential Curvature ◽  
Fitting Model

AbstractAll gradiometers currently operating for exploration in the field are based on Lockheed Martin’s GGI gradiometer. The working of this gradiometer is described and a method for robust non linear inversion of gravity gradients is presented. The inversion method involves obtaining the gradient response of a trial body consisting of vertical rectangular prisms. The inversion adjusts the depth to the tops or bases of the prisms. In the trial model all the prisms are not required to have the same area of cross section or the same density (which can also be allowed to vary with depth). The depth to the tops and bottoms of each prism can also be different. This response is compared with the observed values of gradient and through an iterative procedure, the difference is minimized in a least square sense to arrive at a best fitting model by varying the position of the tops or bottoms of the prisms. Each gradient can be individually inverted or one or more gradients can be jointly inverted. The method is extended to invert gravity values individually or jointly with gradient values. The use of Differential Curvature, a quantity which is directly obtained by current gradiometers in use and which is an invariant under a rotation in the horizontal plane, is emphasized. Synthetic examples as well as a field example of inversion are given.

scholarly journals Zeeman-Doppler imaging: old problems and new methods

2008 ◽  
Vol 4 (S259) ◽  
pp. 633-644 ◽  
Author(s):  
Thorsten A. Carroll ◽  
Markus Kopf ◽  
Klaus G. Strassmeier ◽  
Ilya Ilyin
Keyword(s):  
Radiative Transfer ◽  
Principal Component ◽  
Magnetic Surface ◽  
Least Square ◽  
Doppler Imaging ◽  
Inversion Method ◽  
Reconstruction Process ◽  
Physical Constraints ◽  
Non Linear ◽  
Transfer Method

AbstractZeeman-Doppler Imaging (ZDI) is a powerful inversion method to reconstruct stellar magnetic surface fields. The reconstruction process is usually solved by translating the inverse problem into a regularized least-square or optimization problem. In this contribution we will emphasize that ZDI is an inherent non-linear problem and the corresponding regularized optimization is, like many non-linear problems, potentially prone to local minima. We show how this problem will be exacerbated by using an inadequate forward model. To facilitate a more consistent full radiative transfer driven approach to ZDI we describe a two-stage strategy that consist of a principal component analysis (PCA) based line profile reconstruction and a fast approximate polarized radiative transfer method to synthesize local Stokes profiles. Moreover, we introduce a novel statistical inversion method based on artificial neural networks (ANN) which provide a fast calculation of a first guess model and allows to incorporate better physical constraints into the inversion process.

scholarly journals Improved Magnetotelluric Zohdy-Oldenburg Direct Inversion

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Hui Cao ◽  
Yun Liu ◽  
Kun Peng Wang
Keyword(s):  
Jacobian Matrix ◽  
Least Square ◽  
Ratio Method ◽  
Inversion Method ◽  
Model Parameters ◽  
Sparse Linear Systems ◽  
Linear Inversion ◽  
Direct Inversion ◽  
Rugged Topography ◽  
Linear Systems Of Equations

Based on researches of Baiyao (1995) and Zhang and Xu (2001), this paper proposes an improved 2D MT Zohdy-Oldenburg direct inversion method, in the least-square sense, embodying the features of Zohdy’s ratio method and Oldenburg’s difference method, in the condition of rugged topography, with phase information. It bypasses large calculations of the Jacobian matrix and large sparse linear systems of equations and enables direct modifications and comparisons of the model parameters. According to the calculation and analysis of examples, it shows faster convergence and higher precision. In contrast with the conventional linear inversion, the calculation speed of this new method can be increased by more than 10 times.

scholarly journals Flower Pollination Algorithm for the Inversion of Schlumberger Sounding Curve

2021 ◽  
Vol 873 (1) ◽  
pp. 012018
Author(s):  
F Raflesia ◽  
W Widodo
Keyword(s):  
Synthetic Data ◽  
Least Square ◽  
Flower Pollination Algorithm ◽  
Grey Wolf Optimizer ◽  
Local Optimum ◽  
Initial Model ◽  
Linear Inversion ◽  
Flower Pollination ◽  
Non Linear ◽  
Schlumberger Sounding

Abstract Inversion of schlumberger sounding curve is non-linear, and multi-minimum. All linear inversion strategies can produce local optimum, and depend on the initial model. Meanwhile, the non-linear bionic method for inversion problems does not require an initial model, simple, flexible, derivation-free mechanism and can avoid local optimum. One of the new algorithm of the non-linear bionic method for geophysical inversion problem is the Flower Pollination Algorithm (FPA). The FPA is used for the inversion of schlumberger sounding curve. This algorithm was stimulated by the pollination process for blooming plants. The applicability of the present algorithm was tested on synthetic models A-type and KH-type curve. Numerical tests in MATLAB R2013a for the synthetic data and the observed data show that FPA can find the global minimum. For further study, inverted results using the FPA are contrasted with the damped least-square (DLSQR) inversion program, Particle Swarm Optimization (PSO), and Grey Wolf Optimizer (GWO). The outcomes of the comparison reveal that FPA performs better than the DLSQR inversion program, PSO, and GWO.

scholarly journals Comparison between Tornadic and Nontornadic Mesocyclones Using the Vorticity (Pseudovorticity) Line Technique

2005 ◽  
Vol 133 (9) ◽  
pp. 2535-2551 ◽  
Author(s):  
Huaqing Cai
Keyword(s):  
Fractal Structure ◽  
Accurate Estimate ◽  
Least Square ◽  
Self Similarity ◽  
Best Fitting ◽  
Low Levels ◽  
The Difference ◽  
Similarity Scale ◽  
Linear Least Square ◽  
Horizontal Grid

Abstract Comparisons between tornadic and nontornadic mesocyclones using the concept of fractal geometry are presented. Both the maximum vertical vorticity (ζmax) and pseudovorticity (ζpv) associated with a mesocyclone at low levels are found to be scaling with the horizontal grid spacing (ɛ) according to a power-law relationship. The linear least square best fitting of ln (ζmax) or ln (ζpv) versus ln (ɛ) for different scales can be obtained for each mesocyclone at a certain time, and it is named the vorticity (pseudovorticity) line of a mesocyclone. Different mesocyclones have different vorticity (pseudovorticity) line slopes that are closely related to the fractal dimension of vorticity (pseudovorticity) of a mesocyclone as a possible fractal structure. Various factors that may affect the accurate estimate of the vorticity (pseudovorticity) line of a mesocyclone are also discussed in detail. Differences between tornadic and nontornadic mesocyclones are found in terms of the slope of vorticity (pseudovorticity) lines based on three tornadic and two nontornadic mesocyclones. A possible reason why previous studies were not able to identify the difference(s) between tornadic and nontornadic mesocyclones is discussed. Self-similarity (scale invariance), which is a basic characteristic of a fractal structure, seems to be valid between tornado and mesocyclone scales based on the analysis of the vorticity (pseudovorticity) line of the tornadic Kellerville, Texas, mesocyclone. It is hypothesized that a steeper slope of the vorticity (pseudovorticity) line may be indicative of a tornadic mesocyclone.

165 Effects of Digestible Lysine Level on Growth Performance and Economics of Grow-finish Pigs

2021 ◽  
Vol 99 (Supplement_1) ◽  
pp. 58-59
Author(s):  
Larissa L Becker ◽  
Emily E Scholtz ◽  
Joel M DeRouchey ◽  
Mike D Tokach ◽  
Jason C Woodworth ◽  
...  
Keyword(s):  
Phase 1 ◽  
Information Criterion ◽  
Response Curves ◽  
Phase 3 ◽  
Ileal Digestibility ◽  
Distillers Dried Grains ◽  
Feed Cost ◽  
Best Fitting ◽  
Dietary Treatments ◽  
Fitting Model

Abstract A total of 2,124 barrows and gilts (PIC 1050′DNA 600, initially 48.9 kg) were used in a 32-d study to determine the optimal dietary standardized ileal digestibility (SID) Lys level in a commercial setting. Pigs were randomly allotted to 1 of 5 dietary treatments with 24 to 27 pigs/pen and 16 replications/treatment. Similar number of barrows and gilts were placed in each pen. Diets were fed over 3 phases (48.9 to 58.6, 58.6 to 70.9, and 70.9 to 80.8 kg respectively). Dietary treatments were corn-soybean meal-based and contained 10 (phase 1 and 2) or 5% (phase 3) distillers dried grains with solubles. Diets were formulated to 85, 95, 103, 110, or 120% of the current Pig Improvement Company (PIC, Hendersonville, TN) SID Lys gilt recommendations with phase 1 SID Lys levels of 0.90, 1.01, 1.09, 1.17 and 1.27%, phase 2 levels of 0.79, 0.87, 0.94, 1.03, and 1.10%, and phase 3 levels of 0.71, 0.78, 0.85, 0.92, and 0.99%, respectively. Dose response curves were evaluated using linear (LM), quadratic polynomial (QP), broken-line linear (BLL), and broken-line quadratic (BLQ) models. For each response variable, the best-fitting model was selected using the Bayesian information criterion. Overall (d 0 to 32), increasing SID Lys increased (linear, P< 0.001) BW, ADG, G:F, Lys intake/d, and Lys intake/kg of gain. Modeling margin over feed cost (MOFC), BLL and QP estimated the requirement at 105.8% and 113.7% respectively. In summary, while growth increased linearly up to 120% of the PIC current feeding level, the optimal MOFC was 106% to 114% depending on the model used.

Genetic and Environmental Influences of Dietary Indices in a UK Female Twin Cohort

2020 ◽  
Vol 23 (6) ◽  
pp. 330-337
Author(s):  
Olatz Mompeo ◽  
Rachel Gibson ◽  
Paraskevi Christofidou ◽  
Tim D. Spector ◽  
Cristina Menni ◽  
...  
Keyword(s):  
Healthy Eating ◽  
Menopausal Status ◽  
Healthy Eating Index ◽  
Healthy Diet ◽  
Nutritional Epidemiology ◽  
Best Fitting ◽  
Heritability Estimates ◽  
Fitting Model ◽  
Dietary Indices ◽  
Health Parameters

AbstractA healthy diet is associated with the improvement or maintenance of health parameters, and several indices have been proposed to assess diet quality comprehensively. Twin studies have found that some specific foods, nutrients and food patterns have a heritable component; however, the heritability of overall dietary intake has not yet been estimated. Here, we compute heritability estimates of the nine most common dietary indices utilized in nutritional epidemiology. We analyzed 2590 female twins from TwinsUK (653 monozygotic [MZ] and 642 dizygotic [DZ] pairs) who completed a 131-item food frequency questionnaire (FFQ). Heritability estimates were computed using structural equation models (SEM) adjusting for body mass index (BMI), smoking status, Index of Multiple Deprivation (IMD), physical activity, menopausal status, energy and alcohol intake. The AE model was the best-fitting model for most of the analyzed dietary scores (seven out of nine), with heritability estimates ranging from 10.1% (95% CI [.02, .18]) for the Dietary Reference Values (DRV) to 42.7% (95% CI [.36, .49]) for the Alternative Healthy Eating Index (A-HEI). The ACE model was the best-fitting model for the Healthy Diet Indicator (HDI) and Healthy Eating Index 2010 (HEI-2010) with heritability estimates of 5.4% (95% CI [−.17, .28]) and 25.4% (95% CI [.05, .46]), respectively. Here, we find that all analyzed dietary indices have a heritable component, suggesting that there is a genetic predisposition regulating what you eat. Future studies should explore genes underlying dietary indices to further understand the genetic disposition toward diet-related health parameters.

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