The inverse problem of resistivity sounding

Geophysics ◽  
1984 ◽  
Vol 49 (12) ◽  
pp. 2143-2158 ◽  
Author(s):  
Robert L. Parker
Keyword(s):  
Inverse Problem ◽  
Apparent Resistivity ◽  
Single Point ◽  
Quadratic Program ◽  
Data Set ◽  
Regularization Technique ◽  
Resistivity Sounding ◽  
Best Fitting ◽  
Electrical Data ◽  
Fitting Model

The electric potential due to a single point electrode at the surface of a layered conducting medium is calculated by means of a linear combination of the potentials associated with a set of two‐layer systems. This new representation is called the bilayer expansion for the Green’s function. It enables the forward problem of resistivity sounding to be solved very efficiently, even for complicated profiles. Also, the bilayer expansion facilitates the solution of the resistivity inverse problem: the coefficients in the expansion are linearly related to apparent resistivity as it is measured and they are readily mapped into parameters for a model. Specifically, I consider models comprising uniformly conducting layers of equal thickness; for a given finite data set a quadratic program can be used to find the best‐fitting model in this class for any specified thickness. As the thickness is reduced, models of this kind can approximate arbitrary profiles with unlimited accuracy. If there is a model that satisfies the data well, there are other models equally good or better whose variation takes place in an infinitesimally thin zone near the surface, below which there is a perfectly conducting region. This extraordinary class of solutions underscores the serious ambiguity in the interpretation of apparent resistivity data. It is evident that strong constraints from outside the electrical data set must be applied if reliable solutions are to be discovered. Previous work seems to have given a somewhat overly optimistic impression of the resolving abilities of this kind of data. I consider briefly a regularization technique designed to maximize the smoothness of models found with the bilayer inversion.

Magnetotelluric static shift: Estimation and removal using the cokriging method

Geophysics ◽  
2007 ◽  
Vol 72 (1) ◽  
pp. F25-F34 ◽  
Author(s):  
Benoit Tournerie ◽  
Michel Chouteau ◽  
Denis Marcotte
Keyword(s):  
Apparent Resistivity ◽  
A Priori ◽  
Shift Factor ◽  
Static Shift ◽  
Geostatistical Model ◽  
Data Set ◽  
Resistivity Sounding ◽  
The Difference ◽  
Cross Variogram

We present and test a new method to correct for the static shift affecting magnetotelluric (MT) apparent resistivity sounding curves. We use geostatistical analysis of apparent resistivity and phase data for selected periods. For each period, we first estimate and model the experimental variograms and cross variogram between phase and apparent resistivity. We then use the geostatistical model to estimate, by cokriging, the corrected apparent resistivities using the measured phases and apparent resistivities. The static shift factor is obtained as the difference between the logarithm of the corrected and measured apparent resistivities. We retain as final static shift estimates the ones for the period displaying the best correlation with the estimates at all periods. We present a 3D synthetic case study showing that the static shift is retrieved quite precisely when the static shift factors are uniformly distributed around zero. If the static shift distribution has a nonzero mean, we obtained best results when an apparent resistivity data subset can be identified a priori as unaffected by static shift and cokriging is done using only this subset. The method has been successfully tested on the synthetic COPROD-2S2 2D MT data set and on a 3D-survey data set from Las Cañadas Caldera (Tenerife, Canary Islands) severely affected by static shift.

scholarly journals Asteroseismology of the DAV star R808

2020 ◽  
Vol 500 (4) ◽  
pp. 4703-4709
Author(s):  
Y H Chen ◽  
H Shu
Keyword(s):  
Coulomb Potential ◽  
Model Fitting ◽  
Potential Effect ◽  
Data Set ◽  
Trapped Mode ◽  
Star Models ◽  
Diffusion Scheme ◽  
Best Fitting ◽  
Screened Coulomb Potential ◽  
Fitting Model

ABSTRACT The DAV star R808 was observed by 13 different telescopes for more than 170 h in 2009 April on the WET run XCOV26. 25 independent pulsation frequencies were identified by this data set. We assumed 19 m = 0 modes and performed an asteroseismological study on those 19 modes. We evolve grids of DAV star models by wdec adopting the element diffusion scheme with pure and screened Coulomb potential effect. The core compositions are from white dwarf models evolved by mesa, which are thermal nuclear burning results. Our best-fitting model is from the screened Coulomb potential scenario, which has parameters of log(MHe/M*) = −2.4, log(MH/M*) = −5.2, Teff = 11100 K, M* = 0.710 M⊙, logg = 8.194, and σRMS = 2.86 s. The value of σRMS is the smallest among the four existing asteroseismological work. The average period spacing is 46.299 s for l = 1 modes and 25.647 s for l = 2 modes. The other six observed modes can be fitted by $m\, \ne$ 0 components of some modes for our best-fitting model. Fitting the 25 observed modes, we obtain a σRMS value of 2.59 s. Considering the period spacings, we also assume, that at least in one case, we detect an l = 2 trapped mode.

Spectroscopy-Based Mapping with Scanning Microwave Impedance Microscopy

2018 ◽  
Author(s):  
Peter De Wolf ◽  
Zhuangqun Huang ◽  
Bede Pittenger
Keyword(s):  
Single Point ◽  
Electrical Characterization ◽  
Principal Component ◽  
High Sensitivity ◽  
Data Cube ◽  
Nanometer Scale ◽  
Learning Approaches ◽  
Data Set ◽  
3D Data ◽  
Higher Dimensional

Abstract Methods are available to measure conductivity, charge, surface potential, carrier density, piezo-electric and other electrical properties with nanometer scale resolution. One of these methods, scanning microwave impedance microscopy (sMIM), has gained interest due to its capability to measure the full impedance (capacitance and resistive part) with high sensitivity and high spatial resolution. This paper introduces a novel data-cube approach that combines sMIM imaging and sMIM point spectroscopy, producing an integrated and complete 3D data set. This approach replaces the subjective approach of guessing locations of interest (for single point spectroscopy) with a big data approach resulting in higher dimensional data that can be sliced along any axis or plane and is conducive to principal component analysis or other machine learning approaches to data reduction. The data-cube approach is also applicable to other AFM-based electrical characterization modes.

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.

Comparing productive vocabulary measures from the CDI and a systematic diary study

1999 ◽  
Vol 26 (1) ◽  
pp. 177-185 ◽  
Author(s):  
BYRON F. ROBINSON ◽  
CAROLYN B. MERVIS
Keyword(s):  
Growth Curves ◽  
Diary Study ◽  
Expressive Vocabulary ◽  
Early Language ◽  
Vocabulary Size ◽  
Early Language Development ◽  
Closed Class ◽  
Communicative Development ◽  
Best Fitting ◽  
Fitting Model

Expressive vocabulary data gathered during a systematic diary study of one male child's early language development are compared to data that would have resulted from longitudinal administration of the MacArthur Communicative Development Inventories spoken vocabulary checklist (CDI). Comparisons are made for (1) the number of words at monthly intervals (9;10.15 to 2;0.15), (2) proportion of words by lexical class (i.e. noun, predicate, closed class, ‘other’), (3) growth curves. The CDI underestimates the number of words in the diary study, with the underestimation increasing as vocabulary size increases. The proportion of diary study words appearing on the CDI differed as a function of lexical class. Finally, despite the differences in vocabulary size, logistic curves proved to be the best fitting model to characterize vocabulary development as measured by both the diary study and the CDI. Implications for the longitudinal use of the CDI are discussed.

scholarly journals Identification-Robust Estimates of the Canadian Natural Rate of Interest

2016 ◽  
Vol 91 (1-2) ◽  
pp. 161-176
Author(s):  
Maral Kichian
Keyword(s):  
Interest Rate ◽  
Robust Methods ◽  
Errors In Variables ◽  
Natural Rate ◽  
Real Rate ◽  
Point Estimates ◽  
Natural Rate Of Interest ◽  
Best Fitting ◽  
Estimate Precision ◽  
Fitting Model

The natural rate of interest is an unobservable entity and its measurement presents some important empirical challenges. In this paper, we use identification-robust methods and central bank real-time staff projections to obtain estimates for the equilibrium real rate from contemporaneous and forward-looking Taylor-type interest rate rules. The methods notably account for the potential presence of endogeneity, under-identification, and errors-in-variables concerns. Our applications are conducted on Canadian data. The results reveal some important identification difficulties associated with some of our models, reinforcing the need to use identification-robust methods to estimate such policy functions. Despite these challenges, we are able to obtain fairly comparable point estimates for the real equilibrium interest rate across our different models, and in the case of the best fitting model, also remarkable estimate precision.

Forward  Modelling of Bouguer Anomalies along a transect of the Southern Apennines and the Tyrrhenian back-arc basin.

2021 ◽  
Author(s):  
Assel Akimbekova ◽  
Paolo Mancinelli ◽  
Massimiliano Rinaldo Barchi ◽  
Cristina Pauselli ◽  
Giorgio Minelli
Keyword(s):  
Gravity Anomalies ◽  
Moho Depth ◽  
Positive Trend ◽  
Tyrrhenian Sea ◽  
Southern Apennines ◽  
Bouguer Anomalies ◽  
Crustal Model ◽  
Density Values ◽  
Best Fitting ◽  
Fitting Model

<p>Abstract</p><p> </p><p>In the present study, starting from original measurement stations, we created the Bouguer anomaly map of Southern Italy with a reduction density of 2670 kg m<sup>-3</sup>. We perform a regional gravity modelling at crustal scale along the trace of the CROP-04 (on-shore) and MB6 (off-shore) deep seismic reflection profiles crossing the Southern Apennines and the Southern Tyrrhenian Sea. Along the 320 km-long modelled profile, we investigate crustal-scale sources for the observed gravity anomalies. </p><p>After a compelling review of the published Moho geometries in the area, that were retrieved from either active or passive seismic methods, we test them in the observed gravity field through forward modeling of the Bouguer gravity anomalies. The comparison between the different Moho interpretations shows that the steepness of the subducting slab, the position of the step between the western (Tyrrhenian) and the eastern (Adriatic) Moho and Moho depth represent the main features influencing the observed Bouguer anomalies at crustal scale.</p><p>Finally, we provide a best-fitting model across both onshore and offshore areas. In the proposed best-fitting model, the wide wavelength and strong regional Bouguer anomalies correlate with the geometry of the Moho discontinuity and deep tectonic structures. On the other hand, the small-amplitude oscillations of the gravity anomalies were attributed to the low-density values of the Pliocene-Quaternary deposits both on- (e.g. the Bradanic trough) and off-shore (e.g. recent deposits in the Tyrrhenian sea bottom). Gravity minima correspond to the crustal doubling underneath the Southern Apennines where the Tyrrhenian Moho (~27 km depth) overlies the deeper Adriatic Moho (~50 km depth). The positive trend of the observed anomaly toward NE is related to the shallowing of the Adriatic Moho to depths of ~28 km in the Adriatic. Similarly, towards SW, the observed anomaly follows a positive trend towards the maxima located in the Central Tyrrhenian Sea. We model this trend as representative of crustal thinning and shallowing to values of ~12 km depth of the Tyrrhenian Moho. We also model a crustal transition from geometries and density values typical of a continental crust in the Adriatic domain towards a more oceanic structure and composition in the Tyrrhenian domain. This crustal model locates the westward flexure of the Adriatic Moho, mimicking the subduction of the Adriatic lithosphere beneath the Peri-Tyrrhenian block and locates step between the western (Tyrrhenian) and the eastern (Adriatic) Moho beneath the Apennines range.</p><p>The resulted gravity forward model provide contributions to the tectonic settings understanding of the area by providing a robust crustal model ranging from the Tyrrhenian Sea to the Apulian foreland.</p><p> Finally, we believe that the proposed model can serve as a starting point for future studies investigating the upper crustal geometries in the area and addressing open questions about its relations with seismicity distribution.</p><p> </p>

Semidefinite Programming-Based Method for Implementing Linear Fitting to Interval-Valued Data

2011 ◽  
Vol 1 (3) ◽  
pp. 32-46 ◽  
Author(s):  
Minghuang Li ◽  
Fusheng Yu
Keyword(s):  
Lower Bound ◽  
Semidefinite Programming ◽  
Large Scale ◽  
Experimental Studies ◽  
Optimal Solution ◽  
Data Set ◽  
Linear Fitting ◽  
Optimal Value ◽  
Fitting Model ◽  
Interval Valued

Building a linear fitting model for a given interval-valued data set is challenging since the minimization of the residue function leads to a huge combinatorial problem. To overcome such a difficulty, this article proposes a new semidefinite programming-based method for implementing linear fitting to interval-valued data. First, the fitting model is cast to a problem of quadratically constrained quadratic programming (QCQP), and then two formulae are derived to develop the lower bound on the optimal value of the nonconvex QCQP by semidefinite relaxation and Lagrangian relaxation. In many cases, this method can solve the fitting problem by giving the exact optimal solution. Even though the lower bound is not the optimal value, it is still a good approximation of the global optimal solution. Experimental studies on different fitting problems of different scales demonstrate the good performance and stability of our method. Furthermore, the proposed method performs very well in solving relatively large-scale interval-fitting problems.

scholarly journals Investigation and Validation of the Time-Varying Characteristic for the GPS Differential Code Bias

2019 ◽  
Vol 11 (4) ◽  
pp. 428 ◽  
Author(s):  
Haojun Li ◽  
Jingxin Xiao ◽  
Weidong Zhu
Keyword(s):  
Single Point ◽  
Time Varying ◽  
International Gnss Service ◽  
Data Set ◽  
Differential Code Bias ◽  
Triple Frequency ◽  
Code Bias ◽  
Constant Part ◽  
The Difference ◽  
Better Than

The time-varying characteristic of the bias in the GPS code observation is investigated using triple-frequency observations. The method for estimating the combined code bias is presented and the twelve-month (1 January–31 December 2016) triple-frequency GPS data set from 114 International GNSS Service (IGS) stations is processed to analyze the characteristic of the combined code bias. The results show that the main periods of the combined code bias are 12, 8, 6, 4, 4.8 and 2.67 h. The time-varying characteristic of the combined code bias, which is the combination of differential code bias (DCB) (P1–P5) and DCB (P1–P2), shows that the real satellite DCBs are also time-varying. The difference between the two sets of the computed constant parts of the combined code bias, with the IGS DCB products of DCB (P1–P2) and DCB (P1–P2) and the mean of the estimated 24-h combined code bias series, further show that the combined code bias cannot be replaced by the DCB (P1–P2) and DCB (P1–P5) products. The time-varying part of inter-frequency clock bias (IFCB) can be estimated by the phase and code observations and the phase based IFCB is the combinations of the triple-frequency satellite uncalibrated phase delays (UPDs) and the code-based IFCB is the function of the DCBs. The performances of the computed the IFCB with different methods in single point positioning indicate that the accuracy for the constant part of the combined code bias is reduced, when the IGS DCB products are used to compute. These performances also show that the time-varying part of IFCB estimated with phase observation is better than that of code observation. The predicted results show that 98% of the predicted constant part of the combined code bias can be corrected and the attenuation of the predicted accuracy is much less evident. However, the accuracy of the predicted time-varying part decreases significantly with the predicted time.

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