Reply by the author to G. D. Garland.

Geophysics ◽  
1982 ◽  
Vol 47 (10) ◽  
pp. 1460-1460
Author(s):  
B. A. Sissons
Keyword(s):  
Least Squares ◽  
Standard Error ◽  
Gravitational Constant ◽  
Gravity Data ◽  
Residual Distribution ◽  
Density Measurements ◽  
Least Squares Fit ◽  
Least Squares Adjustment ◽  
Sufficient Precision

Although the Tokaanu experiment does contradict the proposal that the gravitational constant G increases with scale, the result is not significant. The standard error in the least‐squares adjustment is at least 1 percent, which exceeds the predicted variation in G. The uncertainty in mean density is nearer 5 percent. Gravity data with sufficient precision to test for a scale effect in G are obtainable; the main problem appears to be the uncertainty in density determinations. Stacey et al (1981) made a least‐squares determination of G using gravity and density measurements from a mine. However, the pattern of residuals obtained indicated the presence of anomalous masses not adequately accounted for by their density averaging. The method I have used which models the spatial variation in density offers the possibility of obtaining a least‐squares fit for G with a satisfactory residual distribution. However, the problem of the effect on bulk density of joints and voids not sampled in hand specimens remains.

Determination of the Ovality of Crude Oil Storage Tanks Using Least Squares

2011 ◽  
Vol 367 ◽  
pp. 475-483 ◽  
Author(s):  
R. Irughe Ehigiator ◽  
J.O. Ehiorobo ◽  
Ashraf A. Beshr ◽  
M.O. Ehigiator
Keyword(s):  
Crude Oil ◽  
Least Squares ◽  
Unbiased Estimate ◽  
Circular Cross Section ◽  
Field Measurements ◽  
Storage Tanks ◽  
Linear Measurements ◽  
Oil Storage ◽  
Least Squares Adjustment

In the processing of field measurements, the observations are adjusted using the least squares principle which gives unbiased estimate of the parameter sought together with their accuracies. In this paper, the use of the Least Squares model in the determination of the tank radius, centre point coordinates and ovality are discussed. The circular cross section of the crude oil storage tanks was divided into sixteen monitoring stations at equal intervals around the tank and at an elevation of 2m from the tank base. Total station instrument was then used to carry out angular and linear measurements by method of multiple intersection to reflectors held on the studs. The field measurements were post processed and adjustment of observation carried out by Least Squares adjustment method. The adjusted coordinates together with the computed radius were then used to determine tanks ovality. All data processing and adjustment were carried out with the aid of MATLAB Software for the 2003, 2004 and 2008 measurement epochs.The results of the study revealed an expansion of the tank shell between 2004 and 2008 measurement epoch. The radius of the tank was computed to be 38.187m in 2003 and 2004 and 38.205m in 2008 respectively.

Classical Concepts of Least Squares Adjustment

1965 ◽  
Vol 19 (1) ◽  
pp. 16-26
Author(s):  
Gottfried Konecny
Keyword(s):  
Statistical Analysis ◽  
Least Squares ◽  
Standard Error ◽  
Statistical Tests ◽  
Arithmetic Mean ◽  
Method Of Least Squares ◽  
Correlated Observations ◽  
Symmetrical Distribution ◽  
Least Squares Adjustment ◽  
Normally Distributed

A review of the fundamental classical concepts of least squares adjustment, based on the development by Gauss is presented. The method of least squares leads to a most probable value of the adjusted quantity under the assumption that the arithmetic mean yields the most probable result and that the uncorrelated observations are normally distributed. It is shown further that the method of least squares leads to an adjusted value with a resulting smallest standard error for any symmetrical distribution. It is indicated that this is also true for correlated observations and that various statistical tests make least squares adjustment a powerful tool for statistical analysis.

Background Correction in Raman Spectroscopic Determination of Dimethylsulfone, Sulfate, and Bisulfate

1985 ◽  
Vol 39 (3) ◽  
pp. 463-470 ◽  
Author(s):  
Yong-Chien Ling ◽  
Thomas J. Vickers ◽  
Charles K. Mann
Keyword(s):  
Least Squares ◽  
Simulated Data ◽  
Background Correction ◽  
Data Sets ◽  
Raman Spectroscopic ◽  
Dimethyl Sulfone ◽  
Quantitative Measurements ◽  
Least Squares Fit ◽  
Background Curvature

A study has been made to compare the effectiveness of thirteen methods of spectroscopic background correction in quantitative measurements. These include digital filters, least-squares fitting, and cross-correlation, as well as peak area and height measurements. Simulated data sets with varying S/N and degrees of background curvature were used. The results were compared with the results of corresponding treatments of Raman spectra of dimethyl sulfone, sulfate, and bisulfate. The range of variation of the simulated sets was greater than was possible with the experimental data, but where conditions were comparable, the agreement between them was good. This supports the conclusion that the simulations were valid. Best results were obtained by a least-squares fit with the use of simple polynomials to generate the background correction. Under the conditions employed, limits of detection were about 80 ppm for dimethyl sulfone and sulfate and 420 ppm for bisulfate.

On: “A least‐squares approach to depth determination from gravity data” by O.P. Gupta (GEOPHYSICS, 48, 357–360, March 1983)

Geophysics ◽  
1990 ◽  
Vol 55 (3) ◽  
pp. 376-377 ◽  
Author(s):  
El‐Sayed M. Abdelrahman
Keyword(s):  
Nonlinear Equation ◽  
Least Squares ◽  
Gravity Anomaly ◽  
Gravity Data ◽  
Residual Gravity ◽  
Depth Determination ◽  
Residual Gravity Anomaly ◽  
Least Squares Approach

In the article by Gupta, the problem of depth determination of a buried structure from the residual gravity anomaly has been transformed into a problem of finding the solution of a nonlinear equation of the form f(z) = 0. Gupta begins his formulation of the problem with equation (1) from Mettleton (1942) Eq. (1) [Formula: see text]

Nucleon separation and pairing energies, decay energies, and atomic masses for 68 ≤ Z ≤ 72

1977 ◽  
Vol 55 (15) ◽  
pp. 1360-1378 ◽  
Author(s):  
K. S. Sharma ◽  
J. O. Meredith ◽  
R. C. Barber ◽  
K. S. Kozier ◽  
S. S. Haque ◽  
...  
Keyword(s):  
Least Squares ◽  
Nuclear Reaction ◽  
Mass Difference ◽  
Atomic Mass ◽  
Mass Defect ◽  
Pairing Energy ◽  
Least Squares Adjustment ◽  
Proton Pairing ◽  
Q Values

A set of 24 precise determinations of mass spectroscopic doublet spacings, including a new determination of the 176Hf35Cl – 174Hf37Cl mass difference, has been combined with nuclear reaction and decay Q values in a least squares adjustment of the atomic mass differences in the region 68 ≤ Z ≤ 72. The following quantities have been calculated for each nuclide: separation energies for the last neutron and last pair of neutrons (Sn, S2n), the neutron pairing energy (Pn), separation energies for the last proton and last pair of protons (Sp, S2p), the proton pairing energy (Pp), Q values for α and β− decays, and the mass defect. The systematic variations of these quantities with N and Z are discussed.

Curie point depths of the Island of Kyushu and surrounding areas, Japan

Geophysics ◽  
1985 ◽  
Vol 50 (3) ◽  
pp. 481-494 ◽  
Author(s):  
Y. Okubo ◽  
R. J. Graf ◽  
R. O. Hansen ◽  
K. Ogawa ◽  
H. Tsu
Keyword(s):  
Heat Flow ◽  
Least Squares ◽  
Curie Point ◽  
Power Plants ◽  
Gravity Data ◽  
Depth Map ◽  
Curie Point Depth ◽  
Geothermal Resources ◽  
Regional Geology ◽  
Least Squares Fit

As part of a comprehensive, nationwide evaluation of geothermal resources for Japan, the first of the Curie point depth maps, covering the island of Kyushu, has been prepared. The map was created by inverting gridded, regional aeromagnetic data. Two satisfactory algorithms were developed to invert the gridded data based upon a distribution of point dipoles. The first algorithm estimates [Formula: see text],[Formula: see text], and [Formula: see text], the coordinates of the centroid of the distribution, by computing a least‐squares fit to the radial frequency of the Fourier transform; the second algorithm estimates centroid depth only by computing a least‐squares fit to the squared amplitude of the frequency estimates. The average depth to the top, [Formula: see text] of the collection of point dipoles, was estimated by a variation of the second algorithm. The depth to the bottom of the dipoles, inferred Curie point depth, is [Formula: see text]. The depth estimates are hand contoured to produce the final map. The Curie point depth map is then compared to regional geology and heat flow data, and to a limited set of gravity data. Good correlations are found between the Curie point depths and the heat flow and regional geology. A spatial correlation observed between gravity and Curie point depths is considered a secondary, structural effect. Locations of the currently operating geothermal power plants correspond to the shallowest Curie point depths. Based on these comparisons, we conclude that the methods provide geologically reasonable results which are usable in a nationwide geothermal assessment program.

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