A least squares method of estimating length to target strength relationships from in situ target strength distributions and length frequencies

2001 ◽  
Vol 109 (1) ◽  
pp. 155-163 ◽  
Author(s):  
Patrick L. Cordue ◽  
Roger F. Coombs ◽  
Gavin J. Macaulay
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Target Strength ◽  
Strength Distributions

Densities determined from surface and subsurface gravity measurements

Geophysics ◽  
1981 ◽  
Vol 46 (11) ◽  
pp. 1568-1571 ◽  
Author(s):  
B. A. Sissons
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Average Density ◽  
Laboratory Measurements ◽  
Density Estimates ◽  
Direct Inversion ◽  
Gravity Measurements ◽  
The Difference ◽  
Made In

A least‐squares method for the direct inversion of surface and subsurface gravity measurements to obtain in situ density estimates is presented. The method is applied to a set of measurements made in a tunnel through the flank of an andesitic volcano. Densities obtained are [Formula: see text] for material in the top 100 m increasing to [Formula: see text] at about 200 m depth. The average density for rocks penetrated by the tunnel is, from laboratory measurements, [Formula: see text] i.e., about 4 percent higher. The difference is ascribed to joints and voids present in situ and not sampled in the laboratory specimens.

Electromagnetic seismograph constants by least-squares inversion

1969 ◽  
Vol 59 (3) ◽  
pp. 1335-1348
Author(s):  
B. J. Mitchell ◽  
M. Landisman
Keyword(s):  
Least Squares ◽  
Love Wave ◽  
Least Squares Method ◽  
Linear Trend ◽  
Wave Train ◽  
Vertical Component ◽  
Long Period ◽  
Electromagnetic Seismograph ◽  
Before And After

abstract A least-squares method has been developed to determine the free periods and damping constants of an electromagnetic seismograph from its calibration pulse. The resulting values are correct to within a few tenths of one per cent for synthetic calibration pulses, even when moderate levels of microseismic noise are present. The seismograph constants of the long-period vertical component at Dallas, Texas were determined from in situ measurements and compared with those calculated from the calibration pulse. The results agreed to within four per cent or better for the free periods and damping constants, after correcting for the linear trend and the base coordinate system of the observed pulse. The values differed by as much as 30 per cent when the linear trend and base coordinate corrections were ignored. Two sets of instrumental constants from an unmatched pair of horizontal seismographs were determined from their calibration pulses. Directions of particle motion for a Love wave train recorded on the same instruments were computed before and after instrumental corrections; the results differed by as much as 8 degrees.

‘Least squares’ method—theorem or law?

1980 ◽  
Vol 59 (9) ◽  
pp. 8
Author(s):  
D.E. Turnbull
Keyword(s):  
Least Squares ◽  
Least Squares Method

An Augmented Iteratively Re-weighted and Refined Least Squares Method for lp Minimization Problem in Inverse Modeling of Potential Field Magnetic Data

2020 ◽  
Vol 1 (3) ◽  
Author(s):  
Maysam Abedi
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Least Squares ◽  
Minimization Problem ◽  
Potential Field ◽  
Field Data ◽  
Least Squares Method ◽  
Porphyry Copper ◽  
Magnetic Data ◽  
Magnetic Field Data

The presented work examines application of an Augmented Iteratively Re-weighted and Refined Least Squares method (AIRRLS) to construct a 3D magnetic susceptibility property from potential field magnetic anomalies. This algorithm replaces an lp minimization problem by a sequence of weighted linear systems in which the retrieved magnetic susceptibility model is successively converged to an optimum solution, while the regularization parameter is the stopping iteration numbers. To avoid the natural tendency of causative magnetic sources to concentrate at shallow depth, a prior depth weighting function is incorporated in the original formulation of the objective function. The speed of lp minimization problem is increased by inserting a pre-conditioner conjugate gradient method (PCCG) to solve the central system of equation in cases of large scale magnetic field data. It is assumed that there is no remanent magnetization since this study focuses on inversion of a geological structure with low magnetic susceptibility property. The method is applied on a multi-source noise-corrupted synthetic magnetic field data to demonstrate its suitability for 3D inversion, and then is applied to a real data pertaining to a geologically plausible porphyry copper unit.  The real case study located in  Semnan province of  Iran  consists  of  an arc-shaped  porphyry  andesite  covered  by  sedimentary  units  which  may  have  potential  of  mineral  occurrences, especially  porphyry copper. It is demonstrated that such structure extends down at depth, and consequently exploratory drilling is highly recommended for acquiring more pieces of information about its potential for ore-bearing mineralization.

Theoretical accuracy of the last squares method in the isotope dilution analysis

1984 ◽  
Vol 49 (4) ◽  
pp. 805-820
Author(s):  
Ján Klas
Keyword(s):  
Least Squares ◽  
Isotope Dilution ◽  
Least Squares Method ◽  
Isotope Dilution Analysis ◽  
Straight Line ◽  
The One ◽  
Two Parameter ◽  
Theoretical Accuracy

The accuracy of the least squares method in the isotope dilution analysis is studied using two models, viz a model of a two-parameter straight line and a model of a one-parameter straight line.The equations for the direct and the inverse isotope dilution methods are transformed into linear coordinates, and the intercept and slope of the two-parameter straight line and the slope of the one-parameter straight line are evaluated and treated.

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