A least-squares approach to mass transport calculations using the isocon method

Baumgartner, Lukas P.; Olsen, Sakiko N.

doi:10.2113/gsecongeo.90.5.1261

Cited by 97 publications

(78 citation statements)

References 15 publications

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“…It is argued by Grant (1986) that such scaling is not only mathematically valid but it also gives due weight to the elements whose concentration magnitude is low. However, Baumgartner and Olsen (1995) argued and illustrated using a hypothetical example that how scaling can bias the slope of the ISOCON. Inspite of this, Grant (2005) in his recent review article out-right rejected this mathematically proved fact giving an untenable argument that scaling is irrelevant to ISOCON slope because it is (C i s /C i p ) a ratio and the scale factors would cancel out.…”

Section: Ambiguities In Isocon Resultsmentioning

confidence: 99%

“…When a data point of an element is scaled forward by multiplying with an integer, the contribution of the element increases because the squared residue also becomes large. This was termed by Baumgartner and Olsen (1995) as torque exerted by data points on the visually or mathematically determined best fit ISOCON. This would mean that the best fit regression line shall become biased towards the elements that plot away from the origin compared to those near the origin.…”

Section: Ambiguities In Isocon Resultsmentioning

confidence: 99%

“…Even if the best fit is obtained by visual estimates, the eyes also act as least squares integrator. Since scaling is inevitable for obtaining graphical solution by ISOCON analysis, Baumgartner and Olsen (1995) proposed a rational basis for scaling that would minimize the error due to uncertainties. They proposed to do this by scaling down (towards origin) the abundance of an element with larger uncertainties and scaling up (away from origin) the elements that are associated with smaller uncertainties such that the torque on the best fit ISOCON by least squares minimization becomes appropriately weighted and statistically more robust.…”

Section: Ambiguities In Isocon Resultsmentioning

confidence: 99%

“…Under ideal conditions, all the solutions should converge to give a unique solution but in practice, it does not happen. In order to find an acceptable solution, an average value is taken as in case of Gresens (1967) or a best fit line is obtained as in case of Grant's (1986) ISOCON method or weighted least squares regression as in case of Baumgartner and Olsen (1995).…”

Section: Isocon Methods Of Mass Balancementioning

confidence: 99%

“…The scaling influence the best fit ISOCON and hence the reference frame for mass-balance estimates. This has been first pointed out by Baumgartner and Olsen (1995) in an attempt to modify ISOCON method. Instead of arbitrary numbers, they proposed a rational basis to assign scaling…”

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confidence: 95%

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Arbitrary scaling in ISOCON method of geochemical mass balance: An evaluation of the graphical approach

Mukherjee

Gupta²

2008

Geochem. J.

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Rock alteration processes can be studied through geochemical Mass Balance (MB) estimation in several ways. Due to the ease of its adaptability, especially its graphical approach, the ISOCON method of mass balance is extensively used for such studies. However the technique suffers from a serious limitation, in particular with reference to the graphical treatment involving arbitrary scaling, which is explained in this paper with the help of illustrative examples. The reference frame for MB obtained by best fit regression is biased to the element scaled upward that plot away from the origin. The scaling factors actually act as weighting factors which bias the slope of the ISOCON line because it is controlled by data points having higher numerical value in the plot. Since scaling of concentration data are unavoidable in ISOCON analysis, the results of MB may potentially be misleading. The slope of the best fit ISOCON line may vary within the range of slopes defined by individual conserved elements. In case, no scaling is done, the ISOCON shall weight in proportion to the abundance of the immobile elements. The co-linearity of the immobile elements with origin is also subjective in nature with the elements near origin apparently seem to satisfy a wide range ISOCON slopes than those that are away from origin. When equal weight is assigned to all elements, regardless of their concentration level, an average of the slopes of the immobile elements (i.e., concentration ratios in altered to unaltered) may provide better approximation for reference frame without recourse to graphical plot and ISOCON solution. The existing weighted least-squares or equal weight leastsquares ISOCON method is found to be more appropriate in case of higher uncertainty in the protolith compositions. In any case, a proper identification of the conserved species is an essential prerequisite to successful implementation of mass balance computation minimizing the inherent errors of the ISOCON technique.

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Section: Ambiguities In Isocon Resultsmentioning

confidence: 99%

Section: Ambiguities In Isocon Resultsmentioning

confidence: 99%

Section: Ambiguities In Isocon Resultsmentioning

confidence: 99%

Section: Isocon Methods Of Mass Balancementioning

confidence: 99%

mentioning

confidence: 95%

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Arbitrary scaling in ISOCON method of geochemical mass balance: An evaluation of the graphical approach

Mukherjee

Gupta²

2008

Geochem. J.

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Early weakening processes inside thrust fault

et al. 2015

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Observations from deep boreholes at several locations worldwide, laboratory measurements of frictional strength on quartzo-feldspathic materials, and earthquake focal mechanisms indicate that crustal faults are strong (apparent friction μ ≥ 0.6). However, friction experiments on phyllosilicate-rich rocks and some geophysical data have demonstrated that some major faults are considerably weaker. This weakness is commonly considered to be characteristic of mature faults in which rocks are altered by prolonged deformation and fluid-rock interaction (i.e., San Andreas, Zuccale, and Nankai Faults). In contrast, in this study we document fault weakening occurring along a marly shear zone in its infancy (<30 m displacement). Geochemical mass balance calculation and microstructural data show that a massive calcite departure (up to 50 vol %) from the fault rocks facilitated the concentration and reorganization of weak phyllosilicate minerals along the shear surfaces. Friction experiments carried out on intact foliated samples of host marls and fault rocks demonstrated that this structural reorganization lead to a significant fault weakening and that the incipient structure has strength and slip behavior comparable to that of the major weak faults previously documented. These results indicate that some faults, especially those nucleating in lithologies rich of both clays and high-solubility minerals (such as calcite), might experience rapid mineralogical and structural alteration and become weak even in the early stages of their activity.

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Quantifying weathering on variable rocks, an extension of geochemical mass balance: Critical zone and landscape evolution

Fisher

Aufdenkampe

Yoo

2017

Earth Surf Processes Landf

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We present a statistical model of soil and rock weathering in deep profiles to expand the capacity to assess weathering to heterogeneous bedrock types, which are common at the Earth's surface. We developed the Weathering Trends (WT) model by extending the fractional mass change calculation (tau) of the geochemical mass balance model in two important ways. First, WT log transforms the elemental ratio data, to discern the log‐linear patterns that naturally develop from thermodynamic and kinetic laws of chemistry. Second, WT statistically fits log‐transformed element concentration ratio data – log(cj/ci), the only depth‐varying term in tau – as a function of depth to determine characteristic depths of transitions in weathering processes, along with confidence intervals. With no prior assumptions, WT estimates average parent material composition, average composition of the upper weathered zone and mean fractional mass change of each element over the entire weathering profile. WT displays the mean shape of weathering profiles of log‐transformed geochemical data bounded by calculated confidence intervals. We share the WT model code as an open‐source R package (https://github.com/fisherba/WeatheringTrends). The WT model was designed to interpret two 21 m cores from the Laurels Schist bedrock in the Christina River Basin Critical Zone Observatory in the Pennsylvania Piedmont, where our morphological and elemental data provided inconclusive estimates of bedrock depth. The WT model differentiated between rock variability and weathering to delineate the maximum extent of weathering at 12.3 m (CI 95% [9.2, 21.3]) in Ridge Well 1 and 7.2 m (CI 95% [4.3, 13.0]) in Interfluve Well 2. The water table was 5–8 m below fresh rock at Ridge Well 1, but at the same depth as fresh rock at the lower elevation interfluve. We assess statistical approaches to identify the best immobile element for use in WT and tau calculations. Copyright © 2017 John Wiley & Sons, Ltd.

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A least-squares approach to mass transport calculations using the isocon method

Cited by 97 publications

References 15 publications

Arbitrary scaling in ISOCON method of geochemical mass balance: An evaluation of the graphical approach

Arbitrary scaling in ISOCON method of geochemical mass balance: An evaluation of the graphical approach

Early weakening processes inside thrust fault

Quantifying weathering on variable rocks, an extension of geochemical mass balance: Critical zone and landscape evolution

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