Erratum

doi:10.2138/am-2023-E10854

The inverse problem of unpolarized infrared spectroscopy of geological materials: Estimation from noisy random sampling of a quadratic form by Andrew Jackson, Robert L. Parker, Malcolm Sambridge, Catherine Constable, and Aaron S. Wolf (August, vol. 103, p. 1176–1184, 2018). Article DOI: http://doi.org/10.2138/am-2018-6152. Erratum DOI: https://doi.org/10.2138/am-2023-E10854

Recently, the authors discovered that Figure 1, Equation 6, and Equation 27 were improperly presented. Below are the correct Figure and equations.

A_{unpol} = \frac{1}{2} (A_{b} + A_{c}) s i n^{2} φ c o s^{2} ψ + \frac{1}{2} (A_{a} + A_{c}) s i n^{2} φ s i n^{2} ψ + \frac{1}{2} (A_{a} + A_{b}) {c o s}^{2} φ

(6)

F (Q_{0}) = {\begin{matrix} 1 - \frac{2}{π} \int_{0}^{\frac{π}{2}} \sqrt{\frac{a_{1} + a_{2} - 2 Q_{0} + (a_{1} - a_{2}) c o s 2 φ}{a_{1} + a_{2} - 2 a_{3} + (a_{1} - a_{2}) c o s 2 φ}} d φ; Q_{0} \leq a_{2} \\ \frac{2}{π} \int_{0}^{\frac{π}{2}} \sqrt{\frac{2 Q_{0} - a_{2} - a_{3} + (a_{2} - a_{3}) c o s 2 φ}{2 a_{1} - a_{2} - a_{3} + (a_{2} - a_{3}) c o s 2 φ}} d φ; Q_{0} > a_{2} . \end{matrix}

(27)

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