### Abstract

A linear retrieval (spectral deconvolution) algorithm is developed and applied to high-resolution laboratory infrared spectra of particulate mixtures and their end-members. The purpose is to place constraints on, and test the viability of, linear spectral deconvolution of high-resolution emission spectra. The effects of addition of noise, data reproducibility, particle size variation, an increasing number of minerals in the mixtures, and blind end-member input are also examined. Thermal emission spectra of 70 mineral mixtures ranging from 2 to 15 end-members and having particle diameters of 250-500 μm were obtained. Deconvolution results show that the assumption of linear mixing is valid and enables mineral percentage prediction to within 5% on average with residual errors of less than 0.1% total emissivity. One suite (21 distinct mixtures), varying from <10 μm to 500 μm, was also prepared to test the limits of the model at decreasing particle sizes. Incoherent volume scattering at grain diameters less than several times the wavelength (∼60 μm) produces significant changes in spectral band morphology and hence, an increase in the root-mean-squared (RMS) error of the model. Because of this, it appears that spectral mixing remains essentially linear to ∼60 μm (using the 250-500 μm size fraction as end-members). Below this threshold, the linear retrieval algorithm fails. However, with the appropriate particle diameter end-member spectra for the corresponding mixtures, the errors are reduced significantly and linearity continues through to the 10-20 μm size fraction. Additions of increasing amounts of noise cause a deviation of an additional 2.4%, whereas variability due to spectrometer reproducibility produces an average error of 4.0%. The model is also able to detect accurately minerals in mixtures containing 15 end-members, well beyond the number of geological significance. Extensive error analysis and model testing confirm the appropriateness of linear deconvolution as a useful and powerful tool to examine complexly mixed emission spectra in the laboratory and the field. The results of this study provide a foundation for remote sensing analyses of thermal infrared data from current airborne and future satellite instruments planned for Earth and Mars.

Original language | English (US) |
---|---|

Pages (from-to) | 577-596 |

Number of pages | 20 |

Journal | Journal of Geophysical Research: Solid Earth |

Volume | 103 |

Issue number | 1 |

State | Published - Jan 10 1998 |

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### ASJC Scopus subject areas

- Geochemistry and Petrology
- Geophysics
- Earth and Planetary Sciences (miscellaneous)
- Space and Planetary Science
- Atmospheric Science
- Astronomy and Astrophysics
- Oceanography

### Cite this

*Journal of Geophysical Research: Solid Earth*,

*103*(1), 577-596.

**Mineral abundance determination : Quantitative deconvolution of thermal emission spectra.** / Ramsey, Michael S.; Christensen, Philip.

Research output: Contribution to journal › Article

*Journal of Geophysical Research: Solid Earth*, vol. 103, no. 1, pp. 577-596.

}

TY - JOUR

T1 - Mineral abundance determination

T2 - Quantitative deconvolution of thermal emission spectra

AU - Ramsey, Michael S.

AU - Christensen, Philip

PY - 1998/1/10

Y1 - 1998/1/10

N2 - A linear retrieval (spectral deconvolution) algorithm is developed and applied to high-resolution laboratory infrared spectra of particulate mixtures and their end-members. The purpose is to place constraints on, and test the viability of, linear spectral deconvolution of high-resolution emission spectra. The effects of addition of noise, data reproducibility, particle size variation, an increasing number of minerals in the mixtures, and blind end-member input are also examined. Thermal emission spectra of 70 mineral mixtures ranging from 2 to 15 end-members and having particle diameters of 250-500 μm were obtained. Deconvolution results show that the assumption of linear mixing is valid and enables mineral percentage prediction to within 5% on average with residual errors of less than 0.1% total emissivity. One suite (21 distinct mixtures), varying from <10 μm to 500 μm, was also prepared to test the limits of the model at decreasing particle sizes. Incoherent volume scattering at grain diameters less than several times the wavelength (∼60 μm) produces significant changes in spectral band morphology and hence, an increase in the root-mean-squared (RMS) error of the model. Because of this, it appears that spectral mixing remains essentially linear to ∼60 μm (using the 250-500 μm size fraction as end-members). Below this threshold, the linear retrieval algorithm fails. However, with the appropriate particle diameter end-member spectra for the corresponding mixtures, the errors are reduced significantly and linearity continues through to the 10-20 μm size fraction. Additions of increasing amounts of noise cause a deviation of an additional 2.4%, whereas variability due to spectrometer reproducibility produces an average error of 4.0%. The model is also able to detect accurately minerals in mixtures containing 15 end-members, well beyond the number of geological significance. Extensive error analysis and model testing confirm the appropriateness of linear deconvolution as a useful and powerful tool to examine complexly mixed emission spectra in the laboratory and the field. The results of this study provide a foundation for remote sensing analyses of thermal infrared data from current airborne and future satellite instruments planned for Earth and Mars.

AB - A linear retrieval (spectral deconvolution) algorithm is developed and applied to high-resolution laboratory infrared spectra of particulate mixtures and their end-members. The purpose is to place constraints on, and test the viability of, linear spectral deconvolution of high-resolution emission spectra. The effects of addition of noise, data reproducibility, particle size variation, an increasing number of minerals in the mixtures, and blind end-member input are also examined. Thermal emission spectra of 70 mineral mixtures ranging from 2 to 15 end-members and having particle diameters of 250-500 μm were obtained. Deconvolution results show that the assumption of linear mixing is valid and enables mineral percentage prediction to within 5% on average with residual errors of less than 0.1% total emissivity. One suite (21 distinct mixtures), varying from <10 μm to 500 μm, was also prepared to test the limits of the model at decreasing particle sizes. Incoherent volume scattering at grain diameters less than several times the wavelength (∼60 μm) produces significant changes in spectral band morphology and hence, an increase in the root-mean-squared (RMS) error of the model. Because of this, it appears that spectral mixing remains essentially linear to ∼60 μm (using the 250-500 μm size fraction as end-members). Below this threshold, the linear retrieval algorithm fails. However, with the appropriate particle diameter end-member spectra for the corresponding mixtures, the errors are reduced significantly and linearity continues through to the 10-20 μm size fraction. Additions of increasing amounts of noise cause a deviation of an additional 2.4%, whereas variability due to spectrometer reproducibility produces an average error of 4.0%. The model is also able to detect accurately minerals in mixtures containing 15 end-members, well beyond the number of geological significance. Extensive error analysis and model testing confirm the appropriateness of linear deconvolution as a useful and powerful tool to examine complexly mixed emission spectra in the laboratory and the field. The results of this study provide a foundation for remote sensing analyses of thermal infrared data from current airborne and future satellite instruments planned for Earth and Mars.

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UR - http://www.scopus.com/inward/citedby.url?scp=0001300277&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0001300277

VL - 103

SP - 577

EP - 596

JO - Journal of Geophysical Research: Atmospheres

JF - Journal of Geophysical Research: Atmospheres

SN - 2169-897X

IS - 1

ER -