Michael M. Herron

Empirically Minimax Affine Mineralogy Estimates from Fourier Transform Infrared Spectrometry Using a Decimated Wavelet Basis

The Fourier transform infrared (FT-IR) spectrum of a rock contains information about its constituent minerals. Using the wavelet transform, we roughly separate the mineralogical information in the FT-IR spectrum from the noise, using an extensive set of training data for which the true mineralogy is known. We ignore wavelet coefficients that vary too much among repeated measurements on rocks with the same mineralogy, since these are likely to reflect analytical noise. We also ignore those that vary too little across the entire training set, since they do not help to discriminate among minerals. We use the remaining wavelet coefficients as the data for the problem of estimating mineralogy from FT-IR data. For each mineral of interest, we construct an affine estimator ◯ of the mass fraction x of the mineral of the form , where is a vector, is the vector of retained wavelet coefficients, and b is a scalar. We find and b by minimizing the maximum error of the estimator over the training set. When applying the estimator, we “truncate” to keep the estimated mineralogy between 0 and 1. The estimators typically perform better than weighted nonnegative least-squares.

End-Member Feldspar Concentrations Determined by FTIR Spectral Analysis

ABSTRACT Feldspar mineralogy, reported as concentrations of KAlSi3O8, NaAlSi3O8, and CaAl2Si2O8, can be determined from FTIR spectroscopy. In this study end-member FTIR spectra were constructed from sample spectra and their associated K-, Na- and Ca- feldspar concentrations using a least-squares full spectrum program. This was necessary because none of the samples have single-phase, pure end-member composition. The K-, Na-, and Ca-feldspar concentrations are computed by fitting the sample FTIR spectrum to the end-member FTIR spectra using a nonnegative least-squares program. For the feldspar samples examined we found that when the compositions determined from infrared spectroscopy are compared to the compositions deri ed from chemistry, the standard error of estimate for K-, Na-, and Ca-feldspar is 1.0, 0.9, and 0.7 absolute mole %, respectively.

Absolute elemental concentrations estimated from geochemical well logging using neutron-induced gamma-ray spectrometry and a geological model

Elemental concentrations of several inorganic elements were determined on a continuous basis with depth using the Schlumberger gamma-ray spectrometry (GST) log in a Santa Fe Energy Co. well in the Kern Front field, Bakersfield, California, Relative gamma-ray yields of Si, Ca, Fe, S, Cl, H, Ti, Gd + Sm, and K were determined using a weighted least-squares fitting of standard elemental spectra, determined from laboratory measurements, to the measured spectra. The relative yields were then placed on an absolute basis using measured sensitivity coefficients and the assumption that, excluding Cl and H, the abundances of these elements plus Al, considered as oxides and, for Ca, carbonates, total 100% of the rock. This assumption removes variations in porosity and salinity from impacting the denormalization procedure. The output is estimated absolute concentrations in weight percent of the rock that are compared with elemental analyses made on over 60 core plug and sidewall samples by x-ray fluorescence and neutron activation analysis.

Clay and Framework Mineralogy, Cation Exchange Capacity, Matrix Density, and Porosity from Geochemical Well Logging in Kern County, California: ABSTRACT

Elemental concentrations of several inorganic elements were determined in a continuous basis with depth using the Schlumberger gamma-ray spectrometry (GST) and natural gamma-ray spectrometry (NGS) logs in a Santa Fe Energy Company well in the Kern Front field in Bakersfield, California. Logs of Al, Si, Ca, K, Fe, Ti, and non-pore H were processed by a matrix multiplication procedure, used previously for a Venezuelan well, into estimated abundances of quartz, feldspar, calcite, ilmenite, and the clay minerals kaolinite, illite, and smectite. A total of 64 core-plug samples were analyzed for elemental content by x-ray fluorescence and neutron activation analysis and for mineralogy by bulk and < 4 ..mu.. clay x-ray diffraction analyses. Log-derived elemental concentrations and mineral abundances show good agreement with the core values. Cation exchange capacity (CEC) is estimated from the abundances of the clay minerals and typical values for these clays. The CEC log agrees well with CEC values determined on the core samples. The mineral abundance logs also permit an estimation of the average matrix density as a function of depth, derived from typical grain densities for each mineral phase. This matrix density log, combined with the bulk density log, yields a porosity log that comparesmorexa0» well with over 200 measurements on core.«xa0less