The goal for the LAS technique used on Leg 199 was to deliver rapid semiquantitative mineral concentrations for the purpose of studying paleoclimate. In the equatorial Pacific, the minerals with the most important paleoclimate significance are opal and calcite and, to a lesser degree, smectite vs. illite. By using multiple regression and matrix inversion, we were able to use local ground truth to calibrate spectral responses. The result is an algorithm that can be used to rapidly calculate concentrations of calcite, opal, smectite, and illite. Postcruise research will involve improved algorithms, including use of nonlinear mixing models and singular-value decomposition (Fisher and Underwood, 1995).
To provide a calibration of expected LAS mineralogical responses for Leg 199, we used a suite of 71 local ground-truth samples. These samples were chosen from six sites in the equatorial Pacific: ODP Site 846, ODP Site 162, and four Leg 199 site survey cores (EW9709). The sediments at these sites (mainly calcite, opal, and terrigenous materials) resemble those that were encountered during Leg 199. The spectra from these samples were collected using the instrumentation setup shown in Figure F1A because this were the same method used during Leg 199. We enlisted the help of Mitchell W. Lyle and Annette Olivarez Lyle (Olivarez Lyle and Lyle, this volume) to analyze the samples for which calcite and opal concentrations were not already known.
The first 22 samples came from Site 846 (91°W, 2°S). Samples were chosen at the same locations (±3 cm) as ones previously analyzed by Mix et al. (1995) for calcite, opal, and "other" (other = 100% - %calcite - %opal) and range in depth from 4.05 to 183.54 mbsf. Since the source area for the clay is most likely the volcanic regions of Central and South America, we concluded that the dominant clay found at this site is smectite. The second set consists of 35 samples taken from four EW97909 cores (the site survey cores for ODP Leg 199). We chose 8 samples from EW9709-3PC, which range in depth from 0.33 to 13.39 mbsf; 15 samples from EW9709-7PC, which range in depth from 1.22 to 15.20 mbsf; 8 samples from EW9709-12PC, which range in depth from 2.58 to 12.63 mbsf; and 4 samples from EW9709-21GC, which range in depth from 0.2 to 2.37 mbsf. Olivarez Lyle and Lyle (this volume) analyzed calcite and opal concentrations of 5-g/cm3 subsamples of each sample. The dominant clay mineral (illite or smectite) was identified subjectively by LAS interpretation. The third set of ground-truth data consists of 14 samples from DSDP Site 162 (14°N, 140°W), ranging in depth from 0.90 to 150.00 mbsf. These samples were also analyzed by Olivarez Lyle and Lyle (this volume) for calcite and opal concentrations. XRD analyses (Zemmels, 1973) indicate that smectite is the dominant clay mineral throughout Site 162. The terrigenous component of our samples commonly includes minor amounts of quartz and other clay species, but we only refer to the dominant clay mineral. Table T1 displays all the mineralogical ground-truth data used in this study.
The first step in analyzing the ground-truth spectra was to determine portions of the spectral curve that react differently to different minerals. Analysis of the entire spectrum is inappropriate because the broad spectral shape can be sensitive to minor mineralogic components (e.g., quartz, feldspar, and organic matter). Instead, we selected about a dozen spectral features that seem to be significant (e.g., depth of the 1900-nm water trough). We used stepwise multiple regression, with each spectral feature as dependent variable and with known mineral concentrations as independent variables, to identify and quantify the spectral features that are reliably predicted by mineral concentration. It is important that the relationship is robust, fitting data from all three data sets without systematic residuals. Site-dependent residuals increase the likelihood of biased predictions for Leg 199 data. About a third of the potentially useful spectral features were rejected either because they poorly predicted mineral percentage or because of systematic residuals.
After the multiple regression calculations, we had eight spectral features that were usefully predictable (R = 0.66-0.92) (Table T2). These equations, plus the unity equation
form a set of simultaneous equations that can be expressed in matrix form as
where K is a 9 x 4 coefficient matrix determined by multiple regression, F is a 4 x 1 matrix of mineral fractions (or concentrations of the standards), and S is a 9 x 1 matrix of spectral features. For calculation of the mineral fractions (F) of any sample from its spectral responses (S), we inverted the coefficient matrix
With nine equations and only four unknowns, the result is an overdetermined least-squares solution. Before inversion, however, all terms in each spectral-feature equation were divided by the standard deviation of that spectral feature, thereby weighting each equation similarly. For unknowns, values for each spectral feature must be divided by this same standard deviation before applying the matrix equation above.
Our four-mineral solution solves for percentages of calcite, opal, smectite, and illite. Based on the correlation between observed and predicted mineral percentages, this solution is very good for calcite, opal, and illite but only fair for smectite. Reliability of the illite solution is limited, however, by the fact that only 6% of our standards have any significant illite at all. We use these results, therefore, only as a first-pass analysis. If the analysis of independent mineralogical data for a site indicates that illite is rare or absent, we then use revised smectite concentrations based on multiple regression and inversion of a set of three-mineral (calcite, opal, and smectite) equations.
The unity equation is only one of the nine equations involved in the least-squares solution, so the sum of estimated mineral fractions is not exactly 1. For our standards, almost all samples had total estimated fractions of 0.9-1.1. Furthermore, the best-fit mineral percentages may include a predicted negative concentration for a mineral component. Apparent negative concentrations were converted to zero, then concentrations of all components were adjusted to total one. Figure F7 compares known mineral concentrations to LAS-predicted mineral concentrations for our data set of standards. The four-mineral solution is shown for all four minerals along with the three-mineral smectite solution. The correlation coefficients range from a high of 0.95 for calcite to a low of 0.85 for the four-mineral smectite solution. An error of up to ±20% is seen between the predicted and actual concentrations, indicating that LAS will be able to predict overall changes in mineralogy during Leg 199, but actual mineral concentrations will not be as accurate.