Applying geostatistical interpolation methods to studies of environmental contamination of urban soils and image analysis of time-of-flight secondary ion mass spectrometry
Milillo, Tammy M.
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Statistical techniques have been applied to a multitude of disciplines in order to interpret, analyze, and understand a variety of information and data. The field of geostatistics is a branch of multivariate statistics that utilizes spatial distribution information to accurately predict and display correlations that are present in various types of data. Geostatistics is commonly used in the fields of geography and geology. These techniques give insight into areas such as watershed, soil pH, erosion, and many other naturally occurring processes. Geostatistics has not been as widely applied in chemical and environmental analysis to answer important questions, pertaining to what is present, how much is present, and where the chemical concentration of concern is located. Within the field of geostatistics, common interpolation methods such as (i) ordinary kriging, (ii) ordinary co-kriging, (iii) indicator kriging, (iv) indicator co-kriging, and (v) inverse distance squared weighted (IDW) are used to provide accurate estimations of concentrations or other variables of interest by utilizing the correlation that results from known sample points and their geographic location to the point of estimation. These five techniques have thus been applied to analyze the extent of heavy metal concentrations found in the soil of Hickory Woods, a residential neighborhood located in South Buffalo. Hickory Woods has been the site of many ongoing environmental contamination studies. After comprehensive analysis of the data collected concerning the distribution of arsenic and lead in the soil, it was determined for both lead and arsenic that the indicator co-kriging method produced the most representative interpolated surface with the least amount of error for both the lead and arsenic distributions in this area. The in-depth analysis of Hickory Woods provided useful information as to how to establish site-specific background levels for lead and arsenic using these interpolation methods. The results were then translated into proposed remediation plans driven by the scientific data generated by this study instead of the more traditional approach, which is dictated by property lines and areas of jurisdiction. After examining the strengths and weaknesses of each interpolation method, benefits of incorporating geographic locational information into the analysis of chemical image maps created by time-of-flight secondary ion mass spectrometry (ToF-SIMS) analysis were investigated. These interpolation methods are applied to visualizing and analyzing spatial distributions and correlations between the components of a chemical image map. A ToF-SIMS image of a 2-euro coin was obtained to test each interpolation method's ability to accurately predict intensity values. With a series of samplings that removed increasing numbers of pixels from the original images, we evaluate the accuracy of images reconstructed from 99% to 0.5% of the original dataset. Accurately reconstructing images can reduce the time needed for image acquisition and ToF-SIMS chemical analysis. This study showed that these techniques did reduce the number of data points needed to accurately reconstruct an image. For the euro coin sample, the IDW technique performed the best, and allowed for an image reconstruction with 5% of the original data remaining. With the positive results from this study, a sample was created that had pertinent chemical information associated with it. The techniques known as ordinary kriging and IDW were applied to determine the chemical distribution and correlation present in a polymer sample that had been lithographically modified to contain areas rich in siloxane- and fluorine-containing components. This study compared the predicted intensities calculated by ordinary kriging and IDW techniques to determine which method was more advantageous for application in this system. A main goal of the study was to investigate how many points (pixels) could be removed from the original TOF-SIMS image when these methods were applied, thus providing an accurate estimate with minimal error. For this reason, different percentages of the original dataset were removed to evaluate how accurately these methods reconstructed the original image. For this sample, the ordinary kriging method performed the best, resulting in the reconstruction of the CxFy image with only 1% of the original data remaining, and the siloxane image with 10% of the original data remaining. The results of the study support the theory that spatial distribution can be instrumental in accurately determining and displaying spatial distributions present on a chemical image map. The removal of points also allows for clear segregation of the boundaries for different chemical species contained within the chemical image map. ToF-SIMS is valued for its ability to detect trace amounts of chemical species found on the surface of a sample. The instrument creates separate images for both the positive and negative ion spectra. These images are often contrasting images. To evaluate the correlation between different chemical species, the images are often overlaid or one goes through other mathematical processes such as principle component analysis (PCA), multiwavelet curve resolution (MCR), or other statistical processes in order to reduce the amount of noise found within the image. Removal of nonessential information helps to analyze the boundaries of chemical species found within a particular sample. Often, many pre-treatment steps are needed to prepare the spectra for these types of statistical processes. When these pre-treatment steps are performed, important chemical information is lost or mutated. The technique known as image fusion combines an image containing high chemical information but a low spatial resolution with an image that has high spatial resolution but little chemically relevant information associated with it. The image fusion technique would allow chemical, topographic, or morphologic information from both images to be combined in a hybrid image. The hybrid image contains all of the information from the two original images, with improved spatial resolution allowing for the visual inspection of the spatial correlation present. In this study, images were obtained using a copper transmission electron microscope (TEM) grid with a characteristic "A" in the center. Both SEM and ToF-SIMS images were obtained. For this analysis, the SEM image was the high-resolution image, while the SIMS image was the low-resolution image with a large amount of chemically relevant information. There are many barriers to obtaining the desired hybrid image from these two instrumental techniques; these difficulties deal with correlation, registration, interpolation errors, and imaging differences, and will be discussed in detail in Chapter 6.