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A geologic map is both a visual depiction of the lithologies and structures occurring at the Earth’s surface and a representation of a conceptual model for the geologic history in a region. The work needed to capture such multifaced information in an accurate geologic map is time consuming. Remote sensing can complement traditional primary field observations, geochemistry, chronometry, and subsurface geophysical data in providing useful information to assist with the geologic mapping process. Two novel sources of remote sensing data are particularly relevant for geologic mapping applications: decameter-resolution imaging spectroscopy (spectroscopic imaging) and meter-resolution multispectral shortwave infrared (SWIR) imaging. Decameter spectroscopic imagery can capture important mineral absorptions but is frequently unable to spatially resolve important geologic features. Meter-resolution multispectral SWIR images are better able to resolve fine spatial features but offer reduced spectral information. Such disparate but complementary datasets can be challenging to integrate into the geologic mapping process. Here, we conduct a comparative analysis of spatial and spectral scaling for two such datasets: one Airborne Visible/Infrared Imaging Spectrometer—Classic (AVIRIS-classic) flightline, and one WorldView-3 (WV3) scene, for a geologically complex landscape in Anza-Borrego Desert State Park, California. To do so, we use a two-stage framework that synthesizes recent advances in the spectral mixture residual and joint characterization. The mixture residual uses the wavelength-explicit misfit of a linear spectral mixture model to capture low variance spectral signals. Joint characterization utilizes nonlinear dimensionality reduction (manifold learning) to visualize spectral feature space topology and identify clusters of statistically similar spectra. For this study area, the spectral mixture residual clearly reveals greater spectral dimensionality in AVIRIS than WorldView (99% of variance in 39 versus 5 residual dimensions). Additionally, joint characterization shows more complex spectral feature space topology for AVIRIS than WorldView, revealing information useful to the geologic mapping process in the form of mineralogical variability both within and among mapped geologic units. These results illustrate the potential of recent and planned imaging spectroscopy missions to complement high-resolution multispectral imagery—along with field and lab observations—in planning, collecting, and interpreting the results from geologic field work.
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An information-theoretic approach to study spatial dependencies in small datasets
From epidemiology to economics, there is a fundamental need of statistically principled approaches to unveil spatial patterns and identify their underpinning mechanisms. Grounded in network and information theory, we establish a non-parametric scheme to study spatial associations from limited measurements of a spatial process. Through the lens of network theory, we relate spatial patterning in the dataset to the topology of a network on which the process unfolds. From the available observations of the spatial process and a candidate network topology, we compute a mutual information statistic that measures the extent to which the measurement at a node is explained by observations at neighbouring nodes. For a class of networks and linear autoregressive processes, we establish closed-form expressions for the mutual information statistic in terms of network topological features. We demonstrate the feasibility of the approach on synthetic datasets comprising 25–100 measurements, generated by linear or nonlinear autoregressive processes. Upon validation on synthetic processes, we examine datasets of human migration under climate change in Bangladesh and motor vehicle deaths in the United States of America. For both these real datasets, our approach is successful in identifying meaningful spatial patterns, begetting statistically-principled insight into the mechanisms of important socioeconomic problems.
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- Award ID(s):
- 1561134
- PAR ID:
- 10294999
- Date Published:
- Journal Name:
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Volume:
- 476
- Issue:
- 2242
- ISSN:
- 1364-5021
- Page Range / eLocation ID:
- 20200113
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1098/rspa.2020.0113
