Free <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msup><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mo stretchy="false">/</mml:mo><mml:mi>p</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math>-complexes and p-DG modules

Heller, Jeremiah; Stephan, Marc

doi:10.1016/j.jalgebra.2020.07.028

Cited by 1 publication

(1 citation statement)

References 17 publications

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“…Each time a wavelet signal oscillates and crosses an axis boundary, a vanishing moment is established, and the ability of the wavelet to interpret signals with higher order polynomial behavior generated. It is a general rule that for all wavelets with N number of vanishing moments, a support value that is greater than or equal to one less than twice the number of vanishing moments is needed, or 2N-1 (Heller, 1995). A second order wavelet will typically have four vanishing moments, or waveform oscillations, whereas a twelfth order wavelet will have six vanishing moments and a correspondingly higher target frequency.…”

Section: Wavelet Supportmentioning

confidence: 99%

Bedrock to soil: In-situ measurement and analytical techniques for initial weathering of proglacial environments

Lorentz¹

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<p>Dirt. It is more important than one might think. Soil, along with its bedrock-derived components, provides a nexus in the earth system for energy, nutrient, and atmospheric control; yet it is a finite resource. Soils are consumed, transported, and replenished by natural and anthropogenic forces. Weathering—both physical and chemical—is the key process breaking down and regenerating the ions and mineral constituents of soils, facilitating the pathways from solid bedrock to soil to the rest of the global ecosystem. Yet our understanding of weathering is incomplete and the available methods to investigate these processes are limited. Here, the fundamental processes of weathering are questioned by studying them at their origins, the rock surface. New techniques were developed in pursuit of quantifying weathering at small scales in-situ, to obtain the highest resolution measurements possible. These were carried out in the proglacial regions of two New Zealand glaciers, Brewster Glacier and Franz Josef Glacier. Proglacial bedrock environments provided a clean-slate model from which to measure incipient weathering at increasing exposure ages. To mitigate error, a holistic approach encompassing weathering signals from multiple angles was taken. Spatial characterisation was completed through the capture of structure-from-motion photogrammetry (SFM) at multiple scales of observation. The resultant three dimensional surface models had an average error of 1.06x10-1 mm. The models were characterised for weathering using roughness as a novel multi-point analysis of surface features, through two separate novel methods utilising global polynomial interpolation filtering and continuous wavelet transform analysis. Physical samples were collected from the field for cosmogenic radionuclide surface exposure age dating. Compositional analysis was performed through X-ray fluorescence, as well as electron microprobe analysis (EPMA). Nano-scale structural and compositional trends were investigated through optical analysis of backscatter electron imaging and secondary electron imaging. Non-directional roughness and volumetric analysis patterns present compelling information to support negligible weathering occurring on bedrock surfaces in proglacial environments. Lithologic variation was identified as a strong influence on the results. Compositional analysis demonstrated insignificant levels of chemical alteration between sites, corroborating the spatial modelling results. The lack of surficial weathering in highly productive weathering environments necessitates the role of additional weathering factors. Deep subsurface weathering was investigated and presents the strongest case as a major contributor to chemical denudation. Validating the presence of deep weathering in many environments critically alters the knowledge required to evaluate and predict patterns of landscape evolution. By establishing a better understanding of how bedrock weathers in-situ, the groundwork is laid for making more accurate and educated forecasts on how the earth system will respond to changes in the future.</p>

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Section: Wavelet Supportmentioning

confidence: 99%

Bedrock to soil: In-situ measurement and analytical techniques for initial weathering of proglacial environments

Lorentz¹

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Free (Z/p)n-complexes and p-DG modules

Cited by 1 publication

References 17 publications

Bedrock to soil: In-situ measurement and analytical techniques for initial weathering of proglacial environments

Bedrock to soil: In-situ measurement and analytical techniques for initial weathering of proglacial environments

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