Matrix‐rich and associated matrix‐poor sandstones: Avulsion splays in slope and basin‐floor strata

A common facies observed in deep‐water slope and especially basin‐floor rocks of the Neoproterozoic Windermere Supergroup (British Columbia, Canada) is structureless, coarse‐tail graded, medium‐grained to coarse‐grained sandstone with from 30% to >50% mud matrix content (i.e. matrix‐rich). Bed contacts are commonly sharp, flat and loaded. Matrix‐rich sandstone beds typically form laterally continuous units that are up to several metres thick and several tens to hundreds of metres wide, and commonly adjacent to units of comparatively matrix‐poor, scour‐based sandstone beds with large tabular mudstone and sandstone clasts. Matrix‐rich units are common in proximal basin‐floor (Upper Kaza Group) deposits, but occur also in more distal basin‐floor (Middle Kaza Group) and slope (Isaac Formation) deposits. Regardless of stratigraphic setting, matrix‐rich units typically are directly and abruptly overlain by architectural elements comprising matrix‐poor coarse sandstone (i.e. channels and splays). Despite a number of similarities with previously described matrix‐rich beds in the literature, for example slurry beds, linked debrites and co‐genetic turbidites, a number of important differences exist, including the stratal make‐up of individual beds (for example, the lack of a clean sandstone turbidite base) and their stratigraphic occurrence (present throughout base of slope and basin‐floor strata, but most common in proximal lobe deposits) and accordingly suggest a different mode of emplacement. The matrix‐rich, poorly sorted nature of the beds and the abundance and size of tabular clasts in laterally equivalent sandstones imply intense upstream scouring, most probably related to significant erosion by an energetic plane‐wall jet or within a submerged hydraulic jump. Rapid energy loss coupled with rapid charging of the flow with fine‐grained sediment probably changed the rheology of the flow and promoted deposition along the margins of the jet. Moreover, these distinctive matrix‐rich strata are interpreted to represent the energetic initiation of the local sedimentary system, most probably caused by a local upflow avulsion.     

Mapping Submerged Aquatic Vegetation with GIS in the Caloosahatchee Estuary: Evaluation of Different Interpolation Methods

This article evaluates different spatial interpolation methods for mapping submerged aquatic vegetation (SAV) in the Caloosahatchee Estuary, Florida. Data used for interpolation were collected by the Submersed Aquatic Vegetation Early Warning System (SAVEWS). The system consists of hydro-acoustic equipment, which operates from a slow-moving boat and records bottom depth, seagrass height, and seagrass density. This information is coupled with geographic location coordinates from a Global Positioning System (GPS) and stored together in digital files, representing SAV status at points along transect lines. Adequate spatial interpolation is needed to present the SAV information, including density, height, and water depth, as spatially continuous data for mapping and for comparison between seasons and years. Interpolation methods examined in this study include ordinary kriging with five different semivariance models combined with a variable number of neighboring points, the inverse distance weighted (IDW) method with different parameters, and the triangulated irregular network (TIN) method with linear and quintic options. Interpolation results were compared with survey data at selected calibration transects to examine the suitability of different interpolation methods. Suitability was quantified by the determination coefficient (R2) and the root-mean-square error (RMSE) between interpolated and observed values. The most suitable interpolation method was identified as the one yielding the highest R2 value and/or the lowest RMSE value. For different geographic conditions, seasons, and SAV parameters, different interpolation methods were recommended. This study identified that kriging was more suitable than the IDW or TIN method for spatial interpolation of all SAV parameters measured. It also suggested that transect data with irregular spatial distribution patterns such as SAV parameters are sensitive to interpolation methods. An inappropriate interpolation method such as TIN can lead to erroneous spatial representation of the SAV status. With a functional geographic system and adequate computing power, the evaluation and selection of interpolation methods can be automated and quantitative, leading to a more efficient and accurate decision.     

Mutual Potential of Homogeneous Polyhedra

The mutual gravitational potential between a pair of homogeneous polyhedra is expressed using an infinite series. The nested volume integrals are evaluated analytically and result in simple tensor expressions containing no special functions. However, complexity increases as O(6 ⁿ ), where n is the term degree. An alternate formulation due to Liebenthal is also presented.