Optimal, scalable forward models for computing gravity anomalies

We describe three approaches for computing a gravity signal from a density anomaly. The first approach consists of the classical "summation" technique, whilst the remaining two methods solve the Poisson problem for the gravitational potential using either a Finite Element (FE) discretization employing a multilevel preconditioner, or a Green's function evaluated with the Fast Multipole Method (FMM). The methods utilizing the PDE formulation described here differ from previously published approaches used in gravity modeling in that they are optimal, implying that both the memory and computational time required scale linearly with respect to the number of unknowns in the potential field. Additionally, all of the implementations presented here are developed such that the computations can be performed in a massively parallel, distributed memory computing environment. Through numerical experiments, we compare the methods on the basis of their discretization error, CPU time and parallel scalability. We demonstrate the parallel scalability of all these techniques by running forward models with up to $10^8$ voxels on 1000's of cores.Comment: 38 pages, 13 figures; accepted by Geophysical Journal Internationa

Simulating bank erosion over an extended natural sinuous river reach using a universal slope stability algorithm coupled with a morphodynamic model

Meandering river channels are often associated with cohesive banks. Yet only a few river modelling packages include geotechnical and plant effects. Existing packages are solely compatible with single-threaded channels, require a specific mesh structure, derive lateral migration rates from hydraulic properties, determine stability based on friction angle, rely on nonphysical assumptions to describe cutoffs, or exclude floodplain processes and vegetation. In this paper, we evaluate the accuracy of a new geotechnical module that was developed and coupled with Telemac-Mascaret to address these limitations. Innovatively, the newly developed module relies on a fully configurable, universal genetic algorithm with tournament selection that permits it (1) to assess geotechnical stability along potentially unstable slope profiles intersecting liquid-solid boundaries, and (2) to predict the shape and extent of slump blocks while considering mechanical plant effects, bank hydrology, and the hydrostatic pressure caused by flow. The profiles of unstable banks are altered while ensuring mass conservation. Importantly, the new stability module is independent of mesh structure and can operate efficiently along multithreaded channels, cutoffs, and islands. Data collected along a 1.5-km-long reach of the semialluvial Medway Creek, Canada, over a period of 3.5 years are used to evaluate the capacity of the coupled model to accurately predict bank retreat in meandering river channels and to evaluate the extent to which the new model can be applied to a natural river reach located in a complex environment. Our results indicate that key geotechnical parameters can indeed be adjusted to fit observations, even with a minimal calibration effort, and that the model correctly identifies the location of the most severely eroded bank regions. The combined use of genetic and spatial analysis algorithms, in particular for the evaluation of geotechnical stability independently of the hydrodynamic mesh, permits the consideration of biophysical conditions for an extended river reach with complex bank geometries, with only a minor increase in run time. Further improvements with respect to plant representation could assist scientists in better understanding channel-floodplain interactions and in evaluating channel designs in river management projects

Geometric tree kernels: Classification of COPD from airway tree geometry

Methodological contributions: This paper introduces a family of kernels for analyzing (anatomical) trees endowed with vector valued measurements made along the tree. While state-of-the-art graph and tree kernels use combinatorial tree/graph structure with discrete node and edge labels, the kernels presented in this paper can include geometric information such as branch shape, branch radius or other vector valued properties. In addition to being flexible in their ability to model different types of attributes, the presented kernels are computationally efficient and some of them can easily be computed for large datasets (N of the order 10.000) of trees with 30-600 branches. Combining the kernels with standard machine learning tools enables us to analyze the relation between disease and anatomical tree structure and geometry. Experimental results: The kernels are used to compare airway trees segmented from low-dose CT, endowed with branch shape descriptors and airway wall area percentage measurements made along the tree. Using kernelized hypothesis testing we show that the geometric airway trees are significantly differently distributed in patients with Chronic Obstructive Pulmonary Disease (COPD) than in healthy individuals. The geometric tree kernels also give a significant increase in the classification accuracy of COPD from geometric tree structure endowed with airway wall thickness measurements in comparison with state-of-the-art methods, giving further insight into the relationship between airway wall thickness and COPD. Software: Software for computing kernels and statistical tests is available at http://image.diku.dk/aasa/software.php.Comment: 12 page

Scalable wavelet-based coding of irregular meshes with interactive region-of-interest support

This paper proposes a novel functionality in wavelet-based irregular mesh coding, which is interactive region-of-interest (ROI) support. The proposed approach enables the user to define the arbitrary ROIs at the decoder side and to prioritize and decode these regions at arbitrarily high-granularity levels. In this context, a novel adaptive wavelet transform for irregular meshes is proposed, which enables: 1) varying the resolution across the surface at arbitrarily fine-granularity levels and 2) dynamic tiling, which adapts the tile sizes to the local sampling densities at each resolution level. The proposed tiling approach enables a rate-distortion-optimal distribution of rate across spatial regions. When limiting the highest resolution ROI to the visible regions, the fine granularity of the proposed adaptive wavelet transform reduces the required amount of graphics memory by up to 50%. Furthermore, the required graphics memory for an arbitrary small ROI becomes negligible compared to rendering without ROI support, independent of any tiling decisions. Random access is provided by a novel dynamic tiling approach, which proves to be particularly beneficial for large models of over 10(6) similar to 10(7) vertices. The experiments show that the dynamic tiling introduces a limited lossless rate penalty compared to an equivalent codec without ROI support. Additionally, rate savings up to 85% are observed while decoding ROIs of tens of thousands of vertices