John C. Tipper

MINLITH—an experience-based algorithm for estimating the likely mineralogical compositions of sedimentary rocks from bulk chemical analyses ☆

The MINLITH algorithm is a tool for estimating the likely mineralogical compositions of sedimentary rocks, using information from bulk chemical analyses. It is an experience-based algorithm that represents compositions in terms of a simplified set of normative minerals. MINLITH has been designed to be applied principally to mature sedimentary rocks, but it can (with care) be applied also to immature sediments and to metasedimentary rocks; the compositions that MINLITH gives for metasedimentary rocks are approximations to the original (i.e. pre-metamorphic) mineralogical compositions. The experience base on which MINLITH is built is a collection of 600 reference samples of sedimentary rocks. The compositional regularities found in these samples have allowed empirical rules to be developed to predict how the oxides reported in a bulk chemical analysis should be partitioned among the minerals most likely to be present. The discrepancies between MINLITH-estimated compositions and physically determined modal compositions are relatively small for the most widespread types of mature sedimentary rocks; they are comparable in their magnitude to the discrepancies associated with other methods for estimating mineralogical compositions from bulk chemical analyses, and to the discrepancies associated with quantitative X-ray diffractometry. The MINLITH algorithm is of particular value: (1) for providing preliminary estimates of mineralogical composition, prior to precise modal analysis; (2) for identifying systematic compositional variation within suites of samples; (3) in generalised sample classification; (4) in the sedimentological interpretation of metasedimentary rocks.

The importance of doing nothing: stasis in sedimentation systems and its stratigraphic effects

Abstract This paper puts forward the proposition that sedimentation systems generally are in stasis. Three lines of evidence suggest the proposition is largely correct: (1) considerations of how sedimentation systems necessarily operate, (2) observations of active systems, and (3) a re-evaluation of ideas about sedimentation rates. There are of course systems to which the proposition cannot apply. A simulation exercise is used to address questions about the stratigraphic effects of stasis. The results show (1) that sedimentation systems that generally are in stasis can be of a variety of types, (2) that stasis is readily preserved in stratigraphic successions, (3) that successions produced by a system in which the time proportion of stasis is high are markedly more complete than successions produced by other systems of the same type, (4) that the proportion of stasis in a system cannot be estimated reliably from stratigraphic successions produced by that system, and (5) that the stratigraphic succession finally left behind by a system is necessarily a systematically biased and partial record of the history of that system. What is always missing is that part of the history before the oldest preserved horizon, which for systems that are in long-term balance will on average be half of the total time.

The Modified Direct Method: An Iterative Approach for Smoothing Planar Meshes☆☆☆

Abstract The Modified Direct Method (MDM) is an iterative method for smoothing planar triangular, quadrilateral and tri-quad meshes, which has been developed from the non-iterative smoothing method for planar meshes that was originated by Balendran [1] . Its simple aim is to make triangular elements as close to equilateral as possible and quadrilateral elements as close to square as possible. The MDM is the computationally simpler of the two methods. The performance of the MDM for both triangular and quadrilateral meshes is effectively identical to that of Laplacian smoothing; however, it outperforms Laplacian smoothing for tri-quad meshes. Test examples show that the MDM is always convergent for triangular, quadrilateral and tri-quad meshes.

A simple method for representing some univariate frequency distributions, with particular application in Monte Carlo-based simulation

Introduced in this paper is a simple yet effective method for representing some of the types of univariate frequency distribution that commonly are required in Monte Carlo-based simulation. To use the method, an appropriate parent distribution is first chosen; then this distribution is modified by blending a constant value into the density function; the particular value used is the ordinate of the density function at its mode. The advantages of the method are (1) that a wide variety of forms of distribution can be represented, (2) that the number of parameters is low, (3) that the parameters can be varied continuously to let sets of systematically related distributions be constructed, and (4) that the resulting distribution functions are straightforward to invert numerically, thereby letting random deviates be generated quickly and efficiently. The method is potentially of particular value in Monte Carlo-based simulation, because it allows distributions of greatly differing forms to be represented within a single, flexible framework. The paper describes the method, provides the necessary equations for parameter estimation, and gives an example of a simulation exercise in which the method proved valuable. A demonstration program is provided that allows experimentation with the method.

A fractionation model for sediment delivery

Abstract The delivery of sediment into basins can readily be studied using process-independent models. The simplest such model is the discrete fractionation model in two dimensions, without erosion. It represents the path down which sediment is delivered as a simple set of discrete steps, and assumes that the sediment is delivered down those steps in a series of discrete events. This model has two parameters — the feed volume and the fractionation coefficient. The feed volume is the volume of sediment fed to the first step in the delivery path, and the fractionation coefficient is the proportion of the sediment reaching a step that is then moved on. Several variants of this model are described here, each involving restrictions on one or both of these parameters. The model has obvious and important applications, but these will be difficult to realize until the problem of parameter estimation has been solved. Fortunately, it seems possible to solve this problem by removing some of the model’s restrictions; these were built into it initially for analytical reasons. Removing these restrictions also makes the model applicable to a wider range of sedimentation systems.

Ear-Clipping Based Algorithms of Generating High-Quality Polygon Triangulation

A basic and an improved ear-clipping based algorithm for triangulating simple polygons and polygons with holes are presented. In the basic version, the ear with smallest interior angle is always selected to be cut in order to create fewer sliver triangles. To reduce sliver triangles in further, a bound of angle is set to determine whether a newly formed triangle has sharp angles, and edge swapping is accepted when the triangle is sharp. To apply the two algorithms on polygons with holes, ‘Bridge’ edges are created to transform a polygon with holes to a degenerate polygon which can be triangulated by the two algorithms. Applications show that the basic algorithm can avoid creating sliver triangles and obtain better triangulations than the traditional ear-clipping algorithm, and the improved algorithm can in further reduce sliver triangles effectively. Both of the algorithms run in O(n 2) time and O(n) space.

An algorithm for finding convex hulls of planar point sets

This paper presents an alternate choice of computing the convex hulls (CHs) for planar point sets. We firstly discard the interior points and then sort the remaining vertices by x-/y- coordinates separately, and later create a group of quadrilaterals (e-Quads) recursively according to the sequences of the sorted lists of points. Finally, the desired CH is built based on a simple polygon derived from all e-Quads. Besides the preprocessing for original planar point sets, this algorithm has another mechanism of discarding interior point when form e-Quads and assemble the simple polygon. Compared with three popular CH algorithms, the proposed algorithm can generate CHs faster than the three but has a penalty in space cost.

3D geological modeling and visualization of rock masses based on Google Earth: A case study

Google Earth (GE) has become a powerful tool for geological modeling and visualization. An interesting and useful feature of GE, Google Street View, can allow the GE users to view geological structure such as layers of rock masses at a field site. In this paper, we introduce a practical solution for building 3D geological models for rock masses based on the data acquired by use with GE. A real study case at Haut-Barr, France is presented to demonstrate our solution. We first locate the position of Haut-Barr in GE, and then determine the shape and scale of the rock masses in the study area, and thirdly acquire the layout of layers of rock masses in the Google Street View, and finally create the approximate 3D geological models by extruding and intersecting. The generated 3D geological models can simply reflect the basic structure of the rock masses at Haut-Barr, and can be used for visualizing the rock bodies interactively.

T-Base: A Triangle-Based Iterative Algorithm for Smoothing Quadrilateral Meshes

We present a novel approach named T-Base for smoothing planar and surface quadrilateral meshes. Our motivation is that the best shape of quadrilateral element—square—can be virtually divided into a pair of equilateral right triangles by any of its diagonals. When move a node to smooth a quadrilateral, it is optimal to make a pair of triangles divided by a diagonal be equilateral right triangles separately. The finally smoothed position is obtained by weighting all individual optimal positions. Three variants are produced according to the determination of weights. Tests by the T-Base are given and compared with Laplacian smoothing: The Vari.1 of T-Base is effectively identical to Laplacian smoothing for planar quad meshes, while Vari.2 is the best. For the quad mesh on underlying parametric surface and interpolation surface, Vari.2 and Vari.1 are best, respectively.

A hybrid approach for optimizing planar triangular meshes

Modified Direct Method (MDM) is an iterative scheme based on Jacobi iterations for smoothing planar meshes [4]. The basic idea behind MDM is to make any triangular element be as close to an equilateral triangle as possible. Based on the MDM, a length-weighted MDM is proposed and then combined with edge swapping. In length-weighted MDM, weights of each neighboring node of a smoothed node are determined by the length of its opposite edge. Also, the MDM, Laplacian smoothing and length-weighted MDM are all combined with edge swapping, and then implemented and compared on both structured and unstructured triangular meshes. Examples show that length-weighted MDM is better than the MDM and Laplacian smoothing for structured mesh but worse for unstructured mesh. The hybrid approach of combining length-weighted MDM and edge swapping is much better and can obtain more even optimized meshes than other two hybrid approaches.