Acoustic properties of fine‐grained sediments from Emerald Basin: Toward an inversion for physical properties using the Biot–Stoll model

Acoustic data from two long cores, comprising marine clays and silts taken from Emerald Basin off Nova Scotia, are presented. High‐resolution measurements of compressional wavevelocity,attenuation, and power law exponent are made using ultrasonic frequencies between 100 to 1000 kHz. The observed values of the frequency dependence of attenuation suggest that a nonconstant Q mechanism is needed to explain these data, and Biot–Stoll theory is used to model the experimental results. An inversion scheme is used to constrain physical parameters in the Biot–Stoll dispersion relation. The inversion shows that there is a restricted range of permeability and grain size. By assigning reasonable values for grain size in the inversion, the Biot–Stoll model predicts unique values for the permeability and frame bulk modulus that agree well with estimates made by other means

Calculation of acoustic parameters by a filter-correlation method

This paper presents the filter correlation method, a technique for extracting consistent and accurate estimates of attenuation parameters from acoustic waveform data. The method minimizes problems associated with short time windows and multipath secondary arrivals. The method comprises two stages: a causal passband filter stage followed by a cross-correlation step. The results of the filter-correlation estimator are compared to those of the spectral difference approach for short time series with and without a secondary multipath arrival. Preliminary analyses of acoustic data collected on cored marine silts and clays show the attenuation properties of these materials cannot be described by a constant Q mechanism. The filter correlation method refines estimates of frequency-dependent velocity, revealing a small but systematic anisotropy between measurements made parallel and transverse to the sediments\u27 bedding plane. The observed velocity anisotropy can be modeled by assuming layered porosity variations in the cored sediments. No systematic anisotropy in attenuation was observed

Recursive strategy for decomposing Betti tables of complete intersections

We introduce a recursive decomposition algorithm for the Betti diagram of a complete intersection using the diagram of a complete intersection defined by a subset of the original generators. This alternative algorithm is the main tool that we use to investigate stability and compatibility of the Boij-Soederberg decompositions of related diagrams; indeed, when the biggest generating degree is sufficiently large, the alternative algorithm produces the Boij-Soederberg decomposition. We also provide a detailed analysis of the Boij-Soederberg decomposition for Betti diagrams of codimension four complete intersections where the largest generating degree satisfies the size condition

The Last Ice Cube

In the very darkest corner, behind the davenport, there sat a little ice cube. Tears were dripping slowly, monotonously, hopelessly from its block-shaped face. The eerie moonlight peeped around the deserted room and revealed the most pitiful expression one could ever witness en the face of an ice cube. And the reason? The little ice cube was dying. Some careless reveler had flipped it out of a glass in one horrifying fling, and there it lay, in a state of inertia, awaiting the hideous death of an ice cube. Slowly, atom by atom, it was disappearing

Canada GEESE 2: Visualization of Integrated Marine Geoscience Data for Canadian and Proximal Waters

The Geological Survey of Canada has made most of its holdings of marine geoscience data available online with unrestricted access. These holdings constitute the premier collections of geological and geophysical source data for Canadian and proximal waters. Multibeam bathymetric imagery, analog high resolution seismic and sidescan sonar data, seabed photographs, grain size analyses, and radiocarbon dates can be directly downloaded from NRCan’s Geogratis (http://geogratis.cgdi.gc.ca) servers. KML files allow the user to discover and explore these collections, highlighting the building blocks of marine data downloadable from ftp/http servers.SOMMAIRELa Commission géologique du Canada a mis en ligne la plupart de ses fonds de données géoscientifiques marines et y donne accès sans restriction. Ces fonds constituent des collections de premier choix de données géologiques et géophysiques de base des eaux canadiennes ou proximales. On peut ainsi télécharger des serveurs Géogratis de RNCan (http://geogratis.cgdi.gc.ca) des données d’imagerie bathymétrique par secteurs, des données analogiques séismiques haute résolution et de levé de sonar à balayage latéral, des photographies du fond marin, des analyses granulométriques, et des datations au radiocarbone. Le format KML des fichiers permet aux utilisateurs d’exploiter facilement le contenu de ces collections, en mettant en relief les données marines de base téléchargeables depuis les serveurs FTP/HTTP

A Project Approach in Differential Equations Courses

From the late 60\u27s the mathematics department at Harvey Mudd College (HMC) has been active in introducing independent study projects into its math courses, especially courses involving differential equations. This paper describes two such approaches and the features that were constructed to support them. With the change in technology in the late 90\u27s, it was clear that these project approaches needed to be updated. These changes are underway and are described in this article

Pitfalls and Pluses in Using Numerical Software to Solve Differential Equations

Ordinary differential equations (ODEs) are often used to model the behavior of physical phenomena and textbooks today especially demonstrate this fact. Since only a very small collection of ODEs can be solved analytically, there is often no alternative than to use computer software to gain some insight into the behavior of solutions (and sometimes even if solution formulas are available--the formulas are often complicated!). A classic work on the numerical solution of ODEs was authored by (Numerical Solution of Ordinary Differential Equations, Chapman and Hall/CRC,1994). There are some questions about the behavior of solutions of ODEs that are not quite appropriate for numerical solvers. In this paper we present examples which illustrate some of these features. However, there is no disputing the fact that the output of numerical solvers is often useful for portraying and understanding the behavior of solutions of ODEs and their utility in modeling physical phenomena, as our final example shows