A principled approach to programming with nested types in Haskell

Initial algebra semantics is one of the cornerstones of the theory of modern functional programming languages. For each inductive data type, it provides a Church encoding for that type, a build combinator which constructs data of that type, a fold combinator which encapsulates structured recursion over data of that type, and a fold/build rule which optimises modular programs by eliminating from them data constructed using the buildcombinator, and immediately consumed using the foldcombinator, for that type. It has long been thought that initial algebra semantics is not expressive enough to provide a similar foundation for programming with nested types in Haskell. Specifically, the standard folds derived from initial algebra semantics have been considered too weak to capture commonly occurring patterns of recursion over data of nested types in Haskell, and no build combinators or fold/build rules have until now been defined for nested types. This paper shows that standard folds are, in fact, sufficiently expressive for programming with nested types in Haskell. It also defines buildcombinators and fold/build fusion rules for nested types. It thus shows how initial algebra semantics provides a principled, expressive, and elegant foundation for programming with nested types in Haskell

Spherical Earth analysis and modeling of lithospheric gravity and magnetic anomalies

A comprehensive approach to the lithospheric analysis of potential field anomalies in the spherical domain is provided. It has widespread application in the analysis and design of satellite gravity and magnetic surveys for geological investigation

Gravity and magnetic anomaly modeling and correlation using the SPHERE program and Magsat data

The spherical Earth inversion, modeling, and contouring software were tested and modified for processing data in the Southern Hemisphere. Preliminary geologic/tectonic maps and selected cross sections for South and Central America and the Caribbean region are being compiled and as well as gravity and magnetic models for the major geological features of the area. A preliminary gravity model of the Andeas Beniff Zone was constructed so that the density columns east and west of the subducted plates are in approximate isostatic equilibrium. The magnetic anomaly for the corresponding magnetic model of the zone is being computed with the SPHERE program. A test tape containing global magnetic measurements was converted to a tape compatible with Purdue's CDC system. NOO data were screened for periods of high diurnal activity and reduced to anomaly form using the IGS-75 model. Magnetic intensity anomaly profiles were plotted on the conterminous U.S. map using the track lines as the anomaly base level. The transcontinental magnetic high seen in POGO and MAGSAT data is also represented in the NOO data

Gravity and magnetic anomaly data analysis

Progress on the analysis MAGSAT data is reported. The MAGSAT data from 40 deg S to 70 deg N latitude and 30 deg W to 60 E longitude was reduced to radial polarization. In addition, gravity anomaly data from this area were processed and a variety of filtered maps were prepared for combined interpretation of the gravity and magnetic data in conjunction with structural and tectonic maps of the area. The VERSATEC listings and cross-reference maps of variable and array names for the spherical Earth analysis programs NVERTSM, SMFLD, NVERTG, and GFLD were also prepared

Magnetic and gravity anomalies in the Americas

The cleaning and magnetic tape storage of spherical Earth processing programs are reported. These programs include: NVERTSM which inverts total or vector magnetic anomaly data on a distribution of point dipoles in spherical coordinates; SMFLD which utilizes output from NVERTSM to compute total or vector magnetic anomaly fields for a distribution of point dipoles in spherical coordinates; NVERTG; and GFLD. Abstracts are presented for papers dealing with the mapping and modeling of magnetic and gravity anomalies, and with the verification of crustal components in satellite data

Improving the geological interpretation of magnetic and gravity satellite anomalies

Current limitations in the quantitative interpretation of satellite-elevation geopotential field data and magnetic anomaly data were investigated along with techniques to overcome them. A major result was the preparation of an improved scalar magnetic anomaly map of South America and adjacent marine areas directly from the original MAGSAT data. In addition, comparisons of South American and Euro-African data show a strong correlation of anomalies along the Atlantic rifted margins of the continents

Analyzing and modeling gravity and magnetic anomalies using the SPHERE program and Magsat data

Computer codes were completed, tested, and documented for analyzing magnetic anomaly vector components by equivalent point dipole inversion. The codes are intended for use in inverting the magnetic anomaly due to a spherical prism in a horizontal geomagnetic field and for recomputing the anomaly in a vertical geomagnetic field. Modeling of potential fields at satellite elevations that are derived from three dimensional sources by program SPHERE was made significantly more efficient by improving the input routines. A preliminary model of the Andean subduction zone was used to compute the anomaly at satellite elevations using both actual geomagnetic parameters and vertical polarization. Program SPHERE is also being used to calculate satellite level magnetic and gravity anomalies from the Amazon River Aulacogen

Study of gravity and magnetic anomalies using MAGSAT data

The results of modeling satellite-elevation magnetic and gravity data using the constraints imposed by near surface data and seismic evidence shows that the magnetic minimum can be accounted for by either an intracrustal lithologic variation or by an upwarp of the Curie point isotherm. The long wavelength anomalies of the NOO's-vector magnetic survey of the conterminous U.S. were contoured and processed by various frequency filters to enhance particular characteristics. A preliminary inversion of the data was completed and the anomaly field calculated at 450 km from the equivalent magnet sources to compare with the POGO satellite data. Considerable progress was made in studing the satellite magnetic data of South America and adjacent marine areas. Preliminary versions of the 1 deg free-air gravity anomaly map (20 m gal contour interval) and the high cut (lambda approximately 8 deg) filtered anomaly maps are included

Aeromagnetic and satellite magnetic anomally mapping

Efforts to process 2 deg-averaged MAGSAT data for a radially polarized map of Africa and western Europe and investigator B data tapes were initiate

Fast iterative solution of reaction-diffusion control problems arising from chemical processes

PDE-constrained optimization problems, and the development of preconditioned iterative methods for the efficient solution of the arising matrix system, is a field of numerical analysis that has recently been attracting much attention. In this paper, we analyze and develop preconditioners for matrix systems that arise from the optimal control of reaction-diffusion equations, which themselves result from chemical processes. Important aspects in our solvers are saddle point theory, mass matrix representation and effective Schur complement approximation, as well as the outer (Newton) iteration to take account of the nonlinearity of the underlying PDEs