Paul Wessel

New, improved version of generic mapping tools released

Version 3.1 of the Generic Mapping Tools (GMT) has been released. More than 6000 scientists worldwide are currently using this free, public domain collection of UNIX tools that contains programs serving a variety of research functions. GMT allows users to manipulate (x,y) and (x,y,z) data, and generate PostScript illustrations, including simple x-y diagrams, contour maps, color images, and artificially illuminated, perspective, and/or shaded-relief plots using a variety of map projections (see Wessel and Smith [1991] and Wessel and Smith [1995], for details.). GMT has been installed under UNIX on most types of workstations and both IBM-compatible and Macintosh personal computers.

Free software helps map and display data

When creating camera-ready figures, most scientists are familiar with the sequence of raw data → processing → final illustration and with the spending of large sums of money to finalize papers for submission to scientific journals, prepare proposals, and create overheads and slides for various presentations. This process can be tedious and is often done manually, since available commercial or in-house software usually can do only part of the job. To expedite this process, we introduce the Generic Mapping Tools (GMT), which is a free, public domain software package that can be used to manipulate columns of tabular data, time series, and gridded data sets and to display these data in a variety of forms ranging from simple x-y plots to maps and color, perspective, and shaded-relief illustrations. GMT uses the PostScript page description language, which can create arbitrarily complex images in gray tones or 24-bit true color by superimposing multiple plot files. Line drawings, bitmapped images, and text can be easily combined in one illustration. PostScript plot files are device-independent, meaning the same file can be printed at 300 dots per inch (dpi) on an ordinary laserwriter or at 2470 dpi on a phototypesetter when ultimate quality is needed. GMT software is written as a set of UNIX tools and is totally self contained and fully documented. The system is offered free of charge to federal agencies and nonprofit educational organizations worldwide and is distributed over the computer network Internet.

New version of the generic mapping tools

An updated, new version (3.0) of the Generic Mapping Tools (GMT) has just been released. GMT is a public domain collection of UNIX tools that contains programs to manipulate (x,y) and (x,y,z) data and to generate PostScript illustrations, including simple x-y diagrams, contour maps, color images, and artificially illuminated, perspective, shaded-relief plots using a variety of map projections [Wessel and Smith, 1991]. GMT has been installed on super computers, workstations and personal computers, all running some flavor of UNIX. We estimate that approximately 5000 scientists worldwide are currently using GMT in their work.

Gridding with continuous curvature splines in tension

A gridding method commonly called minimum curvature is widely used in the earth sciences. The method interpolates the data to be gridded with a surface having continuous second derivatives and minimal total squared curvature. The minimum-curvature surface has an analogy in elastic plate flexure and approximates the shape adopted by a thin plate flexed to pass through the data points. Minimum-curvature surfaces may have large oscillations and extraneous inflection points which make them unsuitable for gridding in many of the applications where they are commonly used. These extraneous inflection points can be eliminated by adding tension to the elastic-plate flexure equation. It is straightforward to generalize minimum-curvature gridding algorithms to include a tension parameter; the same system of equations must be solved in either case and only the relative weights of the coefficients change. Therefore, solutions under tension require no more computational effort than minimum-curvature solutions, and any algorithm which can solve the minimum-curvature equations can solve the more general system. We give common geologic examples where minimum-curvature gridding produces erroneous results but gridding with tension yields a good solution. We also outline how to improve the convergence of an iterative method of solution for the gridding equations.

Generic Mapping Tools: Improved Version Released

Generic Mapping Tools (GMT) is an open-source software package for the analysis and display of geoscience data, helping scientists to analyze, interpolate, filter, manipulate, project, and plot time series and gridded data sets. The GMT toolbox includes about 80 core and 40 supplemental program modules sharing a common set of command options, file structures, and documentation. Its power to process data and produce publication-quality graphic presentations has made it vital to a large scientific community that now includes more than 25,000 individual users. GMTs website (http://gmt.soest.hawaii.edu/) exceeds 20,000 visits per month, and server logs show roughly 2000 monthly downloads.

Global distribution of seamounts inferred from gridded Geosat/ERS‐1 altimetry

Using a forward modeling approach based on an axisymmetric Gaussian seamount, I characterize the global seamount distribution by locating circular maxima in the gridded vertical gravity gradient field derived from altimetry collected by the Geosat and ERS-1 satellite missions. The global seamount distribution is long-tailed and resembles a power law distribution for seamounts in the height range 2-7 km. Smaller seamounts are not well isolated by my technique nor are they well resolved in the gridded data. Several factors are likely to influence the height of volcanic seamounts, such as melt availability, magma driving pressure, and plate thickness. The observed relationship between seamount gravimetric amplitudes and the age of the underlying seafloor implies that there is an upper limit on seamount heights. Whether a seamount will reach that height depends most likely on supply-side factors, such as melt availability and magma driving pressure, but the limiting height itself seems more likely to be controlled by the strength of the oceanic plate. Specifically, compressional stresses directly beneath the seamount as a consequence of the lithospheres flexural response to loading may eventually exceed the magma driving pressure and prevent magma from reaching the surface, thus limiting the growth of the seamount. Because oceanic plate strength primarily is controlled by plate age, the limit on seamount height is inferred to be a simple function of plate age at the time of seamount emplacement. Using analytical solutions, I present a simple flexural model that predicts the observed global height-age relationship.

Toward a self‐consistent, high‐resolution absolute plate motion model for the Pacific

The hot spot hypothesis postulates that linear volcanic trails form as lithospheric plates move relative to stationary or slowly moving plumes. Given geometry and ages from several trails, one can reconstruct absolute plate motions (APM) that provide valuable information about past and present tectonism, paleogeography, and volcanism. Most APM models have been designed by fitting small circles to coeval volcanic chain segments and determining stage rotation poles, opening angles, and time intervals. Unlike relative plate motion (RPM) models, such APM models suffer from oversimplicity, self-inconsistencies, inadequate fits to data, and lack of rigorous uncertainty estimates; in addition, they work only for fixed hot spots. Newer methods are now available that overcome many of these limitations. We present a technique that provides high-resolution APM models derived from stationary or moving hot spots (given prescribed paths). The simplest model assumes stationary hot spots, and an example of such a model is presented. Observations of geometry and chronology on the Pacific plate appear well explained by this type of model. Because it is a one-plate model, it does not discriminate between hot spot drift or true polar wander as explanations for inferred paleolatitudes from the Emperor chain. Whether there was significant relative motion within the hot spots under the Pacific plate during the last ∼70 m.y. is difficult to quantify, given the paucity and geological uncertainty of age determinations. Evidence in support of plume drift appears limited to the period before the 47 Ma Hawaii-Emperor Bend and, apart from the direct paleolatitude determinations, may have been somewhat exaggerated.

Interpolation with splines in tension : A Green's function approach

Interpolation and gridding of data are procedures in the physical sciences and are accomplished typically using an averaging or finite difference scheme on an equidistant grid. Cubic splines are popular because of their smooth appearances; however, these functions can have undesirable oscillations between data points. Adding tension to the spline overcomes this deficiency. Here, we derive a technique for interpolation and gridding in one, two, and three dimensions using Greens functions for splines in tension and examine some of the properties of these functions. For moderate amounts of data, the Greens function technique is superior to conventional finite-difference methods because (1) both data values and directional gradients can be used to constrain the model surface, (2) noise can be suppressed easily by seeking a least-squares fit rather than exact interpolation, and (3) the model can be evaluated at arbitrary locations rather than only on a rectangular grid. We also show that the inclusion of tension greatly improves the stability of the method relative to gridding without tension. Moreover, the one-dimensional situation can be extended easily to handle parametric curve fitting in the plane and in space. Finally, we demonstrate the new method on both synthetic and real data and discuss the merits and drawbacks of the Greens function technique.

Distribution of large Pacific seamounts from Geosat/ERS-1: Implications for the history of intraplate volcanism

We characterize the seamount distribution on the Pacific Plate using the gridded vertical gravity gradient (VGG, or geoid curvature) derived from Geosat and ERS-1 satellite altimetry. The VGG amplifies short-wavelength information and suppresses longer wavelength components, making it suitable for seamount detection purposes. Furthermore, the VGG over seamounts has a much more pronounced zero crossing than that of the free-air anomaly (FAA); the distance to the zero crossing can be used as a proxy for seamount radius. After removing a regional field obtained by robust median filtering we identify seamount amplitudes and locations from local maxima in the VGG grid. The radius of a seamount is more difficult to estimate since seamounts tend to cluster and overprint each others signals. Individual seamounts are modeled as Gaussian, axisymmetric objects loading an elastic lithosphere; the VGG over such features can be approximated by a simple analytical expression which we use to determine the zero-crossing distances for overlapping seamounts. By using the VGG the maximum amplitude and distance to the zero crossing become largely independent of the elastic plate thickness and infill density. We do forward modeling of Gaussian seamounts and their gravimetric response and create a look up table that relates seamount FAA (in milligals), VGG (in Eotvos), and zero-crossing distance (in kilometers) to actual height and radius (in kilometers). The frequency-size distribution of these predicted seamount heights follows a power law for heights between 2 and 8 km. The seamount density (number of seamounts per area) is greatest in the central Pacific. We confirm earlier results suggesting that the majority of large seamounts are located in the western region of the Pacific Plate, on older crust. As crustal age increases, so does seamount density, peaking on 100–130 m.y. crust, supporting suggestions of high magmatism in the Cretaceous. We demonstrate that there may be an empirical relationship between the seamount VGG amplitude and the age of the lithosphere at the time of seamount formation and invert this relationship to predict seamount ages from VGG amplitudes. These pseudo ages have large uncertainties but, nevertheless, may be used to investigate temporal fluctuations in Pacific intraplate volcanism. Our results indicate that seamount intraplate volcanism attained a maximum level in the mid-Cretaceous to Late Cretaceous, about 70–120 Ma, apparently contemporaneous with the formation of large oceanic plateaus in the Pacific.

An empirical method for optimal robust regional-residual separation of geophysical data

Prior to interpretation and further analysis, many datasets must first be separated into regional and residual components. Traditional techniques are either subjective (e.g., graphical methods) or nonrobust (e.g., all least-squares based methods). Bathymetric data, with their broad spectrum, pose serious difficulties to these traditional methods, in particular those based on spectral decomposition. Spatial median filters offer a solution that is robust, objective, and often defines regional components similar to those produced graphically by hand. Characteristics of spatial median filters in general are discussed and a new empirical method is presented for determining the width of the robust median filter that accomplishes an optimal separation of a gridded dataset into its regional and residual components. The method involves tracing the zero-contour of the residual component and evaluating the ratio between the volume enclosed by the surface inside this contour and the contours area. The filter width giving the highest ratio (or mean amplitude) is called the Optimal Robust Separator (ORS) and is selected as the optimal filter producing the best separation. The technique allows a unique and objective determination of the regional field and enables researchers to undertake reproducible separations of regional and residual components. The ORS method is applied to both synthetic data and bathymetry/topography of the Hawaiian Islands; ways to improve the technique using alternative diagnostic quantities are discussed.