Gamma Design Software, LLC

- Comprehensive Geostatistics Program Software

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GS+ is a comprehensive geostatistics program that is fast, efficient, and easy to use. GS+ provides all geostatistics components, from variogram analysis through kriging and mapping, in a single integrated program widely praised for its flexibility and friendly interface. Many users are surprised that geostatistical analysis can be so easy and intuitive.

Geostatistics is a class of statistical techniques developed to analyze and predict values of a property spatially distributed. It begins with a type of autocorrelation analysis called variography or semivariance analysis, in which the degree of spatial self-similarity is displayed as a variogram. A curve is fit to the variogram, and the equation that describes the curve - called the variogram model - is used to help predict unsampled locations via kriging or conditional simulation. This produces optimal unbiased estimates of the property across the area sampled. The same analysis can also be performed with temporal data such as hourly or daily measures of some property to interpolate through time in an optimal manner.

GS+ was first introduced in 1988. Geostatistics is not an add-on feature of GS+ – it is at the heart of the software. Many of our users have access to other geostatistics tools within their favorite GIS or mapping programs but come to GS+ for their serious geostatistical analyses, especially for exploring geostatistical relationships within data sets. Because GS+ output is compatible with industry standards, GS+ can be used directly with many of these other programs. Or it can be used standalone – GS+ has its own data worksheet (which also accepts Excel®, Access®, and other types of data files) and produces its own maps for those users who are not working with other mapping programs.

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2D Geostatistics
GS+ is geostatistics software used the world over. A robust, fast, and intuitive platform for both new and experienced geostatistics users.

Version 10 now shipping!

  • helps you quickly perform geostatistical analysis
  • creates variograms on the fly
  • provides 11 different autocorrelation measures
  • imports data from a wide variety of sources
  • summarizes your data prior to geostatistical analysis
  • provides kriging, conditional simulation and nearest neighbor interpolations
  • creates output files usable by a wide variety of other programs
  • performs cross-validation to test your interpolation system against sampled data
  • allows you to customize all graph and map details and publish to anywhere

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GS+ Quickly perform geostatistical analysis
Geostatistics provides a way to better understand the autocorrelation inherent in spatial data – and to define and use this variation to make better estimates of values for places not sampled and thereby create optimal, unbiased maps.

GS+ provides easy access to these computationally intense analyses. Whether you are analyzing oil deposits, plankton distributions, sun spot patterns, infectious disease outbreaks, or soil resources, GS+ allows you ready access to the power of geostatistics.

Create variograms on the fly
GS+ gives you complete control over variogram parameters such as the active lag distance and the size of individual lag classes. Default values provide reasonable starting places from which you can optimize an analysis to suit a particular data set.

Model your variograms automatically – GS+ can automatically create a model for kriging that honors your data to the maximum extent possible using iterative techniques to optimize good model fits. A model window lets you override the values that GS+ chooses and slider controls allow you to immediately see the results of changes. GS+ provides models sufficient for almost all kriging applications.

Variograms are sometimes erratic due to data anomalies – outliers that become apparent when they are the only values not autocorrelated with other values at a particular scale. GS+ provides h-Scattergram and Variance Cloud analyses to allow you to visualize and identify outliers fast, and a new masking command allows you to surgically remove (either temporarily or permanently) the offending data record.

Directional (anisotropic) variograms are produced at the same time as isotropic variograms so you can readily evaluate whether autocorrelation is dependent on compass direction. This occurs, for example, when there is a slope effect or some other environmental feature that causes autocorrelation in one direction to be different from autocorrelation in another.

It’s easy to recognize anisotropy in GS+ by creating variogram maps – graphs of semivariance in different compass directions. If present, you can then easily define an angle of maximum variation to use for the anisotropic variogram models.

Calculate 11 different types of autocorrelation measures
Variograms are only one type of autocorrelation provided by GS+. Also included are correlograms, madograms, rodograms, covariograms, drift, Moran’s I, fractal dimension, and standardized, general relative, and pairwise relative variograms. All are evaluated in both isotropic and anisotropic directions.

Import data from a wide variety of sources
The GS+ worksheet can be directly edited and you can import data into the worksheet from a variety of sources – text files formatted in different ways, Excel spreadsheets, Access and other database files, or cut and paste from any other Windows program. There are also several ways to indicate missing values, and any value in the spreadsheet can be removed from a particular analysis by setting a temporary missing value attribute. The worksheet accepts over a billion records.

Summarize your data prior to geostatistical analysis
GS+ also provides basic parametric statistics to enable you to characterize your data prior to geostatistical analysis. When a data set is prepared for analysis, GS+ reports stats such as the mean, range, standard deviation, and kurtosis and skewness, and also creates frequency and probability distributions so you can evaluate departures from normality. Quantile scattergrams provide a visual map of your sample locations and identify the locations of data with particular values.

Interpolation methods to meet every need
Three different types of interpolation are provided by GS+. Ordinary kriging (both block and punctual) provide optimal estimates for a property across the spatial domain. Conditional simulation also provides optimal estimates but honors original data at their locations so can be used to map sharp boundaries in a domain. Inverse distance weighting is probably the best non-geostatistical interpolation technique, based on simple nearest neighbor calculations.

GS+ also provides cokriging, which can be useful when your primary data are supported by secondary data collected at many additional locations. Cokriging is available for both block and punctual kriging and co-located cokriging is available for conditional simulation.

Polygon masks allow you to include or exclude complex shapes in the domain being mapped. Interpolate across an island or avoid interpolating across a parking lot – you can also nest polygons and overlap them.

Create interpolation output files that are usable by many other programs
GS+ creates interpolation output files (from kriging, cokriging, simulation, or inverse distance techniques) that can be read into many other types of mapping programs. GS+ will use these files to create it’s own maps or you can read the data into any GIS or mapping program that supports ArcInfo® or Surfer® input formats.

Cross-validation allows you to test your interpolation system against sampled data
In cross-validation analysis each measured point in a spatial domain is individually removed from the domain and its value estimated via kriging or inverse distance weighting as though it were never there. In this way a graph of estimated vs. actual values for each sample location in the domain can be constructed and used to test the interpolation system.

Customize all details of your GS+ graphs and maps and publish to anywhere
A rich set of graph editing options allow you to change axes, fonts, perspective, titles, symbols and many other graph attributes. Maps and graphs can be printed or sent to the Windows clipboard or to a file that can be read by web browsers, word processors, or any other Windows program that accepts wmf, jpeg, png, or bmp formats.

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Geostatistics is not an add-on feature of GS+ – it is at the heart of the software. Many of our users have access to other geostatistics tools within their favorite GIS or mapping programs but come to GS+ for their serious geostatistical analyses, especially for exploring geostatistical relationships within data sets. Because GS+ output is compatible with industry standards, GS+ can be used directly with many of these other programs. Or it can be used standalone – GS+ has its own data worksheet (which also accepts Excel®, Access®, and other types of data files) and produces its own maps for those users who are not working with other mapping programs.

  • GS+ provides easy access to computationally intense analyses of spatial relationships.
  • Whether you are analyzing oil deposits, plankton distributions, sun spot patterns, infectious disease outbreaks, or soil resources, GS+ allows you to better understand the autocorrelation inherent in spatial data – and use this variation to make better estimates of values for places not sampled.
  • With its intuitive interface and powerful statistical analysis, GS+ delivers the the information you need to make better-informed decisions.

  • Agronomy
  • Anthropology
  • Atmospheric Chemistry
  • Biogeochemistry
  • Civil Engineering
  • Demography
  • Earth System Science
  • Ecology
  • Entomology
  • Environ. Engineering
  • Epidemiology
  • Forestry
  • Geography
  • Geology
  • Hydrology
  • Limnology
  • Marine Science
  • Microbiology
  • Oceanography
  • Plant Physiology
  • Range Science
  • Remote Sensing
  • Soil Science
  • Statistics
  • Toxicology
  • Weed Science
  • Wildlife Biology

GS+ – the premier geostatistical analysis program for desktop systems – was introduced in 1988 as the first integrated geostatistics program for the PC. It quickly became the geostatistics program of choice for users worldwide. Widely praised, GS+ was the first geostatistics package to offer all components – from variogram analysis through kriging and mapping – in an integrated package that provides the flexibility demanded by the specialist and the simplicity needed by the novice. GS+ runs on Windows XP, Vista, and Windows 7/8.

Variogram Analysis (Semivariance Analysis or Variography)
Comprehensive Semivariance Analysis provides both isotropic and anisotropic variograms. You have complete control over separation interval classes – choose constant interval classes or define different break points for every lag class. Anisotropic directions can be individually targeted, and variograms can be scaled to sample variance.

Variograms
Variograms that appear in the Semivariance Analysis window – both isotropic and anisotropic – can be enlarged into their own windows, from which values and graphs can be printed, and from which each point along the curve can be decomposed into the pairs of points on which it is based.

Variogram Map
Variogram Surface Maps identify anisotropy quickly and accurately. Maps of semivariance in every compass direction (the center marks the origin of each variogram) allow the axis of maximum variation to be easily identified.

Model definition
Dynamic Variogram Modeling – GS+ can calculate model parameters for 5 types of models based on least squares (residuals) analysis, or individual model parameters can be specified directly by the user.

Variance clouds
Variance Cloud Analysis provides a graph of variance vs. separation distance for every pair of points that make up a specific lag class. This allows outlying pairs to be quickly identified and edited as needed.

h-Scattergrams
h-Scattergram Analysis provides a graph of differences vs. separation distance for every pair of points that make up a specific lag class. This is another way to quickly identify outlying pairs and edit as needed.

Pair-wise variance
The Variance by Pair listing provides variance values and separation distances for each point in a specific variogram lag class.

Interpolation
GS+ provides four types of interpolation – Kriging, Cokriging, Conditional Simulation, and Inverse Distance Weighting. Output is written to ASCII files that can be read for mapping by GS+, ArcView®, or Surfer®.

Kriging
Kriging provides optimal interpolation of points across a spatial domain for which autocorrelation has been documented and measured with variograms. GS+ provides both block and punctual kriging, and allows the user to choose the most appropriate variogram model to use for the interpolation.

Cokriging
Cokriging is a type of kriging that allows one to better estimate map values using a secondary variate sampled more intensely than the primary variate. If the primary variate is difficult or expensive to measure, then cokriging can greatly improve interpolation estimates without having to more intensely sample the primary variate.

Conditional simulation
Conditional Simulation provides optimal interpolation whereby measured data values are honored at their locations. Other interpolation methods will smooth out local details of spatial variation, which can be a problem when you are trying to map sharp spatial boundaries such as contamination hotspots or fault lines.

Inverse Distance Weighting (IDW)
Inverse Distance Weighting (IDW) provides classical interpolation based on nearest neighbor weighting. It is a simple interpolation method used in mapping programs that do not use geostatistics, and assumes spatial dependence among points close to one another (without measuring it).

Interpolation grid
The Interpolation Grid allows the user to define the boundaries of the interpolated area and the intensity (grid spacing) at which the interpolation will proceed.

Polygon outlines
Polygon Outlines define irregular map boundaries and special areas to exclude from kriging. An unlimited number of polygons can be defined by an unlimited number of vertices (x-y boundary points).

Polygon map
Polygon Maps display the areas that will be included or excluded from kriging. Exclusive and inclusive polygons are colored differently, and polygons can be nested within one another.

Cross Validation Analysis
Cross Validation Analysis allows one to test different variogram models; bootstrapping provides comparisons of the actual value of every point sampled vs. its estimated value when removed from the data set.

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Semivariance analysis in GS+ provides both isotropic and anisotropic variograms (also called semivariograms). Semivariance analysis is done before kriging, cokriging, or conditional simulation. You have complete control over separation interval classes – choose constant interval classes or define different break points for every lag class. Anisotropic directions can be individually targeted, and variograms / semivariograms can be scaled to sample variance.

Variograms and semivariograms that appear in the Semivariance window – both isotropic variograms / semivariograms and anisotropic variograms / semivariograms – can be enlarged into their own windows, from which semivariance values and graphs can be printed, and from which each point along the curve can be disaggregated into the pairs of points on which the semivariance value for that semivariogram position is based.

Variogram / Semivariogram Surface Maps – Identify anisotropic semivariance quickly and accurately. Maps of semivariance in every compass direction (the center marks the origin of each variogram / semivariogram) allow the axis of maximum variation to be easily identified.

Dynamic Variogram / Semivariogram Modeling – GS+ can calculate model parameters for 5 types of variogram / semivariogram models based on least squares (residuals) analysis, or individual model parameters can be specified directly by the user.

Variance Cloud Analysis provides a graph of variance vs. separation distance for every pair of points that make up a specific lag class in a variogram / semivariogram. This allows outlying pairs to be quickly identified and edited as needed.

h-Scattergram Analysis provides a graph of differences vs. separation distance for every pair of points that make up a specific lag class in a variogram / semivariogram. This is another way to quickly identify outlying pairs and edit as needed.

A Variance by Pair listing provides variance values and separation distances for each point in a specific variogram / semivariogram lag class.

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GS+ provides Kriging, Cokriging, Conditional Simulation, and Inverse Distance Weighting for interpolation across an area. Output is written to ASCII files that can be read for mapping by GS+, ArcView®, Surfer®, or other mapping or GIS programs.

Kriging provides an optimal interpolation of points across an area for which autocorrelation (semivariance) has been documented and measured with variograms or semivariograms. GS+ provides both block and punctual kriging, and allows the user to choose the most appropriate variogram / semivariogram model to use for the interpolation.

Cokriging is a type of kriging that allows a better estimate of map values by using a secondary variate that is sampled more intensely than the primary variate. If the primary variate is difficult or expensive to measure, then cokriging can greatly improve kriging estimates without having to more intensely sample the primary variate.

Conditional Simulation provides optimal interpolation whereby measured data values are honored at their locations. Other interpolation methods (including kriging) will smooth out local details of spatial variation, which can be a problem when you are trying to map sharp spatial boundaries such as contamination hotspots or fault lines.

Inverse Distance Weighting (IDW) is a classical interpolation technique based on nearest neighbor weighting. It is a simple interpolation method used in mapping programs that do not use geostatistics, and assumes spatial dependence among points close to one another (without measuring it).

An Interpolation Grid in GS+ allows the interpolation boundaries (whether kriging, conditional simulation, or IDW) to be defined and sets the intensity (grid spacing) at which the interpolation will occur.

Polygon Outlines in GS+ define irregular map boundaries and special areas to exclude from interpolation (whether kriging, conditional simulation, or IDW). An unlimited number of polygons can be defined by an unlimited number of vertices (x-y boundary points). The outline defined by the vertices can be visualized in Polygon Maps, which display the areas that will be included or excluded from interpolation. Exclusive and inclusive polygons are colored differently, and polygons can be nested within one another.

Cross Validation Analysis allows one to test different variogram / semivariogram models used for kriging and conditional simulation. Bootstrapping provides comparisons of the actual value of every point sampled vs. its estimated value when removed from the data set.

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  • Madograms
  • Rodograms
  • Drift
  • Correlograms
  • Covariograms
  • Moran's I
  • Fractals
  • Standardized Variograms
  • General Relative Variograms
  • Pairwise Relative Variograms

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The Data Worksheet holds the GS+ analysis data. Data can be entered from a variety of sources, including spreadsheets, databases, various text formats, and by cutting and pasting from any Windows program. The data worksheet can hold over a million records, and a data filter can limit the range of data to be analyzed.

The Descriptive Statistics window provides information on the active data set, and provides the option to transform the data to a more normalized distribution.
 
Frequency distributions provide information about the normality of a particular data analysis set.

The Coordinate Posting window provides a map of sample locations coded by sample values. Values can be divided into quartiles, percentiles, or a variety of other distributions.

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GS+ can produce 3D, 2D, and 1D maps of spatial data following interpolation. The data to be mapped are contained in output files created during interpolation. Maps can be displayed with different contouring schemes, 3-dimensional maps can be rotated on the fly, and both 2-dimensional and 3-dimensional maps can be zoomed to more closely view a transition or other map feature. Additionally, sample postings (original data locations) can be displayed, and estimation standard errors can be mapped for input files that have been saved in the standard GS+ format.

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GS+ 2D Surface Map
GS+ produces 2D surface maps in addition to 3D maps. The lower right Mouse Location panel reports the location of the mouse when it is moved over the image. Zooming is performed by setting a Mouse Action and outlining part the image with the mouse. The Edit Graph button allows the projection to be changed to 3D, axes to be rescaled, labels and backgrounds to be changed, and titles added.

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GS+ 3D Map Image Window
GS+ produces 3D contour models as well as 2D surface maps for data kriged in 2 dimensions. From this Map Image window the map can be edited, printed, and rotated and zoomed on the fly. A Mouse Location Panel (lower right) reports the location of the mouse when it is moved over the image. The Edit Graph button allows axes to be rescaled, labels to be changed, background colors to be defined, and titles added. Maps can be printed to any Windows device, to the clipboard, or to a file in a variety of formats including web-ready formats like JPEG. The Map Definition window defines how the map is drawn.

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GS+ Estimation Error Map
In addition to maps of a particular variate, you can also map the estimation error associated with the variate. These maps are available from files saved in GS+ format (ArcView and Surfer formats don't support estimation error). The type of map drawn is specified in the Map Design Window.

The lower right Mouse Location panel reports the location of the mouse when it is moved over the image. Rotating and zooming is performed by setting a Mouse Action and grabbing the image with the mouse. The Edit Graph button allows the projection to be changed to 2D, axes to be rescaled, backgrounds and labels to be changed, and titles added, as for all other graphs in GS+.

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GS+ 2D Map Postings
Graph the locations of sample points on top of your maps – each symbol in the image marks an actual sample location in the original data set. A posting is also available for 3D and 1D maps, as is a plain 2D posting without the underlying contour map. As for other maps, the lower right Mouse Location panel reports the location of the mouse when it is moved over the image. Zooming is performed by setting a Mouse Action and grabbing the image with the mouse. The Edit Graph button allows axes to be rescaled, labels to be changed, and titles added.

Quintile maps (scattergrams) provide a posting of data values prior to interpolation.

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Defining Map Contour Intervals in GS+
GS+ gives you complete control over map contour intervals. In the Map Contour Intervals dialog you may change the default break points and colors for map contours. The number of contour intervals (1 - 15) is specified in the Map window. Customized intervals (both break points and color schemes) can be saved to allow different maps to easily share the same contouring schemes. Clicking on a color tab brings up a color dialog window with the full suite of colors that Windows supports. Missing values, including areas within 'exclusive' polygons, are mapped as blank spots (background color).

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GS+ Map Color Schemes
Maps can be given any number of color schemes. Choose among predefined schemes such as this blue scheme or customize contour intervals as you like from the Contour Definition window. Background colors can also be changed.

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GS+ 3D Map Rotation
3D maps can be rotated to any perspective, as noted here for a bottom view of a rotated map of estimation error. Rotations are performed from the Map Image Window.

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GS+ 1D Transects
In addition to 2-dimensional spatial data, 1-dimensional data such as linear transects or sampling through time can also be interpolated, and the resulting data graphed as a 1D transect or time-line image. The symbols in this graph represent actual sample values of temperature vs. day of year and the black line represents a dense grid of block-kriged values interpolated at 0.1 day intervals.

The lower right Mouse Location panel reports the location of the mouse when it is moved over the transect. Zooming is performed by setting a Mouse Action and outlining a portion of the image with the mouse. The Edit Graph button allows axes to be rescaled, labels and backgrounds to be changed, and titles added.

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GS+ 1D Estimation Error
Kriging produces an estimation error term for every value interpolated, and you can graph this error to provide insight on portions of the model for which you may have more confidence than other portions. The blue lines here represent the standard deviations (estimation error) of the kriged values, which are reported as the black line.

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GS+ 3D Map with Black Background, Pedestal
Maps can be drawn with backgrounds of any color provided by Windows, and 3D maps can be drawn with or without base pedestals. This image was printed from the Map Image window to a JPEG file. Pedestals are specified in the Map Design Window.

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GS+ 3D Map with Floor Contours
Maps can be drawn with contours projected onto the ceiling or floor of the image. This image had contours projected below the surface and was printed from the Map Design Window to a JPEG file. Floor contours are specified in the Map Design Window.

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GS+ 3D Map with Floor Bands
Maps can be drawn with contour lines or bands projected onto the ceiling or floor of the image. This image has bands projected below the surface and was printed from the Map Image window to a JPEG file. Note that the wire frame density on this map surface is set to a very high value. Floor bands are specified in the Map Design Window.

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Axis Grids on Maps in GS+
Maps can be drawn with grids projected onto any of the axes. Gridding is available for 1D, 2D, and 3D graphs, as for this 3D graph of estimation variance. In this case, a grid was projected along all three axes before the map was printed to a JPEG file. Grids are specified in the Map Design Window.

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