GEOPHYSICAL TECHNIQUES
| SURFAS Technology |
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The underlying technology used in both GTEDIT and GTGRID consists of a set of procedures and data structures developed over many years ( since 1982) that enable the creation,editing and displaying of gridded surfaces in a very efficient yet flexible manner. Collectively, these are referred to as SURFAS® technology, a GTI exclusive. This methodology supports collections of multiple, bounded surfaces that collectively can represent very complex physical structures that need to be represented in a mathematical modeling environment. GTI's Approach to Gridding Gridding is the application of an algorithm that interpolates a set of z values located at random x,y positions onto a specified set of x,y locations that correspond to positions organized into rows and columns of a matrix . Values in this "grid" result are computed in various manners, but most methods attempt to assign values that represent samples on some unknown function Z of x,y that approaches the known, observed random points z values used to compute them. The various methods used by GTI differ primarily in the way that these grid node values are assigned in the immediate neighborhood of the random input points. There are a number of steps involved in generating grid node values. Click to view a description of each of these steps: pre-averaging
In order to avoid points that are very close together and in some cases to reduce the number of points going into the Primary Estimates phase, a spatial averaging process is performed during the initial data loading. This process is designed to only average points that have similar z values unless the points are very close together relative to the target grid spacing.
primary estimates
This is the first step in determining z values in the grid. Using the selected method, random points are used to estimate an appropriate z value at grid nodes that are very close to any one of these points. Because all other grid nodes are eventually an outgrowth of these initial values, this is a critical step. How well these primary estimates reflect the information contained in the random points will determine the quality of the entire gridding process. Fortunately, choosing the correct method is fairly straightforward, depending primarily on the random point data's distribution and in some cases, size ( no. of points). Using the METHOD keyword discussed later, you can specify how the primary estimates are calculated - the Global, Random-Scattered, Random-clustered, or Weighted Resampling method.
Global gives an excellent solution very quickly for point sets having less than 1000 points. Larger point sets and all point sets having boundaries and/or faults associated with them may be processed quicker using one of the Random methods. Resulting grids are usually quite similar. At the other end of the spectrum is Weighted resampling, a method that is very fast, even for large point sets. It is very useful for quick looks or in dealing with oversampled point sets like 3d seismic. Each of these is described in more detail later. secondary estimates
Once these Primary Estimates are formed, they serve as input to the Secondary gridding process used to populate the rest of the grid. This process has several stages designed to produce an appropriate interpolation between the Primary Estimates as quickly as possible. One interesting detail of this procedure is that only grid nodes adjacent to a defined node are evaluated. Each pass over the grid results in more nodes being computed, growing the surface outward from the original control points. This also affords methods to be relaxed as computation moves away from the Primary Estimates. Secondary Estimates are formed only at those nodes which qualify based on their distance from a primary estimate, and the distribution of any surrounding nodes with assigned values. "Surrounding points" are those points located within a user-specified radius about the point to be calculated. The user may also specify the distance to the nearest neighbor in order to get the desired results. Performance is primarily controlled with the radius parameter, whereas distance has the major effect on the coverage generated. Using a small distance, equal to the grid interval, avoids the calculation of secondary estimates. The number of empty octants allowed also has a major effect on the resulting coverage. Values of 4 or 5 allow extrapolation to occur beyond the convex hull of the input points.
Calculation of each qualified node is done by fitting the surrounding valued nodes to a plane, weighting all points by their relative distance from the node to be calculated. This process is stabilized by only computing nodes that are adjacent to a node that already has a value. Multiple passes over the entire grid range "grows" the grid values about the primary estimates in a very robust manner. smoothing
( optional) Smoothing can be applied as a separate step or as part of the grid calculation. If employed during grid calculation, only the secondary estimates will be affected. Smoothing is employed as a number of passes with a very short filter designed to adjust any points that do not conform to the minimum-curvature model. This recursive, numerical solution to the bi-harmonic equation converges rather slowly, but very pleasing results can be obtained in about 10 passes. Other types of smoothing filters are available instead of the minimum curvature.
It is in the Primary Estimates that the main differences exist. It is in this area that the requirements of different data distributions need different algorithms and rules. Types of Gridding Methods ( Controls primary estimates only) Click on each type of Gridding Method to view a description. Global
The GLOBAL method uses a close relative of the bi-harmonic equation solution to compute a set of equations that allow direct calculation of a function that passes through each input point. This is the default method for GTedit. For point sets that have less than 1000 points without any associated boundaries or faults, one set of equations is determined for the entire map. Up to about 500 points, this is the fastest method. For larger datasets, or those with boundaries and faults, the GLOBAL choice becomes somewhat slower than the others because it must perform many solutions, one at each grid node. A radial search method similar to that used in RANDOM-SCATTERED is employed, but all neighbors are used to form a solution, and more nodes are assigned a value as part of each solution. This gives a better estimate at primary nodes, and at some of the secondaries that are nearby. Because of the high-order surface in use here, little or no averaging occurs prior to grid assignment.
Random-Scattered
This method works well on most datasets except those that are tightly clustered with some noise or error term present. In these cases, better results will be obtained with RANDOM-CLUSTERED, a slightly different approach described below. The reason for this becomes apparent in the methodology employed. For SCATTERED points, only a minimum of spatial averaging is employed on the points. Points closer than a fraction of the grid spacing are averaged together. The resulting points are then ordered into search bins. Each point is taken as a search origin and a collection of neighbors formed by taken the two nearest points in each octant. A least-squares fit of a plane that passes through the origin point is determined as then used to assign any adjacent grid nodes that are within about 1 grid interval from the origin point. This process repeats until all input points have be used as an origin. Depending on the point distribution, averaging may occur during this process since the same grid nodes can be assigned multiple times.
Random-Clustered
Very similar to RANDOM-SCATTERED, this method is tuned to deal with cases where noise exists and averaging of the point data is desirable to avoid excessive gradient extrapolation. If SCATTERED was used and too many anomalies were produced adjacent to clusters of points, you probably need to use CLUSTERED.
Clustered
CLUSTERED differs initially in the degree of pre-averaging that is done on the point set itself. All points that are within a distance of .5 times a grid interval will be averaged prior to gridding. The other primary difference occurs after neighbors are collected. Instead of attempting to force a plane through the center point, all points within a grid interval are ignored except the center point and a least squares fit to a plane is performed. In this way the node values assigned tend to be a projection of the background gradient rather than any local gradient implied by close neighbors. This usually implies more averaging at the grid nodes, but can have a desirable effect if data points contain some noise or error component.
Weighted Re-Sampling
This method was introduced shortly after 3d seismic datasets became a part of computer mapping. In such cases, the amount of input points usually far exceeds the resolution of any grid you may wish to compute for modeling or contouring. The method only performs a spatial resampling of the data, not interpolation. In the context of GTedit, this means the initial estimates are done in a very quick manner, and secondary estimates are not even needed if input point coverage is complete. The method can also be used effectively with sparse datasets since secondary estimates will do the interpolation required between the Initial Estimates formed using WEIGHTED.
At each node that is near to an input point,WEIGHTED RE-SAMPLING forms a weighted combination of the input points with weights that are inversely proportional to the distance the point is from the node. Only points that are within 1 grid node are used at a given node. Thus, each input point contributes to about 5 nodes. If used on sparse data, the effect is to make all points.the location of a flat spot, usually a local maxima or minima on the resulting surface. Reccommended Selection of Gridding Method & Parameters To 'grid ' a set of points means to estimate values of a surface that passes through a set of observed points and is smooth and continuous in-between. By performing this estimating on a rectangular grid mesh it is then easy to make displays such as contours and 3D perspective views that give a good visual impression of the information contained in the point set. (The procedures discussed herein assume the function to be determined is single valued over the selected range of x and y.) Therefore, to select the appropriate method and parameters used in the gridding process is very important if you wish to get the best impression of the data set. The following links provide a rough guide to making these choices. You are ready to make a grid !
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