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Geostatistics

Geostatistics

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Geostatistics

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  1. Geostatistics

  2. Hydrogeologist III / Salary Range: $48,980 - $72,632 per year (DOQ).

  3. Goals

  4. Basic definitions • Variance: • Standard Deviation:

  5. Basic definitions • Number of pairs

  6. Basic definitions • Number of pairs:

  7. h Basic definitions • Lag (h) • Separation distance (and possibly direction)

  8. h Basic definitions • Variance: • Variogram:

  9. The variogram • Captures the intuitive notion that samples taken close together are more likely to be similar than samples taken far apart

  10. Common Variogram Models

  11. Common Variogram Models

  12. Basic definitions Kriging: BLUE

  13. Kriging Estimates

  14. Where to get software: http://sgems.sourceforge.net/ http://sgems.sourceforge.net/doc/ sgems_manual.pdf ftp://globec.whoi.edu/pub/software/ kriging/easy_krig/V3.0.1/ http://www.ucc.ie/gnuplot/ Release 4, gp400win32.zip

  15. S-GeMS Object file format ww (49x30) 3 x y pore 1 1 1 21 1 1 41 1 1 61 1 1 81 1 1 101 1 0 121 1 0 141 1 0 161 1 0 181 1 0 201 1 0 … Load object Import as point set

  16. Random Numbers; Pure Nugget

  17. Unconditioned Simulation • Specify mean and neighborhood • Specify variogram • Simulation should honor variogram

  18. Unconditional Simulation

  19. Simulated Field/Known Variogram

  20. USGS Sections http://sofia.usgs.gov/publications/wri/90-4108/wri904108plates.pdf

  21. http://sofia.usgs.gov/publications/wri/90-4108/wri904108plates.pdfhttp://sofia.usgs.gov/publications/wri/90-4108/wri904108plates.pdf

  22. USGS Aquifer Tests

  23. USGS Site Identification Sites are identified by the standard U.S. Geological Survey (USGS) identification number, which is based on an initial determination of latitude and longitude of the site. The site identification serves as a unique identification number in files and databases of the USGS and indicates the approximate geographic location of each site. The identification consists of 15 digits: the first 6 digits denote the degrees, minutes, and seconds of latitude; the next 7 digits denote degrees, minutes, and seconds of longitude; and the last 2 digits (assigned sequentially) identify the site within a 1-second grid. For example, site 363530116021401 is at approximately 36°35'30" latitude and 116°02'14" longitude, and it is the first site recorded in that 1-second grid. Even if a more precise latitude and longitude are subsequently determined, the site identification number remains unchanged. Latitude and longitude shown for a site, therefore, are the most accurate locators.

  24. Coordinate Extraction

  25. Lat/Lon State Plane NGS Horizontal Blue Book format - *80* (Control Point) Record. Only the *80* records in a Blue Book file are used by NADCON, the other records are passed through without change to the output. On the *80* records, only the latitude and longitude are modified - the rest of the record is unchanged. Thus, this format can be used with either 'old' Blue Book files or 'new' Blue Book files. On the *80* records, the direction of the latitude must be north positive ('N') and the direction of the longitude must be west positive ('W'). The precision of the output will be the same as the precision of the input latitude. For more information on this format, please refer to: 'Input Formats and Specifications of the National Geodetic Survey Data Base' 'Volume 1. Horizontal Control Data'. Published by the Federal Geodetic Control Committee in January, 1989 and available from: the National Geodetic Survey, NOAA, Rockville, MD 20852. The following input example is a *80* record from a Blue Book file with NAD 27 coordinates: 004560*80*096 KNOXVILLE CT HSE 411906578 N0930548534 W 277 The following example is of the output *80* record with the transformed NAD 83 latitude and longitude. 004560*80*096 KNOXVILLE CT HSE 411906566 N0930549268 W 277 http://www.ngs.noaa.gov/cgi-bin/nadcon.prl?explain=Y&input_format=3 http://www.ngs.noaa.gov/

  26. Biscayne Aquifer K

  27. Specific Capacity • Flow per Drawdown, Q/s (gpm/ft) • T (gpd/ft) ~ 2000 Q/s (gpm/ft) • T = 2 x 106 gpd/ft (extreme!) • Q/s = T/2000 = 103 gpm/ft • Q = 100 gpm => • s = 1/10 ft (~3 cm) • Data: Q/s = 7000 gpm/ft Driscoll, F. G. 1986. Groundwater and Wells, Johnson Division, Minneapolis.

  28. Specific Capacity Data

  29. Specific Capacity Variance of data: 3,509,048 (gpm/ft)2 Range: 0.07 degrees Slow initial growth in variance with lag => Gaussian variogram model

  30. Specific Capacity Variance of data: 3,509,048 (gpm/ft)2 Range: 0.07 degrees Slow initial growth in variance with lag => Gaussian variogram model

  31. Conditional Gaussian Simulation • Specify data • Fit and specify variogram • Simulation should honor variogram and be responsive to values at ‘conditioning’ points

  32. Kriging • Specify data • Fit and specify variogram • Simulation should honor variogram and return exact values at sampling points • Optimal estimate too far from sample data is mean

  33. Gaussian Simulation/Kriging

  34. Gaussian Simulation/Kriging Gaussian Kriging

  35. Kriging 1 conditioning point 5 conditioning points

  36. Simulation 1 conditioning point 5 conditioning points