Geostatistics

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

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Goals
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Basic definitions

• Variance
• Standard Deviation

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Basic definitions

• Number of pairs

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Basic definitions

• Number of pairs

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Basic definitions

• Lag (h)
• Separation distance (and possibly direction)

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Basic definitions

• Variance
• Variogram

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The variogram

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

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Common Variogram Models
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Common Variogram Models
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Basic definitions

• Kriging

BLUE
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Kriging Estimates
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Where to get software
http//sgems.sourceforge.net/
http//sgems.sourceforge.net/doc/ sgems_manual.pdf

ftp//globec.whoi.edu/pub/software/ kriging/easy_k
rig/V3.0.1/
http//www.ucc.ie/gnuplot/ Release 4,
gp400win32.zip
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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
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Random Numbers Pure Nugget
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Unconditioned Simulation

• Specify mean and neighborhood
• Specify variogram
• Simulation should honor variogram

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Unconditional Simulation
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Simulated Field/Known Variogram
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USGS Sections
http//sofia.usgs.gov/publications/wri/90-4108/wri
904108plates.pdf
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http//sofia.usgs.gov/publications/wri/90-4108/wri
904108plates.pdf
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USGS Aquifer Tests
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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 3635'30"
latitude and 11602'14" 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.
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Coordinate Extraction
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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
00456080096 KNOXVILLE CT HSE
411906578 N0930548534 W 277 The following
example is of the output 80 record with the
transformed NAD 83 latitude and longitude.
00456080096 KNOXVILLE CT HSE
411906566 N0930549268 W 277
http//www.ngs.noaa.gov/cgi-bin/nadcon.prl?explain
Yinput_format3
http//www.ngs.noaa.gov/
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Biscayne Aquifer K
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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 gt
• s 1/10 ft (3 cm)
• Data Q/s 7000 gpm/ft

Driscoll, F. G. 1986. Groundwater and Wells,
Johnson Division, Minneapolis.
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Specific Capacity Data
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Specific Capacity
Variance of data 3,509,048 (gpm/ft)2
Range 0.07 degrees
Slow initial growth in variance with lag gt
Gaussian variogram model
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Specific Capacity
Variance of data 3,509,048 (gpm/ft)2
Range 0.07 degrees
Slow initial growth in variance with lag gt
Gaussian variogram model
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Conditional Gaussian Simulation

• Specify data
• Fit and specify variogram
• Simulation should honor variogram and be
  responsive to values at conditioning points

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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

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Gaussian Simulation/Kriging
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Gaussian Simulation/Kriging
Gaussian
Kriging
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Kriging
1 conditioning point
5 conditioning points
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Simulation
1 conditioning point
5 conditioning points