Every 3D view, 2D view, and volume estimate on the results page comes from the same interpolation.
A boring only tells you the %RE response at that one location, at
discrete sampled depths. Below we describe the method used to
estimate what's happening in the space between and around your
borings, filling in a full 3D grid from those discrete samples.
What is measured and what is estimated
Only the boring logs are measurements. Everything else on the results
page is built from them, in three steps:
Inputs. Each boring's log is cut into 30 cm
(about 1 ft) depth intervals, and the highest %RE reading in each
interval becomes one input point, at the interval's middle depth and
the boring's coordinates. An interval with no readings, such as a
depth gap, gives no point; it is not treated as zero.
Grid. Kriging (below) estimates %RE on a regular
grid of cells 3 m across and 0.15 m deep. Horizontally the grid
reaches past the outermost borings by the fitted horizontal range;
vertically it starts 1 m above the shallowest input point (but not
above the ground surface).
Trimming. Two kinds of cell are left blank:
cells deeper than the borings were logged at that spot, and cells
too far from the borings to be supported
(the 90% rule). At a boring, "as deep as it
was logged" means its deepest reading; between borings it is
interpolated in a straight line from one boring's depth to the
next, and past the outermost borings it keeps the depth of the
nearest point on the outline joining them. So a shallow boring's column stops where its log stops, and
nothing on the results page is estimated below that from deeper
borings elsewhere.
One consequence is worth knowing before you compare a figure with a
log: the highest value on the grid differs from the highest reading
in the logs, because cells rarely sit exactly on a boring and each
input is already a 30 cm summary. It is usually lower: on the
Example Job the logs peak at 653.8 %RE (SB-02) and the grid at
534.7 %RE. It can also come out slightly higher where kriging
overshoots between high readings. Each job's
readme.txt gives both numbers.
Depths are below each boring's own ground surface.
Ground surface elevations aren't used (the coordinates file's
ground_surface_elev_ft column is optional): every boring
starts at the same level, so the 3D view, 2D view and volumes treat
the ground as flat.
On a site with real relief, a layer at one elevation shows up at
different depths in different borings.
The problem: estimating between borings
A site is only ever sampled at a handful of discrete locations and
depths. To draw a continuous 3D plume, or estimate a volume of
material exceeding some %RE threshold, something has to fill in
the gaps between those samples with a reasonable estimate.
The simplest approaches — connecting the sampled points with
straight lines, or just using whichever sample is nearest — treat
every gap the same way, with no regard for how spatially
correlated the real %RE response actually is, and no sense of how
confident the estimate should be in a sparsely-sampled area versus
a densely logged one.
Kriging
Kriging is a geostatistical interpolation method: it predicts a
value at an unsampled location by weighting the surrounding known
samples, rather than treating every nearby sample equally. The
method rests on a simple geographic principle —
spatial autocorrelation: two locations close
together tend to have more similar %RE responses than two
locations far apart. Kriging turns that principle into real
numbers by looking at the distance between every pair of known
samples.
A schematic, not a computed result: four borings, each a column of input points (one per 30 cm interval; every other one drawn). Every pair of input points has its own 3D distance. Two are labeled: two points in the same boring (the vertical direction) and two borings at the same depth (the horizontal one). Kriging uses the distance between every pair.
To turn those distances into weights, lif-viz builds a
semivariogram: for every pair of known samples, it
plots how different their %RE values are against how far apart
they are. Pairs close together typically land low on that plot
(similar values, low dissimilarity); pairs far apart typically
land higher (less related values) — up to a point, beyond which
distance stops making the pairs any less related.
An illustrative semivariogram — dissimilarity between sample pairs rises with distance, then levels off once pairs are far enough apart that distance no longer explains how related they are.
A mathematical curve is fit to that pattern — lif-viz uses a
spherical model, a standard, well-established
choice in environmental work. That fitted curve is what
actually produces the interpolation weights: a sample gets more
say over a prediction the closer and more correlated it is, and
less the farther and less correlated it is — a more sophisticated
rule than "nearest sample wins," because it reflects the real,
measured spatial structure of this site's own data, not a fixed
assumption applied to every site the same way. Kriging reproduces
each input point exactly at that point's own location, but the grid's
cells rarely sit exactly on one, so values right next to a boring can
differ from its log (see
what is measured and what is
estimated).
lif-viz builds that semivariogram in two directions: from pairs of
readings in the same boring (vertical), and from pairs of borings at
the same depth (horizontal). On real UVOST data the two are very
different. Readings in one boring typically stop being related
within a meter or two, while across borings it takes tens of meters,
because contamination tends to spread in thin layers. So the fitted
model has its own range in each direction, which keeps a thin
contaminated layer thin between borings instead of spreading it
over the whole depth. The horizontal range is fitted on the
logarithm of %RE: with only a handful of borings, one boring
hundreds of times above background would otherwise decide it,
depending on which other borings happen to sit at which distances
from it. Each job's fitted values are listed in its
readme.txt. When a job has too few borings to fit the
horizontal direction, that range is set from the site's size
instead, and the readme says so.
lif-viz uses ordinary kriging — the variant that
assumes an unknown but locally constant mean, rather than requiring
you to already know a trend across the site. The interpolation
runs on the cleaned, canonical dataset described in the audit
report, at every job, before any visualization is drawn.
Like any interpolation method, kriging is only as good as the data
feeding it — it can't invent information about parts of a site with
no nearby samples, and a wide, high-variance area on a real kriging
variance surface is telling you exactly that: more borings would
narrow the uncertainty there. The 3D view and volume estimates
elsewhere on this page are estimates built on real statistics, not
a claim of certainty everywhere on the site. The results page doesn't
show the kriging variance itself, and no figure or volume comes with
an error band.
That uncertainty also decides how far the results reach beyond your
borings; see How far the results reach below.
Kriging can produce an estimate anywhere, even far from every
boring, but far away that estimate tells you little. So lif-viz
draws an estimate only where your borings actually support it,
judged with numbers the kriging already works with:
Sill
The level where the semivariogram above flattens out: the typical
difference between two readings so far apart that they're
unrelated. It is about the variance of all of the job's readings,
in %RE squared. Each job's fitted sill is listed on the
Variogram line of its readme.txt.
Kriging variance
Kriging's own measure of how uncertain each estimate is, in the
same units as the sill. It is small next to a boring and grows
with distance from the borings until it levels off at the no-data
level.
No-data level
The kriging variance of an estimate with no boring nearby, where
the borings no longer inform it and kriging returns roughly the
site's average reading. It is about the sill, a few percent above
it, since ordinary kriging also allows for not knowing the site's
average (4.3% above on the Example Job). Each job's no-data level
is listed on the Interpolated area line of its
readme.txt.
The rule
An estimate is drawn only while its kriging variance is below
90% of the no-data level, meaning the nearby
borings have reduced its variance by more than 10% compared with
having no data there. The fraction is the same for every job; the
no-data level, and so the distance at which this happens, comes
from each job's own data.
Computed from the Example Job (synthetic data): the kriging variance along a line running east from its southeast boring, SB-06, as a share of the job's no-data level. Estimates are drawn out to about 21 m, where the variance reaches 90% of that level, and left blank beyond that.
How far that reaches depends mostly on the fitted
horizontal range in the job's readme.txt: about 21 m
past the Example Job's SB-06 with its 39.8 m range, and 50 m
or more on a site whose fitted range is longer than the site itself.
So:
The edge of the colored area is where the borings stop
supporting estimates, not where the plume ends. If your
highest readings are on the edge of the boring grid, the plume is
often still strong where the colors stop, and its real extent
beyond there is unknown.
Past the outermost borings, estimates are
extrapolated. The 2D view outlines the borings’
footprint, the outline joining the outermost borings, and hatches
the colored area beyond it. There an estimate leans on borings on
one side only. The volume chart and the readme give the volume
between the borings and in this extrapolated area separately.
A very high reading can lift estimates beyond the clean
borings next to it. Each estimate is a weighted average
of the readings out to the fitted range, so a reading tens of
meters away still gets a small share of the weight. Next to a
reading hundreds of times above background, that small share is
enough. On the Example Job, SB-02's layer of 250-650 %RE, 47 m
away, gets about 4% of the weight 12 m south of SB-08 and accounts
for all of the 15 %RE estimated there. So the 10 %RE contour runs
10-20 m south of SB-05 and SB-08 although neither reads above about
6 %RE. These estimates are close enough to a boring that the rule
above doesn't blank them: read them as the reach of the hot
reading, not as contamination found there.
A blank estimate is left out everywhere: the 3D views, the 2D plan
view's colors, the GeoTIFF export and the volume estimates. In the
2D view's contour lines, it is where a line turns from solid to
dashed (see Contour lines below).
3D View
The results page's 3D View tab renders the full
computed kriging grid directly in three dimensions — every
interpolated cell at its own real (easting, northing, depth)
position, colored by %RE using your chosen color ramp. Drag to
rotate, shift-click drag to pan, and scroll to zoom, so you can see
the actual shape of the response in space: which depths carry it,
whether it's a thin layer or a tall column, and how that shape
changes as you adjust the transparency threshold or gamma value
(see the visualization-options
help page for what those controls do).
This is the one view that shows the true vertical structure of the
interpolation — the detail the 2D View below necessarily collapses
away to produce a single flat image.
Its vertical scale is exaggerated 3×, so a
thin layer stays visible next to a site tens of meters across; layers
look three times thicker, and slopes three times steeper, than they
are. The vertical axis, Height above ground (m), is
0 at each boring's ground surface and negative below it, so −5
means 5 m below ground. The black rods are the borings, drawn from
their first reading to their last. The tick labels on all three axes are true,
unexaggerated meters, in the coordinate system of your coordinates
file.
2D View
The results page's 2D View tab is a
top-down projection of the exact same 3D kriging grid used by
the 3D view — it is not a second, separate interpolation, and
it does not use a different statistical model. At every
(easting, northing) location on the grid, the plan view shows
the single highest %RE value found at any depth
below that point, so a plume that is strongest at 4 m depth and
a plume that is strongest at 9 m depth both show up at full
intensity in the same flat image.
Note that the plan view is displayed (and exported as a GeoTIFF)
as a smoothed version of
the underlying grid, using a 2D spline fit purely for display
so the plume reads as a continuous cloud rather than a blocky
grid of cells. The smoothing never changes which cells the
kriging model actually computed — it's the same values, just
interpolated onto a much finer image for a nicer-looking result
— so the plan view and the 3D view always agree on the
underlying plume shape. Areas left blank follow the
90% rule above. A spot is colored if any depth
below it passes the rule.
The 2D view's tick labels are easting (along the bottom) and
northing (up the side), in meters in the coordinate system of your
coordinates file. Two exports from the Export menu take it into GIS:
Plan View (GeoTIFF), a colored image in that same
coordinate system, and Contour Lines (GeoJSON), in
WGS84 longitude/latitude, which every GIS reprojects on the fly; see
the visualization-options page
for what each holds. Both line up with your other layers as long as
the coordinate system in your coordinates file is the one your
borings were surveyed in.
Contour lines. The 2D view can draw contour lines
at 10, 25, 50 and 100 %RE, labeled “10%” to
“100%”. They are traced on the kriging grid
itself (3 m cells, the highest value at any depth) rather than on
the smoothed display image, then gently rounded: the smoothing
overshoots slightly between grid cells, which is invisible in the
colors but would turn a line near a site's background level into
many tiny loops. A line is drawn solid between the
borings, inside their footprint, and dashed in the
extrapolated area past it; where the map is blank, as the estimate
fails the 90% rule, the line isn’t drawn at all, so it can
end at the edge of the colors. Every level stays drawn whatever the
transparency threshold, and the Contour Lines (GeoJSON) export
holds the same lines, each piece marked as extrapolated or not.
