I have a question regarding stationarity. Suppose I am dealing with a
fluvial depositional environment with 3 different kinds of deposits:
* coarse to medium grained sands in point bars and channel deposits
moved and deposited primarily by traction;
* sheetlike or splaylike overbank fine sand to silt levee deposits
which are carried in suspension during flood events and then quickly drop
out as currents subside and;
* swampy or marshy clayey and fine silt floodplain deposits which are
rained down vertically as stagnant muddy water slowly cleans itself up.
As you can see the three types of deposits have very different grain sizes,
the three dimensional shape of each facies is different and they were
deposited by completely different mechanisms but they are all closely
associated with one another spatially.
The section I am looking at is 50 feet thick. The site is 700 acres in size
with one linear channel belt roughly 1000 feet wide cutting across it. The
parameter I am trying to describe with geostatistics is grainsize. I have
500 borings with grain size measurements every 0.5 vertical feet on a
regular spacing (250 horizontal feet) over the entire site.
Here's my question. Does it make any sense to try and describe the grain
size variogram for the entire site (all 3 facies lumped together)? It seems
to me that each facies will have it's own area of stationarity and that it
really only makes sense to model each facies independent of the others. It
makes some intuitive sense to me that deposits deposited by the same
mechanism with generally the same grain size could be stationary and could
be reasonably described with a variogram. But lumping them all together just
But this is what is commonly done, this is what I have done in the past.
What are we really doing when we lump things together like this? What
assumptions are we violating and what are the implications to the resulting
interpretation? Does it even make sense to use the term variogram when
lumping things together like this? Isn't this kind of a misapplication of
the tool? Aren't we asking it to describe something it was never meant to
Fina Oil and Chemical
14950 Heathrow Forest Suite 300
Houston, Texas 77032
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