Ferrari Mailing List: Upscaling

[Rick Lindsay (rolindsay]

Good morning friends,

A major phenomenon in my daily business is 'upscaling' - the translation of 
measurements taken at one scale to those of another.  For example, we log or 
measure, rock properties in a well bore using tools that have a vertical 
resolution of 30cm.  We sample at an interval of 15cm, thereby honoring the 
Nyquist frequency of the signal.  (Translation: correct continuous-to-discrete 
or analog-to-digital conversion.)  The only data collected in well bores which 
measures a smaller interval is provided when we take actual core plugs from the 
rock.  Those plugs are about 2.5cm in diameter - but they are not taken at any 
consistent interval but rather, they are all-but-random 'point measurements'.

The sampled well data needs to be compared to measurements taken from the 
surface with seismic (acoustic) methods.  The vertical resolution of that 
methodology is on the order of 25 meters, on a good day!  That means, the data 
which we consider 'true' is sampled over 1500 times as finely as the wide 
spread seismic data measured from the surface.  The problem then becomes one of 
'upscaling' the well data to the resolution of the seismic data so that we 
might calibrate it to the 'truth'.  One cannot go the other direction, 
independent of how alluring that idea might seem.  One cannot 'process' out of 
data what one did not 'measure'.  That would be like predicting how long it 
took you to brush your teeth by measuring how many hours you are awake each day!

Upscaling takes advantage of the length of the finely sampled information.  
Many samples can be averaged together to give an indication of the properties 
of a larger interval - the interval measured by another instrument, for 
example.  This process is done with a moving average and when done properly, it 
is called 'upscaling'.  Implicit in the technique is the assumption that there 
are very many samples, enough to be statistically representative of the larger 
sample interval.  As silly as it might sound, I do this process every day in my 
rock property modeling.

Here's a little aside, and I promise that this soap-box thesis is NOT the theme 
of this post: So-called scientists use tiny bits of finely sampled data, say, 
average earth temperatures over a couple hundred years, and from that minuscule 
data set, they 'upscale' to enormous proportions.  Its called 'global warming' 
and it is junk science, done for economic or feel-good reasons.  In signal 
theory, it is an abomination, not because it is climate change (true or false) 
but because the math is just wrong!  Aside over.

So why did I write all of this to a Ferrari List?

On the drive in to work, my geeky mind this morning was pondering a 
particularly chewy problem I'm facing here at work.  I have a well that has 
encountered hydrocarbons at an objective interval but the well logs are very 
corrupted.  The drillers had lots of problems with 'the hole', as its called.  
They 'lost circulation', which simply means that the drilling fluids used to 
cool the bit and to carry away rock chips, quit circulating!  And that means 
that the fluids were probably being flushed INTO the rock formation.  Yes, a 
pressure imbalance.  The result for drillers is terrible headaches.  The result 
for the company is delays, at $1,000,000 a day rates.  The result for me is 
really bad data coming from the logging tools because the hole condition 
violates the design criteria of the measuring tools.  This got me thinking 
about cars (escapism perhaps?).

I began to think about the scale of sports cars.  And specifically, I compared 
the two kinds of sports cars that I enjoy: Ferraris and LBCs (Little British 
Cars).  I have said before that the 'thrill factor' of motoring is scale 
dependent, thus the connection to the previous tutorial on sampling.  One might 
argue that the same 'thrill-factor' achieved at 90mph in a Ferrari on an open 
winding highway, might be found in a 40mph run in an LBC on a twisty country 
road.  See the scale thing?  And I think this might just explain why I enjoy 
driving LBCs and don't drive my Ferraris much at all.  I can thrash an LBC to 
its absolute limits and rarely exceed the speed limit!  I can break the speed 
limit in 1st gear in either of my F-cars!  The translation is that because of 
the laws, I have to grossly under-use my F-cars thereby depriving me of the 
'thrill-factor'.

Notice how appearance, sound, pride, etc., have not figured into this argument; 
only 'thrill-factor' induced by spirited driving.  Would I rather have a 
Ferrari than an MG?  Obviously yes.  But given a twisty little country road, I 
can tell you which one I would rather drive, and it isn't Italian.

So there you have it, a total brain dump from a silly scientist in Houston.

Happy Thursday,

rick

PS: Posts like this are the reason we just can't wait for the F1 season to 
start! :-)