Your child is dense for her age
Evan BiancoAlan Cohen, veteran geophysicist and Chief Scientist at RSI, secured the role of provacateur by posting this question on the rock physics group on LinkedIn. He has shown that the simplest concepts are worthy of debate.
From a group of 1973 members, 44 comments ensued over the 23 days since he posted it. This has got to be a record for this community (trust me I've checked). It turns out the community is polarized, and heated emotions surround the topic. The responses that emerged are a fascinating narrative of niche and tacit assumptions seldomly articulated.
Any two will do
Why are two dimensions used, instead of one, three, four, or more? Well for one, it is hard to look at scatter plots in 3D. More fundamentally, a key learning from the wave equation and continuum mechanics is that, given any two elastic properties, any other two can be computed. In other words, for any seismically elastic material, there are two degrees of freedom. Two parameters to describe it.
- P- and S-wave velocities
- P-impedance and S-impedance
- Acoustic and elastic impedance
- R0 and G, the normal-incidence reflectivity and the AVO gradient
- Lamé's parameters, λ and μ
Each pair has its time and place, and as far as I can tell there are reasons that you might want to re-parameterize like this:
- one set of parameters contains discriminating evidence, not visible in other sets;
- one set of parameters is a more intuitive or more physical description of the rock—it is easier to understand;
- measurement errors and uncertainties can be elucidated better for one of the choices.
Something missing from this thread, though, is the utility of empirical templates to makes sense of the data, whichever domain is adopted.
Measurements with a backdrop
In child development, body mass index (BMI) is plotted versus age to characterize a child's physical properties using the backdrop of an empirically derived template sampled from a large population. It is not so interesting to say, "13 year old Miranda has a BMI of 27", it is much more telling to learn that Miranda is above the 95th percentile for her age. But BMI, which is defined as weight divided by height squared, in not particularity intuitive. If kids were rocks, we'd submerge them Archimedes style into a bathtub, measure their volume, and determine their density. That would be the ultimate description. "Whoa, your child is dense for her age!"
We do the same things with rocks. We algebraically manipulate measured variables in various ways to show trends, correlations, or clustering. So this notion of a template is very important, albeit local in scope. Just as a BMI template for Icelandic children might not be relevant for the pygmies in Paupa New Guinea, rock physics templates are seldom transferrable outside their respective geographic regions.
For reference see the rock physics cheatsheet.
Reader Comments (5)
Yeah that post was pretty epic. Castagna's notes on fluid factor were quite interesting.
What would be really interesting is to hear Goodway's comments on the points raised in the thread. He is the principal champion of LMR, and has undoubtably been the biggest influence on the industry's use of these parameters in geophysical analysis. Without his voice, I feel the thread is missing a certain Je ne sais quoi.
@Toastar and @Baboon of London,
It is nice to see the community riled up, and I think there are many spectators scratching their chins and pondering this thread. It seems like Bill Goodway is not very active on LinkedIn, but as enough people talk about it, he may find the motivation yet to chime in. I would like to see more examples comparing the propagation of errors through the algebra, even though it has likely been adequately studied. But I will work on that next chance I get. Separation is great, but not necessarily if it doubles or triples the uncertainty about each data point.
... And now, it's time for a shameless plug: Bill contributed a wonderful essay called, The magic of Lame', to our new "52 Things" book, and it touches on this very theme. He'd probably point people to his essay in the book, so I will do the same, ha!
Great to be having these kinds of discussions out in the open, percolating away over several days and weeks. Thanks for writing in. Oh and for the record, I am sitting on the fence between this great divide. I reserve the right to be an LMR enthusiast and a conventional AVO-er.
Submerged weighing is one method of determining % body fat. A person's weight actually doesn't tell you anything about whether or not they are fat. What is important is how much of their weight is fat. So yes, we should submerge kids.
@TSherry,
That is awesome! Thanks for the factoid. I like the analogy because I can't visualize what height squared actually means; I much prefer density. So it is density that we should strive for, as you say, in studying human morphology. Similarly some algebraic forms of elastic properties are hard to wrap one's head around too. So I think you have started a catchphrase that I will use as often as I can, "Yes, we should submerge kids". Love that as a mandate for any empirical approach.