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Miles vs Kilometer - Easy conversion with Fibonacci

Measurements are important. Even the little one’s want to know how much they grew in the past month. It’s a frame of reference. However, especially in geophysics we have not agreed on the same frame of reference. When you look at your data, you better make sure if it’s meters or feet or miles. It’s quite easy to convert from feet to meter, as it is just 3feet = 1m, however when we go from miles to kilometers it gets more tricky.

Miles and Kilometers

One mile equals 1.6 kilometers. So when we convert from one mile to kilometers, we can multiply by 8 and divide by 5. That is quite a hassle.

Fibonacci

Fibonacci spiral.
The Fibonacci sequence is a fascinating thing. The closer you look you can find it in many areas. One, I want to show you now.

The sequence is pretty simple. You start with 0 and 1 as the first two numbers. Add them together for the third number, so 1. Then you go on and just add the last two digits together and get the next number.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, …

What’s really unique between these, is the division of any two adjacent numbers. The higher you go on this sequence, the closer we come to a very special number: The golden ratio.

Fibonacci imagined. CC-BY-SA Rob the Poor

Quick Conversion

As the gif shows, the golden ratio is somewhere around 1.6. Which makes for a nice coincidence with our miles vs km problem. We can convert from miles to km just taking the next fibonacci number.

  • “So your profile is 5miles long, those are some decent 8km!”
  • “Oh it’s 13 km in that direction? Guess those 8 miles will be worth it!”

Of course it also works with compund numbers. 16km is not in the sequence, but 2 times 8km will give you 2 times 5miles, although this one might have been obvious as 1 mile is still 1.6km. When you’re looking for 18miles, you can also add 13mi and 5mi, which amount to 21km plus 8km, so 29km. Is that close enough for you? For me it’s way easier than multiply8-divide5 or the other way around.

If this is any help for you, let me know in the comments.

The Showroom - Data for my thesis

I’m working on a field data set from the Mediterranean Sea. There are many intellectual reasons for working this data set. However, there are some motivate my inner child as well, let me explain.

The Specs

The data set was recorded by TGS and is of brilliant quality. Almost 8km (5mi) in offset over the entire length of a salt sheet with 11s recording time. The frequency content is quite nice for conventional acquisition. It was recorded in the Eastern Mediterranean to be more exact in the Levantine basin.

The fun reasons

When I hear Eastern Mediterranean this will immediately trigger images as the following:

Kardamos Beach. CC-BY-SA GGia

Blue sea, nice beaches and interesting geology on wonderful islands. This may be a bit simple, but then again I’m looking at white/gray/black wiggles all day long, let it slide. It’s a happy place in my head. Another fun one to think about is that Levante is the Italian word for sunrise.

Sailing vessel at sunrise CC-BY-SA Valerii Tkachenko

La dolce vita.

The intellectual reasons

Enough of the pretty pictures. Why would I use exactly this data set in this geological setting.

The salt sheet in the Levantine Basin is young. Now let the geology jokes roll in, as in geology we usually say something is young when it’s only “a couple million years old”. So they were deposited around five and a half million years ago. Since then there has been comparatively little time for tectonic overprinting and the like. However, basin-ward there are some saltrollers. So in one and the same data set we can compare very simple “fresh” salt geology with some overprinted more complex setting.

Trying subsalt imaging in this rather controlled setting will provide a sandbox1 for algorithms and processing steps to test.

Salt tectonics

The salt itself is very interesting as well. The study of salt tectonics in general is pretty young (not on a geologists scale, on a “normal” human scale). In the beginning of last century salt and its overburden were considered to be fluids (on geological time scales) and buoyancy drove salt to rise through the upper sediment. At some point people started realizing that buoyancy alone could never explain the behavior of salt in our Earth. Instead of considering salt to have some sort of intrinsic motivation to rise and start some salt diapirism, nowadays, evaporites are considered to stay where they are unless there is some driving force that will cause it be displaced. Don’t get me wrong, especially here in Northern Germany, we do have the rare case that salt diapirism is actually buoyancy driven, but that is one process out of five. This paradigm change is considered to be the change from the “fluid era” to the “brittle era”

However, salt is an excellent decoupling mechanism for tectonic stress regimes. Normally, when you look at stress fields you have a superposition of local, regional and global stress fields that act upon your area of interest.

Superposition of local (blue) and regional (red) stress fields combine their influence an a fault (purple).
When we introduce salt, we can have a look if the salt was actually decoupling our stress regimes. Usually, you can say that the regional stress acts deeper than the local stress.
Decoupling of local (blue) and regional (red) stress fields. Only regional stress field acts on fault (now red).
More will follow on salt tectonics but this topic especially in regard to the Levantine basin is so huge, it deserves it’s on article.

The challenges

I started a little on the challenges of subsalt imaging in the initial blog post about my master thesis, but let me repeat that part.

Salt Body with two features marked. One has a complex salt geometry. One is fairly simple.
Simple salt geometry still defocus the beam, lowering the illuminating energy. For simplicity only uppermost reflection shown. (Opacity shows total energy.)

This is not an accurate model of Levantine basin but it represents the general setup. You also have the two zooms with the seismic beam in both settings. As we can see the complex structure has some basic optic effects on the beam. However, the simple structure also defocuses the beam because micro-undulations in the interface are present.

 

Complex salt structures can cause lens effects, spreading the energy. Reflection not shown. (Opacity shows total energy.)

So it seems that the simple salt geometry would be much easier to image, as there are no strong dips and lenses. There’s only a little defocusing. That’s at least what I thought. Oh how wrong I was. In salt the degree of deformation correlates negatively with the degree of anisotropy. So when there is less deformation present in the salt sheets, the anisotropy gets turned up a notch. And as Helbig (one big author on anisotropy) once said:

Anisotropy is a nuisance!

You got to know my data a little bit. I for one am quite excited to try and get all the juicy details from this one. Let’s see how this one turns out.

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