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New on StackExchange: Temporal Resolution of Seismic data

This was an answer on StackExchange, see the question here.

In seismic data analysis we have to distinguish between vertical (temporal) and horizontal resolution.

The (First) Fresnelzone is linked to the vertical resolution and defines the area in which the collected energy will still stack constructively.

The temporal resolution however, defines what the wave “sees”. The events can still be resolved if their thickness is within a fourth of the wavelength (lambda). However, in some cases it can go down to (lambda / 32). This is a matter of detectability of events.

Seismic Resolution

Don’t forget that we’re dealing with superpositions of different frequencies so basically low frequencies will give use the necesseray energy content of general trends, while high frequencies enable us to make a distinction between geologic features.

This file from the university of Oslo gives a nice overview.

(The picture is from a blog post I’ve written on knowing your wavelength it’s CC-BY-SA Source1 Source2

from EarthScience Stackexchange

Do you even math? - Calculus in geophysics and geology

The amount of math in degrees varies throughout every university and even in uni itself, there seldomly is a consensus on how much math is actually needed.

Jascha Polet from Cal Poly Pomona asked a very interesting question on Twitter:

This spawned a big debate on wether or not to include mandatory calculus.

One that hit very close was by Cian Dawson:

I myself hated the math courses when I took them. They were in the beginning of my studies. I had no clue how I would ever benefit from them. However, now finishing my Master’s I have to say I’m tremenduously glad I had that much math in my studies.

Alan Schweetz added the distinction between geology and geophysics:

Which I do agree has quite a bit of a different focus. I myself did a geophysics degree, whereas it is a completely different degree for geology at the University of Hamburg. We geophysicists focus a lot on math and physics, potentials, fields, wave propagation and ray theory. Geologists in our uni do not take a single math course and focus a lot on chemistry (yes without math).

Rich Briggs added

and this is where it started to get interesting for me. I took a lot of geology courses additionally to my degree in geophysics. In courses like sequence stratigraphy or oil and gas geology you were basically lost if you didn’t know the least bit of math. They were quite better at reading maps but calculating depths or well correlation was much easier for people who took some calculus.

Talking to some geologists, some even flat out said “I hate geophysics.” So when I came out as a geophysicist undercover (yes I took that many courses; they accepted me as one of their own.) They were a bit puzzled but it boiled down that the amount of math and physics was just overwhelming.

One example are two seemingly identical courses: Volcanology vs. Volcanism.

Volganology was held by a geophysicist, whereas volcanism was held by a geologist. As a geophysicist it was okay taking the volcanism course, you had to learn about many minerals and some basic chemistry. It wasn’t easy but it was doable. Geologists taking volcanology, however, would not last mor than two lectures. The amount of math and equations was overwhelming and plain intimidating for anyone not used to looking at equations. To be quite honest right here, I believe only taking both courses actually gave you the whole picture but it seemed impossible without proper knowledge in math.

Eric Klemetti, Philippa Demonte and whoever is behind TheEarthStory today (the folks I used to write for) added varying amounts of math to the conversation. The discussion ended with the following summary:

At first glance it might be weird to see this varying degree of math in geology and geophysics. But we have to consider that combining geophysics and geology ends you up in describing the Earth from the first formation to quaternary geology in very local settings. I personally believe a basic grasp of some math will significantly help many people in the fields. However, the three semesters I took would be way out of proportion for other applications. I today find joy in trying to understand paraxial ray theory and Gaussian beams, but I do realize I may be rather alone in that position. Looking at some russian universities that sent some students our way, I don’t have a slight grasp on the math they’re capable of.

What’s your opinion of math in geology or gephysics?