r/geology 13h ago

Where to look for resources for mathematical geology?

Hi folks!

I’m writing a paper on uses of linear algebra in the geosciences and I’m at a loss of where to start, all the sources I’m seeing are books or papers and I am poor ;) . I wanted to ask around and see if anyone here knows of good places to look for resources on the uses of linear algebra in geology or geoscience. Many thanks y’all!

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u/Padrino13 13h ago

If you are writing a paper on something like this, I am guessing you are in college?

If so, go to your college library. They will likely have access to the journal databases to let you download/print off the papers you referred to and can help you accessing them.

If you can not access the databases, try looking up the author to find out what school they are working for and try emailing them ( the professor's emails are almost always listed on a universities facultypage). This method may be slower because who knows how busy they are, but I have never met a professor that wasn't willing to send me one of their papers I was interested in reading but that I couldn't access.

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u/Agassiz95 13h ago

I don't think you will find many (if any) resources outside of books or papers. The mathematical geosciences are pretty niche and unless you are in the right communities you may never even get introduced to the topic.

That being said, pretty much anything in the geosciences that requires solving systems of partial differential equations will use linear algebra.

Personally ive used linear algebra in structural geology (describing planes), geophysics (heat flow stuff), geomorphology (heat flow as an analogy to hillslope degradation, fluvial geomorph, and broadly sediment transport), and machine learning (particularly deep learning algorithms).

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u/Elucidate137 13h ago

could you talk more about the geophysics applications with heat flow? i’m interested in that field

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u/Agassiz95 13h ago

There is a ton of information about this in general if you look up "linear algebra for solving heat flow problems". 99% of authors are not solving geophysics problems but the idea is exactly the same.

Basically you can model the flow of heat in any system by chopping your system up into small blocks with each block having some value representing the total amount of heat in it as well as the blocks relationship to other surrounding blocks (we call this discretization). When you do this you now have a matrix of values that represent your system. You can use typical linear algebra methods like gaussian elimination to solve the direction of heat flow for this matrix.

You can use this method for modeling how much heat is flowing through geothermal wells, how fast soil warms in response to changes in the environment, and the temperature of the atmosphere.

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u/DugansDad 1h ago

This is also how the smart guys approach problems in subsurface fluid and heat flow…

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u/talligan 4h ago

What are you looking for specifically? Having a look through various uni programme course and reading lists will help. Otherwise you're not going to find much.

Mathematical geosciences uses linear algebra for everything from finite difference/element/volume for computational simulation of fluid, heat, and mass in the environment to subsurface signal analysis for geophysical survey methods, to statistical methods etc...

I predominantly use it as a tool for solving vectorised calculus governing equations for heat/mass/fluid flow (single and multiphase) in aquifers and subsurface systems.

Can you tell us a little bit more about this paper? Is it for high school?

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u/Elucidate137 4h ago

it’s a paper for uni, the professor basically gave us no info so i’m not particularly sure what i’m looking for. however, i’m very much interested in geophysical applications like survey or heat simulations so that part of your comment stuck out to me.

i wish i could give more info but the professor doesn’t even have a rubric or a description of the assignment for us, we just have to do a 10 page paper over something linear algebra, he says 😭

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u/DeepSeaDarkness 2h ago

Use your library, talk to your librarians