Should subsection headings sometimes repeat section headings?

Question

In a technical or scientific text, such as a PhD thesis, should headings for (sub)sections be complete and sometimes repeat information from the headings of the levels above, or is it sufficient to have a short heading, assuming that it is implied that section X.Y.Z is still inside X.Y.?

For example, in my PhD thesis, I have a sectioning structure like this:

2. Remote sensing
2.3. Specific technologies
2.3.1. Solar
2.3.2. Terrestrial
2.3.3. Active

My supervisor said that Solar, Terrestrial, Active, or even Specific technologies are not proper section titles, but that I should rather write something along the lines of

2.3. Specific observation technologies
2.3.1. Solar remote sensing
2.3.2. Terrestrial remote sensing
2.3.3. Active remote sensing

even though this repeats the heading for chapter 2. Browsing through some books on my desk, it appears that section and subsection titles often indeed do repeat information from higher level headings, but it makes the mathematician buried (somewhat deep) inside me cringe a little.

Are there any style guides or rules addressing this point explicitly?

Answer 1

As @Lauren Ipsum said, go for clarity. Remember that there are times when you don't see the context, for instance when using a cross-reference. "See section 2.3.2, Terrestrial" is not immediately obvious to the reader.
Approach this as a writer, not a mathematician. Writing section headings that make sense even when viewed in isolation, will help readers understand what you're writing and where they can find what they're looking for. Your audience will probably include people for whom English isn't their native language; giving them a complete expression to parse will make it easier for them to read your thesis.
About "specific technologies"; I'd use the word 'specific' only if you have a heading 2.1 or 2.2 that talks about "general technologies" so you have a juxtaposition. Otherwise the word is redundant.

Answer 2

I'd say that your current sounds fine, though you may want to prepare it as both, just to placate your adviser. Sed would be able to help you do this if you are using something like LaTeX to prepare it.