There are 2 kinds of compression involved in trumpet playing. One is concerned with breath control. And the other has to do with the embouchure.
We all know that high notes require more support (compression) than low notes. This need increases with the range. A low c needs x amount. A middle c needs 2X , high c 4X and super c needs 8X the support that low c needs to sound.
Along with this added air compression is a need to increase the lip compression to fight the air stream and produce the higher notes. If we blow a fast airstream against lips set for a low c then a low c comes out. ( Most of the time Look at overblowing the octave at the bottom of this message.) There are several systems taught here. The main point being that the lips need to form a smaller aperture and be strong enough to resist the air. Compression comes about when the lower lip pushes against the upper lip. In some schools (Stevens and Super Chops) the jaw moves up slightly and aids the lower lip in this action. This need for compression is lessened by adding an inward lip curl.The lip curl adds to the strength of the lip and since it acts as a one way valve less overall compression is needed. The air way MUST remain relaxed and open at all times. The air support can be helped by the use of a modified tongue arch and a pivot action. This long aaaaa tongue arch speeds up the air some without affecting the tone. While the pivot keeps the airstream lined up with the throat hole in the mouthpiece.
As far as aperture size and range go there is an important point to remember. Range is a result of some combination of fast air being blown through a small aperture. This can be accomplished in different ways.
1.The aperture can be made smaller by lip compression. (Using only this method may make it difficult to peel paint as it can impede airflow.)
2. Making the vibrating surface shorter by pulling (bringing ) in the mouth corners.
3. A combination of 1 & 2 which works very well.
4. Mouthpiece pressure (Well there ARE people who use this as a real technique even though it has a number of drawbacks.)
5. What I like to call the Trumpet Octave Key. AIR.
There are several ways air can be used. Everyone talks about air speed but few go into any detail. Remember a very important aspect of lip apertures is that a low note needs a big aperture and a loud note causes a big aperture. If we play a soft second line g there is a certain lip aperture size. If we add air to play louder then the aperture increases in size but the note stays a second line g. If the aperture size stayed the same then the pitch would go higher. This rarely happens on second line g. That note is too familiar to us. However we have all increased the air and over shot notes above the staff. One of the only “important” findings from all of the lipless trumpet machine experiments was finding out about lip tension / aperture size / air ratios.
A simple analogy is overblowing the octave on a childs recorder. That $ 2 toy that some kids learn to play in school. The high octave is overblown by air. This is not as easy on the trumpet but we have all done this to some extent. We learned this technique when we worked on our lip slurs. It smoothed them out and enabled us to play arpeggios like middle c to high c while blowing past that pesky Bb.
What good is this?
Well with practice it can be used to help you learn to peel paint. Try this play a high c at a moderate dynamic level and then add air instantly. One of 2 things will happen. If you allow the aperture to get bigger then you have a very loud high c. If you keep the aperture the same size then you will overblow the octave. Hopefully you can use this feeling and technique to learn to open up the aperture on your upper notes.