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Transgressive sills "jump" between bedding planes, following joints:

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But can dykes do the same?

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Yes, they are. It's not the sills or dykes that "jump", it's the magma. Depending on the various parameters such as viscosity, stress, temperature, pressure, and local conditions and availability of joints, the magma will flow either as a sill or a dyke (or some other intrusive body).

Notice that your two sketches are basically the same thing - it's just the in one case the sill is the dominant structure whereas the dyke is more dominant in the second sketch.

The flow regime can definitely change from a "dyke" to a "sill" and vice versa. Here's a schematic diagram:

enter image description here (source: USGS)

I also had a quick Internet search and came up with this great example from nature:

enter image description here

You can read more about it at Geotripper blog by Garry Hayes.

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