Those are milling/sawing marks. Two ways to remove them, sanding or planing. Two ways to sand, hand(ROS or sanding block) or power sand in a drum sander. Two ways to plane, hand plane or power planer .

The first of each can be done DIY---but that will literally take days.

The second will need to be done on industrial equipment, meaning take the piece to a shop with one or the other machine(most shops like that will have both types).

I agree with Mac,the planer was chattering horribly as the board went through.

It looks like marks from a band resaw, then the wood aged unplaned for a long time, so the oxidation penetrated to whatever depth but following the ridges and valleys. When it eventually got planed (or sanded to thickness, IDK), not enough was removed to get through the oxidation layer. It would need to get planed a whole lot to ever make it disappear. I think a light planing followed by a round or 2 of wood bleach is worth a try.

Thanks to everyone for the comments. I took them to a professional wood worker today who is planing and sanding them.

It's a beautiful chunk of wood and you made the right choice to turn this over to a pro. It'll get done right and you can focus on finishing it rather than spending hours with power tools.