40 years ago I would never have dreamed of turning over ground without using a mouldboard plough, but I have not woned one since 1979 and in the 1980s cultivated up to 2000 acres.
To quote myself:-
For primary cultivations I use an implement that goes by various names around the world, such as scarifier, ripper, chisel plough, and it is a fairly robust implement with legs that are held in position by strong springs so that if a solid underground object such as a very large rock or old tree root is struck, the leg deflects, passes over the top of the object and returns to its working position, although it is surprising how big an object they will move. These implements have light and heavy-duty cousins for lightly cultivating or deep ripping respectively, but the type I use in routine cultivations is capable of primary cultivations or further cultivations for seeding. On many properties this one middleweight is enough, but I have sometimes had all three, and I have a home-made deep ripper too.
With the middleweight I use 2 inch wide points on the tines for general work, but if I want to do a quick shallow run through an area to kill weed growth I use wide ones (sufficient that they cover the full width of the implement) that cut through weed roots a little below the surface and lift the soil slightly at the same time so that the weed roots and soil that they are in dry out very quickly, killing the weeds. Points bolt on for easy changing. In primary cultivations I am looking more to open up the soil, and with tine spacing at about 10 inches there is also some soil inversion and burying of surface trash, crop residue or manure. Not a complete inversion as with mouldboard or disc ploughs, but usually sufficient that vegetation is killed and some of it or some of the manures incorporated pretty well to the full working depth of the implement. This means some manure is left on the surface too, and I am quite happy with that. The implement also leaves a loose soil to the full depth of the incorporation so that air penetrates to this depth. For deeper ripping with the same implement it is a matter of removing some of the legs to give less resistance, and perhaps adding some weight to the frame, but for extra depth the heavy weight ripper is best, or a subsoiler. Subsoilers will not normally incorporate organic material to their full working depth. In fact they act differently due to a different tine profile and little or no inversion or incorporation is normal.
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Sorry, I do not know the US name for these implements.