Beating cold steel on top of the anvil might do that, as might beating hot steal pieces that are way to large for the anvil, or a seriously tough alloy, and there are old anvils that wind up looking like that one with the trough in the center. Colonial Williamsburg supposedly had some "reproduction" anvils made that way to match historic examples. That anvil does look like it has a harder steel plate forge welded, or cast welded, to the body so I don't think it's an "anvil shaped object". The seriously bad shape of the top makes me think the damage might be from something else. Maybe a bad steel alloy was used for the top, or some sort of "chemical" damage. Could some situation like Borax mixed with heat do that, or maybe zinc mixed with really high heat, or maybe "acid damage" of some kind.