Is there a mythological basis of healing petrification by running water?

Question

In the The Heroes of Olympus series, book 1: The Lost Hero, we see petrification (being turned to gold) being healed by running water.

This is referenced again later in the recently released book in the Magnus Chase and The Gods of Asgard series, book 2: The Hammer of Thor. Spoilers:

After being injured by the Skoftung(?) Sword, Blitzen is intentionally turned to stone by Magnus using Sunlight. Later this is healed by using by running water, as noted by Hearth's father.

Is there a mythological reference for this? Or is Rick Riordan just trying to bind together different elements of his stories together? Like he did with The Mist, the Duat, and Ginnungagap. This is discussed in detail in the linked question.

Answer 1

Well, let's see where the idea of reversing the Midas touch with water comes from. It looks like Rick Riordan took this from the retelling of the Midas story in A Wonder Book for Boys and Girls by Nathaniel Hawthorne, which is the first reference that the Internet is giving me for the idea of water reversing it:

"It is hateful to me!" replied Midas.

A fly settled on his nose, but immediately fell to the floor; for it, too, had become gold. Midas shuddered.

"Go, then," said the stranger, "and plunge into the river that glides past the bottom of your garden. Take likewise a vase of the same water, and sprinkle it over any object that you may desire to change back again from gold into its former substance. If you do this in earnestness and sincerity, it may possibly repair the mischief which your avarice has occasioned."
_{-Project Gutenburg}

...and that's really the first I can find about it. The myth has become more popular, and I assume Rick Riordan heard it in this form, and so he adopted that for The Lost Hero.

---

The Norse dwarves turning into stone seems to originate from the work Alvíssmál, from The Poetic Edda. From an online translation:

Thor spake:
"In a single breast
I never have seen More wealth of wisdom old;
But with treacherous wiles
Must I now betray thee:
The day has caught thee, dwarf!
(Now the sun shines here in the hall.)"
_{Edited slightly by me.}

I really can't find anything about reversing this or anything. (And apparently I'm not the only one who has trouble with finding details about these stories.)

So with a lack of anything that may indicate anything else... I'm going to have to assume that Uncle Rick is trying to keep the rules of magic and stuff as similar as possible across the different mythologies; like, we see the similarity of a magician using too much power and a demigod using too much power in The Staff of Serapis. Also, the way that monsters in the Greek and Egyptian stories die - they both explode into yellow sand.

"Poor things," the cat woman purred. "Let me help."
Her knives flashed, and the two monsters' heads thudded to the floor at her feet. Their bodies collapsed and dissolved into enormous piles of sand.
_{The Kane Chronicles, book 1: The Red Pyramid, chapter 8: "Muffin Plays With Knives"}

The bull-man roared in agony. He flailed, clawing at his chest, then began to disintegrate—not like my mother, in a flash of golden light, but like crumbling sand, blown away in chunks by the wind, the same way Mrs. Dodds had burst apart.
_{Percy Jackson & the Olympians, book 1: The Lightning Thief, chapter 4: "My Mother Teaches Me Bullfighting"}

He's trying to keep things as similar as possible while at the same time keeping (mostly) true to the mythology (or at least the popular versions of the myths today, such as with Midas).

Answer 2

This cure was already written down by the Roman poet, Ovid (43 BC – 17/18 AD), in his Metamophoses XI.131-145:

Lifting his shining hands and arms to heaven, he cries out: ‘Father, Bacchus, forgive me! I have sinned. But have pity on me, I beg you, and save me from this costly evil!’ The will of the gods is kindly. Bacchus, when he confessed his fault, restored him, and took back what he had given in fulfilment of his promise. ‘So you do not remain coated with the gold you wished for so foolishly,’ he said, ‘go to the river by great Sardis, make your way up the bright ridge against the falling waters, till you come to the source of the stream, and plunge your head and body at the same moment into the foaming fountain, where it gushes out, and at the same time wash away your sin.’ The king went to the river as he was ordered: the golden virtue coloured the waters, and passed from his human body into the stream. Even now, gathering the grains of gold from the ancient vein, the fields harden, their soil soaked by the pale yellow waters.

The river at Sardis is the Pactolos, so there's indeed an ancient source for this motif. Ovid might have even used older sources for his own retelling of the story, but I don't know where to find older versions of the story where the river Pactolos is mentioned.