runs deep vs goes deep

Some examples from the web:

• Our bond with the Sons runs deep.
• My dislike for gamblers runs deep.
• The stuff that runs deep, I couldn't...
• The poison in this wound runs deep.
• Okay. Not a problem, because this well runs deep.
• His blood runs deep here, too.
• For a true expert still water runs deep.
• So, it seems the pain of 9/11 still runs deep.
• This corruption runs deep and wide.
• Zhou Yu's loyalty to Sun Quan runs deep.
• This runs deep, I need a big shovel.
• A few miles south of Soledad, the Salinas River drops in close to the hillside bank and runs deep and green.
• No way, babe, this runs deep.
• Therefore, my imagination runs deep?
• Our river of influence runs deep or have you forgotten how easily we made Judge Denner suppress first-degree murder charges against you, Agent Keen?
• Building the wall, the security barrier, which runs deep inside the West Bank, is a consequence of both schools of thought, but it does not solve the concerns that lie at the root of either one.
• The area is characterised by a lack of water, as the groundwater runs deep inside the earth and the surface water receives exceptional and highly irregular precipitation mainly in the autumn and spring, with a great shortage of rain in the summer.
• The Dollonds made spectacles of that type for years before Franklin got credit, but misinformation within an elitist, patriarchal society runs deep.
• The belief in true democracy and in the people runs deep, proving that the African is capable of governing himself.
• I know our history runs deep with the Sons, but Jesus, Kellan was John's old lady murdered my boy.

Some examples from the web:

• So cold it goes deep into your bones.
• Instead, he goes deep into the forest with you.
• If you have a minute, you might mention to your Senior Clerk that my diary goes deep into next year.
• When she goes under, she goes deep.
• So this really demonstrates our relationship with honeybees, and that goes deep back for thousands of years.
• The wound goes deep, but no hatred, no rejection of neighbouring Serbia has emerged, but instead an attempt to cooperate anew with the Serbian population there.
• And it goes deep, you know?
• Ann, would you like to... I cannot repeat it to you, but this thing goes deep, Ed.
• But if you ask about their education, they pin you to the wall. Because it's one of those things that goes deep with people, am I right?
• Girl who taught herself to read in a Louisiana swamp house, got into Harvard at 15, goes deep-sea diving in her spare time.
• Nobody goes that deep in the jungle on purpose.
• My hole in the wall goes very deep.
• If this really goes as deep as we think, and he's already watching you...
• It goes really deep, no?
• It goes so deep under German lines, they reckon it almost reaches Berlin.
• There is an anger in some souls that goes so deep into the darkest fields, surrounded by death.
• If this really goes as deep as we think, and he's already watching you...
• And whoever... goes too deep into this... has his share of that curse.
• - Your husband goes off the deep end...
• When your husband goes off the deep end...