You know stuff like Yggdrasil tree but just a normal tree that is the biggest and tallest in the world. If the roots grow to surpass the continental and oceanic plate either it only cover some parts or entire world, can it stop earthquake or make it even worse to the zone covered by the root? Or what effect would it give?
The simple answer is "no"
What we learn from studies like this is that unless the soil is perfect, roots tend to grow out more than they grow down. They would certainly have more trouble getting through solid rock than they would soil, and tend to follow the path of least resistance. Consequently, a super large tree as you describe would have massive stability problems and would easily be blown over in the wind.
But, let's assume that our super-tree's roots can wiggle through anything like the proverbial hot knife through butter. Generally speaking, there's as much tree underground as there is above ground. The Earth's mantle is about 2,900 km thick. This would suggest a 2,900 km tall tree. (We'll also ignore the problems with pressure, heat, and simple nutrition as you descend through the mantle.) But at it's greatest extent, Earth's atmosphere is only about 480 km thick, putting most of the tree into the vacuum of space where it would wither and die for a variety of reasons. This would suggest that the largest our super-tree can be is about 300 km, but let's ignore this for the moment, too, and assume we have a powerful super-tree, 2,900 km tall, which we assume could lock fault lines into place and keep tectonic plates from moving.
The real killer with the idea is the tremendous energy involved with tectonic plates. In my answer to another question I pointed out that the magnitude 9 Sumatra earthquake released energy equivalent to a 2,000 megaton explosion with a blast radius that would devastate an entire hemisphere of our planet. This is why my ultimate answer is no, such a tree would not stop an earthquake. The mass of the Earth is considerably greater than the mass of the tree (even one as large as this).
From a simple point of view. There are a few complexities:
The tree's weight would cause some earthquakes by pressing down on fault lines. It would likely create new fault lines.
The tree's roots would stop small and potentially medium sized earthquakes by locking areas of the earth together.
While the tree would offer some protection against tectonic plates that slide against one another (like rubbing your hands back and forth), it would offer only moderate protection to plates that subduct (one slides under another).
But ultimately the tree would lose. Unable to lock all the tectonic plates and trying to stave off the force of the Earth's shifting fluid mass (which is much, much, much greater than the tree) would ultimately create an earthquake that would rip the tree (and, to an extent, the planet) apart.
All of which make for cool story plots, in my personally biased opinion!
It would have no effect at all. Trees are not stronger than rocks (citation needed) and rocks couldn't stop an Earthquake. The Earth is already full, loaded with old roots and trees. Your tree can only grow down so far. Your tree needs 600km long roots to even reach a spot where it might matter. That puts you well into the upper mantle. https://en.wikipedia.org/wiki/Structure_of_the_Earth It's a bit hot down there, but we don't know if there is any life.
So for this to have any measurable effect, your tree would have to have high pressure magma radiation resistant roots that fill the upper and lower mantle of the Earth. And even then, it's still just wood (or is it, if it can withstand magma?)
To put this another way, your tree would need to be strong enough to: Stop the moons orbit and hold it above the Earth and stop the spin of the Earth. How much energy would that take, someone answered that. https://physics.stackexchange.com/questions/169589/how-much-energy-would-it-take-to-stop-earths-rotation-on-its-axis/169593 To be clear you don't need to actually stop the Earths spinning, but you need to be able to counter the Earths reaction to it's spinning, which is pretty much the same thing.
TL/DR The Earth is really big and heavy and is moving really fast, and you just have a tree.
It's more likely that it would make the earthquake less destructive.
We can model the roots in the rocks like a composite material, which will be stressed by the tectonic movement. The more energy the system stores, the more destructive will be the quake when it breaks up.
A root being less resistant than rock means that the root will break at a lower load, leaving only the rock to resist. Bt having the rock a lower section due to the presence of the root, it means that it will break down earlier.
This will prevent storing more energy, thus the resulting quake will be less destructive.
I think the world tree would make earthquakes worse, since as the roots spread, they’d grow into the fault lines since that is the path of least resistance compared to growing into solid rock.
As the roots in the fault lines grow longer and thicker, they’d let water and other slimy slippery material in. When the faults snapped, these roots, and water and everything would act as lubricant, making more energy available for destruction that would have otherwise been lost to friction.