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The equations that govern the deformation of jointed rocks are the same as those used to describe the motion of a continuum: [13] ˙ + = ˙ = = ˙: + = where (,) is the mass density, ˙ is the material time derivative of , (,) = ˙ (,) is the particle velocity, is the particle displacement, ˙ is the material time derivative of , (,) is the Cauchy stress tensor, (,) is the body force density ...
Given the average density of rocks at the Earth's surface and profiles of the P-wave and S-wave speeds as function of depth, it can predict how density increases with depth. [2] It assumes that the compression is adiabatic and that the Earth is spherically symmetric, homogeneous, and in hydrostatic equilibrium. It can also be applied to ...
The depth of compensation (also known as the compensation level, compensation depth, or level of compensation) is the depth below which the pressure is identical across any horizontal surface. In stable regions, it lies in the deep crust, but in active regions, it may lie below the base of the lithosphere. [ 16 ]
Suppose a rock's weight is measured as 10 newtons when suspended by a string in a vacuum with gravity acting upon it. Suppose that when the rock is lowered into water, it displaces water of weight 3 newtons. The force it then exerts on the string from which it hangs would be 10 newtons minus the 3 newtons of buoyancy force: 10 − 3 = 7 newtons.
Suppose a rock's weight is measured as 10 newtons when suspended by a string in a vacuum with gravity acting on it. Suppose that, when the rock is lowered into the water, it displaces water of weight 3 newtons. The force it then exerts on the string from which it hangs would be 10 newtons minus the 3 newtons of buoyant force: 10 − 3 = 7 newtons.
Here is the thickness of the dike; is its lateral extent; is the excess pressure in the magma relative to the host rock; is the density of the host rock; and is the P-wave velocity of the host rock (essentially, the speed of sound in the rock). This formula predicts that dikes will be longer and narrower at greater depths below the surface.
where is the gravitational constant; is the density of the sediment; is the density of water; is the sediment particle diameter (commonly assumed to be the median particle diameter, often referred to as in field studies); and is the molecular viscosity of water. The Stokes settling velocity can be thought of as the terminal velocity resulting ...
The upper crust is characterized by low density and high porosity, leading to reduced seismic velocity. [23] Two key discontinuities have been observed: one within the crust at a depth of 5 to 10 km, [65] and another which is likely the crust-mantle boundary, occurring at a depth of 30 to 50 km. [22]