Why do seismic waves travel faster through the upper mantle than in the core? Why does a seismic wave travel faster through the upper mantle than it does in the crust?
The densities and temperatures are different.
The material's composition, mineral phase and packing structure, temperature, and pressure of the medium through which seismic waves travel all affect seismic velocities.
Seismic waves are slowed down in abnormally hot locations and move more slowly through liquids than through solids. Seismic waves travel faster through denser materials and, consequently, generally travel faster with depth.
Partially molten areas may attenuate or weaken S waves while partially molten areas may slow down P waves and stop S waves because their shearing motion cannot be transmitted through a liquid. - from https://tutor.hix.ai This page also has some excellent graphics.
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Seismic waves travel faster through the upper mantle than in the core because the upper mantle is composed of solid rock, while the core is primarily made of liquid iron and nickel. In addition, seismic waves travel faster through denser materials, and the core is denser than the upper mantle. Similarly, seismic waves travel faster through the upper mantle than in the crust because the upper mantle is denser and composed of more homogeneous materials compared to the crust, which contains various types of rocks with different densities and compositions.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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