What changes, if any, will occur as seismic waves pass from the Earth’s lower mantle UP into the OVERLYING layer?

Question

BlackTom AI · Accepted Answer

P- and S-wave speeds depend directly on the material’s elastic moduli and density. Mathematically:
- P-wave speed Vp = sqrt[(K + 4/3 μ) / ρ], where K is the bulk modulus, μ is the shear (rigidity) modulus, and ρ is density.
- S-wave speed Vs = sqrt[μ / ρ].

Step-by-step reasoning:
1. Identify the relevant properties: rigidity (μ) controls shear resistance and therefore S-wave speed; both K and μ control P-wave speed. A less rigid layer means μ is smaller; bulk modulus K often also decreases upward from the lower mantle to overlying, less rigid layers.
2. Use the formulas to see the effect of reduced rigidity. For a simple numeric example: assume the lower mantle has K = 1.0×10^11 Pa, μ = 1.0×10^11 Pa, ρ = 5000 kg/m^3. Then
   - Vp(lower) = sqrt[(1.0e11 + 4/3·1.0e11) / 5000] = sqrt[2.333e11 / 5000] ≈ 6830 m/s.
   - Vs(lower) = sqrt[1.0e11 / 5000] = sqrt[2.0e7] ≈ 4472 m/s.
3. Now let the overlying layer be less rigid (K and μ both half) and somewhat less dense (ρ = 4000 kg/m^3): K = 5.0×10^10 Pa, μ = 5.0×10^10 Pa.
   - Vp(overlying) = sqrt[(5.0e10 + 4/3·5.0e10) / 4000] = sqrt[1.1667e11 / 4000] ≈ 5400 m/s.
   - Vs(overlying) = sqrt[5.0e10 / 4000] = sqrt[1.25e7] ≈ 3536 m/s.
Both velocities decrease in this realistic example because the reduction in rigidity (and often bulk modulus) outweighs any density change.

Why the correct answer is correct:
- A loss of rigidity (lower μ) reduces Vs directly and reduces the (K + 4/3 μ) term that controls Vp, so both wave types slow down when entering a less rigid overlying layer.

Why the other options are incorrect:
- “P speeds up but S slows” would require K to increase while μ decreases; that is not consistent with an overall less rigid layer.
- “Both travel more quickly” contradicts the decrease in elastic moduli.
- “S-waves die out” or “both die out” only occur if the overlying material is liquid (μ = 0); then S-waves would vanish but P-waves would still propagate. The question assumes a less rigid solid layer, not necessarily a liquid.

Conclusion: Both P-waves and S-waves could slow down entering a less rigid overlying layer, confirming the provided correct answer.

What changes, if any, will occur as seismic waves pass from the Earth’s lower mantle UP into the OVERLYING layer?单项选择题

类似问题

Which of the following statements concerning the behavior of seismic waves within the Earth is FALSE?

Which type of seismic wave does NOT travel through liquids (such at the liquid outer core of the earth)?

Which of the following statements is FALSE?

Seismic waves are generated from what natural phenomenon?

Which of the following are true about both P- and S- waves? (there are 2 correct answers)

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单