 Solution

ID: past-exam-of-the-year-2-of-the-earth-sciences-geology-course-of-the-university-of-oxford/2023/paper-1/6/o/solution

R_{S} = \frac{2.4 - 3.3}{2.4 + 3.3} = - \frac{3}{19} = - 0.1579, T_{σ S} = \frac{16}{19} = 0.8421 .

At sandstone–salt,

R_{S} = \frac{3.0 - 2.4}{3.0 + 2.4} = \frac{1}{9} = 0.1111, T_{σ S} = \frac{10}{9} = 1.1111 .

A stress-amplitude transmission greater than one does not violate conservation of energy: the transmitted energy fraction includes the seismic impedance ratio. For particle velocity, the corresponding

(R_{v}, T_{v})

pairs are

(3/19, 22/19)

and

(- 1/9, 8/9)

. At normal incidence in isotropic layers, pure P and pure S waves do not undergo seismic mode conversion.

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