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Earth sciences (geology) course of the University of Oxford

Year 2 of the earth sciences (geology) course of the University of Oxford

Past exam of the year 2 of the earth sciences (geology) course of the University of Oxford

2022

Paper 1

Specify the <amplitude> convention. For normal-stress/<pressure> <amplitudes>, the <seismic reflection coefficient> and <seismic transmission coefficient> are
$$
\boxed{R_\sigma=\frac{Z_2-Z_1}{Z_2+Z_1}=\frac{19}{37}=0.51351,\qquad
T_\sigma=\frac{2Z_2}{Z_1+Z_2}=\frac{56}{37}=1.51351.}
$$
For particle displacement or velocity resolved in one fixed normal coordinate, the reflected <amplitude> changes sign and the transmitted ratio is instead
$$
R_v=-\frac{19}{37},\qquad T_v=\frac{2Z_1}{Z_1+Z_2}=\frac{18}{37}=0.48649.
$$
These are alternative conventions, not conflicting energy predictions. The reflected and transmitted <energy flux> fractions are
$$
\mathcal R=\frac{361}{1369}=0.26370,\qquad
\mathcal T=\frac{1008}{1369}=0.73630,
$$
which sum to one for the ideal lossless interface. Thus an <amplitude> transmission coefficient greater than one does not violate <conservation of energy>.

Solution

Past exam of the year 2 of the earth sciences (geology) course of the University of Oxford / 2022 / Paper 1 / 6 / d / ii / Solution

Past exam of the year 2 of the earth sciences (geology) course of the University of Oxford / 2022 / Paper 1 / 6 / d / ii / Solution

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