Seismology: Worked Applications

A station records P at 23:59:50 and S at 00:00:10 the next day. In a homogeneous, zero-depth teaching model, $V_P=6$ and $V_S=3\ \text{km/s}$. Find the delay and conditional range.

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Assume a common straight path, $V_P=6$ and $V_S=3.5\ \text{km/s}$, and an S-P delay of $10\ \text{s}$. Find the path length and check both travel durations.

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A surface station has a conditional straight source path of $50\ \text{km}$. The assumed focus is $30\ \text{km}$ below the common station surface. Find horizontal distance.

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In the same homogeneous model, a station is $60\ \text{km}$ horizontally from the epicenter and the source depth is $45\ \text{km}$. Let $V_P=6$, $V_S=3\ \text{km/s}$. If P arrives at 14:30:00, find the conditional S arrival.

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An S-P pick gives $3\ \text{s}$ with $V_P=6$, $V_S=3\ \text{km/s}$. A separate interpretation assumes source depth $30\ \text{km}$. Can these inputs define a horizontal circle?

In local east/north kilometres, stations are $A(0,0)$, $B(72,0)$ and $C(0,96)$. Each inferred horizontal radius is $60\ \text{km}$. Find and verify the candidate shown in the left panel.

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Keep the same stations, but set all three horizontal radii to $30\ \text{km}$. A subtraction calculation still returns $(36,48)\ \text{km}$. Interpret the right panel of the paired figure.

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Assume $V_P=6$, $V_S=3\ \text{km/s}$ and fixed depth $45\ \text{km}$. An S-P delay is $10.0\pm0.2\ \text{s}$. Find the corresponding horizontal range interval, considering only this supplied timing bound.

An idealized slipping fault patch is $5$ by $4\ \text{km}$ in its own plane, with uniform shear modulus $30\ \text{GPa}$ and mean slip $0.50\ \text{m}$. Find scalar moment and $M_w$ using the SI constant $9.1$.

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Compare moment magnitudes $5$ and $7$. Separately compare two calibrated local-amplitude magnitudes differing by two units at identical distance/instrument correction. What ratios follow, and what site motion remains unknown?

An ideal $50{,}000\ \text{kg}$ mass is rigidly attached to a base and follows its horizontal acceleration. The chosen ground component has PGA $0.40g$, with $g=9.81\ \text{m/s}^2$. Neglect vertical acceleration. Find peak horizontal force magnitude.

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Use the synthetic 5%-damped spectral chart. Oscillator A has $T_n=0.50\ \text{s}$ and PSA $0.80g$; oscillator B has $T_n=1.00\ \text{s}$ and PSA $0.40g$. Find each peak relative displacement with $g=9.81\ \text{m/s}^2$.

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A synthetic study supplies the lesson's 5%-damped PSA comparisons. At $0.2\ \text{s}$ the rock/soil values are $0.30/0.24g$; at $1.0\ \text{s}$ they are $0.20/0.50g$. Can one three-to-five amplification factor describe these data?

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At a point in a reclaimed-land teaching model, hold total vertical stress at $160\ \text{kPa}$. Initial pore pressure is $120\ \text{kPa}$ and a supplied excess rise is $25\ \text{kPa}$. Find effective stresses and $r_u$, then state what remains unresolved.

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