Two earthquakes differ in magnitude by 2.0 units. The ratio of the energy released by the larger to that by the smaller is approximately
Answer: A
Energy rises by about 32 times per magnitude unit, so two units give 32 squared, which is 1024, taken as about 1000. The factor of 100 is the trap: that is the amplitude ratio for two units, since amplitude rises tenfold per unit.
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A seismograph records a wave amplitude 1000 times larger for earthquake X than for earthquake Y at the same distance. The difference in their magnitudes is
Answer: B
Correct answer: 3.0
Magnitude is the base ten logarithm of amplitude, so a difference in magnitude corresponds to a ratio of amplitudes: \[ \Delta M = \log_{10}\left(\frac{A_X}{A_Y}\right) = \log_{10}(1000) = 3.0. \] The condition that both are recorded at the same distance matters, because otherwise the distance correction would have to be applied before the amplitudes could be compared.
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An earthquake has a focal depth of 15 km and its epicentre is 20 km from a site. The hypocentral distance to the site is
Answer: C
The focus, the epicentre and the site form a right-angled triangle with the depth vertical, so the hypocentral distance is the square root of 15 squared plus 20 squared, which is 25 km. Adding or subtracting the two figures is the common error.
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A fault ruptures over an area of 100 square kilometres with an average slip of 1 m, in rock of rigidity 3 × 1010 N/m2. The seismic moment is
Answer: D
Seismic moment is rigidity times area times slip. The area must be in square metres, so 100 square kilometres is 108 m2, and the product is 3 × 1010 × 108 × 1, giving 3 × 1018 N·m. Leaving the area in square kilometres understates it by a million.
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If a site has a design earthquake with a return period of 475 years, the annual probability of exceedance is closest to
Answer: A
The annual probability is the reciprocal of the return period, so 1 divided by 475 is about 0.0021, which is the familiar 10 per cent chance in 50 years. Confusing the return period with a probability is the error the alternatives represent.
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An earthquake of magnitude 6.0 releases energy E. The energy released by a magnitude 7.0 event is closest to
Answer: B
Correct answer: 32E
Energy rises by a factor of about \( 10^{1.5} \) per magnitude unit: \[ 10^{1.5} = 31.6 \approx 32. \] So a magnitude 7 releases roughly 32 times the energy of a magnitude 6, and a magnitude 8 about a thousand times. The factor of 10 that people often quote is the amplitude ratio, not the energy ratio, and confusing the two understates the difference badly.
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Assertion (A): A deep focus earthquake is usually less damaging than a shallow one of the same magnitude.
Reason (R): Seismic waves attenuate as they travel through rock.
Select the correct option.
Answer: C
The greater travel path from a deep focus lets the waves spread and lose amplitude before reaching the surface, so attenuation is precisely why the shaking is weaker. Both statements are true and the second explains the first.
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Assertion (A): The Richter scale is unsuitable for comparing very large earthquakes.
Reason (R): The Richter scale has a fixed upper limit of 10.
Select the correct option.
Answer: D
The assertion is correct, but the reason is not: the scale has no arbitrary ceiling of 10. It becomes unsuitable because it saturates, the amplitude it measures ceasing to grow once the rupture is much longer than the wavelength observed.
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Assertion (A): One earthquake can be assigned several different intensity values.
Reason (R): Intensity describes the shaking at a particular place.
Select the correct option.
Answer: A
Because intensity is assessed where the observer stands, it takes a different value at every location, which is exactly why one earthquake yields many. Magnitude is the single-valued quantity, since it describes the source.
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Consider the following statements about the focus and the epicentre.
1. The focus lies within the earth.
2. The epicentre lies vertically above the focus.
3. The epicentre is always the point of greatest damage.
Which of the statements are correct?
Answer: B
The first two are definitions and hold always. The third does not: soil amplification and the direction in which the rupture travelled can put the worst shaking well away from the epicentre, which is why damage maps and epicentre maps do not coincide.
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