An earthquake measured 3.1 on the Richter scale. How many times as intense as a standard earthquake was this one?

Question

BlackTom AI · Accepted Answer

To compare how many times more intense the 3.1 magnitude earthquake is relative to a standard or reference quake, we use the amplitude-based relationship on the Richter scale: intensity ratio ≈ 10^M, where M is the magnitude.

Option 1: 479.6. This value would correspond to an amplitude ratio of roughly 10^2.68, which would imply a magnitude around 2.68, not 3.1. Therefore this option does not match the 3.1 magnitude.

Option 2: 1258.9. This is obtained by calculating 10^3.1, since 3.1 is the given magnitude. Using the standard reference magnitude of 0, the ratio is 10^(3.1 − 0) = 10^3.1 ≈ 1258.9, which correctly represents how many times more intense the earthquake is compared to a magnitude 0 event. This aligns with the standard interpretation of amplitude-based intensity scaling.

Option 3: 491.0. Similar to option 1, this value would correspond to a magnitude slightly above 2.7, not 3.1. It does not match the stated magnitude and thus is incorrect for this comparison.

Option 4: 81 962.8. This extremely large figure would correspond to a magnitude well above 4 or more (since 10^4.9 ≈ 79,000), which is far from 3.1. This overestimates the ratio and misinterprets the scale.

In summary, the calculation 10^3.1 ≈ 1258.9 directly uses the magnitude difference from the standard reference and yields the correct intensity ratio for a 3.1 magnitude event; the other options arise from misapplying the scale or assuming a different baseline magnitude.

MHF4U - Quattrociocchi - S1 Unit 6 Online Quiz

An earthquake measured 3.1 on the Richter scale. How many times as intense as a standard earthquake was this one?

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