How is the difference in energy release between two earthquakes calculated?

The correct choice involves using a formula that relates the energy released by earthquakes to the difference in magnitude between them. Earthquake magnitudes on the Richter scale or the moment magnitude scale are logarithmic, specifically a base 10 logarithm. This means that for every one unit increase in magnitude, the energy release increases by approximately 31.6 times (which is 10^(3/2), since the energy scale is typically compared on a logarithmic basis).

To calculate the difference in energy release between two earthquakes, we denote the difference in magnitude as deltaM, which is the difference in their magnitudes (M2 - M1). The relationship can be expressed as:

Energy ratio = E2/E1 = 10^(1.5 * deltaM)

In this context, the energy release is proportional to 1000 raised to the power of deltaM because we are expressing the energy releases in a way that accounts for the logarithmic nature of magnitude.

Taking the square root shows up in the context of simplifying this logarithmic energy relationship, where a change in magnitude is squared to arrive at a unit change in energy output. This is why the square root shows up in the subject choice. This understanding unfolds as deltaM relates to energy