A - Seismic energy increases significantly with each unit rise in Ms; a one-unit increase corresponds to a roughly 32-fold rise in energy release. B - The Marcus Bath equation predicts energy release; Mb = 6 yields 28 times more energy than Mb = 5. C - Gutenberg-Richter predicts higher seismic energy increase than Marcus Bath for one-unit surface-wave magnitude rise (difference: 4).
A. To calculate the increase in seismic energy when the surface-wave magnitude (Ms) increases by one unit, we can use the Gutenberg-Richter law:
Log E = 4.8 + 1.5 * Ms
Let's substitute Ms values of 5 and 6 into the equation:
For Ms = 5:
Log E_5 = 4.8 + 1.5 * 5 = 12.3
For Ms = 6:
Log E_6 = 4.8 + 1.5 * 6 = 13.8
The energy release for Ms = 5 is 10^12.3 Joules, and for Ms = 6 is 10^13.8 Joules. The energy ratio (6 to 5) is approximately 32 according to the given data.
B. Now, using the Marcus Bath equation:
Log E = 5.24 + 1.44 * Mb
Let's substitute Mb values of 5 and 6 into the equation:
For Mb = 5:
Log E_5 = 5.24 + 1.44 * 5 = 12.44
For Mb = 6:
Log E_6 = 5.24 + 1.44 * 6 = 13.88
The energy release for Mb = 5 is 10^12.44 Joules, and for Mb = 6 is 10^13.88 Joules. The energy ratio (6 to 5) is approximately 28 according to the given data.
C. Observations:
The energy ratio calculated using Gutenberg-Richter law is 32, while using the Marcus Bath equation, it is 28. The difference between the two ratios suggests that the increase in seismic energy for a one-unit increase in surface-wave magnitude is higher according to the Gutenberg-Richter law compared to the Marcus Bath equation. This indicates a difference in the predictions of these two earthquake energy release models for the given magnitude increase.
Complete question:
A. Calculate the amount by which the seismic energy released by an earthquake increases when the surface-wave magnitude (Ms) increases by one unit. b. Repeat the calculation for an increase of one unit in the body-wave magnitude. c. What are some observations from parts a and b?