SUMMARY
An earthquake with a magnitude of 5.4 is 39 times as intense as its aftershock occurring 5 hours later. The magnitude of the aftershock can be calculated using the formula m=log_10(i/i_0). By simplifying the equation and recognizing that the initial intensity reference (i_0) is irrelevant, the aftershock's magnitude can be determined as m=log_10(39x). The key takeaway is that the intensity reference cancels out, allowing for a straightforward calculation of the aftershock's magnitude.
PREREQUISITES
- Understanding of logarithmic functions and properties
- Familiarity with earthquake magnitude scales
- Basic knowledge of intensity measurements in seismology
- Ability to manipulate algebraic equations
NEXT STEPS
- Study the properties of logarithms, particularly the product rule
- Learn about the Richter scale and how earthquake magnitudes are calculated
- Explore the relationship between earthquake intensity and aftershocks
- Investigate real-world applications of logarithmic equations in seismology
USEFUL FOR
Students studying seismology, educators teaching earthquake science, and anyone interested in understanding earthquake magnitude calculations and their implications.