The problem describes how the Richter scale magnitude, $R$, of an earthquake is determined. The formula is given by $R = \log(\frac{a}{T}) + B$, where $a$ is the amplitude of the vertical ground motion (in micrometers), $T$ is the length of time a seismic wave lasts, and $B$ is a factor that accounts for the weakening of the seismic waves.

Applied MathematicsLogarithmsEarthquakeRichter ScaleFormulaModeling
2025/4/23

1. Problem Description

The problem describes how the Richter scale magnitude, RR, of an earthquake is determined. The formula is given by R=log(aT)+BR = \log(\frac{a}{T}) + B, where aa is the amplitude of the vertical ground motion (in micrometers), TT is the length of time a seismic wave lasts, and BB is a factor that accounts for the weakening of the seismic waves.

2. Solution Steps

The given formula is:
R=log(aT)+BR = \log(\frac{a}{T}) + B
The problem only asks us to restate the formula and explain the variables. There are no computations to perform.

3. Final Answer

The Richter scale magnitude RR is calculated using the formula R=log(aT)+BR = \log(\frac{a}{T}) + B, where aa is the amplitude of the vertical ground motion, TT is the length of time the seismic wave lasts, and BB is a factor that accounts for the weakening of seismic waves.

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