The Richter scale is a logarithmic scale used to quantify the magnitude of an earthquake. It measures the amount of energy released by an earthquake on a base-10 scale.
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The Richter scale is logarithmic, meaning each whole number increase on the scale represents a tenfold increase in measured amplitude and roughly 31.6 times more energy release.
An earthquake measuring 5.0 on the Richter scale has ten times the amplitude of one measuring 4.0.
Magnitude calculations using the Richter scale can be expressed with exponential functions, typically involving base-10 logarithms.
The formula $M = \log_{10}(A) + B$ is often used, where $M$ is the magnitude, $A$ is the amplitude of seismic waves, and $B$ is a constant that accounts for distance from the epicenter.
Understanding how to manipulate and interpret logarithmic functions is crucial for comprehending how magnitudes are compared on this scale.
Review Questions
How does a two-unit increase on the Richter scale affect the measured amplitude?
Write out the relationship between amplitude and magnitude on the Richter scale using a base-10 logarithm.
If an earthquake's magnitude increases from 3.0 to 6.0 on the Richter scale, by what factor does its energy release increase?
Related terms
Logarithm: A mathematical function that determines how many times one number must be multiplied by itself to obtain another number.
A mathematical expression where a constant base is raised to a variable exponent.
$\log_{10}$: $\log_{10}$ denotes a common logarithm, which uses base-10 and is often used in scientific calculations such as those on the Richter scale.