IA idea · Statistics & hypothesis testing
How often do big earthquakes happen? The Gutenberg–Richter law
Research question
Does the number of earthquakes of at least magnitude M in [a region] follow log₁₀N = a − bM, and how does the fitted b-value compare with the typical value of about 1?
Adapt it: change the place, the data or the comparison until the question is yours.
Why it makes a good exploration
Seismologists use this law to estimate how often large earthquakes will occur. USGS data lets you fit it for a region you choose and then use it — carefully — to estimate the frequency of rarer events.
The mathematics you'll need
- Logarithms and exponential relationships
- Linear regression on log-transformed counts
- Cumulative frequency
- Extrapolation and its dangers
Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.
Where the data comes from
Export 20+ years of earthquakes for a region from the USGS catalog (CSV).
- USGS Earthquake Catalog (ComCat) — Every recorded earthquake with time, location, depth and magnitude; filter and export CSV.
Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.
A possible outline
- Explain magnitude as a logarithmic scale.
- Build a cumulative count table.
- Fit the line and interpret a and b.
- Estimate the return period of larger events.
- Reflect on catalogue completeness at small magnitudes.
Pitfalls that cost marks
- Including small magnitudes the network cannot detect reliably.
- Treating the extrapolation as a prediction.
- Mixing magnitude types without comment.
Showing personal engagement
- Choose a region you have lived in or visited.
- Compare two tectonic settings.
- Discuss what your return period means for building codes.
See Criterion C: personal engagement for what examiners look for.
Taking it further
Model time between events with an exponential distribution and test the fit.