Updated 12 October 2026 · By Pete Bromfield, former Head of Maths with IB examining experience

IA idea · Statistics & hypothesis testing

How often do big earthquakes happen? The Gutenberg–Richter law

AI SLAI HLAA SLAA HL Solid Also in: Environment, Modelling

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?

Make it yours, then agree it with your teacher.

Next step: plan this IA free — the planner opens with this question filled in. For feedback on your own draft, the IA package (€39 once) gives you 5 AI feedback credits and every annotated exemplar in full.

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

Modelling the data, step by step

This idea usually needs exponential or straight-line models. See it worked step by step, with a criterion tip at every step: Exponential y = a e^(kx) + c and y = a·bˣ · Straight line y = mx + c.

Model your own data Paste it from Desmos, GeoGebra or a spreadsheet and get the same play-by-play with your numbers. New to modelling? Start with the modelling workflow. Writing it up? The IA modelling planner comments on each paragraph as you draft — it never writes it for 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.

Real data for this idea

Primary source: USGS Earthquake Catalog: Earthquake catalog search. Choose a region, a date range and a minimum magnitude (2.5 is a sensible start), then export CSV and use the mag column. Licence: Check the terms on the USGS site.

Links checked October 2026; we link to the data and never copy it. More free data sets.

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.

Which course is it for?

Course	Fit	Maths to lean on
AA SL	Good fit	Logarithms and exponential relationships; Linear regression on log-transformed counts
AA HL	Good fit	Logarithms and exponential relationships; Linear regression on log-transformed counts
AI SL	Good fit	Logarithms and exponential relationships; Linear regression on log-transformed counts
AI HL	Good fit	Logarithms and exponential relationships; Linear regression on log-transformed counts

Level: Solid. Needs some independent work beyond class examples. See how the IA differs between AA and AI, SL and HL.

How this idea reaches the top bands

Reflection (D)

For this idea, start with the weak points: including small magnitudes the network cannot detect reliably; and treating the extrapolation as a prediction. Say how each one affects your answer.

Use of mathematics (E)

SL: logarithms and exponential relationships; linear regression on log-transformed counts; cumulative frequency; extrapolation and its dangers, each explained in your own words and carried out correctly.

How statistics explorations reach the top bands in general: Statistics & hypothesis testing IA ideas. Guides: A · B · C · D · E · self-grade sheet.

Taking it further

Model time between events with an exponential distribution and test the fit.

Extending it for HL

Add an HL technique the question genuinely needs: what an HL statistics exploration adds.

See a complete IA, marked

Should I lease or buy my first car? (AI SL) is a complete statistics exploration, marked on every criterion.

Frequently asked questions

Which IB Maths course is this IA idea for?

It works for AI SL, AI HL, AA SL and AA HL. We rate it Solid: it needs some independent work beyond class examples.

What mathematics does this IA use?

Logarithms and exponential relationships, linear regression on log-transformed counts, cumulative frequency and extrapolation and its dangers.

Where can I get data for this IA?

Export 20+ years of earthquakes for a region from the USGS catalog (CSV). Checked sources and tools: USGS Earthquake Catalog and USGS Earthquake Catalog (ComCat).

Turn this idea into your IA

The planner opens with “How often do big earthquakes happen? The Gutenberg–Richter law” filled in: the question, the maths and the data sources.

Plan this IA free

Your plan is kept in this browser. A free account keeps it with your drafts on any device: Join free · Sign in

Also: free IA self-check · A–E checklist (PDF) · have a draft? AI feedback or a review with Pete (€100)

Writing it up: how to write a Maths IA, step by step · structure and format · mistakes that cost marks · IA statistics, step by step