Faculty of Risk Science and Methods

013D graph

How its disciplines connect

3D graph

265 nodes1,691 relations9 views

02Maps

Build a twin of any place

Search any place or open the world; the layers and generators follow the faculty's subjects on the planet map, the globe and in 3D.

The central Apennines: L'Aquila, Amatrice and Norcia, Italy. Flat plan of the same data: relief, the three reference epicentres with magnitude and depth, and the numbers below; the sampler's figure shows one precomputed field with its parameters. The 3D twin opens on devices that can draw it, once its data and code have been checked.

Terrain 24 to 2,805 m
3 reference earthquakes, M6.2 to M6.6
Earthquakes M4.5 and above, past week: read live when the 3D twin opens
USGS ShakeMap intensity contours: read live when the 3D twin opens

Credits and dates per layer are listed under the stage. Relief in the twin is exaggerated ×1.5 for legibility.

Drag to move, right drag or Shift with a drag to turn and tilt, Ctrl with the wheel to zoom. Keyboard: arrows move, Shift with arrows turn and tilt, + and – zoom, 0 resets, V steps through the views, Escape clears.

Flat plan of the same data: relief, the three reference epicentres with magnitude and depth, and the numbers below; the sampler's figure shows one precomputed field with its parameters. The 3D twin opens on devices that can draw it, once its data and code have been checked.

Distribution fitter (magnitude-frequency)

The Gutenberg-Richter relation fitted by maximum likelihood to a sample of magnitudes, with the cumulative magnitude-frequency curve, the b-value and its standard error, and a completeness magnitude the learner moves to watch the fit move.

The box's catalogue layer waits for an admitted catalogue, so the fitter runs on the past week's world feed of M4.5 and above (one request to the plan's fixed URL on your press, never polled here) and on the three reference events for the method. Move the completeness magnitude and watch the fit move; the standard error is printed with every value.

Completeness magnitude4.5 Mw

Reference events Three main shocks, M6.2 to M6.6: the estimator is shown on them for the method only; a fit needs a complete catalogue.

Reading	Value
Magnitudes in the extract	M6.3, M6.2, M6.6
Completeness magnitude used	M6.0 (the extract holds main shocks only)
Maximum-likelihood b-value	1.04, standard error 0.6 with n = 3: an illustration of the estimator only, three events say nothing about the regional b-value
Inter-event times	7.4 years, 0.2 years (too few for an exponential fit)

A fit to a sample; its standard error is printed. The box's catalogue layer is pending, so the fitter runs on the past week's world feed of M4.5 and above, read once on the learner's press, and shows the estimator on the three reference events for the method only. A fit to a sample, with its standard error. The past week's world feed stands in for a full catalogue. Method: Gutenberg, B. and Richter, C. F. (1944), Frequency of earthquakes in California, Bulletin of the Seismological Society of America 34; Aki, K. (1965), Maximum likelihood estimate of b in the formula log N = a - bM and its confidence limits, Bulletin of the Earthquake Research Institute 43; Utsu, T. (1966), A statistical significance test of the difference in b-value between two earthquake groups, Journal of Physics of the Earth 14.

Return-period calculator

The annual rate of events at or above a threshold magnitude from the Gutenberg-Richter relation, the return period and the probability of at least one event in an exposure time under a Poisson process, with the rate, the b-value, the threshold and the time on sliders.

The rate, the b-value, the threshold and the exposure time are on sliders; the rate and b-value start as teaching values (not estimates for the box) and take the fitter's values when a fit is made. The calculator shows the difference between a return period and the probability of at least one event in a lifetime.

Annual rate of M4.5 and above0.2 per year

b-value1 per magnitude unit

Threshold magnitude6 Mw

Exposure time50 years

Poisson model With 0.2 events of M4.5 and above a year and b = 1, M6 and above has a return period of 158 years and a 27 percent chance of occurring at least once in 50 years (teaching values).

Reading	Value
Annual rate of M at or above the threshold	0.006 per year
Return period	158 years
Probability of at least one in 50 years	27 percent
Probability in one year	0.6 percent

A Poisson teaching model: clustering (aftershocks) is not modelled, and the rate and b-value are teaching values until the fitter supplies a fit from a sample of thirty or more; not a hazard assessment for any site. A Poisson teaching model, without clustering. Not a hazard assessment for any site. Method: Cornell, C. A. (1968), Engineering seismic risk analysis, Bulletin of the Seismological Society of America 58(5), 1583–1606.

Monte Carlo sampler (the uncertainty field)

Synthetic earthquakes drawn from the magnitude-frequency model over the box, the intensity at every hexagonal cell from a published prediction equation with its sigma, and the probability per cell that an intensity threshold is reached in the exposure time, drawn on the terrain with its sampling error.

Change the prior and resample: the field is redrawn on the terrain of the open twin as hexagonal cells of 1.4 km side (about 5 square km each), with the sampling error in the read-out; the ShakeMap contours of the three reference events show what one realisation looked like.

b-value1 per magnitude unit

Maximum magnitude7 Mw

Annual rate of M4.5 and above0.2 per year

Intensity threshold7 MMI

Samples2000 events

Baseline field Probability of intensity 7 and above at least once in 50 years: highest cell 0.27, mean 0.2 over 156 cells of 4 km side, from 2,000 synthetic events (teaching surface, not a hazard map).

Reading	Value
Source zone	the whole box, locations uniform; depths uniform between the reference events' depths
Prior	rate 0.2 per year of M4.5 and above, b = 1, maximum magnitude M7, intensity threshold 7, 50 years (teaching values)
Samples	2,000 synthetic events, seed fixed at build
Highest cell probability	0.27 (sampling error of the exceedance fraction up to 0.004)
Mean cell probability	0.2

A teaching probabilistic surface, not a hazard map: the source zone is the whole box, the rate and the maximum magnitude are teaching values on the sliders, and the published GEM map's row is pending. Every parameter is on screen and the sampling error is printed; the ShakeMap contours of the three reference events are drawn beside the field as what one realisation looked like. A teaching surface, not a hazard map. Sampling error printed with every field. Method: Cornell (1968); Allen, T. I., Wald, D. J. and Worden, C. B. (2012), Intensity attenuation for active crustal regions, Journal of Seismology 16; McGuire, R. K. (2004), Seismic Hazard and Risk Analysis, EERI monograph MNO-10.

Scenario tree

A decision tree with a decision node (act now or wait) and a chance node (the event comes or not), solved by backward induction for the expected value of each branch and the value of perfect information, with the probability and the consequence values on sliders.

A two-branch tree with one chance node: move the probability and the three consequence values (relative loss units, 0 to 100) and watch the preferred branch and the value of perfect information change. The probability starts from the calculator; the consequence values are teaching values and nothing in the twin supplies them.

Probability of the event6 percent

Cost of acting now20 units

Loss if the event comes after acting30 units

Loss if the event comes after waiting100 units

Backward induction Act now: -21.8; wait: -6; the preferred branch is to wait and perfect information would be worth 3 (teaching values).

Node	Value
Chance node	an M6 and above event within 10 years, p = 0.06 from the calculator's teaching values
Act now (retrofit)	cost 20, loss if the event comes 30: expected value -21.8
Wait	no cost, loss if the event comes 100: expected value -6
Preferred branch	wait
Value of perfect information	3
Probability at which the branches tie	0.29

A teaching tree on learner inputs: the probability starts from the return-period calculator and the consequence values are teaching values in relative loss units; no consequence value is supplied by the twin. A teaching tree on learner inputs. Method: Raiffa, H. (1968), Decision Analysis: Introductory Lectures on Choices under Uncertainty, Addison-Wesley; Howard, R. A. (1966), Decision analysis: applied decision theory, Proceedings of the Fourth International Conference on Operational Research.

The boundaries, names and designations shown do not imply any judgement on the legal status of any territory, or any endorsement or acceptance of such boundaries. Countries: Natural Earth (public domain).

03The faculty's method

From a catalogue to a decision: rates, return periods and the probability that matters

A catalogue of past events gives a rate; a rate at a threshold gives a return period; a return period and a time horizon give the probability of at least one event, and that probability, not the return period, is what a decision needs.

Sources: Gutenberg and Richter, Frequency of earthquakes in California (1944); Cornell, Engineering seismic risk analysis (1968); Wiemer and Wyss, Minimum magnitude of completeness in earthquake catalogues (2000); USGS Earthquake Hazards Program, earthquake catalogue search (2026-10-17).

04Departments

Departments and their disciplines

Each card names the department's disciplines and its open courses.

05Disciplines

Disciplines of the faculty

Each discipline once, in its department.

06Console

How Risk Science and Methods is organised, as a process you can run

Press Play to run this process from this page's own data.

Process explorer

How Risk Science and Methods is organised

32 steps8 stages

07Standards and evidence

Standards and evidence, with 5 related topics

Nexus Standards the faculty teaches toward

The Nexus Standards areas whose standards the faculty's disciplines teach toward, with the number of standards and disciplines in each.

08Learning

Learning and connections

Labs used in the faculty's courses

09Take part

Take part in Risk Science and Methods

Start from who you are.

10Questions

Questions, answers and key terms

Is study here free?

Yes. Every course and learning material of Risk Academy, led by the Nexus Consortium, is free to study, self-paced or with a cohort. Ordinary participation has no fee; paid work, internships and fellowships are separate arrangements.

What does completing a course give me?

A completion record: the course, its version, the date and what was assessed, private by default and shared by you. It stacks into discipline, department and programme achievements. A record states what was studied and assessed and does not certify competence. A record is not a licence, a professional title or an employment status.

Where do the data and the places come from?

Every faculty teaches on a twin of a real place built from open data. Each layer carries its provider, licence and date, and every result on the Academy states its source. Maps and figures are indicators for teaching, never an assessment of a place.

How do I take part beyond the faculty's courses?

Form a competence cell of three to seven people, study a shared pathway, take a supervised assignment in the National Working Groups, or bring a cohort from your institution. Open the page for organisations.

Key terms

Term