Use this seismology calculation to reproduce a stated convention, screen observations, or compare scenarios whose units, coordinate conventions, catalog selection, and model assumptions are known.

λ (1/yr)

Required number in 1/yr. Annual rate of exceedance.

T (yr)

Required number in yr. Window length.

The cited overview of Seismology supplies background for the terminology and domain context used by this tool.^[1]

Convert an annual exceedance rate to the probability of exceeding at least once in T years. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

P_T

Returned number. At-least-once probability.

λT (count)

Returned number in count. Expected number of events.

• Earth structure, source geometry, path effects, site response, instrument response, catalog completeness, uncertainty, and the fitted range can dominate the accuracy of simplified seismic calculations.
• λ must be at least 0.
• T must be at least 0.
• Use finite inputs in the displayed units, preserve source measurements and assumptions, and independently verify consequential decisions.

For analysis or hazard decisions, retain uncertainty and provenance and compare the result with waveform processing, calibrated regional models, and guidance from qualified seismologists or the responsible agency.

• Poisson Return Period Probability Exceedance Calculator

  Probability of at least one exceedance within T years for a Poisson process: P = 1 − exp(−T/TR).

• Hazard Curve Probability Interpolation Log-Log

  Log-log interpolation of annual exceedance probability between hazard-curve anchors.

• Catalog Complete Timespan Denominator Checker

  Verify the catalog window is long enough for stable annual-rate denominators.