Sizing the Invisible
When an earthquake struck before seismometers existed, the only magnitude evidence lies in the rocks. Surface rupture length, fault displacement, and deformation patterns preserved in the geological record can be measured centuries or millennia later. Empirical scaling relations, calibrated against hundreds of instrumentally recorded earthquakes, translate these measurements into magnitude estimates — connecting the geological record to the quantitative framework of modern seismology.
Scaling Relations
The Wells & Coppersmith (1994) study analyzed 244 earthquakes with known magnitudes and measured surface parameters, establishing the field's standard scaling relations. The key insight is that magnitude scales logarithmically with displacement and rupture dimensions: a tenfold increase in displacement corresponds to roughly 0.7 magnitude units. These relations have been refined for different tectonic environments but the original formulations remain widely used for their simplicity and robustness.
Multiple Estimators
Using both displacement and rupture length provides independent magnitude estimates that should agree within ~0.3 units if the data are reliable. Significant disagreement may indicate incomplete rupture mapping, non-characteristic behavior, or distributed deformation not captured at a single trench site. Seismic moment, computed from rigidity, area, and displacement, provides a physically grounded estimate independent of the empirical scaling.
Uncertainty and Consequences
Paleomagnitude uncertainty of ±0.3 units sounds small but corresponds to a factor of ~2 in seismic energy release. For hazard assessment, this uncertainty propagates into ground motion predictions and ultimately into structural design requirements. This simulation lets you explore how the measurable geological evidence constrains the magnitude of ancient earthquakes and how different fault types shift the scaling relationships.