Spatial Methods for Identifying Undocumented Historical Earthquake Damage

Historical earthquake records are inherently incomplete: many sites that were likely damaged were never documented, leaving spatial gaps in the macroseismic record. This study evaluates whether intensity values at unreported sites can be estimated from the spatial relationships of surrounding reports, framing the task as a spatial data imputation problem. Three spatial imputation methods, Linear regression, K-Nearest Neighbors (KNN), and Kriging, were applied to eight macroseismic datasets, comprising two historical Dead Sea Transform earthquakes (1927 Dead Sea, 1837 South Lebanon) and six instrumental events from major strike-slip fault systems. Model performance was assessed with 5-fold cross-validation under random and spatial-block designs, using Mean Squared Error (MSE) and success rate, defined as the percentage of predictions falling within ±0.5 and ±1.0 intensity units of observed values. Under random cross-validation, simple and locally focused models performed on par with the complex geostatistical approaches. For the geographically concentrated historical data, success rates reached up to 90% within ±1.0 intensity units. San Andreas events yielded the strongest results among instrumental datasets, while Caribbean events showed the weakest performance due to spatial reporting biases. Under spatial-block cross-validation, performance declined across all models, with linear regression and Universal Kriging proving most robust to spatial extrapolation. These findings provide a methodological basis for estimating intensity at undocumented sites. While continuous intensity mapping from sparse data remains inadvisable, point-based imputation offers a practical tool for enriching historical earthquake records, with direct implications for seismic research along poorly documented fault systems.