Spatial imputation techniques for identifying historical earthquake damage that probably occurred but was not reported in the historical sources.

Historical earthquake catalogs are essential for understanding long-term seismic patterns. Yet many events are based on sparse and spatially biased damage reports, which can lead to a significant underestimation of hazard levels. This research addresses the problem of undocumented damage by employing spatial data imputation techniques that represent distinct approaches to modelling spatial relationships:  Linear Distance-Gradient assumes a relationship between variance and neighbour’s distance, k-Nearest Neighbors (KNN) relies on similarity between nearby observations, and averages the values from k nearest sites or within a fixed radius, and Kriging applies a complex geostatistical model that refines the spatial pattern through autocorrelation. These methods were used to generate synthetic reports that estimate the intensity value of earthquake damage at undocumented sites, referred to as "negative evidence".

By comparing two historical events with relatively large dataset from the Dead Sea Transform system (the 1837 South Lebanon and 1927 Jericho earthquakes) and six well-documented instrumental earthquakes such as South Napa (2014) and Ridgecrest (2019), the study evaluates model performance through Mean Squared Error (MSE) and success rates, measuring the ratio of synthetic data where predictions fall within ±0.5 and ±1.0 intensity units of true observations. The results show that seismic intensity can be estimated at undocumented locations within boundaries of uncertainty, and that simpler models, such as Fixed-K KNN and Linear regression, achieve higher accuracy than complex statistical approaches, like Kriging models. For example, for the two historical events, Linear regression and KNN models achieved average success rates of 79% and 75% respectively within ±0.5 intensity units, compared to 58% average success rates for Kriging model.

While Kriging models are widely used to create continuous intensity surfaces for historical earthquakes, this research shows that they often lack accuracy for predicting intensity at specific sites. The findings provide a reproducible framework for researchers working with sparse historical datasets, offering an alternative to complex geostatistical methods. By filling gaps in the historical record, this research may improve seismic hazard assessments and ensures that undocumented damage are accurately accounted for in future research.