Prediction of strong ground motion distribution for scenario earthquake is usually performed for several cases of source parameter settings in order to incorporate various kinds of uncertainties. Although actual earthquake event does not necessarily follow the condition of scenario earthquakes, an observed distribution can be associated with the predicted distributions depending on the appropriateness of their varieties and diversities. This study aims to approximate the observed strong ground motion distribution using the predicted distributions. First, the mode decomposition using singular value decomposition was applied to all predicted strong ground motion distributions cases. Then, the observed distribution was approximated using mode synthesis of decomposed orthogonal modal forms. Numerical examples are shown for the observed Japan Meteorological Agency (JMA) seismic intensity distribution of the 2018 Hokkaido Eastern Iburi Earthquake (MW = 6.6) using the four cases of distribution predicted for the Southern Part of the Eastern Boundary Fault Zone of the Ishikari Lowland (MW = 7.1) in Japan. The approximated distribution generally represents the overall JMA seismic intensity spread of the observed distribution. The modal form that gives the biggest contribution to the approximated JMA seismic intensity distribution based on mode synthesis represents the attenuation effect to source-to-site distance. In addition, the multiple regression model was developed for comparison; both models give almost equivalent approximated results. However, the interpretation of orthogonal modes synthesis is easier to understand than that of the multiple regression model which involves the difficulty due to multicollinearity.