Quantifying Uncertainties in Ground Motion-Macroseismic Intensity Conversion Equations. A Probabilistic Relationship for Western China

We analyze the global and local uncertainties of ground motion-macroseismic intensity conversion equations and derive new probabilistic relationships between the macroseismic intensity and peak ground motion parameters (peak ground acceleration and peak ground velocity) for western China based on the assumption that the peak values of ground motion are randomly distributed for each MMI level, bounded by a normal distribution. For this purpose, a strong ground motion database consisting of 37 moderate- to large-magnitude earthquakes that occurred in western China between 1994 and 2017 is employed along with the corresponding modified Mercalli intensity (MMI) information inferred from isoseismal maps and earthquake damage reports. The mean value and standard deviation parameters in the probabilistic formulas are obtained from the result of the analysis of the local uncertainties of the data compiled for Western China. We propose a method for the rapid assessment of computer-generated intensity maps using the new probabilistic formulas. Our method composed of two steps. (1) According to a Bayesian formula, the possibility, expectation and standard deviation of the seismic intensity are calculated by the ground motion parameters recorded at a site station. (2) Furthermore, expectation and standard deviation maps of the seismic intensity throughout an area are obtained through spatial interpolation. Finally, an application is illustrated to validate this new methodology by presenting rapidly estimated (computed) intensity maps of the 8 December 2016 Hutubi (Ms 6.2) earthquake in western China.