Regression analysis and variable selection to determine the key subduction-zone parameters that determine the maximum earthquake magnitude

Abstract

Abstract Large variations in the maximum earthquake magnitude ( $$M_{{\text{max}}}$$ M max ) have been observed among the world’s subduction zones. There is still no universal relationship between $$M_{{\text{max}}}$$ M max and a given subduction-zone parameter, such as plate age, plate dip angle, or plate velocity, which suggests that multiple parameters control $$M_{{\text{max}}}$$ M max . Here, we conduct exhaustive variable selections that are based on three evaluation criteria; leave-one-out cross-validation errors (LOOCVE), Akaike information criterion (AIC), and Bayesian information criterion (BIC) to determine the combination of subduction-zone parameters that best explains $$M_{{\text{max}}}$$ M max . Multiple linear regression analyses are applied using 18 subduction-zone parameters as potential candidates for the explanatory variables of $$M_{{\text{max}}}$$ M max . The minimum BIC is obtained when five variables (trench sediment thickness, existence of an accretionary prism, upper-plate crustal thickness, bending radius of the subducting oceanic plate, and trench depth) are selected as explanatory variables; each variable contributes positively to $$M_{{\text{max}}}$$ M max . Minimum LOOCVE and AIC values are obtained when eight variables (the five parameters for BIC, plus the along-strike plate convergence rate, age of the subducting plate, and maximum depth of the subducting plate) are selected. Our selection of the trench sediment thickness and plate bending radius contributing to $$M_{{\text{max}}}$$ M max is consistent with previous studies. The results show that increasing upper-plate crustal thickness results in a large $$M_{{\text{max}}}$$ M max . In addition to smoothing the subducting-plate interface via subducted sediments, along-dip extension of the crustal area along the convergent plate boundary would be important for generating a large earthquake. Graphic Abstract

Keywords

• Earthquake magnitude
• Subduction zone
• Multiple regression analysis
• Exhaustive model evaluation
• Plate tectonics