The inhomogeneous Cox point process is commonly used for modeling natural disasters, such as earthquake occurrences. The inhomogeneous Cox point process is one of the popular models for the analysis of earthquake occurrences involving geological variables. The standard two-step procedure does not however perform well when such variables exhibit high correlation. Since ridge regularization has a reputation in handling multicollinearity problems, in this study we adapt such a procedure to the spatial point process framework. In particular, we modify the two-step procedure by adding ridge regularization for parameter estimation of the Cox point process model. The estimation procedure reduces to either the Poisson-based regression or logistic-based regression. We apply our proposed method to model the earthquake distribution in Sumatra. The results show that considering ridge regularization in the model is advantageous to obtain a smaller value of the Akaike Information Criterion (AIC). Especially, Cox point process model with a logistic-based regression has the smallest AIC.