We introduce a Bayesian spatial-temporal model for analyzing earthquake magnitudes. Specifically, we define a spatial-temporal Pareto regression model with latent multivariate log-gamma random vectors to analyze earthquake magnitudes. This represents a marked departure from the traditional spatial generalized linear regression model, which uses latent Gaussian processes. The multivariate log-gamma process results in a full-conditional distribution that can be easily sampled from, which leads to a fast mixing Gibbs sampler. Thus, our proposed model is a computationally efficient approach for modeling Pareto spatial data. The empirical results suggest similar estimation properties between the latent Gaussian process model and latent multivariate log-gamma model, but our proposed model has stronger predictive properties. Additionally, we analyze a US earthquake dataset as an illustration of the effectiveness of our approach.