Beyond Classical Geostatistics: Deep Neural Networks For Learning Complex Three-Dimensional Spatial Dependence

Speaker: Dr. RR. Kurnia Novita Sari

Understanding complex spatial dependencies remains a fundamental challenge in geostatistics, particularly when dealing with three-dimensional anisotropic phenomena characterized by heterogeneous spatial structures. The classical semivariogram model has long been used to quantify spatial dependencies by measuring the variance of differences between observed values at different locations. This semivariogram is expressed as a lag function of distance that also includes the angle between locations, which exhibits anisotropic phenomena. The increasing complexity of geospatial datasets, including the large number of distance pairs between these 3D locations, has motivated the exploration of data-driven approaches capable of capturing complex spatial patterns beyond the assumptions of conventional parametric models. This study investigates the integration of Deep Neural Networks (DNNs) into semivariogram modeling, specifically in estimating the nugget effect, sill, and range parameters as semivariogram model parameters. Interpretation of this semivariogram-DNN model allows for a more flexible characterization of anisotropic spatial structures. This methodology is applied to megathrust earthquake data in Java, Indonesia, a region characterized by highly complex tectonic interactions resulting from the convergence of the Indo-Australian and Eurasian plates. Several theoretical semivariogram models are compared and then improved through DNN-based learning. The results show that the spherical semivariogram DNN can provide the most accurate and consistent representation capturing the complex three-dimensional anisotropic spatial variability of earthquakes compared to conventional approaches. These findings highlight the potential of deep learning to extend classical geostatistics and provide a robust framework for advanced spatial modeling in geophysical and seismic applications.