Topographic stress modelling and cone volume analysis at fissure eruptions

This notebook presents the workflow used to analyze the topographic controls on the eruptive fissure morphology (using the Lakagígar case study, but can be applied to other systems). The workflow is divided into three main parts: 1. Pre-eruptive topography: Reconstruction of the pre-eruptive elevation profile by filtering the current elevation profile. Plotting of the cones over the pre-eruptive profile, color coded by log10Vol. 2. Stress Modeling: Computation of the topographic stress tensor using the elevation profile in (1). Plot the confining stress (𝑆𝑦𝑦) induced by the pre-eruptive topographic load (1) using an analytical solution for a 2D elastic half-space. We used analytical solutions for uniform vertical strip loads (50-m-wide) applied on an elastic half-space available in Dahm (2000), derived from Davis and Selvadurai (1996). 3. Statistical Analysis: Evaluation of the horizontal, vertical, and combined stress gradient metrics against eruptive cone volumes using K-Means clustering and ROC curve validation. 4. Quantitative Models: Spatial application of the stress gradient thresholds derived from previous analysis.