Decreases in Entropy and Variance with Progressing Geoscience Survey

Abstract

A model consisting of simple geology is analyzed mathematically in order to understand improvement of accuracy with progress of geological survey. The model is to identify geologic units along a line segment [0, 1]. At Step 1, the midpoint of the segment is identified geologically. At Step 2, the segment is divided into three sub-segments, and the midpoint of each sub-segment is identified geologically. At Step 3, each sub-segment is divided into subordinate subsegments, each of which is also identified. This process is continued to Step K, when it is assumed to identify the geology along the initial segment with necessary and sufficient accuracy. Cell entropy s_k/K and variance V_k/K, which are calculated at each step k for the final step K, can indicate decrease of uncertainty in progressive survey. Especially, the cases using almost binary abundance values suggest that geologist should focus on the survey of high entropy (large variance) cells at the next step.