Quantitative description of internal 3D structure of a geological sample using algebraic topology methods

Area of Science:

• Geology
• Materials Science
• Computational Geometry

Background:

• Qualitative descriptions of geological sample morphology lack accuracy and detail.
• Quantitative methods are needed for compact, comparable, and physically informative sample characterization.
• Integral geometry and algebraic topology offer powerful tools for analyzing complex spatial structures.

Purpose of the Study:

• To develop a quantitative approach for characterizing the internal spatial structure and texture of geological samples.
• To apply integral geometry and algebraic topology for detailed analysis of X-ray density phases in rock samples.
• To create a classifier for geological sample phases based on integral-geometric characteristics.

Main Methods:

• Segmentation of geological samples into X-ray density phases.
• Application of integral geometry for quantitative feature extraction.
• Utilizing algebraic topology for structural analysis of segmented phases.
• Development of a classifier based on integral-geometric characteristics.

Main Results:

• A novel approach for quantitative characterization of spatial structure and texture in geological samples was developed.
• A classifier for X-ray density phases demonstrated stable operation.
• Detailed analysis of algebraic-topological characteristics provided geologically meaningful interpretations.
• The method was successfully demonstrated on a meimechite sample.

Conclusions:

• The developed approach enables accurate, quantitative description of internal spatial structures in geological samples.
• This method allows for the classification and comparison of samples based on their texture.
• The approach is broadly applicable to natural and synthesized substances, and even property distributions, across various scientific fields.