On some comparison metrics between 3D implicit structural models

@inproceedings{caumon:hal-04165710,
 abstract = {During the last two decades, several implicit structural modeling approaches have flourished to automatically build 3D models of complex geological structures from sparse structural data. The essential idea of implicit modeling is to use one or several three-dimensional scalar fields, each of them representing one or several conformable geological interfaces as iso-surfaces (or level sets). In detail, the various implicit methods use different numerical representations of the scalar field and different formulations of the interpolation / extrapolation problem. Consequently, from the same input data, two different implicit methods may lead to different 3D models. In addition to theoretical analyzes, numerical benchmarks are important to better understand these behaviors in multiple geological settings. For such benchmarks, a first approach is to extract the individual surfaces corresponding to the target geological interfaces and then compute the distance between these surfaces. However, for implicit stratigraphic models where a conformable stratigraphic series is modeled at once by one single scalar field, such comparison does not capture variations for horizons corresponding to iso-values not present in the data. A difficulty is also that the absolute scalar field values may be scaled differently from one model to the other. Therefore, we propose, to compare normalized scalar field gradients as a global measure. Inspired by persistent homology, we also use some measures which characterize the topology of the scalar fields. These measures also open interesting perspectives to detect similarities between stochastic structural models and cluster realizations in structural uncertainty studies.},
 address = {Nancy, France},
 author = {Caumon, Guillaume},
 booktitle = {{IAMG 21st annual conference}},
 hal_id = {hal-04165710},
 hal_version = {v1},
 title = {{On some comparison metrics between 3D implicit structural models}},
 url = {https://hal.univ-lorraine.fr/hal-04165710},
 year = {2022}
}