Abstract
Oil & gas exploration requires modeling underground geological objects, notably sediment deposition surfaces called “horizons” which are piecewise-explicit surfaces. Starting from sparse interpretation data (e.g. polylines and heightmap fragments), a denser model must be built by interpolation. We propose here a reconstruction method for multivalued horizons with reverse faults. It uses an abstract graph to provide a unified representation of input interpretation data. The graph is partitioned into simpler (explicit) parts which are then jointly interpolated in the plane by a natural extension of standard horizon interpolation methods.
Work performed in a CIFRE PhD thesis in partnership between ANRT, GIPSA-LAB and TOTAL SA.
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Notes
- 1.
Detailed numerical results are not shown here for brevity.
- 2.
As written, L(f) prevents an exact passage through constraints but this is acceptable in our context.
- 3.
The actual definition of an envelope for monovalued horizons and how it prevents pixels from being gridded are not detailed here for the sake of brevity.
- 4.
This junction process is not detailed here but is in the spirit of the dilated envelope restriction in Sect. 2.3.
- 5.
Exact same number is not reached as it depends on the graph shape for propagation. Moreover, two graph vertices can have a different geometrical extent, e.g. polylines being smaller than heightmap connected components.
- 6.
This is for disk-shaped structural elements and distance maps based on the L2 norm, because the disk is the topological ball associated with the L2 norm in \(\mathbb {R}^2\).
- 7.
Data size and density will be kept low for readability though.
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Baudrillard, J., Guillon, S., Chassery, JM., Rombaut, M., Wang, K. (2019). Reconstruction of Piecewise-Explicit Surfaces from Three-Dimensional Polylines and Heightmap Fragments. In: Ragia, L., Grueau, C., Laurini, R. (eds) Geographical Information Systems Theory, Applications and Management. GISTAM 2018. Communications in Computer and Information Science, vol 1061. Springer, Cham. https://doi.org/10.1007/978-3-030-29948-4_1
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