Systems and methods of multi-scale meshing for geologic time modeling

1. A method for generating a model of one or more geological structures, comprising:

(a) computing a first function for a geological structure, wherein the first function includes a first iso-surface in a transformed coordinate space of an initial coordinate space and generating an initial model of the geological structure having an initial resolution of cells that are divided along the first iso-surface;

(b) detecting if the first iso-surface intersects a set of geological markers within a threshold proximity;

(c) if the first iso-surface does not intersect the set of geological markers within the threshold proximity, correcting the initial model using an induced mesh having an increased cell resolution for computing a second function for the geological structure to improve the accuracy of a location of the geological structure in the initial model, wherein the second function includes a second iso-surface in the transformed coordinate space that intersects the set of geological markers within the threshold proximity;

(d) generating a second model including the second iso-surface, wherein the second model has a locally increased resolution relative to the initial model caused by further dividing cells in the second model along the second iso-surface;

for each new geological structure, repeating steps (a)-(d), using the second model as the initial model; and

displaying a visualization of the second model.

2. The method of claim 1 , wherein the second model is the initial model with the second iso-surface.

3. The method of claim 1 , wherein the second model is the induced mesh.

4. The method of claim 1 , wherein axes of the induced mesh include iso-surfaces of the initial model in the transformed coordinate space.

5. The method of claim 1 , wherein the initial coordinate space models geological structures at a current time period and the transformed coordinate space models geological structures at a time of original deposition.

6. The method of claim 1 , wherein the induced mesh has a cell resolution that is anisotropically increased or decreased, wherein cells in the induced mesh have a finer or coarser resolution in one dimension relative to the resolutions in the other dimensions.

7. The method of claim 6 , wherein the first and second iso-surfaces each have a different constant value in the one dimension.

8. The method of claim 1 , wherein the second model includes a mesh with a relatively greater resolution of cells than a mesh of the initial model.

9. The method of claim 1 , wherein correcting the initial model using the induced mesh comprises increasing the resolution of cells in a volume of interest.

10. The method of claim 1 , comprising, for cells in the second model that intersect the second iso-surface, converting each of the said cells to a sub-mesh comprising polyhedron sub-mesh parts, each sub-mesh part with at least one facet approximating the orientation of the incorporated subsurface structures.

11. The method of claim 10 , wherein at least some of the sub-mesh parts are non-hexahedral polyhedrons.

12. The method of claim 1 , wherein the cells of the model are predominantly hexahedral.

13. The method of claim 1 , wherein the iso-surfaces estimate a configuration of the geological structures at a time of original deposition within the Earth.

14. The method of claim 13 , comprising transforming the iso-surfaces from the transformed coordinate space to a current coordinate space representing a configuration of the geological structures at a current time period.

15. The method of claim 1 , comprising receiving data representing the set of geological markers which describe an observed configuration of geological structures in a current time period.

16. The method of claim 1 , comprising dividing the initial model into N sub-volumes and processing each sub-volume independently for the same or different number of iterations to independently increase resolution in each sub-volume.

17. A system for modeling a geological structure, the system comprising:

one or more processors configured to:

(a) compute a first function for a geological structure, wherein the first function includes a first iso-surface in a transformed coordinate space of an initial coordinate space and generate an initial model of the geological structure having an initial resolution of cells that are divided along the first iso-surface;

(b) detect if the first iso-surface intersects a set of geological markers within a threshold proximity;

(c) if the first iso-surface does not intersect the set of geological markers within the threshold proximity, correct the initial model using an induced mesh having an increased cell resolution for computing a second function for the geological structure to improve the accuracy of a location of the geological structure in the initial model, wherein the second function includes a second iso-surface in the transformed coordinate space that intersects the set of geological markers within the threshold proximity;

(d) generate a second model including the second iso-surface, wherein the second model has a locally increased resolution relative to the initial model caused by further dividing cells in the second model along the second iso-surface; and

for each new geological structure, repeat steps (a)-(d), using the second model as the initial model;

and a display to visualize the second model.

18. The system of claim 17 , wherein the second model is the initial model with the second iso-surface.

19. The system of claim 17 , wherein the second model is the induced mesh.

20. A method, comprising:

receiving geological data representing a configuration of geological structures at a current geological time;

transforming the geological data to a first depositional model comprising an initial division of cells along a first set of iso-surfaces at a first resolution, wherein the cells represent an estimated configuration of a first set of geological structures at a time of original deposition;

in response to detecting that the transformed geological data does not intersect a set of geological markers, updating the first depositional model to create a second depositional model comprising a further division of cells along a second set of iso-surfaces at a second resolution greater than the first resolution to improve the accuracy of a location of the geological structure in the initial model;

re-transforming the geological data to the second depositional model to generate transformed geological data that intersects the set of geological markers; and

displaying a visualization of the second model.

21. The method of claim 20 , wherein the transformation is a three-dimensional transformation from xyz-space to uvt-space.

22. The method of claim 20 , comprising inverse transforming the transformed geological data that intersects the set of geological markers to the current geological time; and inserting the inverse transformed geological data into a current time model.

23. The method of claim 20 , comprising, for cells that intersect the geological structures, dividing each of the cells into a sub-mesh comprising polyhedral sub-mesh parts, each sub-mesh part with at least one facet approximating the orientation of the geological structures.