Systems and methods to build sedimentary attributes
A method and system for computing and visualizing sedimentary attributes may include receiving, by a processor, paleo-geographic coordinates representing predicted approximate positions of particles of sediment deposited at a time period when a layer was originally formed. The processor may numerically compute or determine a sedimentation rate that varies laterally along the layer. The processor may determine a sedimentary attribute based on the lateral variation of the sedimentation rate along the layer with respect to the paleo-geographic coordinates. A monitor or display may display the sedimentary attribute of the layer in the present-day geological space.
1. A method to visualize geological attributes that represent geological properties of particles of one or more geologic horizons, the method comprising:
in one or more computer processors:
receiving, based on measured geological data of the particles of the geological horizons in a present-day configuration of the geological horizons in present-day geological coordinates, a geological-time coordinate representing predicted time periods when the particles of the geologic horizons were originally formed, wherein the geological-time coordinate has level sets that are coincident with the geologic horizons;
determining a vector field tangent to normal-lines of the geologic horizons and parallel to the gradient of the geological-time coordinate;
determining a vector field of curvature of the normal-lines deduced from the vector field tangent to the normal-lines, wherein the vector field of curvature of the normal-lines corresponds to lateral variations of sedimentation rate along a layer; and
displaying on the geological horizons or on a cross-section the geological attribute that is the curvature vector field of the normal-lines or a function derived from the vector field of curvature of the normal-lines within the geological horizons with respect to the present-day geological coordinates.
2. The method of claim 1 , wherein a curvature vector of a normal-line passing through a given point is a function of the derivative of the unit vector tangent to the normal-line defined as the unit vector proportional to the gradient of the geological-time coordinate.
3. The method of claim 1 , wherein the curvature vector field of the normal-lines passing through a given point is a function of the derivative of the unit vector tangent to the normal-line with respect to an arc-length abscissa along the normal-line passing through the point.
4. The method of claim 1 , wherein the geological attribute is the function derived from the curvature vector field of the normal-lines, which is the length of the curvature vector field of the normal-lines.
5. The method of claim 1 , wherein the geological attribute is the function derived from the curvature vector field of the normal-lines, which is the divergence of the curvature vector field of the normal-lines.
6. A system to visualize geological attributes that represent geological properties of particles of one or more geologic horizons, the system comprising:
one or more computer processors configured to:
receive, based on measured geological data of the particles of the geological horizons in a present-day configuration of the geological horizons in present-day geological coordinates, a geological-time coordinate representing predicted time periods when the particles of the geologic horizons were originally formed, wherein the geological-time coordinate has level sets that are coincident with the geologic horizons;
determine a vector field tangent to normal-lines of the geologic horizons and parallel to the gradient of the geological-time coordinate;
determine a vector field of curvature of the normal-lines deduced from the vector field tangent to the normal-lines, wherein the vector field of curvature of the normal-lines corresponds to lateral variations of sedimentation rate along a layer; and
display on the geological horizons or on one or more cross-sections the geological attribute that is the curvature vector field of the normal-lines or a function derived from the vector field of curvature of the normal-lines within the geological horizons with respect to the present-day geological coordinates.
7. The system of claim 6 , wherein the one or more computer processors are configured to determine a curvature vector of a normal-line passing through a given point as a function of the derivative of the unit vector tangent to the normal-line defined as the unit vector proportional to the gradient of the geological-time coordinate.
8. The system of claim 6 , wherein the one or more computer processors are configured to determine the curvature vector field of the normal-lines passing through a given point as a function of the derivative of the unit vector tangent to the normal-line with respect to an arc-length abscissa along the normal-line passing through the point.
9. The system of claim 6 , wherein the one or more computer processors are configured to derive the function from the curvature vector field of the normal-lines to be the length of the curvature vector field of the normal-lines.
10. The system of claim 6 , wherein the one or more computer processors are configured to derive the function from the curvature vector field of the normal-lines to be the divergence of the curvature vector field of the normal-lines.
11. The system of claim 6 comprising a display to visualize the curvature vector field of the normal-lines or the function derived from the vector field of curvature of the normal-lines on the geological horizons or cross-sections.
12. A non-transitory computer readable storage medium that stores instructions, which when executed by one or more processors, causes the one or more processors to:
receive, based on measured geological data of the particles of the geological horizons in a present-day configuration of the geological horizons in present-day geological coordinates, a geological-time coordinate representing predicted time periods when the particles of the geologic horizons were originally formed, wherein the geological-time coordinate has level sets that are coincident with the geologic horizons;
determine a vector field tangent to normal-lines of the geologic horizons and parallel to the gradient of the geological-time coordinate;
determine a vector field of curvature of the normal-lines deduced from the vector field tangent to the normal-lines, wherein the vector field of curvature of the normal-lines corresponds to lateral variations of sedimentation rate along a layer; and
display on the geological horizons or on a cross-section the geological attribute that is the curvature vector field of the normal-lines or a function derived from the vector field of curvature of the normal-lines within the geological horizons with respect to the present-day geological coordinates.
13. The non-transitory computer readable storage medium of claim 12 , wherein the instructions, when executed by the one or more processors, further cause the processors to determine a curvature vector of a normal-line passing through a given point as a function of the derivative of the unit vector tangent to the normal-line defined as the unit vector proportional to the gradient of the geological-time coordinate.
14. The non-transitory computer readable storage medium of claim 12 , wherein the instructions, when executed by the one or more processors, further cause the processors to determine the curvature vector field of the normal-lines passing through a given point as a function of the derivative of the unit vector tangent to the normal-line with respect to an arc-length abscissa along the normal-line passing through the point.
15. The non-transitory computer readable storage medium of claim 12 , wherein the instructions, when executed by the one or more processors, further cause the processors to derive the function from the curvature vector field of the normal-lines to be the length of the curvature vector field of the normal-lines.
16. The non-transitory computer readable storage medium of claim 12 , wherein the instructions, when executed by the one or more processors, further cause the processors to derive the function from the curvature vector field of the normal-lines to be the divergence of the curvature vector field of the normal-lines.