Geological-Time Refinement via Segmented 3D Interpolation
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Solution Overview
Problem
Current interpolation techniques for modeling geological time in subsurface terrains often result in inaccurate data due to violations of principles such as superposition and minimal energy deformations, particularly when dealing with discontinuities in the gradient of the geological time function across fault blocks, leading to the formation of unrealistic 'bubbles' in the model.
Innovation Solution
The Geological-Time Refinement (GTR) technique divides 3D interpolation into two stages: 2D interpolation on reference horizons to reshape them to fit sampling data and 1D piecewise-linear interpolation along iso-paleo-geographic lines, allowing for discontinuities in the gradient of the geological time function while maintaining its monotonicity, thus preventing the formation of bubbles and improving the accuracy of the model.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Stability of the object's composition
If classical C1 continuous interpolation is used to model geological time, then the gradient continuity is maintained, but the interpolation produces unrealistic bubbles and violates geological principles such as superposition and minimal energy deformations
Solution Approach 1:
The patent segments the 3D interpolation problem into two distinct stages: 2D interpolation on reference horizons to reshape them to fit sampling data, and 1D piecewise-linear interpolation along iso-paleo-geographic lines. This segmentation allows the model to handle gradient discontinuities across fault blocks while maintaining monotonicity, thereby preventing unrealistic bubble formations and adhering to geological principles.
Solution Approach 2:
The patent applies different interpolation methods to different spatial locations based on local geological characteristics. Specifically, C0 piecewise-linear interpolation is used along iso-paleo-geographic lines to allow gradient discontinuities at fault blocks, while maintaining C1 continuity in regions without faults. This local adaptation ensures geological accuracy without imposing unrealistic constraints everywhere.
2Device complexity
If 3D interpolation is performed directly to model geological time, then the computational process is simplified, but the model produces gradient discontinuities and unrealistic geometries across fault blocks
Solution Approach 1:
The patent divides the 3D interpolation into two stages: 2D interpolation on reference horizons followed by 1D interpolation along iso-paleo-geographic lines. This segmentation reduces computational complexity by breaking down the 3D problem into manageable 2D and 1D sub-problems, while simultaneously improving accuracy by allowing gradient discontinuities at fault blocks through the 1D piecewise-linear interpolation.
Solution Approach 2:
The patent transforms the 3D interpolation problem by introducing iso-paleo-geographic lines as a new dimensional framework. By performing interpolation along these 1D lines after 2D horizon reshaping, the method effectively reduces the complexity of 3D interpolation while maintaining geometric accuracy and preventing bubble formations.
3Stability of the object's composition
If C1 continuous interpolation is applied across all horizons, then the mathematical smoothness is improved, but the model violates geological principles and creates non-monotonic behavior leading to bubbles
Solution Approach 1:
The patent applies C0 piecewise-linear interpolation specifically along iso-paleo-geographic lines where gradient discontinuities occur at fault blocks, while maintaining C1 continuity in regions without faults. This local differentiation ensures geological reliability by preventing non-monotonic behavior and bubble formations at fault locations, while preserving mathematical smoothness where appropriate.
Solution Approach 2:
Instead of enforcing C1 continuity everywhere and then trying to correct violations, the patent inverts the approach by deliberately using C0 piecewise-linear interpolation along iso-paleo-geographic lines to prevent gradient discontinuities at fault blocks from the outset. This inversion of the traditional approach ensures monotonicity and prevents bubble formations while maintaining overall model smoothness.
Data Source
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AI summary
A device, system and method for performing a 3D interpolation in a 2D interpolation stage and a 1D interpolation stage to generate a refined geological-time. A 3D model may be obtained of a subsurface region defined by an initial geological-time in the past when particles in the subsurface region are determined to have been originally deposited. The stages of the 3D interpolation may include a 2D interpolation along one or more initial 2D reference horizon surfaces to generate one or more reshaped 2D reference horizon surfaces, and a 1D interpolation based on the initial geological-time along one or more 1D interpolation lines to generate a refined geological-time, wherein each 1D interpolation line is approximately orthogonal to the initial 2D reference horizon surfaces. The 3D model may be displayed according to the refined geological-time.