Geobody Inversion via Ultra Low-Dimensional Shape Representation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Traditional cell-based Full Waveform Inversion (FWI) methods struggle with accurately imaging subsurface salt bodies due to their large number of unknowns, leading to ill-posed optimization problems and blurred images, especially in 2D and 3D domains.
Innovation Solution
An ultra low-dimensional representation of salt bodies using a stochastic view as a spatial random process, parameterized by a set of orthogonal basis functions, significantly reducing the dimensionality of the inversion space, allowing for sharper boundary representation and improved imaging.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional cell-based FWI methods are used to image subsurface salt bodies, then the method can process the data, but the large number of unknowns leads to ill-posed optimization problems and blurred images
Solution Approach 1:
The patent segments the salt body representation into a small number of discrete point locations (seeds) rather than using a full cell-based grid. This segmentation reduces the number of unknowns from potentially thousands of cells to just a handful of seed points, transforming the ill-posed optimization problem into a well-posed one while maintaining image accuracy.
Solution Approach 2:
The patent transitions from representing salt bodies in the spatial domain (cell-based 2D/3D grids) to representing them in a parameter space defined by seed locations and growth parameters. This dimensionality change allows the complex geometric representation to be controlled by far fewer parameters, resolving the contradiction between detail and complexity.
2Area of stationary object
If cell-based representation is used, then complete subsurface coverage is achieved, but computational complexity increases and inversion becomes ill-posed
Solution Approach 1:
The patent segments the continuous subsurface domain into discrete salt body regions represented by seed points and growth parameters. This segmentation maintains coverage of all relevant subsurface features while reducing the computational burden from inverting thousands of cell parameters to inverting just a few seed parameters per salt body.
Solution Approach 2:
The patent extracts only the essential features of salt bodies (their locations, shapes, and boundaries) represented by seed points and growth parameters, rather than inverting all cell parameters. This extraction maintains the ability to image complete subsurface structures while dramatically improving inversion efficiency.
3Reliability
If traditional FWI is applied to large homogeneous geobodies, then the method can process the data, but the optimization problem becomes severely ill-posed due to the large number of unknowns
Solution Approach 1:
The patent segments the high-dimensional inversion space into a low-dimensional parameter space defined by seed locations and growth parameters. This segmentation reduces the dimensionality from potentially thousands of cell parameters to just a few parameters per salt body, making the optimization problem well-posed and numerically stable.
Solution Approach 2:
The patent changes the parameters being inverted from cell-based velocity or impedance values to seed-based geometric parameters (locations and growth factors). This parameter transformation fundamentally changes the nature of the optimization problem from ill-posed to well-posed, improving reliability while reducing complexity.
Data Source
AI summary
A two-stage method for iteratively inverting geophysical data for the purpose of subsurface imaging, including: obtaining at least one geophysical dataset and an initial subsurface model; representing subsurface such that a geometry of a geobody is defined using a set of basis functions, and a number of such basis functions is significantly smaller than the number of cells used in cell-based geobody representations, wherein an order of magnitude reduction is two or more for 2-D domains and 3 or more for 3-D domains; in a first stage, successively updating the initial subsurface model, only for the geobody, by performing iterative low-dimensional geophysical inversion based on minimizing a misfit between simulated geophysical data and the geophysical dataset, wherein the simulated geophysical data is generated from a current subsurface model at each iteration; generating a subsurface image from a final updated subsurface model obtained via the low-dimensional geophysical inversion, wherein the subsurface image includes an inverted geobody; in a second stage, successively updating the subsurface model with the inverted geobody by performing iterative cell-based geophysical inversion based on minimizing a misfit between simulated geophysical data and the geophysical dataset, wherein the simulated geophysical data is generated from a current subsurface model at each iteration.