Seismic Inversion via Spherical Elastic Parameter Constraints
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Solution Overview
Problem
Current 4D seismic inversion methods face challenges due to ill-posed problems with multiple solutions, non-uniqueness, and reliance on liberalized approximations, leading to inaccurate and non-unique seismic inversion results, particularly in prestack 4D inversion schemes that are heavily dependent on amplitude information and AVO inversion.
Innovation Solution
The method involves projecting petrophysical data into valid combinations of elastic parameters, creating distance penalties based on geological and dynamic scenarios, and constraining the inversion process using a spherical plot to select model solutions consistent with prior geological and dynamic considerations, thereby stabilizing the inversion and improving the accuracy of elastic parameter determination.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If liberalized approximations are used in prestack 4D inversion schemes, then the inversion process is simplified and easier to perform, but the results become non-unique and inaccurate
Solution Approach 1:
The patent applies preliminary action by computing distance penalties from petrophysical data before the inversion process. Valid combinations of elastic parameters are projected onto a spherical plot and distance penalties are determined in advance, creating a constraint framework that guides the inversion toward geologically realistic solutions without complicating the inversion algorithm itself.
Solution Approach 2:
The patent transforms the inversion constraint by introducing distance penalties in spherical space rather than using traditional linear constraints. This parameter transformation allows the inversion to maintain simplicity while incorporating geological knowledge through the spherical projection of valid elastic parameter combinations, resolving the non-uniqueness issue without requiring complex iterative constraint application.
2Adaptability or versatility
If multiple solutions are allowed in the inversion problem, then the solution space is more comprehensive, but the results become non-unique and harder to interpret
Solution Approach 1:
The patent resolves the non-uniqueness problem by adding a dimensional transformation - projecting elastic parameters onto a spherical plot. This dimensional change allows the inversion to explore multiple solutions while the spherical geometry naturally constrains solutions to geologically valid regions, preserving solution comprehensiveness while restoring uniqueness through the geometric constraint of the spherical manifold.
Solution Approach 2:
The spherical plot of valid elastic parameter combinations acts as an intermediary between the seismic data and the inversion results. This intermediary structure filters the solution space by encoding geological knowledge in the spherical geometry, allowing multiple seismic interpretations to be mapped onto a constrained set of geologically realistic solutions, thereby restoring uniqueness without losing solution comprehensiveness.
3Reliability
If distance penalties are computed from petrophysical data, then the inversion is constrained to geologically valid solutions, but the computational complexity increases
Solution Approach 1:
The patent reduces computational complexity by performing the geologically intensive work of computing distance penalties in advance, before the actual inversion process. The spherical projection and penalty computation are pre-calculated from petrophysical data, creating a lookup framework that the inversion can query efficiently without repeating complex geological calculations during iterative inversion steps.
Solution Approach 2:
The patent uses spherical geometry to simplify the constraint representation. By projecting elastic parameters onto a sphere, the complex multi-dimensional constraint space is transformed into a geometrically intuitive spherical manifold where distance penalties can be computed using simple angular distances rather than complex multi-dimensional Euclidean distances, reducing computational complexity while maintaining geological validity.
Data Source
AI summary
Disclosed is a method a seismic inversion for petrophysical properties of a subsurface volume comprising the steps of: obtaining petrophysical data relating to valid geological and/or dynamical scenarios, converting this data into valid combinations of elastic parameters; projecting the valid combinations of elastic parameters onto a spherical plot; and determining a penalty term from the distances between each cell of the spherical plot and the nearest valid combination of elastic parameters within the subsurface volume. Valid geological and/or dynamical scenarios comprise those which are petrophysically possible. The penalty term is then used to constrain an inversion minimizing a cost function associated with seismic mismatch between two or more seismic surveys.