Global Gravity Inversion via General Local Isostasy
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Solution Overview
Problem
Current methods for modeling the Earth's crust and mantle geometry and density using gravity and isostatic data are limited by their assumption of local isostasy, which does not account for lateral variations in crustal and mantle densities, leading to less accurate and realistic lithospheric models.
Innovation Solution
The implementation of a global inversion algorithm combining gravity data with the principle of general local isostasy, which allows for lateral variations in crustal and mantle densities, enabling the creation of more realistic lithospheric models that best-fit observed gravity data and maintain isostatic equilibrium.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If local isostasy is assumed with constant densities, then the model is simpler and easier to solve, but the accuracy and realism of lithospheric models deteriorates due to inability to account for lateral density variations
Solution Approach 1:
The patent transforms the inversion problem by changing the parameterization from direct density values to isostatic parameters (depth to compensation surface, crustal thickness, density contrasts). This allows the model to account for lateral density variations while maintaining computational tractability through the isostatic constraint that reduces the number of independent parameters.
Solution Approach 2:
The patent applies local isostasy theory to allow different regions to have different density characteristics while maintaining overall isostatic equilibrium. Each location can have its own compensation depth and density contrast values, enabling lateral variations in crustal and mantle properties without requiring a completely complex global model.
2Measurement precision
If lateral variations in crustal and mantle densities are accounted for, then the realism and accuracy of lithospheric models improves, but the complexity of the inversion problem and computational requirements increases
Solution Approach 1:
The patent reduces inversion complexity by changing from inverting multiple density parameters to inverting isostatic parameters (compensation depth, crustal thickness, and a few density contrast values). The isostatic equilibrium condition provides a mathematical constraint that eliminates the need to independently determine densities at every location, significantly reducing the dimensionality of the inverse problem.
Solution Approach 2:
The patent applies isostatic equilibrium as a preliminary constraint before performing the inversion. By pre-establishing the isostatic relationship between crustal thickness, compensation depth, and density contrasts, the algorithm starts with a physically constrained model space, reducing the search space and computational burden during the inversion process.
3Adaptability or versatility
If traditional gravity inversion without isostatic constraint is used, then more freedom in fitting gravity data is available, but the geological realism and physical consistency of the model deteriorates
Solution Approach 1:
The patent incorporates isostatic equilibrium as a feedback constraint in the inversion algorithm. The computed model is continuously checked against isostatic balance conditions, and the inversion adjusts parameters to satisfy both the gravity data fit and the isostatic constraint, ensuring geological realism while maintaining data compatibility.
Solution Approach 2:
The patent pre-establishes isostatic equilibrium relationships as fundamental constraints before the inversion process. By defining the isostatic balance equations a priori, the algorithm ensures that all candidate models satisfy physical consistency requirements, filtering out geologically unrealistic solutions before they can be selected.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach provides more accurate and reliable estimates of crustal geometry, including depth to the top or base of the crust, and mantle properties, while reducing the ambiguity in fitting gravity data, thereby improving the characterization of geological structures.
Implementation Method 1
inverting gravity anomaly data for depth to the top or base of the earth's crust, as well as for densities of the crust and mantle
Implementation Method 2
defining a model space within which all subsurface models are in general local isostatic equilibrium
Data Source
AI summary
A method including: defining a model space within which all subsurface models are in general local isostatic equilibrium; generating a representative set of trial models which span the model space, wherein a requirement that all of the trial models be in isostatic equilibrium provides a constraint that narrows a range of solutions that fit observed gravity data, wherein the trial models provide scenarios of Earth's crustal geometry, and crust and mantle rock properties; and determining, within an inversion process, a model solution based on minimizing a misfit between the observed gravity data and synthetic gravity data generated from at least one of the trial models.