Gravity Inversion Using Hybrid Radial Basis Functions
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Solution Overview
Problem
Current gravity inversion methods in geophysics lack effective solutions for accurately inverting density fields using meshfree methods, which are underdeveloped in this field despite their potential.
Innovation Solution
A gravity model inversion method and system based on a meshfree method utilizing a hybrid radial basis function, combining Multi-Quadric and cubic kernel functions, with parameter evaluation and preconditioned conjugate gradient method for improved accuracy and stability.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional gravity inversion methods are used, then inversion can be performed, but the accuracy is insufficient and prior information cannot be effectively utilized
Solution Approach 1:
The patent applies preliminary action by constructing an initial density model using meshfree method and radial basis functions before performing the main inversion process. This preliminary modeling incorporates prior information about ore body morphology and tendency, creating a better starting point that guides the subsequent inversion toward more accurate results.
Solution Approach 2:
The patent utilizes parameter changes by adjusting the shape parameters of radial basis functions (such as the shape parameter in thin plate spline functions) to optimize the initial density model. By changing these mathematical parameters, the model adapts to better represent the actual geological structures, improving inversion accuracy.
2Productivity
If meshfree method with hybrid radial basis function is used, then the accuracy and efficiency of inversion are improved, but the complexity of the method increases
Solution Approach 1:
The patent applies universality by using radial basis functions that can serve multiple purposes: they act as both interpolation functions for creating the initial density model and as basis functions for the collocation method in solving the inversion equations. This multi-functionality reduces the need for separate processing steps and simplifies the overall methodology despite using advanced meshfree techniques.
Solution Approach 2:
The patent uses radial basis functions as an intermediary between the discrete gravity data and the continuous density distribution model. These functions provide a smooth mathematical bridge that connects observed gravity anomalies with subsided density variations, enabling the meshfree method to work effectively without requiring complex mesh structures.
3Reliability
If only Multi-Quadric radial basis function is used, then the interpolation can be performed, but the condition number becomes too large affecting stability
Solution Approach 1:
The patent applies composite materials concept by creating a hybrid radial basis function that combines Multi-Quadric (MQ) radial basis function with cubic kernel function. This composite function leverages the advantages of both components: MQ provides good interpolation capability while the cubic kernel helps control the condition number, resulting in a stable and accurate hybrid function for the inversion process.
Data Source
AI summary
A gravity inversion method and system based on a meshfree method. The method includes: selecting an appropriate method of constructing an approximate function, and forming a hybrid radial basis function; using an appropriate evaluation method to select suitable parameters of the hybrid radial basis function; selecting a construction form of an equation; and weighting a distance norm of the hybrid radial basis function on the basis of the tendency and morphology of an ore body in the prior information; loading known underground density information and constructing an equation set; solving the equation set, and using a coefficient matrix created with an acquired coefficient vector in combination with a global background grid to obtain a global estimated density distribution; loading observation data and performing inversion by using a preconditioned conjugate gradient method (PCGM) with the estimated density distribution as a constraint; and obtaining an underground density distribution and completing the inversion.