Fast-Constrained 3D Gravity and FTG Inversion via Wavenumber Modeling
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Solution Overview
Problem
Conventional 3D inversion of gravity and FTG data is time-consuming and lacks sufficient constraints, particularly in large-scale applications, and fails to fully utilize prior information such as density, orientation, and spatial extent from seismic data.
Innovation Solution
A method and system employing a biconjugate gradient stabilized method (BiCGSTAB) for one-time forward modeling in the wavenumber domain, integrating prior information through spatial variogram functions, and incorporating topography to enhance computational efficiency and accuracy, while minimizing memory footprint.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional 3D inversion methods are used with smoothness or compactness constraints, then the inversion process is stabilized, but the computational time is excessive and prior information is not fully utilized
Solution Approach 1:
The patent performs preliminary forward modeling to calculate the kernel matrix before the inversion process. This pre-computed kernel matrix is then reused during iterative inversion, eliminating the need to recalculate it in each iteration and significantly reducing computational time while maintaining inversion stability
Solution Approach 2:
The patent transforms the inversion problem from physical space to wavenumber space by computing the kernel matrix in wavenumber domain. This parameter transformation enables more efficient computation and allows better integration of prior information through modified constraint operators that work naturally in the wavenumber domain
2Reliability
If smoothness or compactness constraints are applied, then the inversion is stabilized, but the constraints are too broad and loose to fully utilize prior information from seismic data
Solution Approach 1:
The patent implements depth-dependent weighting functions that apply different constraint strengths at different depths. This allows the inversion to use stronger constraints in regions where prior information is more reliable and weaker constraints where data information dominates, thereby fully utilizing available prior information from seismic data without over-constraining the entire model
Solution Approach 2:
The patent combines multiple types of constraints (smoothness, compactness, and depth-dependent weighting) into a composite constraint framework. This composite approach integrates various sources of prior information in a unified manner, allowing the inversion to simultaneously stabilize the solution while incorporating density information, orientation, spatial extent, and interface data from seismic surveys
3Ease of operation
If the kernel matrix is calculated and stored for gravity and FTG data, then the inversion can proceed, but the calculation and storage are time-consuming and limit large-scale applications
Solution Approach 1:
The patent calculates the kernel matrix in wavenumber space as a preliminary step before inversion. This pre-computed kernel matrix is stored in an efficient format and reused throughout the iterative inversion process, eliminating redundant calculations and reducing the overall computational burden for large-scale applications
Solution Approach 2:
The patent performs forward modeling and kernel matrix calculation in wavenumber space rather than physical space. This dimensional transformation exploits the convolution theorem to simplify computations and reduces the computational complexity from O(N²) to O(N log N), making large-scale gravity and FTG data inversion feasible
Data Source
AI summary
A method for 3D inversion of Full Tensor Gradiometry (FTG) data comprising receiving observed FTG data, performing a kernel matrix calculation on a subset of the observed FTG data and the gravity anomaly data, performing one-time forward modeling in a wavenumber domain to produce predicted FTG data and predicted gravity anomaly data for the reference density model, performing a residual between the observed data and predicted data, performing a depth-weighting function, a model covariance matrix, and data error covariance matrix on the observed FTG data and observed gravity anomaly data, obtaining a model update based on the depth-weighting function, kernel matrix, the model covariance matrix and the data error covariance matrix, and the residual between the observed FTG data and the predicted FTG data in the wavenumber domain, and performing inversion by directly obtaining an inverted model based on the model update and reference model.