Decoupling Electromagnetic Tensor Components Without Matrix Inversion
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Solution Overview
Problem
Rotating multi-sub logging while drilling (LWD) electromagnetic resistivity tools assume a one-dimensional model for formation properties, leading to incomplete data and increased computational costs due to matrix inversion operations for decoupling electromagnetic field tensor components.
Innovation Solution
Numerical and semi-analytical methods are employed to obtain a complete set of nine nonzero electromagnetic field tensor components without matrix inversion, allowing for a three-dimensional inversion process, with decoupling performed downhole and communicated to the surface for more efficient data processing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If matrix inversion operations are used to decouple electromagnetic field tensor components, then complete set of nine nonzero components can be obtained, but computational cost increases
Solution Approach 1:
The patent extracts and removes the matrix inversion operation from the decoupling process by using an alternative computational approach. Specifically, it uses a simplified decoupling method that obtains the nine nonzero electromagnetic field tensor components without requiring full matrix inversion, thereby reducing computational cost while maintaining component completeness
Solution Approach 2:
The patent changes the computational parameters and methodology from traditional matrix inversion to an alternative decoupling approach. By modifying the mathematical operations used to extract tensor components from the electromagnetic data, the system achieves the same measurement precision with reduced computational energy expenditure
2Device complexity
If a one-dimensional model is assumed for formation properties, then inversion process is simplified, but measurement precision of formation modeling decreases
Solution Approach 1:
The patent transitions from a one-dimensional formation model to a three-dimensional formation model. By incorporating additional spatial dimensions in the inversion process, the system captures more complex geological structures and anisotropic properties, thereby improving formation modeling accuracy while using the reduced computational decoupling method
3Loss of time
If downhole decoupling is performed, then data processing time is reduced, but device complexity increases
Solution Approach 1:
The patent performs the decoupling of electromagnetic field tensor components as a preliminary action downhole before the data is transmitted to the surface. By completing the decoupling operation at the source using the simplified method, the system reduces the amount of raw data that needs to be processed later, thereby reducing overall data processing time despite the added downhole computational complexity
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 reduces computational costs and enhances the accuracy of 3-D formation modeling by obtaining a full set of electromagnetic field tensor components, facilitating better geological data recovery and reducing errors associated with 1-D assumptions.
Implementation Method 1
a first transmitter of a set of one or more transmitters transmits an electromagnetic signal into a surrounding formation
Implementation Method 2
a first receiver of a set of one or more receivers detects the transmitted electromagnetic signal
Data Source
AI summary
Numerical and/or semi-analytical methods are leveraged to decouple a complete set of nonzero electromagnetic field tensor components (118) from detected signal data (119). Nine nonzero components can serve as inputs for a three-dimensional inversion process to determine formation properties. A resistivity tool (100) containing at least one transmitter (111) and at least one receiver (108, 109) at tilted angles receives an electromagnetic signal throughout a rotation. A difference in the azimuthal positions of the transmitter(s) and receiver(s) during rotation of the resistivity tool can result in an azimuthal offset between resistivity tool subs. The components (118) are decoupled from the detected signal data (119) numerically or semi-analytically according to whether the azimuthal offset angle is known. If the azimuthal offset angle is known, the nine components are determined numerically through curve fitting. If the azimuthal offset angle is unknown, a semi-analytical process is used to solve for the nine components.