Beam Profile Imaging Using Transfer Matrices
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Solution Overview
Problem
Traditional 3-D simulation approaches for beam profile imaging in rotationally anisotropic targets are computationally inefficient, often requiring extensive time and omitting necessary information due to simplifying assumptions, making real-time processing of acoustic and ultrasonic data impractical, especially in high-wavelength applications with geometric abnormalities like wave mode coupling and varying media thickness.
Innovation Solution
An enhanced form of raytracing that accounts for wave phenomena and geometric abnormalities by encoding properties like energy magnitude, phase, and material variations into transfer matrices, allowing for real-time inversion and calculation of acoustic and ultrasonic properties using GPU processors, which enables fast forward modeling and real-time data processing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional 3-D simulation approach is used, then accuracy in accounting for wave phenomena and geometric abnormalities is improved, but computational time and resource requirements increase significantly
Solution Approach 1:
The patent segments the complex 3-D simulation problem into multiple 1-D simulations by dividing the casing thickness into discrete layers. Each layer is modeled independently with its own transfer matrix, allowing the overall problem to be solved through sequential composition of simpler sub-problems rather than a single computationally intensive 3-D simulation.
Solution Approach 2:
The patent replaces the mechanical/computational burden of full 3-D finite element modeling with an analytical transfer matrix approach. By using closed-form mathematical solutions based on wave propagation theory and transfer matrices, the method eliminates the need for iterative numerical simulations while maintaining accuracy for layered media.
2Productivity
If simplifying assumptions are made in 1-D models, then computational efficiency is improved, but accuracy in treating wave phenomena and geometric abnormalities deteriorates
Solution Approach 1:
The patent applies local quality by allowing different transfer matrices to represent different physical effects at different locations through the casing thickness. Each layer can have its own acoustic properties, thickness, and transfer matrix, enabling the model to capture local variations in wave propagation while maintaining the computational efficiency of 1-D analysis.
Solution Approach 2:
The patent uses composite transfer matrices that combine multiple physical effects (reflection, refraction, wave mode conversion, geometric abnormalities) into a unified mathematical framework. By composing individual transfer matrices for each layer and effect, the method creates a composite model that captures complex wave-casing interactions while retaining 1-D computational efficiency.
3Loss of information
If full 3-D finite element inversion is performed, then comprehensive acoustic property analysis is improved, but processing time for large datasets becomes impractical
Solution Approach 1:
The patent performs preliminary action by pre-calculating and storing transfer matrices for different casing layers and wave modes before actual data processing. These pre-computed matrices capture the essential physics of wave propagation through the casing, allowing rapid forward modeling during inversion without repeated complex simulations, thus enabling fast processing of large datasets while maintaining comprehensive acoustic property analysis.
4Productivity
If traditional raytracing is used, then computational speed is improved, but accuracy in accounting for wave phenomena and geometric abnormalities deteriorates
Solution Approach 1:
The patent changes the fundamental parameters of the raytracing model by incorporating wave phenomena through transfer matrices that account for wavelength, frequency, and wave mode coupling. Instead of treating rays as simple geometric lines, the model uses wave-based transfer matrices that preserve phase information and account for interference effects, thereby maintaining computational speed while significantly improving accuracy for wave-dominated regimes.
Data Source
AI summary
Systems and methods for beam profile imaging by emitting a ray into one or more media; receiving a first signal corresponding to the ray at a first point; encoding a first matrix based at least in part on one or more of a location of the first point, a direction of the ray at the first point, and a first perturbation effect; receiving a second signal corresponding to the ray at a second point; encoding a second matrix based at least in part on one or more of a location of the second point, a direction of the ray at the second point, and a second perturbation effect; and calculating the value of the acoustic property of one or more media based at least in part on a comparison between the first matrix and the second matrix.