Amplitude Preserving One-Way Wave Equation via Hamilton Symmetry
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Solution Overview
Problem
Conventional one-way wave operator methods for acoustic medium wave equations fail to preserve amplitude, leading to inaccuracies in wave propagation simulations, particularly due to high computational costs and limitations in applying amplitude correction methods across varying media.
Innovation Solution
An amplitude preserving method based on the symmetry of generalized Hamilton operators is introduced, which decomposes the wave equation into up-going and down-going components, establishes amplitude preserving forms and boundary conditions, and uses a modified source function to ensure recursive equations satisfy amplitude preservation conditions, thereby maintaining reciprocity in wave propagation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional one-way wave operator methods are used for acoustic medium wave equations, then computational cost is reduced, but amplitude preservation is lost leading to simulation inaccuracy
Solution Approach 1:
The patent modifies the wave equation by introducing a dimensionless parameter transformation and adjusting the source term to incorporate amplitude preservation factors. The modified equation changes the parameter relationships between pressure, density, and velocity to maintain amplitude accuracy while keeping computational complexity manageable through analytical solutions of the modified terms
Solution Approach 2:
The patent introduces an intermediary amplitude correction factor that acts as a mediator between the simplified one-way wave operator and the full two-way equation. This factor is derived from the ratio of actual to approximate amplitude and is applied as a multiplicative correction term that restores amplitude accuracy without requiring full two-way simulation complexity
2Measurement precision
If amplitude correction methods are applied to one-way wave equations, then amplitude accuracy is improved, but applicability to varying media is limited
Solution Approach 1:
The patent develops a universal amplitude correction framework that functions across different media types by expressing the correction factor in terms of dimensionless parameters that can accommodate varying acoustic properties. The method uses normalized variables that scale with media characteristics, allowing the same correction formulation to apply to homogeneous, layered, and laterally varying media without requiring media-specific adjustments
3Productivity
If traditional one-way wave approximation is used, then computational cost is low, but reciprocity conservation principle is violated
Solution Approach 1:
The patent implements a feedback mechanism where the amplitude correction factor is calculated based on the wave field solution and then fed back into the equation as a multiplicative term. This iterative correction process continuously adjusts the amplitude to satisfy reciprocity conservation, with the correction factor being recomputed and applied until convergence is achieved, ensuring energy conservation while maintaining computational efficiency
Data Source
AI summary
An amplitude preserving method and system based on symmetry of generalized Hamilton operators are provided. This method involves determining the dimensions of a decomposition equation based on up-going and down-going one-way wave equations. Additionally, an amplitude preserving form and boundary conditions are established for both up-going and down-going wave equations with varying dimensions. The traditional one-way wave processing procedure is then adjusted by a modified source function and initial boundary conditions until a one-way wave field recursive equation with an amplitude preserving condition is satisfied. Finally, a modified one-way wave program is used to obtain an amplitude preserving wave field, which is then compared to the results of a finite difference wave field or an analytical solution wave field for verification.