MH
M.W. Hogendoorn
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This study introduces a novel quaternion-based approach to solving the scalar Helmholtz equation in a 3D heterogeneous environment, using an analytical Green’s function. The general Green’s function is constructed and validated through comparison with Finite-Difference Time-Domain (FDTD) simulations for a seismic example. The results demonstrate that the quaternionic method accurately models wave propagation, achieving the same performance as the established Green’s function in homogeneous media. Furthermore, the analytical approach offers significant advantages, achieving computational speeds approximately 1000 times faster than FDTD while inherently maintaining numerical stability. The findings highlight the potential of quaternion-based methods for efficient and precise wave modeling, paving the way for future applications in complex heterogeneous media.
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This study introduces a novel quaternion-based approach to solving the scalar Helmholtz equation in a 3D heterogeneous environment, using an analytical Green’s function. The general Green’s function is constructed and validated through comparison with Finite-Difference Time-Domain (FDTD) simulations for a seismic example. The results demonstrate that the quaternionic method accurately models wave propagation, achieving the same performance as the established Green’s function in homogeneous media. Furthermore, the analytical approach offers significant advantages, achieving computational speeds approximately 1000 times faster than FDTD while inherently maintaining numerical stability. The findings highlight the potential of quaternion-based methods for efficient and precise wave modeling, paving the way for future applications in complex heterogeneous media.