Full Waveform Inversion with Angle-Dependent Parameters

The patent applies parameter changes by introducing angle-dependent model parameters into the full waveform inversion process. Instead of using conventional isotropic parameters, the method incorporates parameters that vary with angle (such as α0, α1, α2, α3) to better characterize anisotropic subsurface properties. This parameter transformation enables more accurate representation of complex geological structures while maintaining computational feasibility through systematic parameter substitution in the inversion equations.

The patent applies segmentation by dividing the angle-dependent model parameters into distinct components (α0, α1, α2, α3) that correspond to different physical characteristics. This segmentation allows the complex inversion problem to be broken down into manageable parts, where each parameter can be inverted separately or in small groups. The segmented parameter structure reduces the computational burden compared to inverting all angle-dependent parameters simultaneously, while still capturing the full complexity of anisotropic subsurface properties.

The patent applies partial action by selectively inverting only the necessary angle-dependent parameters for each specific subsurface property being characterized. Rather than inverting all possible angle-dependent parameters simultaneously, the method identifies and inverts only the minimal set required for accurate property determination (such as velocity, density, or elastic moduli). This selective inversion approach reduces processing time while maintaining sufficient accuracy, as excessive parameters would only add computational burden without providing additional useful information.