Direct kriging: A direct optimization based model with locally varying anisotropy

Numerous earth system structures, such as braided rivers and meandering channels, exhibit varying degrees of continuity in different directions, known as locally varying anisotropy (LVA), which poses a challenge in adequately characterizing and expressing such features. In such cases, obtaining the realistic shortest anisotropic path distance (SPD) associated with nonlinear features becomes crucial. However, fully utilizing SPD in geostatistics remains a challenge. In this research, we propose a novel estimation model named "direct kriging, " which directly incorporates SPD in kriging estimation with LVA. Unlike classical kriging, this method does not rely on a system of equations; instead, it formulates the problem of minimizing estimation error variance as a direct optimization model. An objective function is designed to achieve minimum error variance while considering the validity of error variance and estimated values, thereby ensuring model validation and accommodating SPD. The proposed method is implemented using a genetic algorithm and evaluated using two datasets corresponding to a fluvial channel system: a delta deposit and a meandering channel. Our results demonstrate that the proposed method outperforms classical solutions, providing a more explicit representation of curvilinear structures and improving interpolation accuracy, as measured by normalized mean absolute error and normalized root mean square error. Given its capability and flexibility in producing more accurate and realistic results, we anticipate that this method will benefit the field of characterizing more complex geological features in a broader context.