Inverse Modeling of Moving Average Isotropic Kernels for Non-parametric Three-Dimensional Gaussian Simulation

Moving average simulation can be summarized as a convolution between a spatial kernel and a white noise random field. The kernel can be calculated once the variogram model is known. An inverse approach to moving average simulation is proposed, where the kernel is determined based on the experimental variogram map in a non-parametric way, thus no explicit variogram modeling is required. The omission of structural modeling in the simulation work-flow may be particularly attractive if spatial inference is challenging and/or practitioners lack confidence in this task. A non-linear inverse problem is formulated in order to solve the problem of discrete kernel weight estimation. The objective function is the squared euclidean distance between experimental variogram values and the convolution of a stationary random field with Dirac covariance and the simulated kernel. The isotropic property of the kernel weights is imposed as a linear constraint in the problem, together with lower and upper bounds for the weight values. Implementation details and examples are presented to demonstrate the performance and potential extensions of this method.