Two-dimensional Conditional Simulations Based on the Wavelet Decomposition of Training Images

Scale dependency is a critical topic when modeling spatial phenomena of complex geological patterns that interact at different spatial scales. A two-dimensional conditional simulation based on wavelet decomposition is proposed for simulating geological patterns at different scales. The method utilizes the wavelet transform of a training image to decompose it into wavelet coefficients at different scales, and then quantifies their spatial dependence. Joint simulation of the wavelet coefficients is used together with available hard and or soft conditioning data. The conditionally co-simulated wavelet coefficients are back-transformed generating a realization of the attribute under study. Realizations generated using the proposed method reproduce the conditioning data, the wavelet coefficients and their spatial dependence. Two examples using geological images as training images elucidate the different aspects of the method, including hard and soft conditioning, the ability to reproduce some non-linear features and scale dependencies of the training images.