Foreword F. Kalf (2017)
The earlier part of this paper was intended to be published in 2006 but for various reasons, including the author’s commitments, was not resubmitted. A number of anonymous reviewers did provide useful comments that were incorporated in the paper. However these reviewers also seemed to be somewhat surprised by the relative simplicity of the approach, that yielded generation of stochastic images similar to the traditional pixel-based approach with rapid computation that was possible in both 2D and layered 3D using Value-Noise (VN) functions. The traditional pixel based approaches at the time seemed to the current author less realistic and less flexible. VN methodology could and can simulate for example Sequential Gaussian Simulation textures but also include changes in grain factor (matrix coarseness or fineness), anisotropy, warping, warping with decay and rotation. By using trigonometric turbulation (image ‘twisting’) with sin or cos functions, VN can also mimic morphology in a particular form of anastomosing or braided stream depositional sediment facies that were also new and not readily available with traditional methodologies at the time.
Conditioning these Value-Noise images to transmissivity/permeability bore data was overcome by application of the PEST code as described in the original paper that was not a completely satisfactory approach but nevertheless a valid solution. A more recent examination of the methodology uses a different and more simplified approach that achieves conditioning of the VN methodology. This procedure has been outlined in this updated report. This report also contains a more detailed explanation of the basis of the version of VN methodology used by author. Depending on interest additional segments of the associated FORTRAN code and complete code will be posted in due course.
There is no claim that the VN methods presented in the original paper and the updated descriptions herein are the ‘be-all and end-all’ or the ultimate alternative and simpler solution to stochastic simulation rather than using other more extensive and elaborate methodologies that have appeared since the VN computer programs were written. The VN generation was developed and utilized to overcome what the author perceived at the time as a method without the need to understand often challenging geostatistical mathematical notation. Also despite apparent mathematical sophistication of these traditional methods, they did not at the time always result, in the author’s opinion, in particularly convincing images of real hydrogeological depositional systems. To large extent this still holds true today with methodology such as Multiple-Point Geostatistics (Remy et al. 2009, Mariethoz & Caers 2015. M&C) that depends on the creation of a ‘realistic’ training images of mimicked or imagined subsurface sediment deposition which is quite difficult to obtain or to generate as M&C have noted. More recently Pyrcz and Deutsch (2014) have written a comprehensive text review and additional presentation of figures about the various methodologies. This includes in particular modelling geological lithofacies and fluvial processes using geostatistical methods although it focuses on those that are important to the petroleum industry. Nevertheless many concepts also apply to hydrogeological applications.
The VN method used by this author does not pretend to solve the ultimate objective of generating a truly ‘realistic’ image. However, it does compete with many images produced by traditional geostatistical methods. In its basic form VN method does not depend on use of a training image but realizations generated are obtained by applying a range of parameters that can yield a variety of different images with very fast computation (a less than two seconds for 2D and less than a 30 seconds in 3D (3.4 GHz computer) for a model with 8 layers and 256 x 256 arrays or as required – see images below).