AI-GEOSTATS: Simulation and trends

[Chris Lloyd]

Hello,   I am currently using sequential Gaussian simulation (SGS) to generate microtopographic soil surfaces from sparse data. There are nearly 16000 observations,  so I’m using a small search neighbourhood (e.g., 16 observations). The mean of the variable I’m concerned with (heights) increases systematically from the top to the bottom of the data set and R squared for a fitted first order polynomial is 0.885. An obvious choice is to detrend the data, use SGS based on simple kriging and then add the trend back. An alternative might be to use the fitted trend to define the locally-varying mean and apply SGS based on simple kriging with locally-varying means (rather than taking the mean of the residuals as the constant mean and applying standard simple kriging). I suspect that ordinary kriging (using a power model fitted to the raw variogram) would result in predictions as accurate as those obtained through detrending in some way, but given the trend is so obvious I don’t want to ignore it. I am aware that there is a lot of relevant work in the literature about the application of these approaches in the context of kriging. However, I would be interested in details of any case studies that have dealt with large scale trends in a simulation context. I would also be interested in the views of list members about the approaches I’ve mentioned or any others that may be appropriate.   Many thanks in advance,   Chris Lloyd