A direct sequential cosimulation algorithm and its application in hydrogeophysics

After interpretation, geophysical surveys often provide exhaustive maps of secondary information (electric resistivity for example) that are extremely useful to guide the interpolation of a primary variable (hydraulic conductivity for example). However, most often the relation between the variables are modeled with a linear statistical relationship (often between the log of the variables) or with conditional expectation. Here, we argue that these approaches are only special and limited cases of a broader approach in which the relation between the two variables should be modeled by a joint probability density function. An advantage of considering the joint relation in this manner is that it allows to model relatively easily situations in which the conditional probabilities (for example the probability of having a certain hydraulic conductivity knowing the resistivity) is multimodal. In this framework, we present a direct conditional co-simulation technique that allows creating collocated conditional simulations of the primary variable from a set of data points of the primary variable, an exhaustive map of the secondary variable, a numerical description of the joint pdf between the two variables, and a model of spatial correlation for the primary variable. Spatial cross-correlations are neglected at this stage of the work. The approach is illustrated with data from a coastal karstic aquifer located in the Sultanate of Oman.