Inverse modeling of multimodal conductivity distributions

We present a method for the calibration of multimodal hydraulic conductivity distributions and apply this method to the particular case of confining layers with a complex geological architecture. The basis of our technique is the transformation of the original multimodal conductivity distribution to the standard normal distribution, thus fulfilling the condition of normality which is required by the used representer-based inverse algorithm (Valstar et al., 2004). Using this transformation, a calibration that starts from a homogeneous prior field is shown to radically improve the estimation of the protective properties of the confining layer compared to a unimodal approach to the calibration. The method is also used for the calibration of multimodal heterogeneous prior fields. The inevitable distortion of the original parameter covariances in the posterior fields that results from the transformation process is absorbed by an iterative postprocessing procedure, in which lithologic information obtained from the distorted calibrated fields is used to condition the generation of a new multimodal field that complies again with the original geostatistics. After transformation, this new field can be calibrated again, and this process is repeated until the newly generated field agrees with the measurement information sufficiently well. Then, the lithologic distribution of this new field is fixed, and the intrafacies conductivity distributions are calibrated. This approach is shown to preserve the original geostatistics, both of the lithology field and of the intralithology hydraulic conductivity distributions.