Multi-scale alluvial fan heterogeneity modeled with transition probability geostatistics in a sequence stratigraphic framework

Abstract

The complexity of alluvial fan depositional systems makes detailed characterization of their heterogeneity difficult, yet such detailed characterizations are commonly needed for construction of reliable groundwater models. The transition probability geostatistical approach provides a means to quantify the distribution of hydrofacies in the subsurface. However, a key assumption used in this and other geostatistical approaches is that of stationarity. Stratigraphic character often varies within a deposit, making this assumption tenuous. Sequence stratigraphic concepts help us overcome this problem by dividing the strata into units that have similar properties, called sequences, based on recognition of unconformities and timelines within the sedimentary record. By using transition probability geostatistics in a sequence stratigraphic framework, realizations of the alluvial fan facies distributions are produced that account for multi-scale heterogeneity represented by spatially variable hydrofacies within sequences, laterally extensive aquitard units at sequence boundaries, and spatial variability attributes that are unique to each sequence. Incorporation of conceptual geologic information into the Markov chain model of transition probability also allows development of improved coregionalization models in the typically undersampled, lateral directions. The Kings River Alluvial Fan, located southeast of Fresno, California, provides an excellent test case for the approach. Several sequences within the alluvial fan were produced by outwash from Pleistocene glaciations in the Sierra Nevada Mountains. Five sequences, separated by large-scale (>3 km laterally), mature, red paleosols, were recognized in the alluvial fan strata. Markov chain models were developed to characterize the intermediate-scale (0.3–1.5 km laterally) distribution of hydrofacies in each individual sequence and to characterize the spatial distribution of paleosols. Separate conditional simulation of each sequence provides realizations of hydrofacies distributions. Combining these five sequence realizations into a single realization, then overprinting the paleosol distributions onto this realization, produced a geologically plausible image of the subsurface facies distribution that accounts for non-stationarity between stratigraphic units. Importantly, the resulting realization preserves the lateral continuity of the large-scale sequence boundary paleosols, which are potentially important confining beds within the fan deposits. Additionally, facies juxtaposition tendencies (e.g. upward fining tendencies of the fluvial deposits) and known directional anisotropy and dip of units within the fan are preserved in the realization. These physical attributes, accurately reproduced by the geostatistical method, are essential components of the overall hydrogeologic character of the alluvial fan.