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.

[1]  D. Quirk.  ‘Base profile’: a unifying concept in alluvial sequence stratigraphy , 1996, Geological Society, London, Special Publications.

[2]  C. A. Ross,et al.  Sea-level changes: An integrated approach , 1986 .

[3]  C. Payton,et al.  Seismic stratigraphy and global changes of sea level; Part 2, The depositional sequence as a basic unit for stratigraphic analysis , 1977 .

[4]  Clayton V. Deutsch,et al.  GSLIB: Geostatistical Software Library and User's Guide , 1993 .

[5]  Richard D. Miller,et al.  Hydrogeologic Facies Characterization of an Alluvial Fan Near Fresno, California, Using Geophysical Techniques , 1997 .

[6]  Steven F. Carle,et al.  CONDITIONAL SIMULATION OF HYDROFACIES ARCHITECTURE: A TRANSITION PROBABILITY/MARKOV APPROACH1 , 1998 .

[7]  Sheldon M. Ross,et al.  Introduction to probability models , 1975 .

[8]  G. Fogg,et al.  Transition probability-based indicator geostatistics , 1996 .

[9]  R. Ritzi,et al.  Hydrofacies distribution and correlation in the Miami Valley Aquifer System , 1995 .

[10]  T. McCarthy,et al.  The Okavango Fan and the classification of subaerial fan systems , 1993 .

[11]  P. Mccabe,et al.  Perspectives on the Sequence Stratigraphy of Continental Strata , 1994 .

[12]  R. Wasson.  Intersection Point Deposition on Alluvial Fans: An Australian Example , 1974 .

[13]  S. Carle.  Implementation schemes for avoiding artifact discontinuities in simulated annealing , 1997 .

[14]  J. Wagoner,et al.  Siliciclastic sequence stratigraphy in well logs, cores, and outcrops , 1990 .

[15]  Steven F. Carle,et al.  Three‐dimensional hydrofacies modeling based on soil surveys and transition probability geostatistics , 1999 .

[16]  C. Payton.  Seismic Stratigraphy — Applications to Hydrocarbon Exploration , 1977 .

[17]  H. Posamentier,et al.  Siliciclastic Sequence Stratigraphy: Recent Developments and Applications , 1994 .

[18]  Henry W. Posamentier,et al.  Eustatic Controls on Clastic Deposition I—conceptual Framework , 1988 .

[19]  W. C. Krumbein,et al.  Fortran IV program for simulation of transgression and regression with continuous-time markov models , 1968 .

[20]  S. Dreiss,et al.  Hydrostratigraphic interpretation using indicator geostatistics , 1989 .

[21]  B. Smart,et al.  Combining Sequence Stratigraphy, Geostatistical Simulations, and Production Data for Modeling a Fluvial Reservoir in the Chaunoy Field (Triassic, France) , 1998 .

[22]  T. Muto.  Coastal Fan Processes Controlled by Sea Level Changes: A Quaternary Example from the Tenryugawa Fan System, Pacific Coast of Central Japan , 1987, The Journal of Geology.

[23]  M. Jervey.  Quantitative Geological Modeling of Siliciclastic Rock Sequences and Their Seismic Expression , 1988 .

[24]  Roland Westland Page,et al.  Geology, hydrology, and water quality in the Fresno area, California , 1969 .

[25]  G. Fogg,et al.  Modeling Spatial Variability with One and Multidimensional Continuous-Lag Markov Chains , 1997 .

[26]  V. Wright,et al.  Pedostratigraphic models for alluvial fan deposits: a tool for interpreting ancient sequences , 1990, Journal of the Geological Society.

[27]  M. Hutchinson.  A new procedure for gridding elevation and stream line data with automatic removal of spurious pits , 1989 .