TECHNIQUE FOR AREAL POPULATION OF NUMERICAL MODELS WITH GEOHYDROLOGIC PARAMETERS USING TRANSITIONAL PROBABILITIES

Geohydrologic parameters can be geostatistically propagated from known/observed values at one site to populate numerical model grids where values are not available. The results of a gamma-ray geophysical log (surrogate for grain-size distribution and, therefore, hydraulic conductivity and effective porosity) collected in a vertical borehole in alluvium were propagated areally by assuming that horizontal and vertical variation in geohydrologic parameters are the same (Walther's Law). The range of the gamma ray values in the log (0-177 counts per second) was discretized into 5 intervals so that the gamma log value at a given depth was assigned a value of 1, 2, 3, 4, or 5, as appropriate. Transitional probabilities of a gamma log value at a location X2, 1 foot vertically from a reference point, X1, were calculated and plotted by interval, given the gamma log value at the reference point. The histogram of transitional probabilities for the gamma log value at X2, given X1=1, is shown in figure 1. Using Walther's Law, the known gamma log value (1-5) at a specific depth in the logged well is propagated to a point 1 foot radially away by first selecting the transitional probability histogram for the new point (X2) given the known value at the well (X1).

Given this selected histogram representing the “probability density function” at the new point, a “realization” is obtained that represents a random selection from the density function. That “realization” is the propagated gamma value at the new point, which is then considered a known value in the propagation step to the next point, 2 feet radially away from the well. By continuing this pattern of propagating radially from the well 1 foot at a time, the inherent structure in the data of the known vertical gamma log values at the well is probabilistically reproduced areally (figure 2). Because areal propagation is a function only of radial distance from the well, not the direction, the 1-dimensional structure in the vertical gamma log is propagated axisymmetrically onto the 2-dimensional horizontal plane within the assumed area of geostatistical influence of the well (bottom left well in figure 2.)

The areally propagated gamma log values can be converted to equivalent hydraulic conductivity and effective porosity values, using empirical relations between the gamma-ray log and grain size distribution. The hydraulic conductivity and effective porosity values would be initial estimates of the values of these parameters for the cells of a numerical grid for construction of a heterogeneous model to analyze hydraulic and tracer tests conducted, for example, at the 4-well complex shown in figure 2.