Geostatistical simulation is used to create a synthetic three-dimensional geologic environment such that randomly generated values of a physical property have a required covariance and mean. We create a spatially stationary, multivariate Gaussian simulation with a Gaussian covariance. This type of simulation permits modeling of natural variations which may be an important source of noise in geologic investigations, whereas interpolation techniques such as kriging tend to smooth out those variations.Computationally efficient frequency-domain methods allow the rapid creation of multiple scenarios, each having the required statistical distribution. For the particular problem considered, a given porosity distribution is simulated and then functionally related to physical properties needed for input into geophysical models. Additionally, megascopic cavities having random size, shape, and orientation similar to those observed in karst settings are emplaced in the physical model. Geostatistical simulation plays a particularly important role in exploring the degree to which natural variations in physical parameters lower the resolution of target anomalies that have similar signatures. In the accompanying paper, we discuss the geophysical methods tested and the results of the tests.