Stochastic models are valuable and sometimes essential tools for investigating the behavior of complex phenomena. In seismology, stochastic models can be used to describe velocity heterogeneities that are too small or too numerous to be described deterministically. Where analytic approaches are often infeasible, synthetic realizations of such models can be used in conjunction with finite difference algorithms to systematically investigate the response of the seismic wave field to complex heterogeneity. This paper represents a continuing effort at formulating a complete and robust stochastic model of lithologic heterogeneity within the crust, and the means of generating synthetic realizations; ''complete'' implies that the model is flexible enough to describe all types of random heterogeneity within the crust, while ''robust'' implies sufficiently constrained parameterization that an inversion problem may be well-posed. As a basis for investigation we use geologic maps of crustal exposures and petrophysically inferred velocities. Earlier efforts at stochastic modeling have focused on characterization of the univariate probability density function, which is typically modal (i.e., binary, ternary, etc.), and the covariance function, which is typically fit with a von K¿rm¿n function. Here we provide a means of characterizing the property of ''sinuous connectivity'' and for generating realizations that possess this property. Sinuous connectivity is the tendency for individual lithologic units to be continuous over long and highly contorted paths; there is no means in the earlier modeling of either characterizing of synthesizing this property. We generate sinuously connective realizations by mapping regions encompassed by two contours in a Gaussian-distributed surface into the two values of the binary field. This operation is nonunique, as one can choose, in many ways, the values for the contours. ¿ American Geophysical Union 1996