Application of a diffusion model to simulate erosion of scoria cones in the San Francisco volcanic field, Arizona

A computer model for simulating the erosion of scoria (cinder) cones by diffusive processes is being formulated to investigate their long-term degradation. The model uses a two-dimensional diffusion algorithm expressed in finite-difference form to operate upon a three-dimensional scoria cone input as a matrix of elevation values (essentially a DTM). The computer simulation exhibits degradation from an initial conical form, through crater infilling, and finally into a low-relief, shield-like hill. This preliminary and simplest version of the model successfully mimicked the degradation pattern observed in degraded cones of the San Francisco volcanic field, Arizona. The scoria cones in this volcanic field range in age from Early Pliocene to Holocene and demonstrate a decrease in cone height/width ratio and slope with an increase in age. Morphometric relationships offer an opportunity to establish a relative age scheme and to loosely date cones of unknown age in a given volcanic field. The systematic decrease with time of scoria cone height, height/width ratio, and slope is the basis for a relative dating scheme. Morphometry is derived from 1:24,000-scale, 20-ft.-contour topographic maps and from calibrated field photographs. Morphometric parameters obtained from computer simulations and from actual degraded cones are calibrated by a least-squares technique withmore » cones that have been dated by radiometric or other absolute age-dating methods. Comparative morphology of scoria cones is a potentially useful age-dating tool for mapping volcanic fields.« less