LANDFORM MODELING OF ALLUVIAL FANS: A KINEMATIC TOOL FOR ASSESSING QUATERNARY DEFORMATION

Application of a model for analyzing topography of piedmont surfaces is an iterative process requiring repeated validation and analysis at every step from initial data selection through final interpretation. Elevation data employed by the model are typically digitized from 1:24,000-scale topographic maps. The primary assumption for modeling is that a piedmont is composed of radially symmetric elements that can be distinguished and modeled individually. The model generates a radially symmetric conoid surface through specification of five parameters: three for apex position (x,y,z); and two for shape (slope and curvature). Topographic data are compared to the model surface and the parameters are adjusted to decrease the misfit between data and model. The model assesses deformation due to tilt with two additional parameters (tilt east, tilt north) with which the data are transformed with respect to the model-specified apex location. Model fit can be assessed quantitatively with typical regression statistics such as the error variance, which can be expected to be close to 0.21m² for data sets acquired from maps with a 5-foot contour interval, and qualitatively using graphic plots of model misfit such as histograms, residual maps, and regressor plots. Model validation and calibration were conducted using mathematically and graphically constructed data as well as topographic data from Copper Canyon fan in Death Valley, California. If tilt is evident and model results agree with geologic indicators, then analysis of results by means of grid search and confidence interval calculation are justified. Linear dependence between the regressor variables (multicolinearity) greatly exaggerates the size and elongation of confidence regions, which can be adjusted for this effect. In spite of an unreasonably located apex for the best-fit model (global minimum) of the 600ka Tunis Canyon fan, California, the grid search provides a means of assessing model solutions from candidate apex positions that agree with geologic conditions and are statistically indistinguishable from the global minimum at a given significance level. Analysis of this family of model solutions provides a tilt magnitude estimate of 1°±0.5° at an azimuth of 200°±35°. This estimate is compatible with the pattern of Quaternary piedmont dissection along the northern Tehachapi Mountains.