Drainage-Divide Approach to Finding Boundaries of Geologic Bodies Using Gradients of 2D Potential Field Anomalies and 3D Tomographic Velocity Anomalies

The locations of steep horizontal gradients of gravity and magnetic anomalies often approximate the locations of edges of geologic source bodies, especially shallow sources. Typically, colored or contoured plots of horizontal gradient values display curvilinear high ridges that separate regions of low gradient. Various approaches have been suggested for locating ridge points and for connecting them to form continuous boundaries. A common approach for locating ridges is to examine variously oriented cross- sections at each point in the gradient field for parabolic-shaped cross-sections indicative of a ridge, or to attempt to fit a paraboloid to a small grid of points surrounding the point of interest. Although the resulting collection of ridge points determined by these methods yields a set of curvilinear lines, these lines are often disconnected and do not form continuous boundaries around the intervening low-gradient areas, which would be useful if one wished to "terrace" (as with rice fields) the potential field anomalies (e.g., Cordell and McCafferty, 1989), thereby delineating the "bodies" inferred from the ridge lines of steepest gradient. Mother nature has provided a convenient way for discovering ridges using the flow of raindrops. Gradient ridges form "drainage divides" separating "drainage basins" in the gradient field. Our approach is to identify the lows in the gridded gradient field, and then to determine into which low a raindrop falling at each gridpoint will ultimately come to rest, so that each low corresponds to a drainage basin. This can result in a great many drainage basins for noisy data, but consolidating nearby lows or putting "lakes" in low areas can simplify the pattern of basins. Ridge points can also be tagged with the value of the gradient at the point, offering some quality assessment of boundary lines. One advantage is that drainage basins translate directly into terrace regions. The approach can be easily extended to 3D data sets such as tomographic velocity models where 3D anomalies in velocity may, in some cases, be caused by geologic bodies with sharp contacts that it would be desirable to locate.