Gravity Inversion Using A “Shape-Of-Anomaly” Mfxhod: Developments In Three-Dimensional Modeling And Application To Gravity Over An Abandoned Underground Limestone Mlne In Southeastern Indiana

A method is developed for threedimensional modeling of gravity measured at the earth’s surface. The model<br>is built of many rectangular parallelepipeds of constant horizontal dimensions. Each prism is assigned an allowed<br>density contrast; however, all density contrasts are of the same sign. An initial model of filled prisms, or “seed”,<br>is specified. Additional prisms are filled automatically, one for each pass through an algorithm that minimizes the<br>difference between the shapes of the modeled and observed gravity. This “shape-of-anomaly” criterion was<br>previously developed and applied to two-dimensional modeling of gravity profiles (Rene, 1986). Other criteria for<br>controlling the model’s compactness and depth to center of gravity are developed here. Applications are first<br>demonstrated using synthetic gravity. For the gravity of a buried sphere, the inverse model closely approximates<br>a sphere if the depth to center of gravity is unconstrained. Some models are generated by specifying allowed ranges<br>for depths to center of gravity. To treat random noise, including measurement errors and high spatial-frequency<br>“geologic” noise, a filter is applied to both the observed and modeled gravity. Effects of bias are also shown. An<br>inverse model is also derived from a negative 143-pgal gravity anomaly of the flooded underground Gheen’s Mill<br>Cementville Mine in southeastern Indiana. The anomaly is defined by gravity at 837 stations in nineteen profiles<br>with a 3-m (lo-foot) station spacing. The model is constrained by 17 boreholes that penetrated cavities and 39<br>boreholes that did not find cavities.