GEOPHYSICS, VOL. 66, NO. 6 (NOVEMBER-DECEMBER 2001);P. 1774–1780, 9 FIGS. A new method for shape and depth determinations from gravity data El-Sayed M. Abdelrahman, Tarek M. El-Araby, Hesham M. El-Araby, and Eid R. Abo-Ezz ∗ ABSTRACT We have developed a simple method to determine simultaneously the shape and depth of a buried struc- ture from residualized gravity data using filters of suc- cessive window lengths. The method is similar to Euler deconvolution, but it solves for shape and depth inde- pendently. The method involves using a relationship be- tween the shape factor and the depth to the source and a combination of windowed observations. The relation- ship represents a parametric family of curves (window curves). For a fixed window length, the depth is deter- mined for each shape factor. The computed depths are plotted against the shape factors, representing a contin- uous, monotonically increasing curve. The solution for the shape and depth of the buried structure is read at the common intersection of the window curves. This method can be applied to residuals as well as to the Bouguer gravity data of a short or long profile length. The method is applied to theoretical data with and with- out random errors and is tested on a known field ex- ample from the United States. In all cases, the shape and depth solutions obtained are in good agreement with the actual ones. INTRODUCTION One of the most important exploration problems is estimat- ing the shape and depth of a buried structure. Different meth- ods have been developed to determine the shape and depth of the buried structure from gravity data. The methods generally fall into one of two categories. The first category is continu- ous modeling methods (Tanner, 1967; Cordell and Henderson, 1968), which require density information as part of the input, along with some depth information obtained from geological and/or other geophysical data. Thus, the resulting model can vary widely, depending on these factors, and still give a cal- Manuscript received by the Editor February 15, 2000; revised manuscript received January 17, 2001. ∗ Cairo University, Geophysics Department, Giza, Egypt. c  2001 Society of Exploration Geophysicists. All rights reserved. culated curve in close agreement with the observed data. The second category is fixed simple geometry methods, in which the sphere, horizontal-cylinder, and vertical-cylinder models determine the shape and depth of the buried structures from residuals and/or observed data. The models may not be entirely geologically realistic, but usually approximate equivalence is sufficient to determine whether the form and magnitude of the calculated gravity effects are close enough to those observed to make the geological interpretation reasonable. The advantage of fixed geometry methods over continuous modeling meth- ods is that they require neither density nor depth information, and they can be applied if little or no factual information other than the gravity data is available. For interpreting isolated sim- ple source bodies, fixed geometry methods can be both fast and accurate. Several methods have been developed to interpret gravity data using a fixed simple geometry. The methods include, for example, use of the half-g max rule (Nettleton, 1976), Kelvin transformation (Nedelkov and Burnev, 1962), Fourier trans- form (Odegard and Berg, 1965), least-squares minimization approaches (Gupta, 1983; Abdelrahman, 1990; Abdelrahman and El-Araby, 1993a; Abdelrahman and Sharafeldin, 1995a), ratio techniques (Bowin et al., 1986; Abdelrahman et al., 1989), Mellin transform (Mohan et al., 1986), and the Euler decon- volution technique (Klingele et al., 1991; Zhang et al., 2000). These methods all require prior knowledge of a simple shape that can be used to approximate the true form of the source. Efforts have been made to identify the shape of a source for observed data. Shaw and Agarwal (1990) indicate that the Walsh transform can be used. Abdelrahman and Sharafeldin (1995b) have developed a least-squares minimization approach to determine the shape and depth of the buried structure from residual gravity data. Nandi et al. (1997) use quadratic equa- tions to predict the shapes of sources with simple geometry from the gravity anomaly and its gradient. However, the accu- racy of the results obtained by these methods depends on the accuracy with which the residual anomaly can be separated from observed gravity anomaly. 1774